JP6935769B2 - State estimation method, molten metal level control method, program, and state estimation device - Google Patents

Description

The present invention relates to a state estimation method for estimating the state of the molten metal in a mold of a continuous casting machine, a molten metal level control method based on the estimation result of the state estimation method, and a program for causing a computer to execute the state estimation method. And a state estimation device for estimating the state of the molten metal in the mold of the continuous casting machine.

In continuous steel casting, in order to stabilize the operation and improve the quality, the height of the molten metal in the mold is measured with a level meter, and the height of the molten metal is controlled by opening and closing the nozzle to keep the measured value at the target value (spray level). Control) is being performed. That is, control is performed to suppress the entire vertical movement of the molten metal surface (that is, the volume fluctuation of the molten steel in the mold).

In the present specification, the position of the molten metal at a specific point in the width direction in the mold (for example, expressed as a relative position with respect to the upper end of the mold) is defined as the height of the molten metal, and the width of the height of the molten metal in the mold. The distribution in the direction is defined as the height distribution of the molten metal. Further, the height distribution of the molten metal at the position in the inner width direction of the mold based on the case where the molten metal surface is horizontal 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 change in the shape of the molten metal over time including the entire vertical movement of the molten metal (variation in the level of the molten metal) that occurs uniformly in the entire inner width direction of the mold due to the balance of molten steel in the mold (that is, the inner width direction of the mold). The temporal fluctuation of the height of the molten metal as a whole) is called the fluctuation of the molten metal. Further, in the present specification, the state of the molten metal is at least one of the height of the molten metal, the distribution of the height of the molten metal, the shape of the molten metal, the fluctuation of the shape of the molten metal, the fluctuation of the molten metal level, and the overall vertical movement of the molten metal. Means that.

Here, the measured values of the molten metal level meter include not only the overall vertical movement of the molten metal surface to be suppressed, but also standing waves due to the ripples of the molten metal surface, swelling of the molten metal surface due to the influence of molten steel flow, measurement errors, etc. The disturbance component due to is superimposed. Therefore, the measured value of the molten metal level meter does not necessarily accurately represent the entire vertical movement of the molten metal. Therefore, even if the nozzle opening / closing operation or the like is performed based on the measured value of the molten metal level meter, it is difficult to appropriately suppress the entire vertical movement of the molten metal surface.

Therefore, a method of estimating the state of the molten metal based on the measured value of the molten metal level meter has been proposed. For example, in Patent Document 1, in a method of estimating the state of the molten metal based on the measured value of the molten metal level meter, the shape of the molten metal in the mold width direction is expanded by the basis functions of a sine wave and a cosine wave, and then. A method of estimating the expansion coefficient of the basis function by a Kalman filter assuming a vibration model derived from the surface wave equation is disclosed. The state of the molten metal (shape of the molten metal, overall vertical movement of the molten metal, etc.) is estimated by the method described in Patent Document 1, and the level of the molten metal is controlled based on the estimation result. It becomes possible to perform with higher accuracy.

Japanese Unexamined Patent Publication No. 2016-182607

However, the natural frequency of the vibration model used in Patent Document 1 does not match the actual phenomenon as much as the higher-order one. Therefore, in the method described in Patent Document 1, when the molten metal surface shape fluctuation or the molten metal surface fluctuation includes a high-order vibration component, the estimation accuracy is deteriorated.

Therefore, the present invention has been made in view of the above problems, and an object of the present invention is a novel method capable of more accurately estimating the state of the molten metal in a mold in a continuous casting machine. It is an object of the present invention to provide an improved state estimation method, a molten metal level control method, a program, and a state estimation device.

In order to solve the above problems, according to a certain viewpoint of the present invention, the measured values of the height of the molten metal at a plurality of measurement points in the width direction of the mold in the continuous casting machine are used to determine the surface of the molten metal in the mold. A state estimation method for estimating a state, in which a term relating to a difference between a measured value of the molten metal level and an estimated value of the molten metal level at the measurement point obtained from the measured value and a term relating to the height of the molten metal On a two-dimensional rectangular region with respect to time and space, including a term for the second-order differential in the time direction of the molten metal height estimation function representing an estimated value and a term for the second-order differential in the spatial direction of the spine height estimation function. By constructing a variation problem for the defined evaluation function, expanding the molten metal height estimation function using the base function defined on the two-dimensional rectangular region, and terminating the base function in a finite dimension. , The variation problem is converted into a coefficient estimation problem of a linear regression model that estimates the expansion coefficient of the base function, the expansion coefficient is estimated by solving the coefficient estimation problem, and the estimated expansion coefficient is estimated. Provided is a state estimation method for estimating the state of the molten metal using the above.

Further, in the state estimation method, the term relating to the difference between the measured value of the molten metal level and the estimated value of the molten metal level may be the sum of squares of the difference.

Further, in the state estimation method, the term relating to the difference between the measured value of the molten metal level and the estimated value of the molten metal level may be the sum of the absolute values of the difference.

Further, in the state estimation method, the basis function may be composed of trigonometric functions.

Further, in order to solve the above-mentioned problems, according to another viewpoint of the present invention, in the above-mentioned state estimation method, the entire vertical movement of the molten metal surface is estimated as the state of the molten metal surface, and the estimated molten metal surface is used. Provided is a molten metal level control method for controlling the molten metal level in the mold by using the whole vertical movement.

Further, in order to solve the above-mentioned problems, according to another viewpoint of the present invention, the mold is used in a computer by using the measured values of the height of the molten metal at a plurality of measurement points in the width direction of the mold in the continuous casting machine. It is a program that executes a state estimation method for estimating the state of the molten metal inside, and in the state estimation method, the measured value of the molten metal level and the height of the molten metal at the measurement point where the measured value is obtained. A term related to the difference from the estimated value, a term related to the second-order differential in the time direction of the molten metal height estimation function representing the estimated value of the molten metal level, and a term related to the second-order differential in the spatial direction of the molten metal height estimation function. Construct a variation problem for the evaluation function defined on the two-dimensional rectangular region with respect to time and space, including, and estimate the height of the molten metal using the base function defined on the two-dimensional rectangular region. By expanding the function and terminating the base function in a finite dimension, the variation problem is converted into a coefficient estimation problem of a linear regression model that estimates the expansion coefficient of the base function, and the coefficient estimation problem is solved. This provides a program that estimates the expansion coefficient and estimates the state of the molten metal using the estimated expansion coefficient.

Further, in order to solve the above problems, according to another viewpoint of the present invention, the measured values of the height of the molten metal at a plurality of measurement points in the width direction of the mold in the continuous casting machine are used in the mold. It is a state estimation device that estimates the state of the molten metal, and includes a term relating to the difference between the measured value of the molten metal level and the estimated value of the molten metal level at the measurement point from which the measured value is obtained, and the molten metal surface. A two-dimensional rectangle with respect to time and space, including a term for the second-order differential in the time direction of the molten metal height estimation function that represents the estimated value of the height, and a term for the second-order differential in the spatial direction of the molten metal height estimation function. Construct a variation problem for the evaluation function defined on the region, expand the molten metal height estimation function using the base function defined on the two-dimensional rectangular region, and expand the base function in finite dimensions. By terminating, the variation problem is converted into a coefficient estimation problem of a linear regression model that estimates the expansion coefficient of the base function, and the expansion coefficient is estimated and estimated by solving the coefficient estimation problem. Provided is a state estimation device including a calculation unit that estimates the state of the molten metal using the expansion coefficient.

As described above, according to the present invention, in the continuous casting machine, the state of the molten metal in the mold can be estimated more accurately.

It is a figure which shows the configuration example of the system which concerns on this embodiment. It is a flow chart which shows the processing procedure of the method of estimating the state of the molten metal which concerns on this Embodiment, which is executed by the state estimation apparatus. It is a block diagram which shows the functional structure of the state estimation apparatus which concerns on this embodiment. It is a block diagram which shows an example of the hardware composition of the state estimation apparatus which concerns on this embodiment. It is a graph which shows the example (1 sec) of the estimation result of the molten metal surface shape variation in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (2 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (3 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (4 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (5 sec) of the estimation result of the molten metal surface shape variation in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (6 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (7 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (8 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (9 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (10 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (11 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (12 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (13 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (14 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (15 sec) of the estimation result of the molten metal surface shape variation in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (16 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (17 sec) of the estimation result of the molten metal surface shape variation in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (18 sec) of the estimation result of the molten metal surface shape variation in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (19 sec) of the estimation result of the shape change of the molten metal in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the example (20 sec) of the estimation result of the molten metal surface shape variation in the Example which executed the state estimation method which concerns on this Embodiment. It is a graph which shows the result of having calculated the RMSE of the estimation result and the measurement result of the molten metal surface shape in the Example which executed the state estimation method which concerns on this Embodiment.

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.

(1. System configuration)
The configuration of the system according to the embodiment of the present invention will be described with reference to FIG. FIG. 1 is a diagram showing a configuration example of a system according to the present embodiment. Referring to FIG. 1, the system 1 according to the present embodiment includes a molten metal level meter 3 installed in a mold 2 of a continuous casting machine, a state estimation device 4, a display device 5, a continuous casting control device 6, and the like. To be equipped.

The molten metal level meter 3 measures the height of the molten metal at a predetermined position of the mold 2. The type of the molten metal level meter 3 is not limited, and as the molten metal level meter 3, various known ones such as a vortex type level meter and a thermocouple level meter may be used. In the present embodiment, a plurality of molten metal level gauges 3 are installed side by side in the mold width direction. That is, a plurality of measurement points for the height of the molten metal are provided in the width direction of the mold 2.

The state estimation device 4 estimates the state of the molten metal in the mold 2 based on the measured values of the height of the molten metal by the plurality of molten metal level meters 3. The state estimation device 4 can estimate the state of the molten metal surface in real time during continuous casting. The estimation result of the state of the molten metal is transmitted to at least one of the display device 5 and the continuous casting control device 6.

The display device 5 displays the estimation result by the state estimation device 4. For example, the display device 5 displays the shape of the molten metal at an estimated time as a graph. In this case, the display device 5 may superimpose the measured value by the molten metal level meter 3 on the molten metal surface shape which is the estimation result and display it. In addition, instead of the display device 5, or together with the display device 5, a printing device that prints the estimation result on a paper medium may be used.

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, since the molten metal surface shape estimated as described above is output in real time by the display device 5, it is possible to grasp the molten metal surface shape variation, and based on the molten metal surface shape variation, before the completion of casting. It becomes possible to grasp the distribution of slab defects in the slab width direction. As a result, slab quality control can be speeded up.

Based on the estimation result by the state estimation device 4, the continuous casting control device 6 controls the molten metal level so as to keep the height of the molten metal in the mold at the target value during continuous casting. Specifically, since the total vertical movement of the molten metal is generated by the balance of molten steel in the mold, the continuous casting control device 6 is based on the estimation result of the total vertical movement of the molten metal by the state estimation device 4. The opening / closing control of the immersion nozzle 8 for injecting molten steel into the mold 2 and the rotation speed control of the pinch roll for pulling out the slab from below the mold 2 are executed so as to suppress the overall vertical movement of the mold 2.

The specific content that the state estimation device 4 estimates as the state of the molten metal may be appropriately set by the user according to the purpose. Further, the destination to which the state estimation device 4 transmits the estimation result can also be appropriately set by the user according to the specific content to be estimated. For example, if the main purpose is to control the quality of the above-mentioned slabs, fluctuations in the shape of the molten metal can be the target of estimation. Then, the estimation result of the change in the shape of the molten metal is transmitted to the display device 5 and used by the user for quality control. Alternatively, for example, when the main purpose is to control the molten metal level as described above, the entire vertical movement of the molten metal surface can be an estimation target. Then, the estimation result of the overall vertical movement of the molten metal level is transmitted to the continuous casting control device 6 and used for the molten metal level control. In addition, the specific contents of the state of the molten metal to be estimated may be appropriately set for various purposes.

Further, in the above configuration example, the state estimation device 4 estimates the state of the molten metal in real time during continuous casting, and transmits the estimation result to at least one of the display device 5 and the continuous casting control device 6. However, this embodiment is not limited to such an example. For example, the estimation result may be transmitted to each of these devices and stored in a storage unit (storage unit 44 shown in FIG. 3 to be described later) included in the state estimation device 4. The estimation result stored in the storage unit functions as, for example, a backup of the output by the display device 5, and is cast after the fact when the occurrence of slab defects is overlooked in the real-time output by the display device 5. It is used to identify the occurrence of one-sided defects and their causes. Further, even when the real-time output by the display device 5 is not performed, the estimation result stored in the storage unit may be referred to in order to identify the cause after the occurrence of the slab defect. Further, the state estimation device 4 does not necessarily have to estimate the state of the molten metal in real time during continuous casting. For example, when it is desired to confirm the state of the molten metal during operation for the purpose of identifying the cause after the occurrence of the slab defect as described above, the state estimation device 4 is used to obtain the height of the molten metal during operation. The state of the molten metal may be estimated ex post facto based on the measured value.

(2. Method of estimating the state of the hot water surface)
The method of estimating the state of the molten metal executed by the state estimation device 4 of the system 1 described above will be described in detail. Since the width of the mold 2 is sufficiently larger than the thickness, in the present embodiment, the variation of the height of the molten metal in the thickness direction is not considered, and only the variation in the width direction is considered. Estimate the state of.

(2-1. Principle of estimation method)
The state estimation device 4 uses the measured values of the height of the molten metal at a plurality of measurement points arranged in the width direction of the mold 2, and the time variation of the height distribution of the entire surface in the width direction including the position where the measurement point does not exist. (That is, the fluctuation of the molten metal level) can be estimated. At this time, in the present embodiment, the fluctuation of the molten metal level is estimated by using the property that the height distribution of the molten metal fluctuates smoothly in time and space.

Specifically, in the present embodiment, as shown in the following mathematical formula (1), the estimated value of the height of the molten metal is used as a regularization term representing "the temporal and spatial smoothness of the height distribution of the molten metal". We define an evaluation function J [d (x, t)] whose regularization term is the second-order differential of the hot water surface height estimation function d (x, t) with respect to time and space. Then, by solving the variational problem for the J [d (x, t)], the molten metal height estimation function d (x, t) is obtained (d (x, t) is the molten metal surface height. Since it is a temporally and spatially continuous function representing the estimated value of, to obtain d (x, t) is to estimate the fluctuation of the molten metal level). In the following, the molten metal height estimation function d (x, t) representing the estimated value of the molten metal surface height is also simply referred to as the estimated value d (x, t) of the molten metal surface height.

_{Here, y (x j, t i} ) is a measure of the molten metal surface height at position _{x j,} the time _{t i.} d _(x j, _{t i)} is an estimate of the molten metal surface height at position _{x j,} the time _{t i.} I is the time sampling point. J is the number of spatial sampling points in the width direction of the mold 2. λ is an adjustment parameter. W is the mold width. T is the time width to be estimated, that is, the time from time t _{1 to time t I.} In the following, the time width T that is the target of this estimation will also be described as a time window. In the present embodiment, the time interval [t ₁ , t _I ] is replaced with the time interval [-T / 2, T / 2] for the sake of uniformity of notation.

The first term on the right side in the equation (1) is a section on the difference between the molten metal surface height measurement values _{y (x} j, _{t i)} and the molten metal surface level of the estimated value _{d (x} j, _{t i)} (Hereinafter, also referred to as restoration error term). As shown in the equation (1), in the present embodiment, restore the error term, melt-surface height measurements _{y (x} j, _{t i)} and the molten metal surface level of the estimated value _{d (x} j, _{t i} ) Is the sum of squares. Further, the second term on the right side in the above mathematical formula (1) is a regularization term, and as described above, in order to express "temporal and spatial smoothness of the height distribution of the molten metal", the height of the molten metal. comprising the estimated values d (x _{j, t i)} the section on terms and spatial second derivative with respect to time second order differential of.

The above mathematical formula (1) can be rewritten as the following mathematical formula (2) by using the delta function.

In the following, for the sake of simplicity, the description of the integration range in the mathematical formula will be omitted.

Here, the solution of the variation problem defined on the two-dimensional rectangular region can be expanded by the orthonormal basis function system (for example, "Coolant, Hilbert," Method of Mathematical Physics ", Maruzen Publishing Co., Ltd., p. .190-p.191 ”). Since the variational problem shown in the above mathematical formula (2) is defined on the two-dimensional rectangular region [-W / 2, W / 2] x [-T / 2, T / 2], the present embodiment. Then, using this method, the solution d (x, t) of the variational problem is developed by an orthonormal basis function system using trigonometric functions as shown in the following mathematical formula (3).

Here, in the above example, a basis function composed of trigonometric functions is used, but the present embodiment is not limited to such an example. Other functions may be used as basis functions as long as they are orthonormal functions in the temporal and spatial directions. However, as a result of studies by the present inventors, it has been found that both ends in the width direction become antinodes in the fluctuation of the molten metal level in the mold 2. Therefore, as the basis function, one that satisfies the boundary condition that the mold 2 becomes antinodes at both ends in the width direction is selected in the spatial direction. In the above example, the basis function is selected so as to satisfy the boundary condition shown in the following mathematical formula (4). Examples of other basis functions will be described in detail below (5. Modifications).

In the following, in order to simplify the notation, the above formula (3) is used in the following formula (5) using the ^{basis functions d (1)} _mn (x, t) and d ⁽²⁾ _{mn (x, t).} It will be expressed as.

The basis functions d ⁽¹⁾ _mn (x, t) and d ⁽²⁾ _mn (x, t) are defined as the following mathematical formulas (6) to (13).

In the following, the above mathematical formula (1) is transformed by using the above mathematical formula (5). As a result, the above mathematical formula (1) is represented by a linear regression model using the ^{basis functions d (1)} _mn (x, t) and d ⁽²⁾ _{mn (x, t). ) Can} be transformed into a coefficient estimation problem of a linear regression model that estimates the expansion coefficients of the basis functions d ⁽¹⁾ mn (x, t), d ⁽²⁾ _{mn (x, t).}

First, the second term (regularization term) on the right side of the above formula (1) is calculated. Substituting the above formula (5) and sequentially calculating the terms included in the regularization term as shown in the following formulas (14) to (17), the regularization term is finally obtained by the following formula (18). It can be expressed as.

Here, since the basis functions d ⁽¹⁾ _mn (x, t) and d ⁽²⁾ _mn (x, t) have orthogonality, the following mathematical formulas (19) to (22) are established.

^{Using the orthonormality of the basis functions d (1)} _mn (x, t), d ⁽²⁾ _mn (x, t) shown in the above formulas (19) to (22), the above formula (18) is as follows. It is expressed as the formula (23).

Subsequently, the first term (restoration error term) on the right side of the above formula (2) is calculated. By substituting the above equation (5), the restoration error term can be expressed as the following equation (24).

Therefore, from the above mathematical formulas (23) and (24), the above mathematical formula (1) can be expressed as the following mathematical formula (25). As shown in the following formula (25), by transforming the formula using the above formula (5), J [d (x, t)] in the above formula (1) is set to a _mn and b _mn as variables. It can be transformed into a function J [a _mn , b _mn].

In the present embodiment, the following mathematical formula (26) is obtained by truncating the infinite series at an appropriate dimension (n = 0,1, ... N, m = 0,1, ... M). As a result, the infinite dimensional variational problem (the above mathematical formulas (1) and (2)) is replaced by the finite dimensional coefficient estimation problem (the following mathematical formula (26)). That is, the variational problem for J [d (x, t)] shown in the above mathematical formulas (1) and (2) has a quadratic function J [a] having a regularization term with _{a mn} and b _{mn as variables. It} was replaced by the minimization problem of [mn, b _mn].

Expressed using a matrix, the above mathematical formula (26) is expressed as the following mathematical formula (27).

Here, u = (a ₀₀ , a ₀₁ , b ₀₁ , ..., a ₁₁ , b ₁₁ , ..., a _mn , b _mn , ..., a _MN , b _MN ). y = (y (x ₁ , t ₁ ), y (x ₁ , t ₂ ), ..., y (x ₁ , t _J ), y (x ₂ , t ₁ ), ..., y (x) _I , t _J )). A and L are matrices that are appropriately determined according to the sequence of u.

The retention condition of J [u] shown in the above mathematical formula (27) is represented by the following mathematical formula (28).

U that satisfies this retention condition is u ^* = (a ₀₀ ^* , a ₀₁ ^* , b ₀₁ ^* , ... a ₁₁ ^* , b ₁₁ ^* , ... a _mn ^* , b _mn ^* , ... a _MN ^* , b _MN ^* ). This u ^* can be obtained analytically as in the following mathematical formula (29).

In the present embodiment, the state estimator 4, the measured value _{y (x} j, _{t i)} by melt-surface level gauge 3 by substituting the above equation (29), J shown in the equation (27) [u] Calculate u = u ^* that minimizes (ie, basis functions d ⁽¹⁾ _mn (x, t), d ⁽²⁾ _mn (x, t) that minimize J [u]. Estimate the expansion coefficient of).

The state estimation device 4 has obtained this u ^* = (a ₀₀ ^* , a ₀₁ ^* , b ₀₁ ^* , ... a ₁₁ ^* , b ₁₁ ^* , ... a _mn ^* , b _mn ^* , ... The state of the _{molten metal} can be estimated using a _MN ^* and b ^{MN *).} For example, when it is desired to obtain an estimated value ^{of the molten metal level fluctuation, the state estimation device 4 substitutes the obtained u *} into the above equation (5) to obtain an estimated value d ^* (x, of the molten metal level fluctuation). t) (that is, the estimated value of the molten metal level fluctuation) is calculated. In this specification, in order to distinguish from the estimated value d (x, t) of the molten metal used in the above description, the estimated height of the molten metal obtained ^{by the state estimation device 4 using u *.} The value ^{shall be described as d *} (x, t). That is, the estimated value d ^* (x, t) of the height of the molten metal can be calculated by the following mathematical formula (30).

The state estimation device 4 can also estimate the overall vertical movement of the molten metal surface. Specifically, assuming that the estimated value of the overall vertical movement of the molten metal surface is d ₀ (t), the d ₀ (t) is a basis function of m = 0 (that is, in the spatial direction) in the above mathematical formula (5). By considering only the term about (uniform basis function), it can be expressed as the following mathematical formula (31).

^{By substituting the obtained u *} into the above formula (31), the state estimation device 4 _{similarly performs the estimated value d 0} ^* (t) (d ^* (x, t)) of the overall vertical movement of the molten metal surface. In order to distinguish it from the general estimated value of the total vertical movement of the molten metal d ₀ ^{(t), the estimated value of the total vertical movement of the molten metal obtained by the state estimation device 4 using u *} is d _0. ^* (T)) can be requested. _{That is, the estimated value d 0} ^* (t) of the total vertical movement of the molten metal surface can be calculated by the following mathematical formula (32).

Further, the state estimation device 4 obtains an estimated value d ^* (x, t) of the height of the molten metal (that is, an estimated value of the fluctuation of _{the molten metal), and an estimated value d 0} ^* (t) of the overall vertical movement of the molten metal. ) Can be subtracted to obtain the estimated value of the change in the shape of the molten metal. Further, the state estimation device 4 may obtain an estimated value of the molten metal level distribution at a certain time from the estimated value of the molten metal level fluctuation, or the hot water at a certain position from the estimated value of the molten metal level distribution. An estimated value of surface height may be obtained. Further, the state estimation device 4 may obtain an estimated value of the molten metal surface shape at a certain time from the estimated value of the molten metal surface shape fluctuation. As described above, what the state estimation device 4 specifically estimates as the state of the molten metal may be appropriately set by the user.

Here, with respect to various parameters used for estimation (time sampling point I, spatial sampling point J, time window T, adjustment parameter λ, and basis function numbers N, M, etc.), sufficient estimation accuracy can be obtained. In addition, it may be appropriately set by the user in consideration of the calculation load and the like.

For example, for the time sampling point I, the spatial sampling point J, and the adjustment parameter λ, appropriate values may be appropriately selected so as to satisfy the above conditions by using a water model experiment or the like. For example, the adjustment parameter λ may be set by cross-validation or the like using data of a water model experiment or the like. The number of spatial sampling points J is set so as not to become excessive in consideration of installation cost, maintenance cost, etc. in order to correspond to the measurement point of the height of the molten metal, that is, the number of installed units of the molten metal level meter 3. It is preferable to be done.

Further, for example, the time window T may be selected so as to include a main fluctuation period assumed as the fluctuation of the molten metal level.

Further, for example, for the number N of basis functions in the time direction, N = [(J-1) / 2] ([・] is a Gaussian symbol). Further, for the number M of basis functions in the spatial direction, M = I-1 may be set. However, in general, the estimation accuracy does not change significantly by slightly increasing or decreasing the number of basis functions. Therefore, if some knowledge is obtained in advance, the values of N and M may be appropriately increased or decreased from the above values. You may. If there is no significant increase in the number of basis functions, there will be no significant change in the calculation time in practice, so it is not necessary to limit the number of basis functions in consideration of the calculation time.

As described above, in the present embodiment, the height of the molten metal is solved by solving the variation problem of the evaluation function including the term related to the difference between the measured value of the height of the molten metal and the calculated value of the height of the molten metal. Find the estimated value of. At this time, assuming "temporal and spatial smoothness of the height distribution of the molten metal", the term related to the second derivative of the estimated value of the height of the molten metal regarding the time and space is used as the regularization term of the evaluation function. Introduce. By introducing such a regularization term, it becomes possible to estimate a smoothly fluctuating water level distribution (that is, smooth water surface fluctuation) based on the measured value of the water surface height.

Here, the actual fluctuation of the molten metal level includes fluctuation components different from the natural frequency of the standing wave, such as disturbance. In the method described in Patent Document 1, the state of the molten metal is estimated by assuming a surface wave equation model. Therefore, for example, when the fluctuation component is a high-order component, the estimation is highly accurate. Was difficult to do. On the other hand, in the present embodiment, since the surface wave equation model is not assumed, even if the estimation accuracy deteriorates due to the model error in the method described in Patent Document 1, the state of the molten metal can be accurately obtained. It becomes possible to estimate.

(2-2. Specific procedure of estimation method)
With reference to FIG. 2, a specific processing procedure of the method of estimating the state of the molten metal executed by the state estimation device 4 will be described. FIG. 2 is a flow chart showing a processing procedure of a method for estimating the state of the molten metal according to the present embodiment, which is executed by the state estimation device 4. When the processor of the state estimation device 4 executes arithmetic processing according to a predetermined program, each processing shown in FIG. 2 can be executed.

As shown in FIG. 2, in the method of estimating the state of the molten metal according to the present embodiment, first, a basis function is set (step S101). In step S101, as the basis functions used in the estimation process, for example, the basis functions d ⁽¹⁾ _mn (x, t) and d ⁽²⁾ _mn (x, t) shown in the above formulas (6) to (13) are used. Set. The basis function may be created in advance by the user and input to the state estimation device 4.

Then, the measured value _{y (x} j, _{t i)} of the molten metal surface level is obtained (step S103). In step S103, the measured value y (x _{j, t i)} of have been melt-surface height measured by the molten metal surface level gauge 3, which are more established in the width direction of the mold 2 shown in FIG. 1, obtained by the state estimating device 4 Will be done.

Then, the measured value y (x j, t i) of the obtained molten metal surface level with the coefficient of the linear regression model is estimated (step S105). In step S105, the equation (26), for the linear regression model shown in (27), J [a mn , b mn] (= J [u]) that minimizes the, basis function d (1) mn ( The expansion coefficients a mn and b mn (that is, u * ) of x, t), d (2) mn (x, t) are calculated according to the above formula (29).

Next, the state of the molten metal is estimated using ^{the u *} obtained in step S105 (step S107). The specific content of the estimated hot water surface state can be appropriately set by the user. For example, in step S107, ^{by substituting u *} obtained in step S105 into the above mathematical formula (30), the estimated value d ^* (x, t) of the height of the molten metal, that is, the estimated value of the fluctuation of the molten metal is calculated. NS. Further, for example, in step S107, _{the estimated value d 0} ^* (t) ^{of the overall vertical movement of the molten metal surface is calculated by substituting the u *} obtained in step S105 into the above mathematical formula (32). Further, in step S107, at least one of the estimated values of the height of the molten metal, the distribution of the height of the molten metal, the shape of the molten metal, and the variation in the shape of the molten metal may be calculated based on these estimated values.

Then, the estimation result is output (step S109). In step S109, the state of the molten metal estimated in step S107 is transmitted to at least one of the display device 5 and the continuous casting control device 6 shown in FIG.

Here, the process in step S101 is executed only once at the beginning when executing a series of processes. Then, while performing continuous casting, the processes in steps S103 to S109 are sequentially executed at predetermined time intervals. In the present embodiment, the time interval for performing the processing in step S103~ step S109 (hereinafter, also referred to as time interval estimating process), method (1) melt-surface height measurements _{y (x} j, _{t i)} of the Set either for each sampling interval or for each method (2) time window T. Which method is used may be appropriately set by the user.

For example, the time when the number of sampling points I = 10, T = 1 ( sec), the measured value of 10 molten metal surface level sampled every 0.1 seconds _{y (x} j, _{t i)} with an estimated Processing will be performed. If this case, when adopting the method (1), for each 0.1 seconds, the measured value y (x _{j, t i)} ten molten metal surface level of the last second with , The estimation process is performed. On the other hand, when adopting the method (2), for each T = 1 (sec), the measured value _{y (x} j, _{t i)} ten molten metal surface level of the last second with an estimated Processing is done.

According to the method (1), the estimation results are sequentially output in a shorter cycle, so that the estimation results can be sequentially displayed on the display device 5 while being overwritten with the latest results. That is, the estimation result of the current time is displayed on the display device 5 while being updated at any time. Therefore, the user can preferably adopt the method (1) when he / she wants to confirm the estimation result in real time.

On the other hand, in the method (2), the estimation results are sequentially output in a longer cycle, so that the calculation load of the state estimation device 4 can be made smaller than that in the method (1). Therefore, when the calculation load in the method (1) is excessive in consideration of the calculation capacity of the state estimation device 4, the user can preferably adopt the method (2).

However, the time interval of the estimation process is not limited to the above methods (1) and (2). In the present embodiment, the time interval of the estimation process, melt-surface height measurements y (x _{j, t i)} as a minimum unit sampling intervals, as an integer multiple of the spacing of the sampling interval, is set to any good.

(3. Functional configuration of state estimation device)
A functional configuration of the state estimation device 4 that executes the above-described processing will be described with reference to FIG. FIG. 3 is a block diagram showing a functional configuration of the state estimation device 4 according to the present embodiment. Referring to FIG. 3, the state estimation device 4 has a measurement value acquisition unit 41, a calculation unit 42, an output unit 43, and a storage unit 44 as its functions. The functions of each part will be described below.

The measured value acquisition unit 41 is realized by, for example, a processor such as a CPU (Central Processing Unit) or a DSP (Digital Signal Processor), and a communication device that receives the measured value of the molten metal level from the molten metal level meter 3. As shown in FIG. 1, the measured value acquisition unit 41 acquires measured values from a plurality of molten metal level meters 3 arranged side by side in the mold width direction. The process by the measured value acquisition unit 41 corresponds to the process in step S103 shown in FIG. When the processor constituting the measurement value acquisition unit 41 executes the arithmetic processing according to a predetermined program, the above processing can be executed via the communication device. The measured value acquisition unit 41 provides the acquired measured value to the calculation unit 42.

The calculation unit 42 is realized by a processor such as a CPU. The calculation unit 42 estimates the state of the molten metal using the measured value of the height of the molten metal acquired by the measured value acquisition unit 41. The specific content of the hot water surface state estimated by the calculation unit 42 may be appropriately set by the user, and the calculation unit 42 may set the hot water surface state desired by the user, for example, the shape of the hot water surface, according to the setting. Performs estimation processing. The processing by the calculation unit 42 corresponds to the processing in steps S101 and S105 to S107 shown in FIG. At this time, the calculation unit 42 uses various parameters (time sampling point I, spatial sampling point J, time window T, adjustment parameter λ, and basis function numbers N, M, etc.) stored in the storage unit 44. And execute the estimation process. These processes can be executed when the processor constituting the arithmetic unit 42 executes the arithmetic processes according to a predetermined program. Since the details of these processes have already been described, the description thereof will be omitted here.

The calculation unit 42 provides the output unit 43 with an estimation result regarding the state of the molten metal. Alternatively, the calculation unit 42 may store the estimation result of the state of the molten metal in the storage unit 44.

The output unit 43 is realized by a processor such as a CPU and a communication device that transmits a signal to an external device. The output unit 43 outputs the estimation result of the state of the molten metal by the calculation unit 42 to an external device. For example, the output unit 43 outputs the estimation result of the state of the molten metal (for example, the shape of the molten metal) by the calculation unit 42 to the display device 5 shown in FIG. The display device 5 displays the estimated shape of the molten metal on a display or the like. Further, for example, the output unit 43 outputs the estimation result of the state of the molten metal (for example, the entire vertical movement of the molten metal) by the calculation unit 42 to the continuous casting control device 6 shown in FIG. Based on the estimated total vertical movement of the molten metal surface, the continuous casting control device 6 makes at least one of the molten steel injection amount into the mold 2 and the slab withdrawal speed from the mold 2 the total vertical movement of the molten metal surface. Is controlled so as to suppress. The process by the output unit 43 corresponds to the process in step S109 shown in FIG. When the processor constituting the output unit 43 executes the arithmetic processing according to a predetermined program, the above processing can be executed via the communication device.

The storage unit 44 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 (Hard Disk Drive). The storage unit 44 is used for estimation processing by the calculation unit 42, for example, various parameters used for the estimation processing of the state of the molten metal by the calculation unit 42 described above, information about the basis function, progress of the estimation processing, and the like. Various related data are stored. The parameter is input to the storage unit 44 in advance by the user before the estimation process is executed. Further, the storage unit 44 may temporarily or permanently store the estimation result of the state of the molten metal by the calculation unit 42. This estimation result may be output by the output unit 43 to at least one of the display device 5 and the continuous casting control device 6 shown in FIG. 1 at an arbitrary timing.

The example of the functional configuration of the state estimation device 4 according to the present embodiment has been described above. The functional configuration of the state estimation device 4 described above is merely an example, and the state estimation device 4 may be configured to have the same functions as those described above, and the specific device configuration is It may be changed arbitrarily. For example, the state estimation device 4 does not necessarily have to be one device, and may be realized by the cooperation of a plurality of devices. In this case, each function of the state estimation device 4 is distributed and mounted on a plurality of devices, and the plurality of devices operate while exchanging various information with each other, thereby forming the state estimation device 4 as a whole. The function can be realized.

Further, it is possible to create a computer program for realizing the function of the state estimation device 4 as described above, particularly the function of the calculation unit 42, 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, for example, a network without using a recording medium.

(4. Hardware configuration)
FIG. 4 is a block diagram showing an example of the hardware configuration of the state estimation device 4 according to the present embodiment. Referring to FIG. 4, the state estimation device 4 includes a CPU 901, a ROM 903, and a RAM 905. The state estimation device 4 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 state estimation device 4 according to various programs recorded in the ROM 903, the RAM 905, the storage device 913, or the removable recording medium 921. 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 measured value acquisition unit 41, the calculation unit 42, and the output unit 43 shown in FIG. Further, the ROM 903 and the RAM 905 may form the storage unit 44 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, keyboard, 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. 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 state estimation device 4 can input various data to the state estimation device 4 and instruct the processing operation. The input device 909 may be replaced by an externally connected device 923 such as a tablet terminal having an operation function of the state estimation device 4.

The output device 911 is composed of a device capable of visually or audibly notifying the user of the acquired information. Examples of such a device include a display using a liquid crystal display, a CRT, or the like, an indicator such as a lamp, an audio output device such as a speaker or headphones, a printer device, or the like. The output device 911 outputs, for example, the results obtained by various processes performed by the state estimation device 4. For example, the display displays the results obtained by various processes performed by the state estimation device 4 on the screen as text or an image. Further, for example, the voice output device outputs the results obtained by various processes performed by the state estimation device 4 as an alarm or a dialog. As described with reference to FIG. 1, the system 1 according to the present embodiment includes a display device 5 as a means for presenting information to the user. Since the display device 5 has the same function as the output device 911, the output device 911 is not necessarily provided in the state estimation device 4 when the display device 5 can substitute the function of the output device 911. It does not have to be.

The storage device 913 is a data storage device configured as an example of the storage unit of the state estimation device 4. 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 programs 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 44 shown in FIG.

The drive 915 is a reader / writer for a recording medium, and is built in or externally attached to the state estimation device 4. 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 a record 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 state estimation device 4. 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 state estimation device 4 acquires various data directly 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, a LAN, or the like. The communication device 919 may constitute the measured value acquisition unit 41 and the output unit 43 shown in FIG.

The above is an example of a hardware configuration capable of realizing the function of the state estimation device 4 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.

(5. Modification example)
Some modifications of the embodiments described above will be described.

(5-1. Evaluation function)
In the above-described embodiment, the evaluation function J [d (x, t)] is defined as in the above mathematical formula (1), and finally the evaluation function J [d (x, t)] is obtained by transforming the equation. The optimization problem of the evaluation function J [u] shown in the above mathematical formula (27) was solved. However, this embodiment is not limited to such an example, and the evaluation function may be appropriately defined according to the purpose. Other examples of the evaluation function J [u] include the following.

For example, when the measured value of the height of the molten metal includes non-normal noise (absolute value that occurs suddenly, etc.), the restoration error term is set as the L1 loss function (that is, the restoration error term is defined as the height of the molten metal). the measurements _{y (x} j, _{t i)} and the molten metal surface level of the estimated value _{d (x} j, _{t i)} and the absolute value sum of the difference between), the evaluation function J shown in the following equation (33) [U] may be used.

For example, in the method described in Patent Document 1, since the state of the molten metal is estimated using a Kalman filter, if the measured value contains non-normal noise, the error of the estimation result may become large. be. On the other hand, in the present embodiment, as shown in the above equation (33), by constructing the evaluation function J [u] using the L1 loss function, non-normality noise is included. However, it is possible to make an estimation with high accuracy.

^{Further, for example, when it can be assumed in advance that the solution u = u *} of the optimization problem of the evaluation function J [u] is close to a specific value u ₀ , a regularization term is used as in the following mathematical formula (34). The replaced evaluation function J [u] may be used.

In this case, for example, it is considered that "the solution u ^* in the current calculation cycle is close to ^{the solution u *} one calculation cycle before", and the value ^{of the solution u *} one calculation cycle before is set as _{u 0.} Can be used.

(5-2. About basis functions)
In the above-described embodiment, the functions composed of the sine waves shown in the above equations (6) to (13) are used as the basis functions, but the present embodiment is not limited to such an example. In this embodiment, other basis functions may be used as long as they are orthonormal basis functions in the temporal direction and the spatial direction. However, in the spatial direction, it is necessary to be a basis function that satisfies the boundary condition shown in the above formula (4).

For example, as another basis function, a function composed of orthogonal polynomials such as Legendre polynomials can be used. Here, as an example, a basis function composed of Legendre polynomials will be described.

Table 1, as an example of a Legendre polynomial _P n (x), shows a specific form of Legendre polynomials _P n (x) to the zero-order 5 order.

In the following, for the sake of simplicity, P _n (x) will be described as being defined on the interval [-1, 1]. Even if it is treated in this way, it does not lose its generality.

A method of constructing an orthonormal basis function by combining the _{Legendre polynomials P n} (x) as shown in Table 1 above will be described. Formed by combining the Legendre polynomials _P n (x), the basis functions of the space direction and _f m (x). The basis functions f _{m (x),} as described above, satisfies the boundary conditions shown in the equation (4) (i.e., the boundary condition that f _{m (x)} is the antinode in the width direction of both ends of the mold 2) There is a need. Assuming that P _n (x) is defined on the interval [-1, 1] as described above, the boundary condition can be expressed by the following mathematical formula (35).

For example, Legendre polynomials P _n by combining the "odd order components together" or "even order components between" certain superposition coefficient _(x), satisfies the boundary condition basis functions shown in the equation (35) f _m (X) can be newly configured. Here, as an example, f ₁ (x) is a basis function composed of a combination of the linear and cubic components _{of the Legendre polynomial P n (x), and f 2} (x) is the Legendre polynomial P _n ( _{A specific method for creating f 1} (x) and f ₂ (x) will be described as a basis function composed of a combination of the secondary component and the quaternary component of x).

( _{How to create f 1} (x))
f ₁ (x) is defined as the following mathematical formula (36) by combining the linear component and the cubic component of the Legendre polynomial P _{n (x).} Here, a ₁ and b ₁ are superposition coefficients.

When the _first derivative in the spatial direction of f 1 (x) is calculated, the following mathematical formula (37) is obtained.

From the above formula (37), in order for f ₁ (x) to satisfy the boundary condition shown in the above formula (35), the superposition coefficients a ₁ and b ₁ must satisfy the following formula (38).

Further, in order to satisfy the normality, the superposition coefficients a ₁ and b ₁ must satisfy the following mathematical formula (39).

_{As a 1} and b _{1 that} satisfy both the above mathematical formulas (38) and (39), the _{superposition coefficients a 1} and b ₁ shown in the following mathematical formulas (40) and (41) can be obtained. By substituting these a ₁ and b ₁ into the above mathematical formula (36), f ₁ (x) can be obtained.

( _{How to create f 2} (x))
f ₂ (x) is defined as the following mathematical formula (42) by combining the quadratic component and the quaternary component of the Legendre polynomial P _{n (x).} Here, a ₂ and b ₂ are superposition coefficients.

When the _{first derivative of f 2} (x) in the spatial direction is calculated, the following mathematical formula (43) is obtained.

From the above formula (43), in order for f ₂ (x) to satisfy the boundary condition shown in the above formula (35), the superposition coefficients a ₂ and b ₂ must satisfy the following formula (44).

Further, in order to satisfy the normality, the superposition coefficients a ₂ and b ₂ need to satisfy the following mathematical formula (45).

_{As a 2} and b ₂ satisfying both the above mathematical formulas (44) and (45), the _{superposition coefficients a 2} and b ₂ shown in the following mathematical formulas (46) and (47) can be obtained. By substituting these a ₂ and b ₂ into the above mathematical formula (42), f ₂ (x) can be obtained.

Here, a method of creating two base functions (f ₁ (x), f ₂ (x)) has been described as an example, but in the same manner, M base functions f ₁ (x), ..., F have been described. _M (x) may be created.

When the basis function f _{m (x) in the spatial direction is created as described above, the basis function d mn} (x, t) which is orthonormal in the temporal direction and the spatial direction is defined by the following mathematical formula (48). be able to.

_{That is, when trying to create a basis function d mn} (x, t) that is normally orthogonal to the temporal and spatial directions using the Legendre polynomials, the _{basis function d mn} (x, t) is of the nth order. A newly obtained basis function f by synthesizing the Legendre polynomials P _n (t) and the "odd-order components" or "even-order components" of the Legendre polynomials so as to satisfy the boundary condition shown in the above equation (35). _It can be created by multiplying m (x) and.

At this time, the estimated value d (x, t) of the height of the molten metal can be expressed as the following mathematical formula (49) as a superposition of the _{basis functions d mn (x, t).}

By using the above formula (49) instead of the above formula (5) and performing the same calculation as in the above-described embodiment, the expansion coefficient _cmn is obtained as a solution to the coefficient estimation problem in the linear regression model, and the expansion coefficient c mn is obtained. By substituting c _mn into the above equation (49), the estimated value d (x, t) of the height of the molten metal (that is, the estimated value of the fluctuation of the molten metal) can be obtained.

Here, the conditions to be satisfied by the temporal and spatial basis functions d _mn (x, t) that can be used in the present embodiment are reorganized in Table 2 below. _{In the present embodiment, any form of function may be used as the basis function d mn} (x, t) as long as it satisfies the conditions shown in Table 2 below.

In the above, as an example of basis functions _d mn (x, t), basis functions _d mn (x, t) constituted by a sinusoidal, and Legendre polynomials _P basis function constructed by n (x) _d mn (x , T) has been described. These are summarized in Table 3 below.

Examples of the present invention will be described. In this example, a water model experiment simulating the flow of molten steel in a mold (experimental conditions: casting speed 1.6 m / min, mold width 1630 mm) was carried out to confirm the effectiveness of the present invention.

In the water model experiment, it is possible to calculate the fluctuation of the water surface height at an arbitrary position in the width direction in time series by analyzing the image of the water surface captured by the video camera. In this example, the water surface heights at a plurality of positions in the width direction obtained by analyzing the captured image were virtually regarded as the measured values of the molten metal level at the plurality of measurement points in the mold width direction. The number of measurement points (that is, the number of spatial sampling points J) was set to the following 9 patterns. In addition, it was decided to use the measured value of the water surface height for 150 seconds measured every 0.1 seconds at each measurement point.

・ A total of 4 points, 2 points at both ends in the width direction and 2 points set at equal intervals between them ・ A total of 6 points at 2 points at both ends in the width direction and 4 points set at equal intervals between them ・ 2 points at both ends in the width direction A total of 8 points of points and 6 points set at equal intervals between them ・ A total of 10 points of 2 points at both ends in the width direction and 8 points set at equal intervals between them ・ 2 points at both ends in the width direction and between them, etc. A total of 12 points of 10 points set at intervals ・ 2 points at both ends in the width direction and 12 points set at equal intervals in between 14 points in total ・ 2 points at both ends in the width direction and 14 points set at equal intervals between them 16 points in total ・ 2 points at both ends in the width direction and 16 points set at equal intervals between them, total 18 points ・ 2 points at both ends in the width direction and 18 points set at equal intervals between them, total 20 points

Measured value y (x _{i, t j)} of the measured value of the water surface height at each measurement point bath level height is regarded as was performed method of estimating the state of the molten metal surface according to the present embodiment described above. The specific conditions of the estimation method are as follows.

The adjustment parameter λ was set to λ = 1.

For the time window T, T = 1 (sec). That is, the estimation process was performed using the measured values of 10 water surface heights every 0.1 seconds (that is, the time sampling point I is I = 10). In the water model experiment conducted this time, the fluctuation of the water surface is mainly the fluctuation of the standing wave, so considering the period, it is considered that sufficient accuracy can be obtained at about T = 1 (sec).

As the basis functions d ⁽¹⁾ _mn (x, t) and d ⁽²⁾ _mn (x, t), those shown in the above formulas (6) to (13) were used. _{Then, the expansion coefficients a mn} ^* and b _mn ^* were estimated by solving the optimization problem of the _{evaluation function J [amn} , b _mn ] shown in the above formula (26) (that is, the above formula (29) was used. I asked for u ^*). Then, from these expansion coefficients a _mn ^* and b _mn ^{* , the estimated value d *} (x, t) of the height of the molten metal (that is, the estimated value of the fluctuation of the molten metal) was obtained by using the above formula (30). ..

Such estimation processing of the shape change of the molten metal was continuously executed every 0.1 seconds for 150 seconds by the above-mentioned method (1).

An example of the estimated value of the molten metal surface shape variation obtained in this way is shown in FIGS. 5 to 24. 5 to 24 are graphs showing the estimation result of the shape change of the molten metal in the example in which the state estimation method according to the present embodiment is executed. In FIGS. 5 to 24, the horizontal axis is the position in the width direction, the vertical axis is the height of the molten metal, and the estimation result of the shape of the molten metal at a predetermined time is shown by a broken line. In addition, for comparison, the measurement results of the shape of the molten metal obtained by image analysis are shown by superimposing them with solid lines. In FIGS. 5 to 24, as an example, the result of 20 seconds out of 150 seconds of the estimation process in the case where the number of measurement points is 4 is displayed for 20 frames in 1 second units.

With reference to FIGS. 5 to 24, it can be confirmed that the molten metal surface shape obtained by the state estimation method according to the present embodiment accurately represents the measurement result.

Further, in order to quantitatively evaluate the estimation accuracy, a mean square error (RMSE: Root Mean Square Error) was calculated for the estimation result and the measurement result of the molten metal surface shape for 150 seconds. In this embodiment, RMSE is defined by the following mathematical formula (50).

here,
・ T'is the number of sampling points in the time direction.
・ Δt is the sampling interval,
・ P is the number of sampling points in the width direction.
Y (p, kΔt) is the height of the water surface at the position p in the width direction at sampling time t = kΔt, which was obtained as a result of image analysis.
D (p, kΔt) is the height of the molten metal (water surface height) at the position p in the width direction at the sampling time t = kΔt, which is estimated by the state estimation method according to the present embodiment.
Is.

The results are shown in FIG. 25 and Table 4 below. FIG. 25 is a graph showing the result of calculating the RMSE between the estimation result of the molten metal surface shape and the measurement result in the example in which the state estimation method according to the present embodiment is executed. In FIG. 25, in order to confirm the difference in estimation accuracy depending on the number of measurement points, the number of measurement points is taken on the horizontal axis, the RMSE value is taken on the vertical axis, and the RMSE value corresponding to the estimation result at each measurement point is plotted. doing. Note that FIG. 25 is a graph of the contents of Table 4 below.

With reference to FIGS. 25 and 4, it can be confirmed that as the number of measurement points increases, the RMSE value decreases and the measurement accuracy improves. However, the degree of reduction of RMSE is almost saturated when the number of measurement points exceeds 10.

Further, if the accuracy is about RMSE = 1 (mm), it is considered that there is no problem in practical use. However, referring to FIGS. 25 and 4, RMSE is less than 1 mm even when the number of measurement points is 4. ing. That is, according to the state estimation method according to the present embodiment, even when the number of measurement points is 4, it is possible to obtain a high level of estimation accuracy that does not cause a problem in practical use. As described above, since a sufficiently high estimation accuracy can be obtained even if the number of the molten metal level meters 3 installed is small, the state estimation method according to the present embodiment has high accuracy without significantly increasing the cost. It also has the advantage that the state of the molten metal can be estimated.

(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.

1 System 2 Mold 3 Hot water level meter 4 State estimation device 5 Display device 6 Continuous casting control device 8 Immersion nozzle 41 Measurement value acquisition unit 42 Calculation unit 43 Output unit 44 Storage unit

Claims (7)

This is a state estimation method for estimating the state of the molten metal in the mold by using the measured values of the height of the molten metal at a plurality of measurement points in the width direction of the mold in the continuous casting machine.
A term relating to the difference between the measured value of the molten metal level and the estimated value of the molten metal level at the measurement point obtained from the measured value, and the molten metal level estimation function representing the estimated value of the molten metal level. The variation problem for the evaluation function defined on the two-dimensional rectangular region related to time and space, including the term related to the second-order differential in the time direction and the term related to the second-order differential in the spatial direction of the height estimation function. Configure and
By expanding the molten metal height estimation function using the basis function defined on the two-dimensional rectangular region and terminating the basis function in a finite dimension, the variation problem can be solved by solving the expansion coefficient of the basis function. The expansion coefficient is estimated by converting to the coefficient estimation problem of the linear regression model to be estimated and solving the coefficient estimation problem.
The state of the molten metal is estimated using the estimated expansion coefficient.
State estimation method. The term relating to the difference between the measured value of the height of the molten metal and the estimated value of the height of the molten metal is the sum of squares of the difference.
The state estimation method according to claim 1. The term relating to the difference between the measured value of the height of the molten metal and the estimated value of the height of the molten metal is the sum of the absolute values of the difference.
The state estimation method according to claim 1. The basis function is composed of trigonometric functions.
The state estimation method according to any one of claims 1 to 3. In the state estimation method according to any one of claims 1 to 4, the entire vertical movement of the hot water surface is estimated as the state of the hot water surface.
Using the estimated total vertical movement of the molten metal, the level of the molten metal in the mold is controlled.
Hot water level control method. A program that causes a computer to execute a state estimation method for estimating the state of the molten metal in the mold by using the measured values of the height of the molten metal at a plurality of measurement points in the width direction of the mold in the continuous casting machine.
In the state estimation method,
A term relating to the difference between the measured value of the molten metal level and the estimated value of the molten metal level at the measurement point obtained from the measured value, and the molten metal level estimation function representing the estimated value of the molten metal level. The variation problem for the evaluation function defined on the two-dimensional rectangular region related to time and space, including the term related to the second-order differential in the time direction and the term related to the second-order differential in the spatial direction of the height estimation function. Configure and
By expanding the molten metal height estimation function using the basis function defined on the two-dimensional rectangular region and terminating the basis function in a finite dimension, the variation problem can be solved by solving the expansion coefficient of the basis function. The expansion coefficient is estimated by converting to the coefficient estimation problem of the linear regression model to be estimated and solving the coefficient estimation problem.
The state of the molten metal is estimated using the estimated expansion coefficient.
program. It is a state estimation device that estimates the state of the molten metal in the mold by using the measured values of the height of the molten metal at a plurality of measurement points in the width direction of the mold in the continuous casting machine.
A term relating to the difference between the measured value of the molten metal level and the estimated value of the molten metal level at the measurement point obtained from the measured value, and the molten metal level estimation function representing the estimated value of the molten metal level. The variation problem for the evaluation function defined on the two-dimensional rectangular region for time and space, including the term for the second-order differential in the time direction and the term for the second-order differential in the spatial direction of the height estimation function. Configure and
By expanding the molten metal height estimation function using the basis function defined on the two-dimensional rectangular region and terminating the basis function in a finite dimension, the variation problem can be solved by solving the expansion coefficient of the basis function. The expansion coefficient is estimated by converting to the coefficient estimation problem of the linear regression model to be estimated and solving the coefficient estimation problem.
It is provided with a calculation unit that estimates the state of the molten metal using the estimated expansion coefficient.
State estimator.

Images