JP7657416B2 - Water level estimation program, water level estimation system, and water level estimation method - Google Patents

Description

The present invention relates to a water level estimation program, a water level estimation system, and a water level estimation method.

For example, Patent Document 1 discloses a state prediction device capable of accurately predicting the water level state of a known tsunami or the like in real time. The device includes a prediction unit that predicts a state vector at the next time using two-dimensional shallow water equations that represent the propagation of a tsunami for a state vector composed of the flow rate and water level of the tsunami at multiple points set two-dimensionally in an area including the radar coverage area, a smoothing unit that uses a Kalman filter to collectively smooth the state vector predicted by the prediction unit within the coverage area using a Kalman gain, the state vector predicted by the prediction unit, and an observation vector composed of sea surface flow velocity observation values in multiple cells spanning multiple range directions and multiple beam directions within the coverage area, and a setting unit that sets an initial value used to predict the state vector in the prediction unit.

However, not only is it important to predict the water level at the time of a tsunami, but it is also important from the perspective of disaster prevention and mitigation to always be aware of the water level conditions at each point in a specific area, i.e., the water level situation. As a technology for estimating the water level situation over a wide area without actually observing the water level situation at each point, the inventors of the present invention have developed a tidal current prediction technology for rivers and bays that uses a shallow water area flow condition estimation analysis technology based on a Kalman filter finite element method (FEM) that takes into account the movement of the waterfront, as described in Non-Patent Document 1.

Patent No. 6641532

Proceedings of the 32nd Computational Mechanics Conference (2019) Vol. 32, No. 013

When grasping the water level situation over a wide area, it is desirable to use actual observation values from each point, but from the perspective of system scale, there is a need for flow regime estimation analysis technology that can match all actual observation values in real time as closely as possible using as few observation values as possible.

While the inventors were investigating the development of the above analysis technology, they performed a flow regime estimation analysis using water level data obtained using conventional observation technology in addition to data acquired by a water level gauge installed in an actual bay. They discovered a problem in that the resulting water levels differed from the actually measured water levels, even when a numerical analysis method that included the effects of high numerical viscosity was used.

In view of the above problems, the present invention aims to provide a water level estimation program, a water level estimation system, and a water level estimation method that can grasp the water level conditions over a wide area in real time with greater accuracy.

The inventors of the present invention conducted intensive research into the above-mentioned problem and discovered that it is possible to grasp the water level situation over a wide area in real time by performing estimation analysis using an extended Kalman filter (FEM) that takes into account the movement of the waterfront using observed water levels, which led to the completion of the present invention.

In other words, a water level estimation program according to one aspect of the present invention that solves the above-mentioned problems executes on a computer the steps of recording image data of an observation point located upstream of the flow of a water body , recording water level data based on the image data, and creating water level estimation data using the extended Kalman filter finite element method based on the estimation conditions and the water level data.
The extended Kalman filter finite element method uses equation (1) for the system equation, and has the steps of: calculating an estimation error covariance matrix [P _(- ) n+ ¹ ] at the time step n+1 following time step n based on a state transition matrix [F ⁿ ] after linear approximation at time step n and a prediction error covariance matrix [P ₍₊₎ ⁿ ]; calculating a Kalman gain matrix [K ₁ ⁿ⁺¹ ] at the next time step n+1 based on the estimation error covariance matrix [P ( _{- )} ^{n +1} ]; and calculating a prediction error covariance matrix [P (+) n+1 ] at the next time step _n +1 based on the estimation error covariance matrix [P _(-) ^{n+1 ]} and the Kalman gain matrix [K 1 n+1 ];
Further, the method includes a step of providing minute water depths to adjacent junctions in elements including nodes of waterfront boundaries consisting of wet and dry regions;
Furthermore, it is preferable to have a step of calculating an estimate vector {φ^ _(- ) ^{n +1} } at the next time step n+1 based on the state transition matrix [A] and the estimate vector {φ^ _(-) n } at time step n, and calculating an optimal estimate vector {φ^ ₍₊₎ ⁿ⁺¹ } at the next time step n+1 based on the estimate vector {φ^ _(-) ⁿ⁺¹ }, water level data, and the Kalman gain matrix [K ₁ ⁿ⁺¹ ].

In addition, in this aspect, it is preferable that the step of recording the water level data includes performing at least one of a binarization process and a noise removal process on the image data.

In addition, in this respect, it is preferable that the water level condition estimation data is generated by an extended Kalman filter finite element method in which minute water depths are given to elements including nodes of the waterfront boundary consisting of wet areas and dry areas .

Furthermore, in this respect, it is preferable that the water level condition estimation data includes water area estimation data and water depth estimation data.

In addition, in this aspect, it is preferable that the step of recording image data records image data of the state before the flooding or inundation occurred and image data at the time of estimation, and that the step of recording water level data records water level data based on the image data at the time of estimation.

In addition, in this respect, it is preferable to have a step of displaying the water level situation estimation data.

In addition, a water level estimation system according to another aspect of the present invention comprises a plurality of detection units installed at different observation points upstream of the flow of a water body , an image data recording unit that records image data based on output from the detection units, a water level data recording unit that records water level data based on the image data, and a water level estimation data acquisition unit that acquires water level estimation data using the extended Kalman filter finite element method based on the estimation conditions and the water level data.
In addition, the water level state estimation data acquisition unit uses equation (1) as the system equation in the extended Kalman filter finite element method, and calculates the estimation error covariance matrix [P _{(-) n+} ¹ ] at the time step n+1 following time step n based on the state transition matrix [F ⁿ ] after linear approximation at time step n and the prediction error covariance matrix [P ₍₊₎ ⁿ ], calculates the Kalman gain matrix [K ₁ ⁿ⁺¹ ] at the next time step n+1 based on the estimation error covariance matrix [P ₍ -) ^{n +} 1 ], and calculates the prediction error covariance matrix [P ₍₊₎ n ⁺¹ _] at the next time step n+1 based on the estimation error covariance matrix [P _(-) n+1 ] and the Kalman gain matrix [K ^{1 n+1} ],
Furthermore, for elements that include nodes on the waterfront boundary consisting of wet and dry areas, a small water depth is given to the adjacent junctions,
Furthermore, it is preferable to calculate the estimate vector {φ^ _(-) ^{n +1} } at the next time step n+1 based on the state transition matrix [A] and the estimate vector {φ^ _(-) n } at time step n, and to calculate the optimal estimate vector {φ^ ₍₊₎ ⁿ⁺¹ } at the next time step n+1 based on the estimate vector {φ^ _(-) ⁿ⁺¹ } , water level data, and the Kalman gain matrix [K ₁ ⁿ⁺¹ ] .

A water level estimation program according to another aspect of the present invention causes a computer to execute a water level estimation method .

As described above, the present invention provides a water level estimation program, a water level estimation system, and a water level estimation method that can grasp water level conditions over a wide area in real time with greater accuracy.

FIG. 2 is a schematic diagram of functional blocks of the water level estimation system. This is an example of a connection including the hardware of a water level estimation system. 13 is a connection example including hardware relating to another example of a water level situation estimation system. 13 is a flowchart showing a water level status estimation procedure. 13 is a flowchart showing a water level data recording procedure. 13 is a flowchart showing a procedure for acquiring water level estimation data. 1 is an example of image data for acquiring water level data. 13 is an example of the water level data obtained. This is an example of comparing water level estimation data (estimated values) with observed values. This is an example of comparing estimated water level data with observed values. 1 is an example showing distribution of flow velocity and water level fluctuation amount in an embodiment. This is an example of a condition for estimating and analyzing water level conditions using water level data obtained from image analysis. 13 is an example showing a comparison between a measured water level and an estimated water level in the embodiment. 13 is an example showing a comparison between a measured water level and an estimated water level in the embodiment.

The following describes in detail the embodiments of the present invention with reference to the drawings. However, the present invention can be implemented in many different forms, and is not limited to the specific examples mentioned in the embodiments and examples shown below.

(Water level estimation system)
Fig. 1 shows an outline of the functional blocks of the water level estimation system S according to this embodiment (hereinafter referred to as "this system"). As shown in this figure, this system S includes a detection unit 1, an image data recording unit 2 for recording image data based on the output from the detection unit 1, a water level data recording unit 3 for recording water level data based on the image data, a water level estimation data acquisition unit 4 for acquiring water level estimation data by the extended Kalman filter finite element method (FEM), an estimation condition acquisition unit 5 for acquiring analysis conditions such as mesh data and observation point data that are the initial values for the calculation of the extended Kalman filter FEM, and estimation variables such as flow velocity and water level fluctuation, and a display unit 6 for displaying the water level estimation data. Furthermore, this system S includes a recording medium 7 for recording a water level estimation program for executing the extended Kalman filter FEM and the various data described above, and a volatile recording medium 8 for performing various calculations such as executing the extended Kalman filter FEM.

The effects of this system S will be described in detail later, but this system makes it possible to grasp the flood damage situation in real time by estimating the water level in flooding conditions that occur on land such as residential areas due to floods, typhoons, tsunamis, etc. for a wide area other than the observation point, and to grasp the damage situation around the river or bay area in real time by estimating the water level for a wide area other than the observation point when the water level in a river or bay rises due to a typhoon, etc. In particular, because water level data can be obtained based on image data obtained by the output of the detection unit, it is easy to obtain various information on the water level situation at the observation point, and by using this information, the system can estimate the water level situation with high accuracy.

Figure 2 shows an example of connections including the hardware of this system S. This system S can be roughly divided into two groups of components, although this is not limited to these. One is a detection unit as a mechanical device that is actually installed at an observation point, and the other is an image data recording unit 2, a water level data recording unit 3, and a water level situation estimation data acquisition unit 4 that are virtually installed in an information processing device that processes various data based on the output of the detection unit. This system S may also be equipped with an additional group of components, a display unit 6 as a mechanical device that displays flood situation estimation data to grasp the damage situation at various points in real time.

Figure 3 shows an example of connections including hardware of the system S' according to one variation of the system S according to the present embodiment. The system S' is characterized in that each element is connected via a network N, and in particular, processing is possible even if the information processing device and the detection unit are in different positions or at different locations.

The detection units 1 are installed at multiple observation points different from the points where the information processing devices are installed, and are connected to each element such as the information processing devices via a network N.

The image data recording unit 2, water level data recording unit 3, and water level status estimation data acquisition unit 4, which are virtually provided within the information processing device, may be located within a single information processing device, or may be distributed within multiple information processing devices connected via a network N.

The display unit 6 can be provided within an information processing device, such as a mobile information terminal such as a smartphone, and multiple display units can be provided directly on the information processing device or indirectly via a network N.

(Detection Unit 1)
As described above, the detection unit 1 in the present system S can operate at the same observation point as the information processing device, but it is preferable to install a plurality of detection units at observation points different from the point where the information processing device is installed. By providing at least one detection unit at each of the plurality of observation points, it is possible to perform output according to the surrounding situation. A specific example of the detection unit 1 is a so-called video camera, and it is preferable that the camera can output the surrounding situation as an electrical signal, preferably image data.

It is also preferable that the detection unit 1 is connected to an electric communication line, i.e., a so-called network N, so that the image data can be output to an external device directly or indirectly via another device. This has the advantage that it becomes easier to synchronize multiple detection units, and it becomes possible to accurately obtain a wide range of information. In addition to a video camera, the detection unit 1 can be anything that can obtain the situation at the observation point as image data as described above and output it directly or indirectly to an external device, such as a so-called smartphone with a camera, a tablet terminal with a camera, or a high-speed camera.

The more detection units 1 installed at multiple different observation points, the more accurately it will be possible to estimate the water level conditions over a wider area. However, it is preferable to install multiple units along the lines of riverbanks or bays where levee breaches or overtopping are expected, i.e., along areas expected to be the origins of flooding. This will increase the accuracy of the estimation, as the water level condition estimation data described below will match the data actually observed.

When a video camera is used for the detection unit 1 in this system, it is preferable that the camera be capable of high-speed processing. For example, if a camera capable of taking 200 images per second is used, the time increment Δt in the extended Kalman filter FEM can be set small, which is advantageous in terms of improving the accuracy of estimating water level and flow velocity.

In addition, in this system, the detection unit 1 may be provided with an information processing device for processing image data separately. By recording the image data acquired by the detection unit 1 and further recording the water level data, it is possible to reduce the processing load on the centrally managed information processing device.

In this system, the image data recording unit 2, water level data recording unit 3, and water level status estimation data acquisition unit 4 are virtually installed within an information processing device, i.e., a computer. More specifically, the calculation program, estimation program, and various data are recorded on a recording medium 7 such as a computer's hard disk, and are loaded into a volatile recording medium 8 such as a memory as needed, and executed to form virtual units.

In this system, the image data recording unit 2, water level data recording unit 3, and water level status estimation data acquisition unit 4 may be configured to be installed inside the same computer, but they may also be configured to be connected via an electric communication line, i.e., a so-called network N, or other means that allow data to be exchanged and arranged separately and distributed. Therefore, the example in Figure 3 shows an example of a configuration in which a computer with an image data recording unit 2 installed inside is directly connected near the detection unit 1, an example of a configuration in which a computer with an image data recording unit 2 and a water level data recording unit 3 installed inside are directly connected, and an example of a configuration in which another computer is installed at a location (remote location) away from the detection unit (observation point) via the network N and the image data recording unit 2, water level data recording unit 3, and water level status estimation data acquisition unit 4 are installed inside it, and each unit is executed as needed.

The computer in this system is not limited as long as it has the above functions, but it is preferable that it includes, for example, a central processing unit (CPU), which is a component of a typical computer, a non-volatile recording medium such as a hard disk or flash memory, a volatile recording medium such as memory, a bus connecting these, input devices such as a keyboard or mouse, and a display device such as a monitor, but is not limited to these.

The computer may be a so-called notebook computer or desktop computer, but if high-speed calculations are required, it may be a so-called workstation or supercomputer, or, in consideration of portability, may be a mobile information terminal, which has become increasingly popular in recent years, specifically a so-called smartphone or tablet terminal. A typical mobile information terminal is an integrated device in which the above-mentioned CPU, display device, and other components are housed in a single terminal cover, and a sensor is placed on the display device to make it a so-called touch panel, which is very easy to use and is preferable. In the case of a mobile information terminal, a program for executing the present method is recorded and displayed as a so-called app on the mobile information terminal, and the present method can be easily executed by starting the app. It can also serve as the display unit 6 described below.

(Water level estimation program)
As described above, the image data recording unit 2, water level data recording unit 3, and water level status estimation data acquisition unit 4 are established as virtual units by storing the program in a recording medium 7 such as a computer's hard disk, reading it into a volatile recording medium 8 such as a memory, and executing it. That is, in this system, a water level status estimation program (hereinafter referred to as "this program") is stored in a computer, and by executing this, the image data recording unit 2, water level data recording unit 3, and water level status estimation data acquisition unit 4 are virtually provided in the computer, making it possible to carry out each process.

Focusing on this program, we will explain it in more detail using Figure 4. This program causes a computer to execute the following steps: (S1) acquiring calculation conditions for the extended Kalman filter FEM by inputting analysis conditions such as mesh data and observation point data, and estimation conditions including at least one of estimation variables such as flow velocity and water level fluctuation; (S2) recording image data; (S3) recording water level data based on the image data; (S4) creating water level status estimation data using the extended Kalman filter FEM based on the estimation conditions and water level data; and (S5) displaying the water level status estimation data. Note that when this program is executed, the above step (S1) is performed by the estimation condition acquisition unit 5, step (S2) is performed by the image data recording unit 2, step (S3) is performed by the water level data recording unit recording unit 3, and step (S4) is performed by the water level status estimation data acquisition unit 4.

(Water level estimation method)
As is clear from the above description, when this program is executed on an information processing device, i.e., a computer, it can realize a water level estimation method (hereinafter also referred to as "this method") having the steps of: (S1) acquiring analysis conditions such as mesh data and observation point data, and estimation conditions including estimation variables such as flow velocity and water level fluctuation; (S2) recording image data; (S3) recording water level data based on the image data; (S4) creating water level estimation data using an extended Kalman filter FEM based on the estimation conditions and the water level data; and (S5) displaying the water level estimation data.

Next, we will explain in detail the processing of each recording unit and acquisition unit in accordance with the steps of this method.

(S1: Obtain estimation conditions)
First, this method includes a step (S1) of acquiring calculation conditions for the extended Kalman filter FEM by inputting analysis conditions such as mesh data and observation point data, and estimation conditions including estimation variables such as flow velocity and water level fluctuation, and by executing this step, an estimation condition acquisition unit 5 is virtually provided. These data are recorded in a recording medium 7.

Examples of analytical conditions, which are estimation conditions, include mesh data (total number of nodes, total number of elements, coordinate values of each node on the x-y plane), observation point data (coordinate points of observation points and observed water level data), as well as time increment Δt, number of time steps, gravitational acceleration, reference water depth (data in the z direction), parameters set to prevent numerical calculations from diverging (e.g., ramping parameters), initial values of estimation variables, initial values of the estimation error covariance matrix, system error covariance matrix, observation error covariance matrix, boundary conditions related to flow velocity and water level given at the boundaries of the analysis target area, etc. It is important to use at least one of these, and preferably multiple.

The estimated variables are also one of the estimation conditions required in the extended Kalman filter FEM, and include information on the flow velocity and water level fluctuation, for example. The estimated variables are sometimes called observed variables.

The estimated conditions can be inputted into a computer using an input device such as a keyboard, mouse, or scanner. Information can also be read out from optical recording media such as CDs (Compact Discs) and DVDs (Digital Versatile Discs), magneto-optical recording media such as MOs (Magneto-Optical disks), tape media, magnetic recording media, or semiconductor memories. The estimated conditions can also be acquired from external storage media such as USB memory, and these devices can be acquired directly through an interface that allows input of the estimated conditions to an information processing device, such as USB (Universal Serial Bus) or Bluetooth (registered trademark), or can be acquired via a network or communication line.

The mesh data, which is one of the analysis conditions that serves as the initial values for the extended Kalman filter FEM, specifically includes information that indicates the x, y position on the map for a certain area on the map (observation target area) where the water level situation is estimated, as well as information z on the depth from the reference plane at a certain x, y point. The mesh can be set by dividing the observation target area using a finite element mesh. When dividing the mesh, it is preferable to set it for the observation point where the detection unit 1 is installed and the area that includes the river or bay that is the observation target. Note that the area that includes the river or bay is sometimes simply called the water area.

The observation point data, which is one of the analysis conditions that serves as the initial value for the extended Kalman filter FEM, is information related to the observation point where the detector 1 is installed, specifically information such as the actual water level and the actual flow velocity in the x and y directions. Although calculations using the extended Kalman filter FEM are possible using only the actual water level or the actual flow velocity in the x and y directions, previous studies have shown that calculations can be performed with higher accuracy when using "observation values of both (actual flow velocity in the x and y directions and actual water level)" compared to when using "observation values of only the actual water level". In the estimation analysis of the flow field using the extended Kalman filter FEM, it has been confirmed that the influence of the observation value is transmitted to the downstream side, so it is preferable that the observation point data include water level information on the upstream side of the water body in the observation area.

(S2: Image data recording)
This method also includes a step of recording image data (S2). By executing this step, an image data recording unit 2 is virtually provided.

In this step, it is preferable to record calm time image data, which is image data during calm times, and estimated time image data, which is image data during times other than calm times. "Calm time image data" is data that includes information on the state before flooding or inundation occurs, and can be used to estimate water levels in calm conditions at a time when flooding or inundation damage has not occurred. Furthermore, "estimated time image data" is data that includes information other than calm times at at least one observation point of the multiple detection units, specifically, data that includes information at an observation point from immediately after flooding or inundation occurs, and by using this to estimate water levels from the time flooding or inundation occurs, it becomes possible to grasp the damage situation in real time.

(S3: Water level data recording)
This method also includes a step (S3) of recording water level data based on image data, and by executing this step, a water level data recording unit 3 is virtually provided.

In addition, in the step of recording the water level data, it is preferable to perform at least one of binarization processing (S31) and noise processing (S32) on the image data recorded in the image data recording step (S2). Note that, in the step of recording the water level data (S3), if both binarization processing (S31) and noise processing (S32) are performed, it is preferable to perform noise processing (S32) after binarization processing (S31).

In addition, the image data for recording the water level data used to create the water level estimation data described later can be used to grasp the water level situation in real time by using the image data at the time of estimation. In this case, it is desirable to add synchronized time information to the image data from the multiple detection units. This makes it easy to set the time when flooding or inundation is detected at at least one observation point of the multiple detection units as the water level estimation reference time. Examples of methods for adding time information include a method of shooting a synchronized signal, such as a synchronized blinking light or an accurate radio clock, at a fixed position in a part of the camera's field of view that is not the water surface. This makes it possible to record the time information as part of the image. If the signal position in the captured image does not change, the time can be obtained by the same process in each camera.

(S31: Binarization process)
Here, the binarization process (S31) will be described. Identification of the water surface position by the binarization process (S31) involves taking the difference between two consecutive image data. Specifically, in an image including the water surface obtained by a detection unit with a fixed angle of view, the difference between each pixel information that changes over time can be taken to extract the water surface position and remove the background. Then, a brightness threshold is determined for the difference information of the two extracted image data, and binarization is performed. Note that, for binarization, it is preferable to convert the image including the water surface or the difference information into a grayscale in advance, since this reduces the number of variables for determining the brightness threshold. In addition, when using grayscaled difference information, for example, the brightness threshold is preferably determined so as to distinguish between image noise caused by a slight brightness difference in the background and a slight brightness difference caused by changes in the water surface. The brightness threshold may be determined manually or automatically in an information processing device by machine learning, and any means may be used. Then, binarization is possible by setting values below the threshold as black = 0 and values above the threshold as white = 1. As described above, using the brightness after grayscaling for binarization is advantageous in terms of reducing the load on the computer, but color information may be used individually, and the parameters used for binarization are not limited.

(S32: Noise processing)
In addition, in the noise processing (S32), when using image data after binarization processing, it is preferable to repeat a process (expansion process) of making the pixel of interest white if there is at least one white pixel among the eight pixels adjacent to the pixel of interest, and a process (contraction process) of making the pixel of interest black if there is at least one black pixel adjacent to the pixel of interest. In addition, in this noise processing, it is preferable to perform a process (closing process) of performing the contraction process multiple times and then the expansion process the same number of times. For example, a process of performing the contraction process twice and then the expansion process twice (contraction → contraction → expansion → expansion) corresponds to this. On the other hand, it is also preferable to perform a process (opening process) of performing the contraction process multiple times and then the contraction process the same number of times (for example, expansion → expansion → contraction → contraction). If an opening process is performed on image data that has been binarized and then a closing process is performed, there is an advantage that white dot noise can be removed. Note that, in the noise processing, noise can also be removed by repeating the expansion process and contraction process in the same way when color information is used.

(S33: Water level acquisition)
By comparing the image after noise processing with an image showing an object where the water level can be confirmed before binarization, such as a water level board with a water level scale engraved on it, water level data at the observation point can be obtained. Either calm time image data or estimated time image data can be used as the image showing the object where the water level can be confirmed, but it is preferable to use calm time image data in order to obtain accurate water level data without being affected by binarization or noise processing. This step is the water level acquisition step (S33).

(S4: Obtaining water level status estimation data)
In addition, this program has a step (S4) of acquiring water level condition estimation data using an extended Kalman filter FEM based on analysis conditions such as mesh data and observation point data, estimation conditions including estimation variables such as flow velocity and water level fluctuation, and water level data, and a water level condition estimation data acquisition unit 4 that executes this step is virtually provided.

In particular, this method has the advantage that it can obtain highly accurate water level estimation data over a wide range of water areas by estimating water level conditions using an extended Kalman filter FEM that takes into account the movement of the water shoreline. Here, "movement of the water shoreline" refers to creating a mesh of the entire observation area in advance, dividing the area into a wet area with water and a dry area without water, and assigning minute water depths to elements that include nodes on the water shoreline boundary, which makes it possible to analyze shallow water flows that take into account the movement of the water shoreline.

In addition, in this method, the "water level condition estimation data" preferably includes water area estimation data and water depth estimation data. The water area estimation data is data that indicates a planar extent, and more specifically, it is preferable that the data includes "information on planar coordinates x, y." On the other hand, the water depth estimation data is data that indicates the water depth at a certain x, y point, and includes "information on the depth z direction" at that x, y point.

In addition, in the step (S4) of creating or acquiring water level condition estimation data, the water area estimation data and water depth estimation data can be obtained by performing the steps of (S41) Kalman gain matrix calculation, (S42) water area estimation and (S43) water depth estimation.

(S41, S42: Kalman gain matrix calculation, water area estimation)
Incidentally, the Kalman gain matrix calculation (S41) in the extended Kalman filter FEM is preferably performed so as to minimize the trace norm of the estimation error covariance matrix. The calculation and calculation order for minimizing the trace norm of the estimation error covariance matrix are not limited, but can be performed using, for example, the specific procedure disclosed in Transactions of the Japan Society of Mechanical Engineers, Vol. 82, No. 835, p. 15, 2016.

Water area estimation (S42) can be output by calculating the system equation and then correcting it using the Kalman gain matrix shown in the following equation (4) and the observed value shown in the following equation (2). Specifically, the system equation describing the water area estimation can be expressed as the following equation (1), and the observation equation describing the observed value can be expressed as the following equation (2). The following equation (1) is expressed by an equation in which the shallow water long wave equation (motion equation and continuity equation including advection terms (nonlinear terms)) is discretized in the spatial direction based on the finite element method and discretized in the time direction using the finite difference method.

Here, {φ} is the state vector representing the flow velocity and water level, n is the time step, [A] is the state transition matrix (the reference water depth h and gravitational acceleration g are also included in the matrix [A]), [Γ] is the driving matrix, and {q} is the system noise vector. Also, {z} is the observation value vector, [H] is the observation matrix, and {r} is the observation noise vector.

The estimation error covariance matrix before assimilation is expressed by the following formula (3), the estimation error covariance matrix after assimilation is expressed by the following formula (4), the Kalman gain matrix is expressed by the following formula (5), the calculation of the estimated value is expressed by the following formula (6), and the calculation of the optimal estimated value is expressed by the following formula (7).

Here, [P _(-) ] is the error covariance matrix before assimilation, [F] is the state transition matrix after linear approximation, [Q] is the system error covariance matrix, [K ₁ ] is the Kalman gain matrix, [R] is the observation error covariance matrix, [P ₍₊₎ ] is the error covariance matrix after assimilation (prediction error covariance matrix), [P _(-) ] is the error covariance matrix before assimilation (estimated error covariance matrix), T is the transpose symbol, {φ^ _(-) } is the estimated value vector, and {φ^ ₍₊₎ } is the optimal estimated value vector. Here, ^ (hat) indicates the estimated value. The waterfront processing is performed before formula (6), and in the element (mesh) that includes the node representing the waterfront, the micro water depth is given to the adjacent node. In the right side of formula (6), the estimated value vector in the nth step corrected by the micro water depth is used to calculate the left side of formula (6) (estimated value vector in n+1 step), making it possible to calculate the water level situation taking into account the movement of the waterfront.

Then, the procedure for estimating and analyzing the water level situation using the extended Kalman filter FEM, taking into account the movement of the waterfront line, can be carried out, for example, as follows: 1 to 9.

(Water level analysis procedure)
1. Input the calculation conditions such as the analysis mesh, the time step Δt for the water level estimation analysis of the water level situation, the time interval ΔT for the water level measurement, the reference water depth, and the initial conditions (flow velocity, water level fluctuation). In the water level estimation analysis of the water level situation, it is preferable that Δt and ΔT have the same value, but if Δt and ΔT are different, adjust so that the measured water level value is given for every time step Δt.
2. Input the water level measurements {z ⁿ⁺¹ }.
3. Calculate the estimation error covariance matrix [P _(-) ⁿ⁺¹ ] at a certain time step n+1 (Equation (3)).
4. Calculate the Kalman gain matrix [K ₁ ⁿ⁺¹ ] at a certain time step n+1 (Equation (4)).
5. Calculate the prediction error covariance matrix [P ₍₊₎ ⁿ⁺¹ ] at a certain time step n+1 (Equation (5)).
6. In elements (mesh) that contain nodes on the waterfront, minute water depths are assigned to adjacent nodes.
7. Calculate the estimated flow velocity and water level fluctuation amount {φ^ _(-) ⁿ⁺¹ } at a certain time step n+1 (Equation (6)).
8. Using the measured water level value {z ⁿ⁺¹ } at a certain time step n+1, calculate the optimal estimated value {φ^ ₍₊₎ ⁿ⁺¹ } of the flow velocity and water level fluctuation. (Equation (7))
9. Update the time step (add a time step Δt to the current time) and go back to step 2 above.

The specific calculation sequence of the Kalman filter FEM that does not consider the movement of the waterfront can be performed using, for example, the specific procedure disclosed in Transactions of the Japan Society of Mechanical Engineers, Vol. 82, No. 835, p. 15, 2016.

(S43: Water depth estimation)
On the other hand, water depth estimation (S43) can be performed using the same process as water area estimation, and after calculating the above equation (1), the result can be output by correcting it using the Kalman gain matrix shown in the above equation (4) and the observed value shown in the above equation (2).

(S5: Display of estimated water level data)
This method also includes a step of (S5) displaying the water level status estimation data. This refers to displaying the water level status estimation data on a display unit such as a monitor or display that a computer necessarily has, or a display of a smartphone.

The display unit 6 may be directly connected via an interface that enables the output of water level status estimation data from an information processing device having the water level status estimation data acquisition unit 4, or may be connected via a network or communication line.

Here, the water level estimation method according to the above embodiment was processed using actual data to confirm its effectiveness. A detailed explanation is given below.

(Evaluation experiment 1: Water level data recording section)
A gate was installed at one end of a waterway (10 m long, 0.4 m wide) to hold the water mass. A detector capable of measuring the water level was installed 0.25 m, 1 m, and 2 m from the gate. The detector consisted of a water level board installed in the waterway and a high-speed camera (taking 200 images per second).

The gate was opened momentarily to release the water mass into the waterway. The time when the gate was opened was set to zero seconds, and measurements were started simultaneously for all detection parts. After measurements started, the image data was recorded in a computer with an image data recording unit. Two consecutive images (illustrated in Figure 7) were read out from the recorded image data, and images of the same range near the water level plate were cut out from both images. Next, the cut-out images were each grayscaled, and both grayscaled images were binarized using the same brightness threshold. After noise processing, the water level engraved on the water level plate was compared with the water surface position clarified by noise processing to obtain the water level.

Figure 8 shows the results of recording the change in water level over time at each point. Even in a situation where the gate was opened momentarily and a large amount of water splashed onto the water surface, it was confirmed that the peak water level became lower and the time it took to reach the peak became slower the further away from the gate.

(Evaluation experiment 2-1: Water level estimation data acquisition section)
The accuracy of estimating flow fields in shallow water areas using the Kalman filter finite element method was verified by changing the settings of observation variables in the water area and the number and locations of observation points.

The verification used water level information provided by tide gauge stations to estimate the water level conditions in Tokyo Bay, and then compared this with water level information provided by tide gauge stations that were not used in the water level estimation. The water level data used was from three locations: Tokyo (2313), Chiba (3305), and Yokohama New Port (3308) (numbers in parentheses are all tide gauge station registration numbers). The water level data used for comparison after estimating the water level conditions was from the tide gauge station in Yokosuka (3301). In this study, one type of mesh data was used, and one set of observation point data was also adopted.

Depth estimation data was obtained using data from nautical charts. The calculation parameters were as shown in Table 1.

Figure 9 shows the results of the flow estimation analysis, i.e., water level estimation. The estimated water level data (estimated value) in Yokosuka (3301), estimated using water level data from three locations, Tokyo (2313), Chiba (3305), and Yokohama New Port (3308), was confirmed to be in good agreement with the water level data (observed value) observed in Yokosuka (3301).

Figure 10 shows the results of a flow estimation analysis using a numerical analysis method that includes the effect of high numerical viscosity, without using the water level data from the three locations mentioned above, but instead using water level data obtained using conventional observation techniques. The estimated water level data for Yokosuka did not match the results.

As a result of estimating the water level conditions, we were also able to estimate the distribution of flow speed and water level fluctuations within Tokyo Bay. (Figure 11)

This example shows that using the x- and y-direction flow velocities on a two-dimensional plane and the water level fluctuation as observed variables produces more accurate flow field estimates than using only the water level fluctuation as an observed variable. It also shows that it is more important to place the observation point upstream of the flow than downstream.

(Evaluation experiment 2-2: Water level estimation data acquisition section)
Using the water level data obtained from image analysis, we conducted an estimation analysis of the water level situation for the dam break problem, taking into account the moving boundary of the waterfront (Figure 12).

The results are shown in Figures 13 and 14. Figure 13 shows the results for (x = 1.1 m, y = 0.2 m), and Figure 14 shows the results for (x = 1.8 m, y = 0.2 m). From these results, it was confirmed that the water level estimation results obtained were close to the water level data obtained from image analysis.

As a result of this example, the usefulness of this method was confirmed.

The present invention has industrial applicability as a water level estimation program, a water level estimation system, and a water level estimation method. Flood areas can be estimated with high accuracy and in real time, and by preparing the water level estimation system developed according to the present invention, it is possible to appropriately guide evacuation in the event of river flooding or flooding disasters caused by sudden heavy rain, for example.

S, S'... System 1... Detection section 2... Image data recording section 3... Water level data recording section 4... Water level condition estimation data acquisition section 5... Estimation condition acquisition section 6... Display section

Claims (7)

recording image data from an observation point located upstream of a flow of a body of water ;
recording water level data based on the image data;
A step of creating water level state estimation data by an extended Kalman filter finite element method based on the estimation conditions and the water level data ,
The extended Kalman filter finite element method uses the following equation (1) as a system equation:
A step of calculating an estimated error covariance matrix [P _{(−) n+} ¹ ] at the time step n+1 following the time step n based on the state transition matrix [F ⁿ ] after linear approximation at the time step n and the prediction error covariance matrix [P ₍₊₎ ⁿ ];
calculating a Kalman gain matrix [K ₁ ⁿ⁺¹ ] at the next time step n+1 based on the estimated error covariance matrix [P ₍₋₎ ⁿ⁺¹ ];
calculating a prediction error covariance matrix [P ₍₊₎ ⁿ⁺¹ ] at the next time step n+1 based on the estimation error covariance matrix [P ₍₋₎ ⁿ⁺¹ ] and the Kalman gain matrix [K ₁ n ⁺¹ ];
Further, the method includes a step of providing minute water depths to adjacent junctions in elements including nodes of waterfront boundaries consisting of wet and dry regions;
Furthermore, an estimate vector {φ^ _(-) ⁿ +1 } at the next time step n+1 is calculated based on the state transition matrix [A] and the estimate vector {φ^ _(-) ⁿ } at the time step n, and an optimal estimate vector {φ^ ₍₊₎ ⁿ⁺¹ } at the next time step n+1 is calculated based on the estimate vector {φ^ _(-) ⁿ⁺¹ } , the water level data, and the Kalman gain matrix [K ₁ ⁿ⁺¹ ].
Method for estimating water level conditions.
where {φ} is the state vector, n is the time step, [A] is the state transition matrix, [Γ] is the driving matrix, and {q} is the system noise vector. 2. The method for estimating water level conditions according to claim 1, wherein the step of recording the water level data includes performing at least one of a binarization process and a noise removal process on the image data. The water level estimation method according to claim 1, wherein the water level estimation data includes water area estimation data and water depth estimation data. The step of recording the image data includes recording image data of a state before the inundation or flooding occurs and image data at the time of estimation,
2. The method for estimating water level conditions according to claim 1 , wherein the step of recording the water level data includes recording the water level data based on the image data at the time of estimation. The water level status estimation method according to claim 1, further comprising a step of displaying the water level status estimation data. A plurality of detection units are installed at different observation points on the upstream side of the flow of the water body ;
an image data recording unit that records image data based on an output from the detection unit;
a water level data recording unit that records water level data based on the image data;
a water level state estimation data acquisition unit that acquires water level state estimation data by an extended Kalman filter finite element method based on the estimation conditions and the water level data ;
In the water level state estimation data acquisition unit, the following equation (1) is used as a system equation in the extended Kalman filter finite element method,
Calculate an estimated error covariance matrix [P ₍₋₎ n+ ¹ ] at the time step n+1 following the time step n based on the state transition matrix [F ⁿ ] after linear approximation and the prediction error covariance matrix [P ₍₊₎ ⁿ ] at the time step n;
Calculating a Kalman gain matrix [K ₁ ⁿ⁺¹ ] at the next time step n+1 based on the estimation error covariance matrix [P ₍₋₎ ⁿ⁺¹ ];
calculating a prediction error covariance matrix [P ₍₊₎ ⁿ⁺¹ ] at the next time step n+1 based on the estimation error covariance matrix [P ₍₋₎ ⁿ⁺ 1 ] and the Kalman gain matrix [K ₁ n ⁺¹ ];
Furthermore, for elements that include nodes on the waterfront boundary consisting of wet and dry areas, a small water depth is given to the adjacent junctions,
Furthermore, an estimate vector {φ^ _(-) ⁿ +1 } at the next time step n+1 is calculated based on the state transition matrix [A] and the estimate vector {φ^ _(-) ⁿ } at the time step n, and an optimal estimate vector {φ^ ₍₊₎ ⁿ⁺¹ } at the next time step n+1 is calculated based on the estimate vector {φ^ _(-) ⁿ⁺¹ } , the water level data, and the Kalman gain matrix [K ₁ ⁿ⁺¹ ].
Water level estimation system.
where {φ} is the state vector, n is the time step, [A] is the state transition matrix, [Γ] is the driving matrix, and {q} is the system noise vector. A water level estimation program that causes a computer to execute the water level estimation method according to any one of claims 1 to 5 .