JP6809202B2 - Hot water surface shape estimation method and hot water surface shape estimation device - Google Patents

Description

The present invention relates to a molten metal surface shape estimation method for estimating the molten metal surface shape in a mold of a continuous casting machine and a molten metal surface shape estimation device.

In continuous casting, molten metal (for example, molten steel) once stored in the tundish is supplied into the mold from above via a dipping nozzle, and the outer peripheral surface is cooled and the solidified slab is pulled out from the lower end of the mold. The casting is continuously performed. In the following description, for a mold for continuous casting with a rectangular opening, the long side direction of the opening is referred to as the mold width direction or simply the width direction, and the short side direction of the opening is the mold thickness direction or It is simply called the thickness direction, and the vertical direction is called the casting direction.

Here, the time variation of the position (also referred to as the height of the molten metal or the level of the molten metal) of the surface (spray surface) of the molten metal in the mold during continuous casting is the flux on the molten metal (the powder is melted). Causes entanglement inside the molten metal. Then, this entrained flux can become a surface defect after slab rolling. Therefore, in order to stabilize the operation and improve the quality, during continuous casting, the inflow amount of molten metal injected into the mold via the immersion nozzle and the outflow amount of molten metal drawn out from the mold as slabs. The height of the molten metal is measured with a molten metal level meter so that the height of the molten metal is kept constant, and the inflow amount of molten metal provided in the immersion nozzle is controlled by feedback control based on the measured value. Control (that is, molten metal level control) for adjusting the opening degree of the sliding nozzle and the stopper, which are the adjusting devices of the above, is performed.

In the present specification, the position of the molten metal at a specific point in the width direction in the mold is referred to as the height of the molten metal, and the distribution of the height of the molten metal in the width direction is referred to as the height distribution of the molten metal. Further, the height distribution of the molten metal in the width direction based on the case where the molten metal surface is horizontal in the mold is called the molten metal surface shape, and the temporal variation of the molten metal surface shape is called the variation of the molten metal surface shape. In addition, the variation in the shape of the molten metal includes the temporal variation including the entire vertical movement of the molten metal that is uniformly generated in the entire width direction in the mold due to the balance difference of the molten metal in the mold (that is, in the entire width direction in the mold). Temporal fluctuation of the height of the molten metal) is called fluctuation of the molten metal level.

Here, when a water model experiment simulating the injection and extraction of molten metal into a mold using water instead of molten metal, the discharge flow from the immersion nozzle collides with the short side of the mold and then reverses upward. Due to the influence of the above, the water surface in the mold is not always horizontal, and many waviness and movement in the left-right direction are observed, and it can be observed that the shape of the molten metal fluctuates greatly. This variation in the shape of the molten metal causes the above-mentioned flux entrainment and the resulting slab defects. That is, in order to improve the quality of the slab, it is important to control not only the above-mentioned molten metal level control but also the behavior of the molten metal surface shape fluctuation, and by extension, the behavior of the molten metal level fluctuation. Therefore, if the shape of the molten metal at an arbitrary time can be known, detailed information on the fluctuation of the molten metal can be obtained, and the casting conditions that can prevent flux entrainment can be optimized more finely, and the quality of the slab can be improved. It is considered to be beneficial to.

Here, conventionally, a technique has been proposed in which a plurality of molten metal level meters are installed in a mold and the behavior of the molten metal in the mold is detected based on these measured values. For example, in Patent Document 1, the flow pattern of molten metal on the molten metal is detected by using the molten metal heights detected in each of a plurality of regions by a plurality of molten metal height detecting units, and the slab is based on this. A method of predicting the quality of a metal is disclosed.

Further, in Patent Document 2, a plurality of temperature sensors are installed at predetermined intervals on the inner wall of the mold along the vertical direction and the mold width direction around the control target position of the molten metal surface height, and the measurement by these temperature sensors is performed. From the values, the mold copper plate temperature at the position corresponding to the meniscus is obtained for each temperature measurement column in the vertical direction, the position in the vertical direction corresponding to the copper plate temperature is specified as the meniscus position, and the mold at each meniscus equivalent position in the mold width direction is specified. Based on the heat flux, a method of determining the flow velocity of the molten metal for all the temperature measuring trains in the mold width direction by heat transfer engineering is shown.

Further, Non-Patent Document 1 includes thermocouples arranged in a row in the vertical direction in the vicinity of the position corresponding to the control target position of the height of the hot water, and the hot water at the installation position is based on the temperature distribution of these thermocouples. A method of installing a plurality of molten metal level meters for measuring the surface height in the mold width direction and estimating the time variation of the molten metal level distribution based on the measured values of these molten metal level meters is disclosed. ..

In order to estimate the shape of the molten metal at an arbitrary time, it is effective to use the measured values by a plurality of molten metal level meters as in the techniques described in Patent Documents 1 and 2 and Non-Patent Document 1. Conceivable.

Special Table 2015-522428 Japanese Unexamined Patent Publication No. 2004-291060

A. Yamauchi, et al. , "Estimation of meniscus profile by mold temperature temperature measurement in continuous casting of steel slaves", CAMP-ISIJ, 2002, Vol. 15, p. 843

Here, in order to estimate the shape of the molten metal at an arbitrary time with higher accuracy, it is considered that the molten metal level meters should be arranged in the mold width direction and installed as many as possible. However, in reality, the number of molten metal level meters that can be installed on the mold is limited due to cost and other factors. Therefore, assuming that the shape of the molten metal is estimated using the values measured by M (M ≧ 2) molten metal level meters, the hot water is located at an appropriate position in order to estimate the shape of the molten metal more accurately. It is considered important to install a surface level meter (that is, to arrange the observation points properly).

In this regard, the techniques described in Patent Documents 1 and 2 and Non-Patent Document 1 all describe the molten metal surface of the molten metal in the mold based on the measured values of a plurality of molten metal level meters installed in the mold. Although it is a technique for detecting behavior, Patent Documents 1 and 2 and Non-Patent Document 1 do not specify an appropriate installation position of the molten metal level meter. Specifically, Patent Document 1 does not mention an inappropriate or appropriate distribution of a plurality of regions for detecting the height of the molten metal in the mold width direction. Further, Patent Document 2 does not describe the arrangement of an inappropriate or appropriate temperature sensor for detecting the meniscus position in the mold width direction. Further, Non-Patent Document 1 only describes that the distance between the rows of thermocouples arranged in the vertical direction constituting the molten metal level meter is 150 to 200 mm, and the basis of the numerical value and this The effect of placement on estimation accuracy is not described.

In view of the above circumstances, it can be said that conventionally, an appropriate installation position of the molten metal level meter for more accurately estimating the molten metal surface shape in the mold at an arbitrary time has not been sufficiently examined. Therefore, the present invention has been made in view of the above problems, and an object of the present invention is a mold at an arbitrary time by appropriately determining the installation position of the molten metal level meter in continuous casting. It is an object of the present invention to provide a new and improved method for estimating the shape of the molten metal and an apparatus for estimating the shape of the molten metal, which can estimate the inner shape of the molten metal with higher accuracy.

In order to solve the above problem, according to a certain viewpoint of the present invention, the height of the molten metal in the mold of the continuous casting machine at M (M ≧ 2) observation points arranged side by side in the mold width direction. based on the measured values, a melt surface shape estimation method molten metal surface is estimated melt surface shape which is the reference and the distribution in the mold width direction of the molten metal surface level where it is horizontal, the M observations includes a method for determining a point, the determination method, based on said molten metal surface level estimates of the candidate position of the observation point of M (M ≧ 2), and estimating the melt surface shape estimation It has a step of calculating the estimation error of the molten metal surface shape and a step of determining the positions of the M observation points so that the estimation error becomes small, and was determined in the determination step. the M observation point, the mold width direction and the x-axis direction, the center of the mold width direction in a coordinate system with x = 0, - located in the W / 2 or more and W / 2 or less of the range, and each for the n, at least one of the observation point values x n which you express by the following equation (101) _is in other than the position of _k, the molten metal surface shape estimation method is provided.

here,
W: Mold width N: Indicates the number of wavelength components of a sine wave having a wavelength of 2 W / n (n is an integer from 1 to N) constituting the molten metal surface shape and having both ends in the width direction of the mold as wave antinodes. It is an integer greater than or equal to 2.

The estimated value of the molten metal level may be calculated by using a state space model representing the fluctuation of the molten metal level in the mold of the continuous casting machine. Further, in the step of calculating the estimation error of the molten metal surface shape, the estimated mean square error RMSE of the molten metal surface shape may be calculated as the estimation error of the molten metal surface shape.

Further, in the molten metal shape estimation method, a predetermined level for the co-dispersion matrix regarding the observed noise in the measurement of the molten metal surface height at the observation point and the co-dispersion regarding the disturbance for each wavelength component constituting the molten metal surface shape are used. For each level combination that is a combination of a predetermined level for the matrix and a predetermined level for the number M of the observation points , the candidate positions x ₁ , ..., X _M of the observation points are set by a uniform random error. and pre-estimated Kiyumen shape, as the estimation error of the melt-surface shape, to calculate the mean square error RMSE for the estimated the melt-surface shape, the time variation of the melt surface shape which is the RMSE estimated target wherein the calculating the ratio RMSE / sigma of standard deviation sigma of the RMSE / sigma may determine whether it satisfies a preset adopted criteria RMSE / sigma, corresponding to the RMSE / sigma to meet the inclusion criteria A series of processes in which candidate positions x ₁ , ..., X _M of observation points are adopted as the positions of M of the observation points are repeated a predetermined number of times, and RMSE / σ satisfying the adoption criteria for each of the level combinations. With respect to the candidate positions x ₁ , ..., X _M of the observation point corresponding to, the mold short side on the side closer to itself of the observation point corresponding to the position x ₁ of the coordinates closest to any of the template short sides. At the maximum value z ₁ of the ratio of the distance from the mold short side of 1 to the mold width and the position x _M closest to the second mold short side which is the mold short side opposite to the first mold short side. It is calculated, and the maximum value z _M of the ratio of the distance and the mold width from the corresponding said second mold short side of the observation point, for each of the levels for the number M of the observation point, relating to the observation noise levels for the covariance matrix, and in the case of changing the level of the covariance matrix for the disturbance, and calculates the minimum value minz ₁ of the maximum value z _1, the minimum value minz _M of the maximum z _M, a , The position where the distance from the first mold short side is equal to or less than the distance from the first mold short side to the position in the mold width direction corresponding to the minimum value minz ₁ , and from the second mold short side. Corresponds to the observation point and position x _M corresponding to position x ₁ at positions where the distance is equal to or less than the distance from the short side of the second mold to the position in the mold width direction corresponding to the minimum value minz _M , respectively. so that the observation points are located, the remaining M-2 pieces of the observation points are located in a evenly spacing between the observation point corresponding to the observation point and the position x _M corresponding to the position x ₁ In addition, M of the above observations The position of the point may be determined.

Further, in the molten metal shape estimation method, when the adoption standard of RMSE / σ is 0.25 and M ≦ 5, the first mold short of the observation point corresponding to the position × ₁ is short. The ratio of the distance from the side to the mold width is 0.01 or less, and the ratio of the distance from the second mold short side of the observation point corresponding to the position x _M to the mold width is 0.12 or less. as described above, to determine the position of the observation point corresponding to the observation point and the position x _M corresponding to the position x _1, the case of M ≧ 6, the first of the observation point corresponding to the position x ₁ The ratio of the distance from the short side of the mold to the mold width is 0.19 or less, and the ratio of the distance from the second short side of the mold to the mold width of the observation point corresponding to the position x _M is 0.4 or less. The position of the observation point corresponding to the position x ₁ and the position of the observation point corresponding to the position x _M may be determined so as to be.

Further, in the molten metal shape estimation method, when the adoption standard of RMSE / σ is 0.20 and M ≦ 6, the first mold short of the observation point corresponding to the position × ₁ is short. The ratio of the distance from the side to the mold width is 0.01 or less, and the ratio of the distance from the second mold short side of the observation point corresponding to the position x _M to the mold width is 0.01 or less. as described above, to determine the position of the observation point corresponding to the observation point and the position x _M corresponding to the position x _1, the case of M ≧ 7, the first of the observation point corresponding to the position x ₁ The ratio of the distance from the short side of the mold to the width of the mold is 0.01 + 0.03 × (M-6) or less, and the distance of the observation point corresponding to the position × _M from the short side of the second mold. The positions of the observation point corresponding to the position x ₁ and the observation point corresponding to the position x _M are determined so that the ratio to the mold width is 0.01-0.05 × (M-6) or less. May be good.

Further, the step of estimating the molten metal surface shape is expressed by a state space model including at least the wavelength component of a sinusoidal wave having a wavelength of 2 W / n whose both ends in the width direction of the mold are antinodes of the wave. The step includes a step of sequentially estimating the shape of the molten metal by applying a Kalman filter to the state space model using the heights of the molten metal measured at the M observation points as observation values. The state space model expresses the amplitude of the wavelength component by a standing wave component and a disturbance component, and the Kalman filter may treat the disturbance component as system noise. Further, the M observation points determined in the determination step may include the positions of both short sides of the template.

Further, in order to solve the above problem, according to another viewpoint of the present invention, the molten metal surface in the mold of the continuous casting machine at M (M ≧ 2) observation points arranged side by side in the mold width direction. based on the measurements of height, a melt surface shape estimating device molten metal surface is estimated melt surface shape is the distribution in the mold width direction of the molten metal surface height from the case is horizontal, the M The casting surface shape is estimated based on the estimated value of the casting surface height at the candidate positions of the number (M ≧ 2) observation points, and the estimated casting surface shape estimation error is calculated, and the estimation error is calculated. Is configured to determine the positions of the M observation points so that is smaller, and the determined M observation points have the mold width direction as the x-axis direction and the center in the mold width direction as the center. in coordinate system with x = 0, - W / 2 or more and is in W / 2 or less of the range, and, for each n, the value x _n at least one of the observation points you express by the following equation (101) _is in other than the position of _k, the molten metal surface shape estimating device is provided.

here,
W: Mold width N: Indicates the number of wavelength components of a sine wave having a wavelength of 2 W / n (n is an integer from 1 to N) constituting the molten metal surface shape and having both ends in the width direction of the mold as wave antinodes. It is an integer greater than or equal to 2.

As described above, according to the present invention, in continuous casting, by appropriately determining the installation position of the molten metal level meter, it is possible to more accurately estimate the molten metal surface shape in the mold at an arbitrary time. Become.

It is a figure which shows the configuration example of the molten metal surface shape estimation system which concerns on this embodiment. It is a figure for demonstrating the wavelength component which comprises the molten metal surface shape. It is a figure which shows roughly the position of the node in the mold width direction of each wavelength component. It is a block diagram which shows the functional structure of the molten metal surface shape estimation apparatus which concerns on this embodiment. It is a block diagram which shows an example of the hardware structure of the molten metal surface shape estimation apparatus which concerns on this embodiment. It is a flow chart which shows an example of the processing procedure of the method of determining the installation position of a molten metal level meter. It is a flow chart which shows an example of the processing procedure of the method of determining the installation position of a molten metal level meter. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. When the number of observation points M = 8, when the value of the adoption standard of RMSE / σ is 0.25, the coordinate values of the observation points that satisfy the adoption criteria x ₁ , ..., For x ₈ , x ₁ , ..., it is a histogram showing the distribution in the mold width direction of each x _8. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a graph which shows the boundary of the existence range of the coordinate values x ₁ and x _M of the observation point when the value of the adoption standard of RMSE / σ is 0.25. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a figure which shows the value of the adoption standard of RMSE / σ, and the distribution of the coordinate values x ₁ , x _M of the observation point adopted in the adoption standard in the mold width direction. It is a graph which shows the boundary of the existence range of the coordinate values x ₁ and x _M of the observation point when the value of the adoption standard of RMSE / σ is 0.20.

Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings. In the present specification and the drawings, components having substantially the same functional configuration are designated by the same reference numerals, so that duplicate description will be omitted.

Specifically, in the following, first, the configuration of the molten metal shape estimation system according to the embodiment of the present invention will be described in (1. Configuration of the molten metal surface shape estimation system). Next, in (2. Hot water surface shape estimation processing), the details of the hot water surface shape estimation processing according to the present embodiment, which is performed in the hot water surface shape estimation system, will be described. Next, in (3. Installation position of the molten metal level meter), an appropriate installation position of the molten metal level meter will be described in consideration of the content of the molten metal shape estimation process according to the present embodiment. Next, in (4. Functional configuration of the molten metal shape estimation device), the functional configuration of the molten metal surface shape estimation device that executes the molten metal shape estimation process in the molten metal surface shape estimation system according to the present embodiment will be described. Next, in (5. Hardware Configuration), an example of a specific hardware configuration of the molten metal surface shape estimation device will be described.

(1. Configuration of molten metal shape estimation system)
The configuration of the molten metal surface shape estimation system according to the present embodiment will be described with reference to FIG. FIG. 1 is a diagram showing a configuration example of a molten metal surface shape estimation system according to the present embodiment. Referring to FIG. 1, the molten metal level estimation system 1 according to the present embodiment includes a molten metal level meter 105 installed in a mold 101 of a continuous casting machine, a molten metal shape estimation device 201, an output device 203, and storage. The device 205 is provided. Note that FIG. 1 also shows a dipping nozzle 103 for injecting molten metal into the mold 101 for the sake of explanation. As shown in the figure, the immersion nozzle 103 is installed at substantially the center in the mold width direction with respect to the mold 101.

The molten metal level meter 105 is, for example, a vortex type level meter, and measures the height of the molten metal at a predetermined position in the mold 101. As shown in the figure, in the present embodiment, a plurality of molten metal level meters 105 are installed in the mold width direction with respect to the mold 101, and each molten metal level meter 105 measures the height of the molten metal at its own installation position. To do. The type of the molten metal level meter 105 is not limited, and various known ones may be used. The measured values by each molten metal level meter 105 are sequentially transmitted to the molten metal surface shape estimation device 201 at predetermined intervals.

Although FIG. 1 shows that nine molten metal level meters 105 are installed symmetrically with respect to the center in the mold width direction at substantially equal intervals, the molten metal level meter 105 is installed. The number and installation position are not limited to such examples. The number and position of the hot water level meter 105 installed in FIG. 1 is merely an example of the number and position of the hot water level meter 105 installed. Actually, in the present embodiment, the number of installed hot water level gauges 105 may be appropriately determined according to the cost and the like, and the installation positions thereof will be described below (3. Installation position of the hot water level gauges). Determined according to the method.

The molten metal shape estimation device 201 estimates the molten metal surface shape at an arbitrary time in the mold 101 based on the measured values of the plurality of molten metal level meters 105. The details of the molten metal shape estimation process by the molten metal surface shape estimating device 201 will be described later. The molten metal shape estimation device 201 sequentially estimates the molten metal surface shape each time a measured value by a plurality of molten metal level meters 105 is input. That is, the molten metal shape estimation device 201 can estimate the time variation of the molten metal surface shape, that is, the variation of the molten metal surface shape in real time. The molten metal shape estimation device 201 transmits the estimation result for the molten metal surface shape (that is, the estimation result for the variation in the molten metal surface shape) sequentially estimated to the output device 203 and the storage device 205.

The output device 203 is, for example, an output device capable of visually presenting information such as a display device, a projector, and / or a printing device. The output device 203 outputs the estimation result of the molten metal surface shape by the molten metal surface shape estimating device 201 in real time, for example, by displaying it on a display, projecting it on a screen, printing it on a paper medium, or the like.

Here, from the conventional knowledge, it is known that in continuous casting, many slab defects occur at a position where the time variation of the height of the molten metal is particularly large. Therefore, by outputting the molten metal surface shape estimated as described above in real time by the output device 203, it is possible to grasp the current molten metal surface shape fluctuation at any time during continuous casting, and the molten metal surface shape can be grasped at any time. Based on the variation, it becomes possible to grasp the distribution of the existence probability of slab defects in the slab width direction before the completion of casting. As a result, slab quality control can be speeded up.

The storage device 205 is a device capable of storing various types of information. As the storage device 205, various known devices capable of storing information such as a magnetic storage device such as an HDD (Hard Disk Drive), a semiconductor storage device, an optical storage device, or an optical magnetic storage device can be used. .. The storage device 205 stores the estimation result of the molten metal surface shape by the molten metal surface shape estimating device 201. As a result, even if the estimation result of the output device 203 is not output in real time, the molten metal surface stored in the storage device 205 during the past operation is stored in the storage device 205 in order to identify the cause after the occurrence of the slab defect. You can refer to the estimation result of the shape.

(2. Hot water surface shape estimation process)
The molten metal shape estimation process executed by the molten metal surface shape estimating device 201 will be described in detail.

(Modeling of change in surface shape)
First, modeling of the shape variation of the molten metal will be described. In the present embodiment, the height of the mold 101 is considered to be sufficiently larger than the width, and the deep water wave approximation is used in modeling the change in the shape of the molten metal. Further, it is considered that the width of the mold 101 is sufficiently larger than the thickness, and when modeling the variation in the shape of the molten metal, the variation in the height of the molten metal in the thickness direction is not considered, but only the variation in the width direction is considered. And.

Since the horizontal velocity of the molten metal = 0 always holds at the boundary between both short sides of the mold on the molten metal surface, any time t and any position x in the width direction in the mold 101 (the center in the mold width direction is x = 0). The height of the molten metal y (x, t) in) is defined as the sinusoidal shape of the wavelength λ _n = 2 W / n (mold width W, n = 1, 2, ...) As the base function f _n (x). Can be represented by a linear model. As a result, the shape of the molten metal at an arbitrary time can be expressed by superimposing the basis functions f _n (x) having both ends in the width direction of the mold 101 as antinodes. In this embodiment, the basis function f _n (x) is also referred to as an nth-order wavelength component.

FIG. 2 is a diagram for explaining the wavelength components constituting the molten metal surface shape. FIG. 2 shows a cross section of the mold 101 in the width direction, and shows waveforms of wavelength components S _{1 to} S ₃ from the first order to the third order as an example of the wavelength components constituting the molten metal surface shape in the mold 101. (For the sake of explanation, the amplitude of each wavelength component is equalized). Wavelength lambda ₁ of the first-order wave component _{S 1} is a lambda ₁ = 2W, the wavelength lambda ₂ of the second wavelength component _{S 2} is a lambda ₂ = W, the wavelength lambda ₃ of third-order wave component _{S 3} is λ ₃ = 2W / 3.

Specifically, the nth-order wavelength component, that is, the basis function f _n (x) is expressed by the following mathematical formula (1).

When the wavelength component is defined as described above, the height y (x, t) of the molten metal considering the wavelength component up to the Nth order (n = 1, 2, ..., N) is as shown in the following equation (2). It can be expressed by a linear equation. The specific value of N is appropriately set so that sufficient estimation accuracy can be obtained from the operational knowledge of the continuous casting machine to which the molten metal surface shape estimation method according to the present embodiment is actually applied.

Here, y ₀ (t) indicates the overall vertical movement component included in the height of the molten metal due to the volume balance of the molten metal in the mold 101. _{Further, a} n (t) denotes the amplitude of time varying with respect to _f n (x).

Since the purpose of this embodiment is to estimate the shape of the molten metal, that is, the height distribution of the molten metal based on the case where the molten metal is horizontal, y ₀ (t) = in the above mathematical formula (2). It is assumed to be 0. That is, in the present embodiment, y (x, t) when y ₀ (t) = 0 in the above mathematical formula (2) is used as an estimation target. When y ₀ (t) = 0, y (x, t) represents the shape of the molten metal at an arbitrary time and at an arbitrary position, that is, corresponds to the variation in the shape of the molten metal.

Since the wavelength of each wavelength component is obtained from the width W of the mold 101, f _n (x) can be calculated for any time. Therefore, if the amplitudes a ₁ (t), a ₂ (t), ..., A _N (t) of the nth-order wavelength component are obtained, the molten metal surface shape variation y (x, t) can be estimated. ..

Here, since the wave motion of the molten metal follows the so-called water surface wave motion equation, if the motion of the molten metal is considered as a non-viscous, incompressible perfect fluid vortex-free flow, the frequency is a value associated with the wavelength by the dispersion relation equation. Limited to. Wavelength angular frequency omega _n of the wave is 2W / n is expressed by the following equation (3).

Thus, _a n (t) in the equation (2) is represented by the following equation (4).

Here, _An is a constant corresponding to a wavelength of 2 W / n, and φ _n is a constant representing the phase at time t = 0.

If f _n amplitude _a n to time changes to (x) (t) is expressed as the equation (4), molten metal surface height at an arbitrary position x y (x, t) is the equation (2 ), It can be expressed by superimposing a sine wave with a limited angular frequency ω _n . Since the sinusoidal component of the angular frequency ω _n represented by the above equation (4) can always be observed at the height of the molten metal y (x, t), the sinusoidal component is called a standing wave component. However, when the time series data of the measured values by the molten metal level meter 105 actually installed in the mold 101 of the continuous casting machine is frequency-analyzed, components other than the angular frequency shown in the above mathematical formula (3) are included. It is considered that this is because the external force due to the disturbance caused by the discharge flow from the immersion nozzle acts on the molten metal surface. Accordingly, the time variation of the amplitude _a n (t), using an external force term due to the disturbance _w n (t), can be expressed as following equation (5).

That is, in this _{embodiment, a} n a (t), expressed by the standing wave component and the disturbance component _(w n _(t)). The disturbance component _w n (t) corresponds to the system noise in the state space model of _a n (t) to be described later.

The solution of the above equation (5) includes frequency components other than the angular frequency ω _n included in w _n (t) and changes with time. Incidentally, the expression of the time variation of the amplitude _a n (t) in the equation (4) corresponds to the case _w n (t) is always zero in the above equation (5).

(State-space model of the amplitude _a n (t))
n order wavelength amplitude _a n (t) is the equation for the component (5) expressed in linear differential equations, melt surface shape variation as shown in the equation (2) _f n (x) and _a n (t) Since it is represented by the linear sum of and, the value measured by the molten metal level meter 105 is sampled at predetermined time intervals, and the differential equation shown in the above equation (5) is converted into a model of the difference equation to change the shape of the molten metal. Can be represented by a discrete time state space model. In the following, the discrete time of the interval Δt (sec) is expressed as t = 0, 1, 2, ... At this time, the amplitude _a n (t), and time variation of the amplitude _a n (t) _{(i.e., a} 1-order differential with respect to time of n _{(t)) b} n a (t), the following equation (6) It can be expressed by the model formula of the discrete time shown.

Here, w _n (t) (n = 1, ..., N) is a value of the external force term in the above mathematical formula (5) at a discrete time. Here, it is assumed that the vector w (t) = [w ₁ (t) ... w _N (t)] ^T is an irregular signal according to a multivariate normal distribution having a mean of 0 and a covariance matrix of Q. Further, R _n and G _n are coefficient matrices represented by the following mathematical expressions (7) and (8).

If the variable vector q _n (t) is defined as the following mathematical expression (9), the above mathematical expression (6) can be expressed as the following mathematical expression (10).

Each component of the vector [q ₁ (t) ... q _N (t)] ^{T in} the above formula (10) is rearranged and converted into a vector X (t) as shown in the following formula (11). The transformation of this vector [q ₁ (t) ... q _N (t)] ^T to the vector X (t) can be expressed using a regular matrix T.

At this time, the equation of state representing the time change of X (t) is expressed by the following mathematical formula (12).

(Modeling of measured values with a hot water level meter)
It is assumed that M (M ≧ 2) molten metal level gauges 105 are installed side by side with respect to the mold 101 in the width direction. The coordinate values of the installation positions in the mold width direction (x-axis direction) of the M molten metal level meters 105 in the coordinate system in which the center in the width direction is x = 0 (that is, the coordinate values of the observation points) are set. Assuming that x _m (1 ≤ m ≤ M, x ₁ <x ₂ <... <x _M ) and the height of the molten metal y (x _m , t) at each coordinate can be measured by the molten metal level meter 105, each models of molten metal surface height at the coordinate value _{x m y (x m, t} ) is the expression of the superimposition shown in the equation (2) measurement noise _v m (t) is applied, the following equation (15) expressed.

Here, the observed noise v _m (t) is a measurement error signal of the molten metal level meter 105. Here, it is assumed that the observed noises v _m (t) with respect to the measured values at each observation point are uncorrelated, and v _m (t) is a Gaussian noise signal represented by an average of 0 and a variance of R ₀ .

When the above mathematical formula (15) is expressed as a vector, the following mathematical formula (16) is obtained.

(Estimation processing by Kalman filter)
Above obtained equation (12), it is (16) is an equation representing a state space model of the amplitude _a n (t) for each wavelength component. In the present embodiment, the molten metal shape estimation device 201 uses the state space model generated as described above to measure the height of the molten metal with M molten metal level meters 105 (that is, y (x _m ,). From t)), X (t) is sequentially estimated using a stationary Kalman filter.

In the sequential estimation process using the stationary Kalman filter, when the statistical properties of the time series data do not change with time, the optimum Kalman gain K in the Kalman filter calculation is determined in advance by the discrete time Ricatch equation shown in the following mathematical formula (18). It is calculated according to the following equation (19) using a stable stationary matrix solution P that satisfies.

Kalman filter to calculate the estimated value X ^est of the thus Kalman gain is calculated by K and molten metal surface height measurement values y (x _{m, t)} by using the state variable X (t) ^(t) is represented by the following formula ( It is represented by 20).

The molten metal shape estimation device 201 sequentially starts from t = 1 each time the molten metal level meter 105 measures the height of the molten metal y (x _m , t) (that is, Y (t)). Using the mathematical formula (20), the estimated value ^Xest (t) of the state variable X (t), that is, the estimated value of q ₁ (t), ..., Q _N (t) is calculated, and a ₁ (t), ..., a _N (t) is estimated. Further, the shape of the molten metal is estimated by substituting these calculated values into the above mathematical formula (2). Since the sequential estimation of the state variable X (t) using the stationary Kalman filter can be performed by a known method, detailed description of the specific method will be omitted here.

(3. Installation position of hot water level meter)
As described above, in the present embodiment, the molten metal surface shape estimating device 201 estimates the molten metal surface shape based on the measured values of the molten metal surface height by the M molten metal level meters 105. Here, the installation positions of these M molten metal level meters 105 in the mold width direction (coordinate values x ₁ , ..., X _{M of the} observation points in the mold width direction) have a great influence on the estimation accuracy of the molten metal surface shape. It is an important factor to give. Therefore, in the present embodiment, the installation positions of these M molten metal level meters 105 used for estimating the molten metal surface shape in the mold width direction are appropriately determined. As a result, the molten metal shape estimation process by the molten metal surface shape estimating device 201 can be performed more accurately. Hereinafter, a method for determining the installation position of the molten metal level meter 105 in the present embodiment will be described in detail.

(3-1. Method of determining the installation position of the molten metal level meter based on the position of the node of the wavelength component)
The height of the molten metal y (x, t) at an arbitrary time t in the mold 101 and an arbitrary position x in the width direction in the mold 101 is a wavelength of 2 W / n (n) as shown in the above formula (2). It can be expressed by superimposing N wavelength components of = 1, ..., N). Here, in each wavelength component, there may be a point, that is, a node whose amplitude is always 0 at a predetermined position in the mold width direction. The coordinate values x _{n and k} of the nodes in each wavelength component are expressed by the following mathematical formula (21). Here, k is an integer indicating the order of wave nodes in the wavelength component of wavelength 2 W / n (k = 0, ..., N-1).

FIG. 3 is a diagram schematically showing the positions of nodes in the mold width direction of each wavelength component obtained from the above mathematical formula (21). In FIG. 3, the x-axis, which is the coordinate axis in the mold width direction, is taken as the horizontal axis, and as an example, the positions corresponding to the nodes on the x-axis when n = 1, 2, 3, and 8 are shown.

Here, when all of the M water level gauges 105 are installed at the node positions x _{n and k} shown in the above formula (21) for a certain n, the water level gauge 105 has the height of the water level. The component of the amplitude of the wavelength component of the wavelength 2 W / n for the n, which is included in y (x, t), cannot be observed. That is, when all of the M molten metal level gauges 105 are installed at the positions x _{n and k} shown in the above equation (21) for a certain n, the amplitude of the wavelength component of the wavelength 2 W / n for the n. Therefore, it is not possible to accurately estimate the shape of the molten metal.

Therefore, in the present embodiment, based on such knowledge, with respect to the observation points of the height of the hot water surface for estimating the shape of the hot water surface, the coordinate values of these M observation points in the template width direction x ₁ , ... , X _M are not included in the set of coordinate values x _{n, k} defined by the above equation (21) for a certain n, and the positions of these M observation points (that is, the installation of the molten metal level meter 105). Position) is determined. In other words, for each n, at least one of the coordinate values x ₁ , ..., X _M of _M observation points is other than the coordinate values x _{n, k} represented by the above equation (21). The positions of these M observation points are determined so as to have the value of. By installing the molten metal level meter 105 at such a position, it becomes possible to perform the estimation process of the molten metal surface shape with high accuracy.

(3-2. Method of determining the installation position of the molten metal level meter based on the estimation error)
As described above, in the present embodiment, the installation position of the molten metal level meter 105 is determined based on the position of the node of the wavelength component, but in order to further improve the estimation accuracy of the molten metal surface shape, there are other methods. The installation position of the molten metal level meter 105 may be determined based on the idea. Specifically, in the present embodiment, in addition to the method based on the position of the node of the wavelength component described above, the estimation error of the molten metal surface shape is calculated, and the molten metal level meter 105 so that the estimation error becomes sufficiently small. You may decide the installation position of. This makes it possible to further improve the estimation accuracy of the molten metal surface shape.

Hereinafter, the estimation method based on the method of determining the installation position of the molten metal level meter based on this estimation error will be described in detail. The deviation e (t) between the state variable X (t) and its estimated value _Xest (t) in the _calculation process of the molten metal surface shape is different on both sides of the above formula (12) and the above formula (20), respectively. By further substituting the above mathematical formula (16), it can be expressed as the following mathematical formula (22).

On the other hand, the height of the molten metal y (x ^any , t) at an arbitrary position x = x ^any in the mold width direction can be expressed from the above formula (15) as the following formula (23).

Here, the variance _{V e} of the deviation e (t) of the state variables X (t) is an estimated value ^{X est} (t) and the estimated target by the Kalman filter is a positive discrete-time Lyapunov equation shown in following equation (25) Teikai (See, for example, "Toru Katayama," New Edition Applied Kalman Filter, "Asakura Shoten, February 2000").

Using this _{V e,} arbitrary position ^{x = x} bath level in ^any height ^{y (x any,} t) of the mean square error ^RMSE (x any) estimates (RMSE: Root Mean Square Error) is represented by the following formula It is represented by (27). Here, trace means an operation of summing the diagonal components of a square matrix.

Therefore, the mean square error RMSE of the molten metal surface shape in the entire mold width direction is approximated by the following equation (30) using the errors at the _L evaluation points x = x ^any ₁ , ..., X ^any _L. be able to.

If the evaluation score L is sufficiently large, the approximation error of RMSE can be reduced. Therefore, in the present embodiment, the evaluation score L is sufficiently increased, the RMSE is calculated according to the above formula (30), and the estimation error of the molten metal surface shape is evaluated by the RMSE. Here, since the stationary Kalman filter is defined so as to minimize the RMSE for the observation point where the value of the given coordinates is x _m (m = 1, ..., M), the RMSE shown in the above equation (30) is shown. If is small, it can be said that the coordinate value x _m of the observation point is appropriate. Therefore, in the present embodiment, the estimation error of the molten metal surface shape is evaluated by the RMSE obtained from the above mathematical formula (30), and the coordinate value x _m of the observation point, that is, the molten metal level meter is used so that this estimation error becomes small. The installation position of 105 is determined.

(3-3. Specific procedure for determining the installation position of the hot water level meter)
Based on the two ideas explained above, a specific procedure for determining the installation position of the molten metal level meter 105 will be described. In the present embodiment, for the M molten metal level meters 105, the coordinates shown in the above formula (21) for n having a coordinate value x _m in the mold width direction corresponding to the installation position of each molten metal level meter 105. Installation positions of these M molten metal level gauges 105 so as not to be included in the set of values x _{n and k} and the RMSE shown in the above mathematical formula (30) is sufficiently smaller than the fluctuation amount of the molten metal surface shape ( The coordinate values x _m ) of the M observation points will be searched by simulation.

Specifically, the covariance matrix R of the observed noise v (t) with respect to the measured value of the molten metal surface height and the covariance matrix Q (state variable X (t)) relating to the disturbance for each wavelength component constituting the molten metal surface shape. Several levels are set for each of the covariance matrix Q) regarding the disturbance to the above and the number of observation points M at the height of the molten metal. Then, for each of the combinations of these levels, the series of processes shown in the following (A) to (D) are repeatedly executed a sufficiently large number of times.

(A) The coordinate values x _m of M observation points in the mold width direction are set by uniform random numbers. However, this time, the coordinate value x _m of the M observation point, coordinate values x _m of the M observation point, the coordinates x _n shown in the equation (21) for a certain _n, a set of _k Set so that it is not included in. In addition, for M observation points, considering the symmetry of the shape variation of the molten metal with respect to the center in the mold width direction, the observation points corresponding to m = 1 (that is, for the coordinate values x _m of these observation points) (that is, , X ₁ ) is the observation point closest to any of the short sides of the template, and the m of the observation point corresponding to m = M (that is, the observation point corresponding to x _M ). The short side of the mold near the observation point corresponding to = 1 (hereinafter referred to as the first short side of the mold for convenience) and the short side of the mold on the opposite side (hereinafter referred to as the short side of the second mold for convenience). ) Can be assumed to be greater than or equal to the distance between the observation point corresponding to m = 1 and the short side of the first template. Therefore, when setting the coordinates of the value x _m of the M observation point, if the coordinate values x _m observation points set by the uniform random numbers do not meet the assumptions of each observation point The process of moving the coordinate value x _m to a position symmetrical with respect to the center in the mold width direction is performed.

(B) For the coordinate value x _m of the observation point set in the above (A), the RMSE shown in the above formula (30) is calculated. Further, for each level of the covariance matrix Q, the standard deviation σ of the change in the shape of the molten metal in the mold caused by the disturbance over the time and the entire range of the position in the mold width direction is 0 on average and the covariance matrix is Q. By simulating the shape fluctuation of the molten metal using the irregular signal of the dimensional normal distribution as a disturbance (corresponding to the case where the actual data of the time variation of the height of the molten metal cannot be obtained in advance in the examples described later), or as the basis of Q. It is calculated from the measured value (actual data) of the molten metal surface height in the mold width direction (corresponding to the case where the actual data of the time variation of the molten metal surface height can be obtained in advance in the examples described later). Then, these ratios RMSE / σ are calculated.

(C) For each level of the number of observation points M, the value of the adoption standard for RMSE / σ is set so that the estimation accuracy of the desired molten metal surface shape can be obtained, and the RMSE / σ calculated in (B) above is Determine if this recruitment criterion is met. That is, the RMSE / σ calculated in (B) above is compared with the value of this adoption standard.

(D) When RMSE / σ satisfies the adoption standard in (C) above (that is, when RMSE / σ is equal to or less than the value of the adoption standard), the coordinate value x _m of the observation point is estimated as desired. It is used as the coordinate value of the observation point where accuracy can be obtained.

By repeating the series of processes shown in (A) to (D) above a sufficiently large number of times for each combination of R, Q, and M levels, RMSE is sufficiently larger than the fluctuation amount of the molten metal surface shape. It is possible to obtain the coordinate value x _m of the observation point that becomes smaller than the above for each combination of levels.

Here, as a result of the examination by the present inventors, the template width direction for each of the coordinate values x ₁ , ..., X _M of the observation points such that the RMSE / σ obtained as a result of the above calculation satisfies the adoption criteria. When checking distribution in, regardless of the value of the observation points M, as the value of inclusion criteria of RMSE / sigma increases, the existence range of the present range and x _M of x _1, both the center of the mold width direction It was confirmed that the tendency to spread toward (see FIGS. 16-19 and 21-24 described later for details). In other words, when high estimation accuracy is obtained regardless of the value of the number of observation points M (that is, when the value of the adoption standard is small), x ₁ , x _M are the first template short side and x _M , respectively. It was found that it often exists near the short side of the second mold. Similarly, when the present inventors investigated the distribution of the coordinate values x ₁ , ..., X _M of the observation points such that RMSE / σ satisfied the adoption criteria in the template width direction, the number of observation points M was increased. Regardless of the value, it was confirmed that the peak positions indicating the frequency of x _{2 to} x _M-1 can appear at approximately equal intervals between x ₁ and x _M in the mold width direction (for details, refer to. 8-15, which will be described later). In other words, x ₂ to x _M-1 often exist at approximately equal intervals between x ₁ and x _M when high estimation accuracy can be obtained regardless of the value of the number of observation points M. Do you get it.

Therefore, in the present embodiment, the coordinate values x _m of the appropriate M observation points for obtaining the desired estimation accuracy are determined as follows. For each combination of R, Q, and M levels, if a sufficient number of coordinate values x _m of the observation points where RMSE / σ satisfies the adoption criteria are obtained, they are closest to one of the short sides of the template. Maximum value z of the ratio (W / 2 + x ₁ ) / W of the ratio of the distance from the mold short side (that is, the first mold short side) of the observation point (that is, the observation point corresponding to x ₁ ) to the mold width W. ₁ and, second of the mold short side opposite the nearest observation points in the mold short side (i.e., the observation point corresponding to x _M) of the distance and the mold width W from the second mold short side of The maximum value z _M of the ratio (W / 2-x _M ) / W is calculated (that is, z ₁ , z _M is obtained for each combination of R, Q, and M levels). Then, calculated from the thus _z 1 obtained, _{z M,} the minimum value minz ₁ of _{z 1,} and the minimum value minz _M of _{z M} for each level of M. As a result, a set of minz ₁ and minz _M can be obtained for a certain number of observation points M.

Then, with these minz ₁ and minz _M as the boundary of the setting range, the distance from the short side of the first mold in the mold width direction is equal to or less than the distance from the short side of the first mold to the position corresponding to the minz _1. At the position, the value x ₁ of the coordinates of the first observation point is determined. Further, the value of the coordinates of the second observation point is at a position where the distance from the short side of the second mold is equal to or less than the distance from the short side of the second mold to the position corresponding to the minz _M in the mold width direction. Determine x _M. Then, for values _x 2 _{~x M-1} of the remaining M-2 pieces of observation point coordinates, substantially uniform spacing between _{x 1} and _{x M} These _x 2 _{~x M-1} is in the mold width direction Determine to be located at.

Here, when x _{2 to} x _M-1 are set between x ₁ and x _M at completely even intervals, x _{2 to} x _M-1 is the above formula (21) for a certain n. There is a risk that it will be included in the set of coordinates x _{n, k} shown in. Accordingly, in the present _embodiment, for x 2 _{~x M-1,} these _x 2 _{~x M-1} is the value _{x n} of coordinates shown in the equation (21) for a certain _n, in the set of _k as no and, as will become possible even spacing between x ₁ and x _M, determined. In the above, in that sense, it is described as "almost" evenly spaced.

Specifically, x _{2 to} x _M-1 are determined according to the following mathematical formula (31).

Here, α _m is a positive constant, and its specific values include x _{2 to} x _{M-1 in} the set of coordinate values x _{n and k} shown in the above equation (21) for a certain n. It is appropriately determined so as not to prevent the estimation and to obtain the desired estimation accuracy. Here, the larger the alpha _m, the position of the x 2 _{~x M-1} becomes a to go out from a position which is equally spaced between the x ₁ and x _M, also the estimation accuracy of the molten metal surface shape It will drop. From this, as a result of the examination by the present inventors, it is preferable that α _m is set in the range of α _m <0.25 in order to obtain the desired estimation accuracy.

Hereinafter, a method for determining the installation position of the molten metal level meter 105 in the present embodiment has been described in detail. As described above, the coordinate value x _m of the observation point, that is, the installation position of the molten metal level meter 105 is determined, and the molten metal shape is estimated based on the measured value by the molten metal level meter 105 at such an installation position. By doing so, the estimation accuracy can be improved. Therefore, it is possible to improve the prediction accuracy of slab defects caused by flux entrainment and the like based on the estimation result of the molten metal surface shape, so that slab quality control can be performed more reliably.

In the present embodiment, as described above, the coordinate value x ₁ is determined at a position where the distance from the short side of the first mold is equal to or less than the distance to the position corresponding to minz ₁ in the mold width direction, and the mold is formed. The coordinate value x _M is determined at a position where the distance from the short side of the second mold in the width direction is equal to or less than the distance to the position corresponding to minz _M. In this _case, as x 1 = -0.5W, established the melt-surface level meter 105 corresponding to _{x 1} to the first mold short _side, as x M = 0.5 W, molten metal surface level gauge corresponding to _{x M} The 105 may be placed on the short side of the second mold. As shown in the above mathematical formula (2), in the present embodiment, the molten metal surface shape is expressed by superposition of the basis functions f _n (x) having both ends in the width direction of the mold 101 as antinodes. Therefore, it can be said that both short sides of the mold 101 where the antinodes of f _n (x) are located are places where the time variation of the height of the molten metal is relatively large. Therefore, by installing the molten metal level meter 105 at such positions, Since the height of the molten metal used for estimating the shape of the molten metal can be measured in a wider range, the effect of further improving the estimation accuracy of the shape of the molten metal can be obtained. Further, when the molten metal level meters 105 are installed on both short sides of the mold 101, it is not necessary to move these molten metal level meters 105 when changing the width of the mold 101, so that the work is simplified. You can also get the effect of becoming.

(4. Functional configuration of the molten metal surface shape estimation device)
The functional configuration of the molten metal surface shape estimation device 201 shown in FIG. 1 will be described with reference to FIG. FIG. 4 is a block diagram showing a functional configuration of the molten metal surface shape estimation device 201 according to the present embodiment. Referring to FIG. 4, the molten metal shape estimation device 201 according to the present embodiment has a measurement value acquisition unit 251, a calculation unit 253, an output unit 255, and a storage unit 257 as its functions. The functions of each part will be described below.

The measured value acquisition unit 251 is realized by a communication device that receives measured values from a plurality of molten metal level meters 105. The measured value acquisition unit 251 acquires the measured value of the height of the molten metal from each of the plurality of molten metal level meters 105. In the present embodiment, the installation positions of the plurality of molten metal level meters 105 are determined according to the method described in (3. Installation position of the molten metal level gauge). The measured value acquisition unit 251 provides the acquired measured value to the calculation unit 253.

The arithmetic unit 253 is realized by a processor such as a CPU (Central Processing Unit) or a DSP (Digital Signal Processor). In the calculation unit 253, when the processor constituting the calculation unit 253 operates according to a predetermined program, the calculation process described in (2. Hot water surface shape estimation process) is executed, and a plurality of hot water level meters 105 The variation in the shape of the molten metal is estimated based on the measured value of the height of the molten metal. Since the details of the estimation process have already been described, the description thereof will be omitted here.

The calculation unit 253 provides the output unit 255 with the estimation result of the change in the shape of the molten metal. The arithmetic unit 253, various kinds of information obtained in the course of the process of estimating the molten steel surface shape variation (e.g., amplitude a _{n (t)} of each wavelength component) to, provide the output unit 255, storage unit 257 It may be stored in.

The output unit 255 is realized by a communication device that transmits a signal to an external device. The output unit 255 outputs the estimation result of the change in the shape of the molten metal by the calculation unit 253 to the output device 203 shown in FIG. The output device 203 displays the estimation result of the change in the shape of the molten metal on a display or the like. Further, the output unit 255 may output the estimation result of the change in the shape of the molten metal by the calculation unit 253 to the storage device 205 shown in FIG.

The storage unit 257 is realized by, for example, a memory such as a ROM (Read Only Memory) or a RAM (Random Access Memory), and various storage devices such as an HDD. In the storage unit 257, for example, various data such as a program for causing the calculation unit 253 to execute the calculation process, various parameters used for the estimation process of the shape change of the molten metal surface by the calculation unit 253, and the progress of the estimation process. Is stored. The calculation unit 253 executes the calculation process while exchanging various information with the storage unit 257.

As described above, an example of the function of the molten metal surface shape estimation device 201 according to the present embodiment has been described. Each of the above components may be configured by using general-purpose members or circuits, or may be configured by hardware specialized for the function of each component. Further, the functions of the plurality of components may be collectively realized by a processor such as a CPU. The configuration for realizing the molten metal surface shape estimation device 201 can be appropriately changed according to the technical level at each time of implementation.

Further, it is possible to create a computer program for realizing each function of the molten metal surface shape estimation device 201 according to the present embodiment as described above and implement it on a personal computer or the like. It is also possible to provide a computer-readable recording medium in which such a computer program is stored. The recording medium may be, for example, a magnetic disk, an optical disk, a magneto-optical disk, a flash memory, or the like. Further, the above computer program may be distributed via a network, for example, without using a recording medium.

(5. Hardware configuration)
FIG. 5 is a block diagram showing an example of the hardware configuration of the molten metal surface shape estimation device 201 according to the present embodiment. Referring to FIG. 5, the molten metal shape estimation device 201 includes a CPU 901, a ROM 903, and a RAM 905. The molten metal shape estimation device 201 further includes a bus 907, an input device 909, an output device 911, a storage device 913, a drive 915, a connection port 917, and a communication device 919.

The CPU 901 functions as an arithmetic processing device and a control device, and controls all or a part of the operation in the molten metal shape estimation device 201 according to various programs recorded in the ROM 903, the RAM 905, the storage device 913, or the removable recording medium 921. To do. The ROM 903 stores programs, calculation parameters, and the like used by the CPU 901. The RAM 905 primarily stores the program used by the CPU 901, parameters that change as appropriate in the execution of the program, and the like. These are connected to each other by a bus 907 composed of an internal bus such as a CPU bus. The CPU 901 can constitute the calculation unit 253 shown in FIG. Further, the ROM 903 and the RAM 905 may form the storage unit 257 shown in FIG.

The bus 907 is connected to an external bus such as a PCI (Peripheral Component Interconnect / Interface) bus via a bridge.

The input device 909 is an operating means operated by the user, such as a mouse, a keyboard, a touch panel, buttons, switches, and levers. Further, the input device 909 may be, for example, a remote controller using infrared rays, radio waves, or the like, or an externally connected device 923 such as a tablet terminal having an operation function of the molten metal shape estimation device 201. Further, the input device 909 is composed of, for example, an input control circuit that generates an input signal based on the information input by the user using the above-mentioned operating means and outputs the input signal to the CPU 901. By operating the input device 909, the user of the molten metal shape estimation device 201 can input various data to the molten metal shape estimation device 201 and instruct the processing operation.

The output device 911 is composed of a device capable of visually or audibly notifying the user of the acquired information. Such devices include displays using liquid crystals, CRTs, indicators such as lamps, audio output devices such as speakers or headphones, printer devices, and the like. The output device 911 outputs, for example, the results obtained by various processes performed by the molten metal surface shape estimation device 201. For example, the display displays the results obtained by various processes performed by the molten metal shape estimation device 201 as text or an image on the screen. Further, for example, the voice output device outputs the results obtained by various processes performed by the molten metal surface shape estimation device 201 as an alarm or a dialog. As described with reference to FIG. 1, the molten metal surface shape estimation system 1 according to the present embodiment includes an output device 203 as a means for presenting information to the user. Since the output device 203 has the same function as the output device 911, when the output device 203 can substitute the function of the output device 911, the output device 911 is not always included in the molten metal surface shape estimation device 201. It does not have to be provided.

The storage device 913 is a data storage device configured as an example of the storage unit of the molten metal surface shape estimation device 201. The storage device 913 is composed of, for example, a magnetic storage device such as an HDD, a semiconductor storage device, an optical storage device, an optical magnetic storage device, or the like. The storage device 913 stores a program executed by the CPU 901, various data, various data acquired from the outside, and the like. The storage device 913 may constitute the storage unit 257 shown in FIG.

The drive 915 is a reader / writer for a recording medium, and is built in or externally attached to the molten metal surface shape estimation device 201. The drive 915 reads the information recorded on the removable recording medium 921 such as the mounted magnetic disk, optical disk, magneto-optical disk, or semiconductor memory, and outputs the information to the RAM 905. The drive 915 can also write records to a removable recording medium 921 such as a mounted magnetic disk, optical disk, magneto-optical disk, or semiconductor memory.

The connection port 917 is a port for directly connecting the device to the molten metal surface shape estimation device 201. Examples of the connection port 917 include a USB (Universal Serial Bus) port, an IEEE1394 port, a SCSI (Small Computer System Interface) port, an RS-232C port, and the like. By connecting the externally connected device 923 to the connection port 917, the molten metal surface shape estimating device 201 directly acquires various data from the externally connected device 923 and provides various data to the externally connected device 923. ..

The communication device 919 is, for example, a communication interface composed of a communication device or the like for connecting to the communication network 925. The communication device 919 may include, for example, a communication card for a LAN (Local Area Network). Further, the communication device 919 may include a router or a modem for various wired communications. The communication device 919 can transmit and receive signals and the like to and from the Internet and other communication devices in accordance with a predetermined protocol such as TCP / IP. Further, the communication network 925 connected to the communication device 919 is configured by a network or the like connected by wire or wirelessly, and may include, for example, the Internet or a LAN. The communication device 919 may constitute the measured value acquisition unit 251 and the output unit 255 shown in FIG.

The above is an example of a hardware configuration capable of realizing the function of the molten metal surface shape estimation device 201 according to the present embodiment. Each of the above-mentioned components may be configured by using general-purpose members, or may be configured by hardware specialized for the function of each component. Therefore, it is possible to appropriately change the hardware configuration to be used according to the technical level at each time when the present embodiment is implemented.

As an embodiment of the present invention, the installation position of the molten metal level meter is such that the method described in (3. Installation position of the molten metal level meter) is actually executed and the estimation accuracy of the desired molten metal level can be obtained. The result of determining the above will be described.

In this embodiment, the covariance matrix R for the observed noise with respect to the measured value of the height of the molten metal is set at two levels, and the covariance matrix Q for the disturbance with respect to the state variable is set at 13 levels.

For the covariance matrix R, the observed noise was not correlated between the measurement positions of the height of the molten metal, and the magnitude of the dispersion was set to R ₀ . At this time, the covariance matrix R is represented by a square matrix having a diagonal component of R ₀ and an off-diagonal component of 0, as shown in the following mathematical formula (32).

In this embodiment, the value of R ₀ is set as a representative value that covers the actual operating conditions indicating the magnitude of the measurement error. Specifically, as the covariance matrix _R, and set two levels of R 0 = 0.02778mm or _R 0 = _0.1089mm. Here, R ₀ = 0.02778 mm assumes a case where the measurement error of the height of the molten metal is ± 0.5 mm, so that the standard deviation of the measured value is 0.167 mm, which is 1/3 of this error range. (That is, the measured value of 3σ is ± 0.5 mm), and the value is set as a value corresponding to the square value of 0.167 mm. Similarly, R ₀ = 0.1089 mm assumes a case where the measurement error of the height of the molten metal is ± 1.0 mm, so that the standard deviation of the measured value is 0.33 mm, which is 1/3 of this error range. (That is, the measured value of 3σ is ± 1.0 mm), and the value is set as a value corresponding to the square value of 0.33 mm.

As the covariance matrix Q, there are cases where the actual data of the time variation of the molten metal surface height cannot be obtained in advance, the actual data of the time variation of the molten metal surface height in the actual machine, the water model of the flow in the mold, or the low temperature melting. The case where the experimental data of the time variation of the height of the molten metal by the metal model etc. can be obtained in advance and the case corresponding to each are set.

As the covariance matrix Q corresponding to the case where the actual data of the time variation of the height of the molten metal cannot be obtained in advance, it is assumed that each component of the disturbance term is uncorrelated, as shown in the following mathematical formula (33). A square matrix with an angular component of Q ₀ and an off-diagonal component of 0 was created. The Q ₀ represents the strength of the disturbance that causes the shape of the molten metal to fluctuate. In this embodiment, five levels of Q ₀ = 0.0001, Q ₀ = 0.01, Q ₀ = 1, Q ₀ = 100, or Q ₀ = 10000 are set as the covariance matrix Q.

On the other hand, the covariance matrix Q corresponding to the case where the actual data of the change in the shape of the molten metal can be obtained in advance was created by using the result of the water model experiment, assuming that each component of the disturbance term has a correlation. Specifically, first, a water model experiment simulating continuous casting was carried out, and experimental data of the change in the shape of the molten metal was obtained. The water model experiment was performed twice under four conditions in which the mold width and the casting speed were different from each other. That is, eight experimental data were obtained as the experimental data of the change in the shape of the molten metal. The conditions of the mold width and casting speed in the water model experiment are as shown in Table 1 below. The columns marked with "○" in Table 1 correspond to the conditions of the mold width and casting speed in which the water model experiment was conducted.

By estimating the disturbance term based on each of the eight experimental data, a covariance matrix Q based on each experimental data was generated. The specific procedure is as follows.

First, a Kalman filter capable of estimating the shape variation of the molten metal surface is designed by using a covariance matrix in which each component of the disturbance is uncorrelated and the off-diagonal component is 0. Next, using the measurement data of the time variation of the molten metal level in the water model experiment, the estimated value of the state variable of the molten metal surface shape variation model by this Kalman filter is Xest ^' (t) (t = 2, ..., T). And. However, an arbitrary initial value is given as ^Xest' (1), and w (1) = 0. At this time, with respect to the estimated value ^Xest' (t) of the state variable, it can be considered that the following mathematical formula (34) is approximately established as in the operation expressed by the above mathematical formula (12).

The time t = 2, ..., in the measurement data of the T, approximate value _Q ^{d app} of the covariance matrix of w (t), using the average ^{w mean} of w (t), the following formula (35) It is expressed as.

Assuming that the second term on the right side of the above mathematical formula (34) is represented by ξ (t), the relationship shown in the following mathematical formula (37) holds.

Further, the approximate value ξ ^mean of the average value of ξ (t) can be expressed by the following mathematical formula (38).

On the other hand, the approximate value Q _ξ ^app of the covariance matrix of ξ (t) is expressed by the following mathematical formula (40) using ξ ^mean .

By substituting ξ (t) = G _d w (t) and ξ ^mean shown in the above formula (38) into the above formula (40), the following formula (41) can be obtained.

Comparing the above formula (35) with the above formula (41), the following formula (42) is obtained.

Here, the vector w (t) indicating the disturbance is N-dimensional, and the state variable X is 2N-dimensional. Further, since each dimension of the vector w (t) corresponds to each wavelength component of the change in the shape of the molten metal, the matrix G _d is a column full rank. Therefore, G _d ^T G _d is regular, and there is an inverse matrix (G _d ^T G _d ) ^-1 . Multiplying both sides of the above formula (42) by (G _d ^T G _d ) ^-1 G _d ^T from the left and G _d (G _d ^T G _d ) ^-1 from the right gives the following formula (43).

_Thus, the ^{Q d app,} can be calculated as following equation (44).

In this example, Q _d- ^app was calculated using the above mathematical formula (44) based on each of the eight experimental data corresponding to the conditions shown in Table 1, and this was used as the covariance matrix Q.

The covariance matrix Q is summarized in Table 2 below. As shown in Table 2 below, a total of 13 levels of covariance matrix Q were generated.

Using the covariance matrices Q and R set as described above, the desired method is performed by a computer according to the method described in (3-3. Specific procedure for determining the installation position of the molten metal level meter). The value x _m of the coordinates of the observation point in the mold width direction was determined so that the estimation accuracy of was obtained. The processing procedure of the processing is shown in FIGS. 6 and 7. 6 and 7 are flow charts showing an example of a processing procedure of a method for determining an installation position of a molten metal level meter. Each of the processes shown in FIGS. 6 and 7 can be executed by operating the processor of the computer according to a predetermined program.

With reference to FIGS. 6 and 7, in the method of determining the installation position of the molten metal level meter according to the present embodiment, first, the covariance matrix R of the observed noise is set (step S101). As described above, since the covariance matrix R is set to two levels in this embodiment, one of the levels is set as the covariance matrix R in step S101.

Next, the covariance matrix Q of the disturbance is set (step S103). As described above, since the covariance matrix Q is set at 13 levels in this embodiment, one of the levels is set as the covariance matrix Q in step S103.

Next, the number of observation points M is set (step S105). In this example, the number of observation points M was set to four levels of M = 5-8. Therefore, in step S105, one of these levels is set as the number of observation points M.

Next, i = 1 is set as the parameter i (step S107). The parameter i is a natural number and is a parameter representing the number of calculations. In this embodiment, the calculation is performed 10,000 M times (that is, i = 1 to 10000 M times) for each combination of R, Q, and M levels.

Next, the coordinate values x _m of the M observation points in the mold width direction are determined by a uniform random number (step S109). However, at this time, as described above, the coordinate values x _m of the M observation points are the coordinates of the coordinates x _m of the coordinates of the M observation points shown in the above equation (21) for a certain n. It is determined not to be included in the set of values x _{n, k} .

Next, RMSE is calculated according to the above formula (30) (step S111).

Next, the ratio RMSE / σ between the RMSE calculated in step S111 and the standard deviation σ of the surface shape fluctuation generated by the disturbance corresponding to the covariance matrix Q is set in advance for each observation point M. It is determined whether or not the condition is satisfied (step S113). Specifically, RMSE / σ is compared with the value of the adoption criteria. The value of the adoption standard can be appropriately set as a value that can obtain a desired estimation accuracy, that is, a value that makes RMSE sufficiently smaller than the fluctuation amount of the molten metal surface shape.

When RMSE / σ satisfies the adoption criteria in step S113 (that is, when RMSE / σ is equal to or less than the value of the adoption criteria), the desired estimation accuracy can be obtained by the coordinates of the observation point corresponding to the RMSE. Means that. Therefore, in this case, the coordinate value of the observation point corresponding to the RMSE is adopted as an appropriate coordinate value (step S115). Specifically, the coordinate value of the observation point is stored in a storage device or the like as an appropriate coordinate value. Then, the process proceeds to step S117.

On the other hand, when RMSE / σ does not satisfy the adoption criteria in step S113 (that is, when RMSE / σ is larger than the value of the adoption criteria), the coordinates of the M observation points corresponding to the RMSE are desired. It means that the estimation accuracy cannot be obtained. Therefore, in this case, the coordinate value of the observation point corresponding to the RMSE is not adopted as an appropriate coordinate value, and the process proceeds to step S117.

In step S117, it is determined whether or not the parameter i has reached the upper limit of 10000M. If the parameter i has not reached 10000M in step S117, i is updated, i = i + 1 (step S119), and the process returns to step S109. Then, the processes of steps S109 to S117 are executed again. On the other hand, when the parameter i reaches 10000M in step S117, the process proceeds to step S121.

In step S121, it is determined whether or not the calculation has been performed for all the levels of the number of observation points M. If all levels of M have not been calculated in step S121, M is updated (ie, M is changed to another level that has not yet been calculated) (step S123), and step S107 is performed. Return. Then, the processes of steps S107 to S121 are executed again. On the other hand, if the calculation is performed for all the levels of M in step S121, the process proceeds to step S125.

In step S125, it is determined whether the calculations have been performed for all levels of the covariance matrix Q of the disturbance. If all levels of Q have not been calculated in step S125, update Q (ie, change Q to another level that has not yet been calculated) (step S127) and go to step S105. Return. Then, the processes of steps S105 to S125 are executed again. On the other hand, if the calculation is performed for all the levels of Q in step S125, the process proceeds to step S129.

In step S129, it is determined whether the calculations have been performed for all levels of the observed noise covariance matrix R. If all levels of R have not been calculated in step S129, update R (ie, change R to another uncalculated level) (step S131) and go to step S103. Return. Then, the processes of steps S103 to S129 are executed again. On the other hand, if the calculation is performed for all the levels of R in step S129, the process proceeds to step S133.

In step S133, the coordinate value of the observation point obtained as a result of the above steps S101 to S131 and capable of obtaining the desired estimation accuracy (that is, the coordinate value of the observation point adopted in step S115). Based on the above, minz ₁ and minz _M described above are calculated for each observation point M. Since the content of the process is described in the above (3-3. Specific procedure for determining the installation position of the molten metal level meter), the detailed description thereof will be omitted here.

Then, using the calculated minz ₁ and minz _M , an appropriate installation position of the molten metal level meter is determined for each observation point M (step S135). Specifically, for each observation point M, the distances from the two mold short sides (the first mold short side and the second mold short side) are less than or equal to the distances to the positions corresponding to minz ₁ and minz _M , respectively. At a certain position, x ₁ and x _M are determined. Then, according to the above mathematical formula (31), x ₂ to x _M-1 are determined so as to be located at substantially equal intervals between x ₁ and x _M. Since the content of the process is described in the above (3-3. Specific procedure for determining the installation position of the molten metal level meter), the detailed description thereof will be omitted here.

In this embodiment, as a result of executing the above method for determining the installation position of the molten metal level meter, the following facts could be confirmed.

First, the present inventors examined the distribution of the coordinate values x ₁ , ..., X ₈ of the observation points where RMSE / σ satisfies the adoption criteria in the template width direction. 8 to 15 show the coordinate values of the observation points that satisfy the adoption criteria when the value of the adoption criteria of RMSE / σ is 0.25 when the number of observation points M = 8 x ₁ , ..., X ₈ ( that, RMSE / σ ≦ 0.25 that satisfies the observation point coordinate values _x 1, ..., for _{x 8), x 1, ...} , is a histogram showing the distribution in the mold width direction of each _{x 8.} In the histograms shown in FIGS. 8 to 15, x ₁ , ..., X ₈ are normalized by the mold width W on the horizontal axis, respectively (that is, x _m / W (m = 1, ..., 8). -0.5 ≤ x _{m /} W ≤ 0.5) is taken, and the frequencies of x ₁ , ..., X ₈ adopted on the vertical axis are taken.

Referring to FIGS. 8 through 15, the _{x 1} it can be _seen that the frequency employed closer to x 1 /W=-0.5 is large. This means that when x ₁ is close to the short side of the mold (the short side of the first mold), it is highly possible that high estimation accuracy can be obtained for the estimation of the shape of the molten metal. Similarly, for x ₈ (ie, x _M ), it can be seen that the peak is located near x _{8 /} W = 0.5. This is because when x ₈ is close to the mold short side (second mold short side) on the side opposite to the side where x ₁ is located, it is highly possible that high estimation accuracy can be obtained for the molten metal surface shape estimation. Means. Note that _{x 8,} the frequency thereof is not the highest in x 8 /W=0.5 _is imply a can not be obtained high estimation accuracy in x 8 /W=0.5 is However, in this embodiment, when the value x _m of the coordinate of the observation point is set by a uniform random number in order to calculate RMSE / σ, the second template short side corresponding to x ₈ and x = 0.5 W the distance between the first to be longer than the distance between the mold short side corresponding to the x ₁ and x = -0.5W, since that sets the value of these observations point coordinates, originally x in the vicinity of ₈ /W=0.5 it is because the low frequency _{with which x 8} is present.

On the other _hand, looking at the histogram for x 2 ~x _7, the peak position of the _x 2 / W~x 7 / W _is between the peak position of the peak position and _x 8 / W of _x 1 / W, It can be confirmed that they exist at approximately equal intervals. Therefore, as described above, according to the above equation (31), by determining the x ₂ ~x ₇ substantially evenly spaced between x ₁ and x _8, to obtain a high estimation accuracy for the melt surface shape estimation You can.

In addition, in FIGS. 8 to 15, the result when the number of observation points M = 8 is shown as an example, but as a result of the examination by the present inventors, the same result is shown even when the value of M is different. It has been confirmed that.

Next, the present inventors examined the distribution of x ₁ , x _M , which are the coordinate values of both ends in the mold width direction, in more detail. The present inventors repeatedly executed the series of processes shown in FIG. 6 while changing the value of the RMSE / σ adoption standard, and the value of the RMSE / σ adoption standard and x ₁ adopted in the adoption standard. We investigated the relationship between the distribution in the mold width direction x _M. FIG. 16-19 is a diagram showing the values of the RMSE / σ adoption criteria and the distribution of the coordinate values x ₁ and x _M of the observation points adopted in the adoption criteria in the template width direction. In FIGS. 16-19, the horizontal axis is the value of the adoption standard of RMSE / σ, and the vertical axis is the coordinate value x / mold width W in the mold width direction, which corresponds to the adopted x ₁ and x _M. The points are plotted with circles. The black circle is the point corresponding to x ₁ , and the white circle is the point corresponding to x _M. Further, FIGS. 16 to 19 show the results when the number of observation points M = 5 to 8, respectively. Further, in order to avoid a large number of plot points and complicated figures, in each of FIGS. 16 to 19, one level (specifically, R ₀ = 0.02778 mm) for the covariance matrix R is set. Set and set one level for the covariance matrix Q (specifically, when each component of the disturbance term of Q has a correlation, water at a casting speed of 2.2 m / min and a mold width of 1.425 m. Only the result when Q) generated based on one result in the model experiment is set is shown.

Referring to FIGS. 16 19, regardless of the value of the observation points M, as the value of inclusion criteria of RMSE / sigma increases, the existence range of the present range and x _M of x _1, none, mold width direction You can see the tendency to spread toward the center of. Since x ₁ , x _M adopted when the value of the adoption standard of RMSE / σ is smaller, that is, x ₁ , x _M capable of obtaining higher estimation accuracy, FIG. 16-FIG. 19 shows. From the results shown, x ₁ and x _M should be set in the vicinity of the mold short side corresponding to x = -0.5 W and the mold short side corresponding to x = 0.5 W, respectively, in any M. Therefore, it can be seen that higher estimation accuracy can be obtained. Therefore, as described above, by calculating minz ₁ and minz _M and determining the setting range of x ₁ and x _M based on these, higher estimation accuracy can be obtained for x ₁ and x _M. The placement can be determined.

More specifically, for example, try to examine for the presence range of _x 1, _{x M} when the value of the inclusion criteria of RMSE / sigma is 0.25. In this case, among the points corresponding to x ₁ / W located on the straight line indicating that the value of the adoption standard of RMSE / σ shown in FIGS. 16 to 19 is 0.25, x / W = −0. The distance from the x / W = −0.5 at the point farthest from 5 corresponds to z ₁ described above. Similarly, among the points corresponding to x _M / W located on the straight line indicating that the value of the adoption standard of RMSE / σ is 0.25, the point farthest from x / W = 0.5. , the distance from the x / W = 0.5 corresponds to _{z M} described above. Since the results shown in FIGS. 16 to 19 are the results when R and Q are at certain levels, z ₁ and z _M can be obtained for each combination of R and Q levels. .. The smallest of these z ₁ and z _M is minz ₁ and minz _M , which correspond to the boundaries of the existence range of x ₁ / W and x _M / W, respectively.

In this manner was obtained, the _x 1, _{x M} existing range bounds of the case where the value of the inclusion criteria of RMSE / sigma is 0.25, shown in Figure 20. FIG. 20 is a graph showing the boundary of the existence range of the coordinate values x ₁ and x _M of the observation points when the value of the adoption standard of RMSE / σ is 0.25. In FIG. 20, the number of observation points M is taken on the horizontal axis, the coordinate value x / the mold width W in the mold width direction is taken on the vertical axis, and x ₁ / corresponding to minz ₁ and minz _M obtained as described above, respectively. The values of W and x _M / W (that is, the values corresponding to the boundary of the existence range of x ₁ / W and x _M / W) are plotted.

From the results shown in FIG. 20, in the case of M ≦ 5 is higher estimation accuracy can be obtained for _x 1 / _W, the range of _x M / W _is, x 1 /W≦-0.49 and _x M / a W ≧ 0.38, in the case of M ≧ 6 is higher estimation accuracy can be obtained for _x 1 / _W, the range of _x M / W _is, x 1 /W≦-0.31 and _{x M} It was found that / W ≧ 0.10. In addition, although only the simulation result in the case of 5 ≦ M ≦ 8 is shown in FIG. 20, as a result of the examination by the present inventors, in the case of M ≦ 4, the same conditions as in the case of M = 5 may be satisfied. It has been confirmed that when M ≧ 9, the same conditions as when M = 8 should be satisfied.

Similarly, for example, the result of investigation for the presence range of _x 1, _{x M} when the value of the inclusion criteria of RMSE / sigma of 0.20, shown in Figure 21 Figure 25. 21-24 are diagrams corresponding to FIGS. 16-19, in which the values of the RMSE / σ adoption criteria and the coordinate values of the observation points adopted in the adoption criteria x ₁ , x _M mold widths. It is a figure which shows the distribution in a direction. As an example, FIGS. 21 to 24 show the distribution of x ₁ and x _{M in} the mold width direction based on the same calculation results as in FIGS. 16 to 19 (that is, x ₁ and x _{M in} the mold width direction). The plot itself showing the distribution is similar to FIGS. 16-19). However, in FIGS. 21 to 24, in order to pay attention to the case where the value of the RMSE / σ adoption standard is 0.20, a straight line indicating that the RMSE / σ adoption standard value is 0.20 is added. doing.

Further, FIG. 25 is a diagram corresponding to FIG. 20, and shows the boundary of the existence range of the coordinate values x ₁ and x _M of the observation point when the value of the adoption standard of RMSE / σ is 0.20. It is a graph diagram. In FIG. 25, minz ₁ and minz _M are obtained when the value of the adoption standard of RMSE / σ is 0.20, and the values of x ₁ / W and x _M / W corresponding to these minz ₁ and minz _M , respectively ( That is, the values corresponding to the boundaries of the existence range of x ₁ / W and x _M / W) are plotted.

From the results shown in FIG. 25, in the case of M ≦ 6 is higher estimation accuracy can be obtained for _x 1 / _W, the range of _x M / W _is, x 1 /W≦-0.49 and _x M / a W ≧ 0.49, in the case of M ≧ 7 is higher estimation accuracy can be obtained for _x 1 / _W, the range of _x M / W _is, x 1 _{/W≦-0.49+0.03} ( It was found that M-6) and x _{M /} W ≧ 0.49-0.05 (M-6). Note that FIG. 25 shows only the simulation results when 5 ≦ M ≦ 8, but as a result of examination by the present inventors, when M ≦ 4, the same conditions as when M = 5 may be satisfied. It has been confirmed that when M ≧ 9, the same conditions as when M = 8 should be satisfied.

(6. Supplement)
Although the preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, the present invention is not limited to such examples. It is clear that a person having ordinary knowledge in the field of technology to which the present invention belongs can come up with various modifications or modifications within the scope of the technical ideas described in the claims. , These are also naturally understood to belong to the technical scope of the present invention.

For example, in the above embodiment, the shape of the molten metal is estimated by a sequential estimation process using a Kalman filter, but the present invention is not limited to this example. In the present invention, a plurality of measurements of the molten metal surface level at a certain time, by estimating the value of the amplitude a _{n (t)} which satisfies the above equation (2), in the process of estimating the melt surface shape, the hot water By appropriately determining the positions of the plurality of observation points of the surface height in the template width direction, it is possible to obtain better estimation accuracy, and the content of the estimation process is not limited. Regardless of the content of the estimation process, the same effect can be obtained by determining the positions of multiple observation points in the mold width direction according to the method described in (3. Installation position of the molten metal level meter). is there. For example, the value of the amplitude a _{n (t)} which satisfies the above equation (2) from a plurality of measurements of the molten metal surface level at a certain time may be determined by using a regularization method.

1 Hot water surface shape estimation system 101 Mold 103 Immersion nozzle 105 Hot water level meter 201 Hot water surface shape estimation device 203 Output device 205 Storage device 251 Measured value acquisition unit 253 Calculation unit 255 Output unit 257 Storage unit

Claims (10)

Based on the measured values of the height of the molten metal in the mold of the continuous casting machine at M (M ≧ 2) observation points arranged side by side in the width direction of the mold, the case where the molten metal surface is horizontal was used as a reference. This is a method for estimating the shape of the molten metal, which is the distribution of the height of the molten metal in the mold width direction.
Including the method for determining the M observation points,
The determination method is
A step of the M based on a molten metal surface level estimate of at candidate positions (M ≧ 2) of the observation point, estimates the molten metal surface shape,
The step of calculating the estimated error of the molten metal surface shape and
The step of determining the positions of the M observation points so that the estimation error becomes small, and
Have,
The M observation points determined in the determination step are − W / 2 or more and W / 2 or less in a coordinate system in which the mold width direction is the x-axis direction and the center in the mold width direction is x = 0. in the range of, and, for each n, at least one of the observation point is in other than the position of the value x _{n, k} that you express by the following equation (101),
Hot water surface shape estimation method.

here,
W: Mold width N: Indicates the number of wavelength components of a sine wave having a wavelength of 2 W / n (n is an integer from 1 to N) constituting the molten metal surface shape and having both ends in the width direction of the mold as wave antinodes. It is an integer greater than or equal to 2. The method for estimating the shape of the molten metal according to claim 1, wherein the estimated value of the height of the molten metal is calculated using a state space model representing fluctuations in the height of the molten metal in the mold of the continuous casting machine. The molten metal shape estimation according to claim 1 or 2, wherein in the step of calculating the estimation error of the molten metal surface shape, the estimated mean square error RMSE of the molten metal surface shape is calculated as the estimation error of the molten metal surface shape. Method. A predetermined level for the covariance matrix related to the observed noise in the measurement of the height of the molten metal at the observation point, a predetermined level for the covariance matrix related to the disturbance for each wavelength component constituting the molten metal surface shape, and the observation. For each level combination that is a combination of a predetermined level for the number M of points
Candidate position x 1 of the previous SL observation _point, ..., to estimate the Kiyumen shape before set by uniform random numbers x _M,
As the estimation error of the surface shape, the estimated mean square error RMSE of the surface shape is calculated, and the ratio RMSE / σ of the RMSE and the standard deviation σ of the time variation of the surface shape to be estimated is calculated. Calculate and
It is determined whether or not the RMSE / σ satisfies the preset RMSE / σ adoption criteria.
A series of processes in which the candidate positions x ₁ , ..., X _M of the observation points corresponding to the RMSE / σ satisfying the adoption criteria are adopted as the positions of the M observation points are repeated a predetermined number of times.
For each of the level combinations, the candidate positions x ₁ , ..., X _M of the observation points corresponding to RMSE / σ satisfying the adoption criteria correspond to the positions x ₁ of the coordinates closest to any of the short sides of the mold. The maximum value z ₁ of the ratio of the distance from the first mold short side, which is the mold short side near itself of the observation point, to the mold width, and the mold short side opposite to the first mold short side. The maximum value z _M of the ratio of the distance from the second mold short side of the observation point to the mold width corresponding to the position x _M closest to the second mold short side is calculated.
For each of the levels for the number M of the observation points, the minimum value minz _{1 of the} maximum value z ₁ when the level for the covariance matrix for the observation noise and the level for the covariance matrix for the disturbance are changed. And the minimum value minz _M of the maximum value z _M are calculated.
A position where the distance from the first mold short side is equal to or less than the distance from the first mold short side to the position in the mold width direction corresponding to the minimum value minz ₁ , and from the second mold short side. The observation point and the position x _M corresponding to the position x ₁ correspond to the positions where the distance is equal to or less than the distance from the short side of the second mold to the position in the mold width direction corresponding to the minimum value minz _M , respectively. the observation point is located, so the remaining M-2 pieces of the observation points are located in a evenly spacing between the observation point corresponding to the observation point and the position x _M corresponding to the position x ₁ ,
Determine the positions of the M observation points,
The method for estimating the shape of the molten metal according to any one of claims 1 to 3 . When the adoption standard of RMSE / σ is 0.25,
When M ≦ 5, the ratio of the distance from the short side of the first mold to the mold width of the observation point corresponding to the position x ₁ is 0.01 or less, and the observation point corresponding to the position x _M. The position of the observation point corresponding to the position x ₁ and the position of the observation point corresponding to the position x _M are determined so that the ratio of the distance from the short side of the second mold to the mold width is 0.12 or less. And
When M ≧ 6, the ratio of the distance from the short side of the first mold to the mold width of the observation point corresponding to the position x ₁ is 0.19 or less, and the observation point corresponding to the position x _M. The position of the observation point corresponding to the position x ₁ and the position of the observation point corresponding to the position x _M are determined so that the ratio of the distance from the short side of the second mold to the mold width is 0.4 or less. To do,
The method for estimating the shape of the molten metal according to claim 4 . When the adoption standard of RMSE / σ is 0.20,
When M ≦ 6, the ratio of the distance from the short side of the first mold to the mold width of the observation point corresponding to the position x ₁ is 0.01 or less, and the observation point corresponding to the position x _M. The position of the observation point corresponding to the position x ₁ and the position of the observation point corresponding to the position x _M are determined so that the ratio of the distance from the short side of the second mold to the mold width is 0.01 or less. And
When M ≧ 7, the ratio of the distance from the first mold short side of the observation point corresponding to the position x ₁ to the mold width is 0.01 + 0.03 x (M-6) or less. Position x ₁ so that the ratio of the distance from the second mold short side of the observation point corresponding to the position x _M to the mold width is 0.01-0.05 x (M-6) or less. The position of the observation point corresponding to x _M is determined.
The method for estimating the shape of the molten metal according to claim 4 . The step of estimating the shape of the molten metal is
A step of expressing the molten metal surface shape by a state space model including at least a wavelength component of a sinusoidal wave having a wavelength of 2 W / n whose both ends in the width direction of the mold are wave antinodes.
A step of sequentially estimating the shape of the molten metal by applying a Kalman filter to the state space model using the heights of the molten metal measured at the M observation points as observation values.
Including
In the state space model, the amplitude of the wavelength component is expressed by a standing wave component and a disturbance component.
The Kalman filter treats the disturbance component as system noise.
The method for estimating the shape of the molten metal according to any one of claims 1 to 6 . The M observation points determined in the determination step include the positions of both short sides of the template.
The method for estimating the shape of the molten metal according to any one of claims 1 to 7 . Based on the measured values of the height of the molten metal in the mold of the continuous casting machine at M (M ≧ 2) observation points arranged side by side in the width direction of the mold, the case where the molten metal surface is horizontal was used as a reference. A molten metal shape estimation device that estimates the molten metal shape, which is the distribution of the height of the molten metal in the mold width direction.
The molten metal shape is estimated based on the estimated value of the molten metal surface height at the candidate positions of the M observation points (M ≧ 2), and the estimated error of the molten metal surface shape is calculated. It is configured to determine the positions of the M observation points so that the estimation error becomes small.
The determined M observation points are
The mold width direction and the x-axis direction, the center of the mold width direction in a coordinate system with x = 0, - W / 2 or more and is in W / 2 or less of the range, and, for each n, at least one of the observation point is other than the position of the value x _{n, k} which are Ru represented by the following equation (101),
Hot water surface shape estimation device.

here,
W: Mold width N: Indicates the number of wavelength components of a sine wave having a wavelength of 2 W / n (n is an integer from 1 to N) constituting the molten metal surface shape and having both ends in the width direction of the mold as wave antinodes. It is an integer greater than or equal to 2. Based on the measured values of the height of the molten metal in the mold of the continuous casting machine at M (M ≧ 2) observation points arranged side by side in the width direction of the mold, the case where the molten metal surface is horizontal was used as a reference. A method for estimating the shape of the molten metal, which is the distribution of the height of the molten metal in the width direction of the mold.
In a coordinate system in which the mold width direction is the x-axis direction and the center in the mold width direction is x = 0, the coordinate values of the M observation points are −W / 2 or more and W / 2 or less, and For each n, the coordinate value of at least one of the observation points is the coordinate value x represented by the following equation (105). _{n, k} Is a value other than
A predetermined level for the covariance matrix related to the observed noise in the measurement of the height of the molten metal at the observation point, a predetermined level for the covariance matrix related to the disturbance for each wavelength component constituting the molten metal surface shape, and the observation. For each level combination that is a combination of a predetermined level for the number M of points
Coordinate values x of M observation points in the coordinate system ₁ , ..., x _M Is set by a uniform random number,
Set coordinate value x ₁ , ..., x _M The mean square error RMSE of the estimated value of the molten metal surface shape estimated based on the above is calculated, and the ratio RMSE / σ of the RMSE and the standard deviation σ of the time variation of the molten metal surface shape to be estimated is calculated.
It is determined whether the calculated RMSE / σ satisfies the preset RMSE / σ adoption criteria.
Coordinate value x corresponding to RMSE / σ satisfying the above adoption criteria ₁ , ..., x _M Is used as the coordinate values of the M observation points, and a series of processes is repeated a predetermined number of times.
For each of the level combinations, the coordinate value x corresponding to RMSE / σ that satisfies the adoption criteria. ₁ , ..., x _M The value of the coordinates closest to the short side of any mold x ₁ The maximum value z of the ratio of the distance from the first mold short side, which is the mold short side on the side close to itself of the observation point corresponding to, and the mold width. ₁ And the value x of the coordinates closest to the second mold short side, which is the mold short side opposite to the first mold short side. _M The maximum value z of the ratio of the distance from the second mold short side of the observation point corresponding to the mold width to the mold width. _M And, calculate
For each of the levels for the number M of the observation points, the maximum value z when the level for the covariance matrix for the observation noise and the level for the covariance matrix for the disturbance are changed. ₁ Minimum value minz ₁ And the maximum value z _M Minimum value minz _M And, calculate
The distance from the short side of the first mold is the minimum value minz from the short side of the first mold. ₁ The position that is equal to or less than the distance to the position in the mold width direction corresponding to, and the distance from the second mold short side are the minimum value minz from the second mold short side. _M Coordinate values x at positions that are less than or equal to the distance to the position in the mold width direction corresponding to ₁ The observation point and coordinate values x corresponding to _M The observation points corresponding to are located, and the remaining M-2 observation points are the coordinate values x. ₁ The observation point and coordinate values x corresponding to _M So that they are located at approximately even intervals between the observation points corresponding to
Coordinate values x of M of the observation points ₁ , ..., x _M To decide,
Hot water surface shape estimation method.

here,
W: Mold width
N: Two or more indicating the number of wavelength components of a sine wave having a wavelength of 2 W / n (n is an integer from 1 to N) having both ends in the width direction of the mold forming the surface shape of the molten metal. integer
Is.

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