Sensor arrangement determination device and sensor arrangement determination method

Abstract

To predetermine sensor arrangement for simulation of thermal processing equipment using data assimilation.SOLUTION: A sensor arrangement determination method generates a simulation model that includes a plurality of locations of a thermal processing device 10. The method calculates, on the basis of a configuration of the thermal processing device 10, a first evaluation value for each location on the thermal processing device 10. The method acquires sensor information related to specifications of a sensor 12. The method calculates a second evaluation value for each position of the thermal processing device 10 by performing data assimilation calculation on the basis of a predicted value of a state of the thermal processing device 10 estimated by simulation and a measurement value estimated to be obtained by the sensor 12 at any of a plurality of locations. The method calculates, on the basis of the first evaluation value and the second evaluation value, a composite evaluation value for each location of the thermal processing device 10. The method determines, on the basis of the sensor information and the composite evaluation value, a sensor location where the sensor 12 is installed.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present disclosure relates to a sensor placement determination device and a sensor placement determination method.

Background Art

[0002] Regarding a manufacturing process using a heat treatment apparatus, that is, heat treatment, it may be required to grasp in advance phenomena occurring in the heat treatment apparatus, such as temperature distribution and flow velocity distribution, using a thermal fluid simulation.

[0003] Phenomena during heat treatment are generally difficult to grasp by direct measurement. Although thermal fluid simulation is a powerful means for grasping phenomena during heat treatment, it needs to be appropriately constructed. To construct an appropriate thermal fluid simulation, for example, it is necessary to appropriately set parameters such as boundary conditions or initial conditions of heat treatment. These conditions are usually set by installing sensors in the heat treatment apparatus, acquiring measurement values from the sensors, and repeatedly fine-tuning the parameters manually by a simulation engineer based on the measurement values. However, manual adjustment of parameters based on measurement values takes time. Also, manual adjustment of parameters greatly depends on the intuition and know-how of the simulation engineer.

[0004] As a method for setting and adjusting simulation parameters, there is a technique called "data assimilation". Data assimilation is a technique for statistically estimating a phenomenon of interest based on a predicted value obtained by simulation and a measurement value obtained by a sensor, and thereby, the parameters of the simulation can be corrected to improve the accuracy of the simulation.

[0005] For example, Patent Document 1 discloses a system for estimating the state of a liquefied gas tank installed on a ship, which incorporates a data assimilation technique. Also, Patent Document 2 discloses an apparatus for evaluating sensor placement based on the viewpoint of measurement accuracy of human flow and determining a sensor placement suitable for human flow measurement, which incorporates a data assimilation technique.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Patent Document 2

Non - Patent Documents

[0007]

Non - Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] When applying data assimilation to the simulation of a heat treatment apparatus, the accuracy of the simulation depends on the sensor placement. Therefore, it is required to determine the sensor placement so as to achieve a high - accuracy simulation. If the sensor placement can be determined in advance so as to achieve a high - accuracy simulation before actually installing the sensors, it is more advantageous from the viewpoints of labor and cost.

[0009] The technology of Patent Document 1 simulates and estimates the state of an object by a computer, but cannot estimate the sensor placement in advance so as to achieve a high - accuracy simulation. Also, the technology of Patent Document 2 determines a sensor placement suitable for human flow measurement, but cannot determine the sensor placement in advance so as to achieve a high - accuracy simulation.

[0010] An object of the present disclosure is to provide a sensor placement determination device and a sensor placement determination method capable of determining in advance the placement of sensors so as to achieve a highly accurate simulation before actually installing sensors in a heat treatment apparatus for performing a simulation of the heat treatment apparatus using data assimilation.

Means for Solving the Problems

[0011] A sensor placement determination method according to one aspect of the present disclosure is a sensor placement determination method for determining the placement of at least one sensor in a heat treatment apparatus, generating a simulation model including a plurality of positions of the heat treatment apparatus, calculating a first evaluation value for each position of the heat treatment apparatus based on the structure of the heat treatment apparatus, acquiring sensor information regarding the specifications of the sensor, performing data assimilation calculation based on a predicted value of the state of the heat treatment apparatus estimated by simulation and a measured value estimated to be acquired by a sensor at any of the plurality of positions, thereby calculating a second evaluation value for each position of the heat treatment apparatus, calculating a composite evaluation value for each position of the heat treatment apparatus based on the first evaluation value and the second evaluation value, and determining a sensor position where the sensor is to be installed based on the sensor information and the composite evaluation value.

Advantages of the Invention

[0012] According to one aspect of the present disclosure, it is possible to determine in advance the placement of sensors so as to achieve a highly accurate simulation before actually installing sensors in a heat treatment apparatus for performing a simulation of the heat treatment apparatus using data assimilation.

Brief Description of the Drawings

[0013]

Figure 1

Figure 2

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Figure 6B

Figure 6C

Figure 6D

Figure 7

Figure 8

Figure 9

Figure 10

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Figure 14

Figure 15

Embodiment for Carrying Out the Invention

[0014] Hereinafter, a sensor arrangement determination device and a sensor arrangement determination method according to an embodiment will be described with reference to the drawings.

[0015] [Embodiment] [Configuration of Sensor Arrangement Determination Device] FIG. 1 is a block diagram showing a configuration example of a system including a sensor arrangement determination device according to an embodiment. The system of FIG. 1 includes a heat treatment apparatus 10, at least one sensor 12, and an arithmetic unit 100. The arithmetic unit 100 is an example of a sensor arrangement determination device according to an embodiment.

[0016] The heat treatment apparatus 10 includes a heater 11 and performs heat treatment by heating a material using the heater 11. The heat treatment apparatus 10 is provided with at least one sensor 12 for measuring the state of the heat treatment apparatus 10 during heat treatment, for example, the temperature distribution and / or the flow velocity distribution in the space heated by the heater 11. The sensor 12 may include, for example, a thermocouple and / or an anemometer.

[0017] The arithmetic unit 100 performs data assimilation calculation based on the predicted value of the state of the heat treatment apparatus 10 estimated by simulation and the measured value acquired by the sensor 12 in order to estimate the state of the heat treatment apparatus 10 during heat treatment. Further, the arithmetic unit 100 determines the arrangement of the sensor 12 in advance so as to realize a high-precision simulation before actually installing the sensor 12 in the heat treatment apparatus 10 in order to perform a simulation of the heat treatment apparatus 10 using data assimilation.

[0018] The arithmetic unit 100 includes a storage device 110, a processor 120, an input device 130, and an output device 140.

[0019] The storage device 110 stores a program 111, a simulation model 112, a first evaluation value 113, sensor information 114, a second evaluation value 115, and a composite evaluation value 116. The program 111 includes machine-readable instructions executed by the processor 120, and includes, for example, instructions corresponding to each step of the sensor arrangement determination process in FIG. 2. As will be described later, the other data 112 to 116 are generated by the processor 120 executing the sensor arrangement determination process and stored in the storage device 110. The storage device 110 may include, for example, a semiconductor storage device such as a flash memory or a solid state drive (SSD), a magnetic storage device such as a hard disk drive (HDD), or any combination of other recording media. Further, the storage device 110 may include a non-volatile storage device or recording medium, and may include volatile memories such as SRAM (Static Random Access Memory) and DRAM (Dynamic Random Access Memory).

[0020] The processor 120 controls the overall operation of the arithmetic unit 100, and in particular, determines the arrangement of the sensor 12 in the heat treatment apparatus 10 by executing the sensor arrangement determination process in FIG. 2. The processor 120 functions as a simulation model generation unit 121, a simulation unit 122, a data assimilation unit 123, and a data processing unit 124 by executing the program 111. The processor 120 includes, for example, a control circuit or an arithmetic circuit such as a central processing unit (CPU), an MPU (Microprocessing Unit), or an FPGA (Field Programmable Gate Array).

[0021] The input device 130 acquires user input associated with the sensor arrangement determination process in FIG. 2. The input device 130 includes, for example, a keyboard, a pointing device, and / or a communication interface.

[0022] The output device 140 outputs the arrangement of the sensors 12 determined by executing the sensor arrangement determination process of FIG. 2. The output device 140 includes, for example, a display and / or a communication interface.

[0023] [Operation of Sensor Arrangement Determination Device] FIG. 2 is a flowchart illustrating the procedure of the sensor arrangement determination method executed by the processor 120 of FIG. 1.

[0024] As described above, the processor 120 functions as a simulation model generation unit 121, a simulation unit 122, a data assimilation unit 123, and a data processing unit 124 by executing the program 111.

[0025] First, the simulation model generation unit 121 generates a simulation model of the heat treatment apparatus 10 (step S1). The simulation model of the heat treatment apparatus 10 includes, for example, a plurality of positions in the space heated by the heater 11, such as the positions of lattice points. To generate the simulation model, the storage device 110 may previously store data indicating the dimensions and shape of the space heated by the heater 11, which is acquired via the input device 130. Based on this data, the simulation model generation unit 121 may generate a simulation model by setting a plurality of lattice points in the space heated by the heater 11. The simulation model generation unit 121 stores the generated simulation model in the storage device 110.

[0026] Subsequent to step S1, the data processing unit 124 calculates a first evaluation value for each position of the heat treatment apparatus 10 based on the structure of the heat treatment apparatus 10 (step S2). The first evaluation value quantitatively indicates the ease of installing the sensor 12 at each position of the heat treatment apparatus 10. The larger the first evaluation value, the easier it is to install the sensor 12, and the smaller the first evaluation value, the more difficult it is to install the sensor 12. The structure of the heat treatment apparatus 10 is characterized by, for example, the dimensions and shape of the space heated by the heater 11, the mechanism (such as screws, fixtures, etc.) for installing the sensor 12 in the heat treatment apparatus 10, the distance from the wall, floor, or ceiling of the heat treatment apparatus 10 to the position where the sensor 12 is installed, and so on. Therefore, the ease of installing the sensor 12 varies depending on the position in the heat treatment apparatus 10. The first evaluation value is calculated corresponding to each of a plurality of positions included in the simulation model. The data processing unit 124 stores the calculated first evaluation value in the storage device 110.

[0027] Subsequent to step S2, the data processing unit 124 acquires sensor information regarding the specifications of the sensor 12 via the input device 130 (step S3). The sensor information includes the type of physical quantity acquired by the sensor 12 and the minimum value of the distance between the sensors 12. The type of physical quantity includes, for example, temperature and / or wind speed, etc. The type of physical quantity is used when performing data assimilation calculation in the next step S4. Also, the minimum value of the distance between the sensors 12 is used when determining the sensor positions where the sensors 12 are installed in a later step S6. The minimum value of the distance between the sensors 12 is used to control the degree of proximity between the sensors 12 when a plurality of sensors 12 are arranged in the heat treatment apparatus 10. The larger the minimum value of the distance between the sensors 12, the sparser the sensors 12 are arranged, and the smaller the minimum value of the distance between the sensors 12, the denser the sensors 12 are arranged. By appropriately setting the minimum value of the distance between the sensors 12, it is possible to avoid, for example, the sensors 12 being arranged too densely. The data processing unit 124 stores the acquired sensor information in the storage device 110.

[0028] Subsequent to step S3, the processor 120 calculates a second evaluation value for each position of the heat treatment apparatus 10 by performing data assimilation calculation based on a predicted value of the state of the heat treatment apparatus 10 estimated by simulation and a measured value estimated to be acquired by the sensor 12 at any of a plurality of positions (step S4). Here, the simulation unit 122 calculates a predicted value of the state of the heat treatment apparatus 10 by estimating the state of the heat treatment apparatus 10 by simulation. Further, the simulation unit 122 assumes that the sensor 12 is installed at any of a plurality of positions included in the simulation model, and calculates an estimated measurement value by estimating the measurement value acquired by the sensor 12 by simulation. The simulation unit 122 performs simulation based on, for example, a heat advection equation representing a change in heat, a Navier-Stokes equation representing the motion of a fluid, etc. in order to calculate the predicted value and the estimated measurement value. The simulation unit 122 may determine an equation to be used in the simulation based on the type of physical quantity acquired by the sensor 12. The type of physical quantity acquired by the sensor 12 is included in the sensor information acquired in the aforementioned step S3. The data assimilation unit 123 calculates a second evaluation value for each position of the heat treatment apparatus 10 by performing data assimilation calculation based on the predicted value and the estimated measurement value. The second evaluation value indicates the influence of the estimated measurement value on the accuracy of the predicted value. In other words, the second evaluation value quantitatively represents the degree to which the selection of the position where the sensor 12 is installed contributes to the improvement of the accuracy of the simulation using data assimilation. The larger the second evaluation value, the easier it is to improve the accuracy of the simulation, and the smaller the second evaluation value, the more difficult it is to improve the accuracy of the simulation. Therefore, based on the second evaluation value, it is possible to determine the position of the sensor 12 that is expected to improve the accuracy of the simulation using data assimilation. The second evaluation value is calculated corresponding to each of a plurality of positions included in the simulation model. The data assimilation unit 123 stores the calculated second evaluation value in the storage device 110.

[0029] Subsequent to step S4, the data processing unit 124 calculates a composite evaluation value for each position of the heat treatment apparatus 10 based on the first evaluation value and the second evaluation value (step S5). The composite evaluation value is, for example, the sum of the first evaluation value and the second evaluation value. Therefore, the composite evaluation value represents a position suitable for installing the sensor 12, taking into account both the ease of installing the sensor 12 and the degree to which installing the sensor 12 contributes to improving the accuracy of the simulation using data assimilation. The composite evaluation value is calculated for each of a plurality of positions included in the simulation model. The data processing unit 124 stores the calculated composite evaluation value in the storage device 110.

[0030] Subsequent to step S5, the data processing unit 124 determines the sensor position where the sensor 12 is to be installed based on the sensor information and the composite evaluation value (step S6). First, the data processing unit 124 determines, as the first sensor position, the position associated with the maximum composite evaluation value among a plurality of positions included in the simulation model. Next, the data processing unit 124 determines, as the second sensor position, the position associated with the maximum composite evaluation value among the positions where no other sensor 12 exists within a predetermined distance range. Here, the predetermined distance is the minimum value of the distance between sensors 12 included in the sensor information acquired in step S3 described above. Thereafter, the data processing unit 124 repeats the same process to determine all positions where the sensor 12 can be installed as the sensor positions.

[0031] Subsequent to step S6, the data processing unit 124 outputs the sensor position determined in step S6 via the output device 140 (step S7).

[0032] By executing the sensor arrangement determination process of FIG. 2, the arithmetic unit 100 can determine in advance the arrangement of the sensors 12 so as to realize a high-precision simulation before actually installing the sensors 12 in the heat treatment apparatus 10 for performing the simulation of the heat treatment apparatus 10 using data assimilation.

[0033] The user installs the sensor 12 at the sensor position determined by executing the sensor arrangement determination process of FIG. 2. The arithmetic unit 100 performs data assimilation calculation based on the predicted value of the state of the heat treatment apparatus 10 estimated by simulation and the measured value acquired by the sensor 12, thereby estimating the state of the heat treatment apparatus 10 during the heat treatment. By installing the sensor 12 at the sensor position determined by executing the sensor arrangement determination process of FIG. 2, a highly accurate simulation can be realized.

[0034] As described above, the composite evaluation value takes into account both the ease of installation of the sensor 12 and the degree to which installing the sensor 12 contributes to improving the accuracy of the simulation using data assimilation, and represents a position suitable for installing the sensor 12. Therefore, according to the embodiment, based on the composite evaluation value, the arrangement of the sensor 12 can be determined so as to realize a highly accurate simulation while avoiding positions where it is difficult to install the sensor 12.

[0035] According to the embodiment, without relying on the intuition and know-how of simulation engineers, the parameters of the simulation of the heat treatment apparatus 10 using data assimilation can be appropriately set, and the simulation of the heat treatment apparatus 10 can be performed with high accuracy.

[0036] Next, with reference to the examples of FIGS. 3 to 15, the sensor arrangement determination process of FIG. 2 will be specifically described.

[0037] [Generation of Simulation Model (Step S1)] FIG. 3 is a diagram showing an example of the simulation model generated in step S1 of FIG. 2. The simulation model includes a plurality of grid points P(x, y) in the space heated by the heater 11. Here, 0 ≦ x ≦ 4 and 0 ≦ y ≦ 4. In the example of FIG. 3, each sensor 12 has a distance of 1 from each other with respect to each of the x coordinate and the y coordinate. Actually, the simulation model includes grid points arranged three-dimensionally, but in the following description, a simulation model including grid points P(x, y) arranged two-dimensionally will be referred to.

[0038] [Calculation of the First Evaluation Value (Step S2)] FIG. 4 is a diagram showing an example of the first evaluation value calculated in step S2 of FIG. 2. The first evaluation value indicates the ease of installing the sensor 12 at each lattice point P(x, y) included in the simulation model. The first evaluation value has, for example, any numerical value in the range from 0 to 1, and the larger the numerical value, the easier it is to install the sensor 12, and the smaller the numerical value, the more difficult it is to install the sensor 12. As described above, the structure of the heat treatment apparatus 10 is characterized by, for example, the dimensions and shape of the space heated by the heater 11, the mechanism (screws, fixtures, etc.) for installing the sensor 12 in the heat treatment apparatus 10, the distance from the wall, floor, or ceiling of the heat treatment apparatus 10 to the position where the sensor 12 is installed, and the like. Based on the structure of the heat treatment apparatus 10, the data processing unit 124 calculates the first evaluation value for each lattice point P(x, y) included in the simulation model, for example, as shown in FIG. 4.

[0039] The data processing unit 124 may set the first evaluation value as described with reference to FIGS. 5 to 8.

[0040] FIG. 5 is a flowchart showing a subroutine of step S2 in FIG. 2.

[0041] It is considered that the ease of installing the sensor 12 at lattice points close to each other among the plurality of lattice points P(x, y) included in the simulation model is substantially the same. Therefore, in the example of FIG. 5, in order to assign the same first evaluation value to lattice points close to each other, the space heated by the heater 11 is divided into a plurality of sub-regions.

[0042] First, the data processing unit 124 sets the number Ndiv of sub-regions (step S11). The data processing unit 124 may obtain and set the number Ndiv of sub-regions from the user via the input device 130.

[0043] Subsequent to step S11, the data processing unit 124 selects one partial region (step S12). For example, when Ndiv - 1 partial regions are rectangular parallelepipeds, the partial region may be selected by specifying the coordinates of its eight vertices. The data processing unit 124 may select the partial region by acquiring the coordinates of the vertices of the partial region from the user via the input device 130.

[0044] Subsequent to step S12, the data processing unit 124 sets a first evaluation value for each lattice point included in the partial region (step S13). The data processing unit 124 sets the same first evaluation value for a plurality of lattice points included in the partial region. The data processing unit 124 may acquire and set the first evaluation value from the user via the input device 130.

[0045] Subsequent to step S13, the data processing unit 124 determines whether the first evaluation value has been set for the Ndiv - 1 partial regions (step S14). If YES, it proceeds to step S15. If NO, it returns to step S12.

[0046] Subsequent to step S14, the data processing unit 124 sets the first evaluation value for the remaining lattice points, that is, the plurality of lattice points included in the last partial region (step S15). The data processing unit 124 sets the same first evaluation value for the plurality of lattice points included in the last partial region. The data processing unit 124 may acquire and set the first evaluation value from the user via the input device 130.

[0047] FIG. 6A is a diagram showing an example of one partial region A1 and its first evaluation value set by executing the process of FIG. 5. FIG. 6B is a diagram showing an example of two partial regions A1 to A2 and their first evaluation values set by executing the process of FIG. 5. FIG. 6C is a diagram showing an example of three partial regions A1 to A3 and their first evaluation values set by executing the process of FIG. 5. FIG. 6D is a diagram showing an example of four partial regions A1 to A4 and their first evaluation values set by executing the process of FIG. 5.

[0048] Figures 6A to 6D show the case of Ndiv = 4. Also, since it refers to a simulation model including two-dimensionally arranged lattice points, the Ndiv - 1 = 3 partial regions A1 to A3 are rectangular, and the partial regions are selected by specifying the coordinates of their four vertices.

[0049] First, as shown in FIG. 6A, the partial region A1 is selected by specifying the coordinates (2, 2), (2, 4), (4, 4), (4, 2) of the four vertices. Further, the same first evaluation value "0.8" is set for all lattice points included in the partial region A1.

[0050] Next, as shown in FIG. 6B, the partial region A2 is selected by specifying the coordinates (0, 3), (0, 4), (1, 4), (1, 3) of the four vertices. Further, the same first evaluation value "0.9" is set for all lattice points included in the partial region A2.

[0051] Next, as shown in FIG. 6C, the partial region A3 is selected by specifying the coordinates (3, 0), (3, 1), (4, 1), (4, 0) of the four vertices. Further, the same first evaluation value "0.6" is set for all lattice points included in the partial region A3.

[0052] Finally, as shown in FIG. 6D, the same first evaluation value "0.4" is set for all lattice points included in the remaining partial region A4.

[0053] According to the process of FIG. 5, by setting the same first evaluation value for a plurality of lattice points included in one partial region, the process can be simplified compared to the case of individually setting the first evaluation value for all lattice points included in the simulation model.

[0054] FIG. 7 is a flowchart showing a subroutine according to a modification of step S2 in FIG. 2.

[0055] The sensor 12 is generally considered to be easily installed on the wall surface, floor surface, or ceiling of the heat treatment apparatus 10, and it becomes more difficult to install as it moves away from the wall surface or the like. Therefore, in the process of FIG. 7, the first evaluation value is set based on the distance from the wall surface 10a of the heat treatment apparatus 10 to each grid point P(x, y).

[0056] First, the data processing unit 124 sets the first evaluation value w a on the wall surface 10a of the heat treatment apparatus 10 (step S21). The data processing unit 124 may set the first evaluation value w a having a predetermined fixed value, or may obtain and set the first evaluation value w a from the user via the input device 130.

[0057] Subsequent to step S21, the data processing unit 124 calculates the distance L(x, y) from the wall surface 10a to each grid point P(x, y) (step S22).

[0058] Subsequent to step S22, the data processing unit 124 determines the maximum value L max of the distance L(x, y) (step S23).

[0059] Subsequent to step S23, the data processing unit 124 sets the first evaluation value w max at the grid point having the maximum distance value L b (step S24). The first evaluation value w b in step S23 is set to be smaller than the first evaluation value w a in step S21. The data processing unit 124 may set the first evaluation value w b having a predetermined fixed value, or may obtain and set the first evaluation value w b from the user via the input device 130.

[0060] Subsequent to step S24, the data processing unit 124 calculates the correction coefficient k = (w b - w a ) / L max (step S25).

[0061] Subsequent to step S25, the data processing unit 124 calculates a first evaluation value w = k·L(x, y) for each grid point based on the distance L(x, y) and the correction coefficient k (step S26). As a result, the maximum value of the first evaluation value w is equal to the first evaluation value w set in step S21, and the minimum value of the first evaluation value w is equal to the first evaluation value w set in step S23. a b

[0062] FIG. 8 is a diagram showing an example of the first evaluation value set by executing the process of FIG. 7. In the example of FIG. 8, the first evaluation value is maximized in the vicinity of the wall surface 10a of the heat treatment apparatus 10, decreases as it moves away from the wall surface 10a, and is minimized at the center of the space to be heated.

[0063] According to the process of FIG. 7, the first evaluation value for each grid point P(x, y) can be automatically set based on the distance from the wall surface 10a of the heat treatment apparatus 10 to each grid point P(x, y).

[0064] [Calculation of the second evaluation value (step S3)] FIG. 9 is a diagram for explaining the concept of data assimilation. By performing a simulation based on the initial value P0 using the prediction model f, a predicted value P1 is calculated. Also, a measured value M1 is acquired by a sensor. By performing a data assimilation calculation based on the predicted value P1 and the measured value M1, an analysis value A1 is calculated. In data assimilation, it is assumed that each of the predicted value P1 and the measured value M1 contains an error, and the phenomenon of interest is statistically estimated. Next, by performing a simulation based on the analysis value A1 using the prediction model f, a new predicted value P2 is calculated. Also, a measured value M2 is acquired by a sensor. By performing a data assimilation calculation based on the predicted value P2 and the measured value M2, an analysis value A2 is calculated. Thereafter, by repeating the same calculation process, analysis values A1, A2,... that are expected to be close to the true values T1, T2,... are obtained.

[0065] ​​In the present embodiment, the data assimilation calculation may include a sequential data assimilation calculation, for example, a sequential data assimilation calculation using an ensemble Kalman filter.

[0066] FIG. 10 is a diagram for explaining the concept of sequential data assimilation. In sequential data assimilation, a plurality of simulations are executed in parallel under different conditions to obtain a plurality of simulation results. These simulation results are called "ensemble". Also, for these simulations, a plurality of different initial conditions are set. These initial conditions are called "initial ensemble". In sequential data assimilation, a plurality of simulations each having a plurality of different initial conditions are developed in time, and at the time when a measurement value is obtained, while appropriately adjusting each simulation, an average value of the plurality of simulation results is obtained as a predicted value.

[0067] In the present embodiment, calculating the second evaluation value includes evaluating the influence of the measurement value on the accuracy of the predicted value by performing a sequential data assimilation calculation. This method is called FSO (Forecast Sensitivity to Observations). Assuming that the sensor 12 is installed at any one of a plurality of positions included in the simulation model, an estimated measurement value is calculated by estimating the measurement value acquired by the sensor 12 by simulation. In the present embodiment, the sequential data assimilation calculation is particularly based on EFSO (Ensemble Forecast Sensitivity to Observations), which is an FSO method based on an ensemble.

[0068] Here, a specific calculation method of the second evaluation value will be described. The following example shows the calculation method disclosed in Non-Patent Document 1.

[0069] The time evolution / analysis equation in the state space model is represented by the following equation.

[0070]

Equation

[0071] In formulas (1) to (3), the following symbols are used.

[0072] [Number]

[0073] Formula (1) shows the calculation of the predicted value by simulation. Formula (2) shows the calculation of the measured value that is assumed to be obtained by sensor 12 when sensor 12 is installed at any of a plurality of positions included in the simulation model. K in formula (3) represents the Kalman gain. In EFSO, as shown in formula (3), the analysis error covariance P a is approximated using the analysis ensemble perturbation Y a in the measurement space.

[0074] The second evaluation value is calculated as the difference between the prediction error from the analysis time to the evaluation time and the prediction error from t hours before the analysis time to the evaluation time. The second evaluation value may be expressed, for example, as the following Δe 2 based on formulas (1) to (3).

[0075] [Number]

[0076] In formula (4), the following symbols are used.

[0077] [Number]

[0078] According to formula (4), the second evaluation value Δe 2can be obtained by calculating the ensemble prediction values from t hours before the analysis time to the evaluation time and the ensemble analysis values in the measurement space.

[0079] FIG. 11 is a diagram for explaining the second evaluation value calculated in step S4 of FIG. 2. FIG. 11 shows the time evolution of the prediction error. The second evaluation value Δe 2 is the prediction error e from the analysis time to the evaluation time t|0 and the prediction error e from t hours before the analysis time to the evaluation time t|-t is calculated as the difference between them. That is, the second evaluation value Δe 2 can be obtained by calculating the ensemble-based prediction value from t hours before the analysis time to the evaluation time and the ensemble-based prediction value in the analysis space.

[0080] FIG. 12 is a diagram showing an example of the second evaluation value calculated in step S4 of FIG. 2. The second evaluation value represents the degree to which the selection of the grid point where the sensor 12 is installed among each grid point P(x, y) included in the simulation model contributes to improving the accuracy of the simulation using data assimilation. The larger the second evaluation value, the easier it is to improve the accuracy of the simulation, and the smaller the second evaluation value, the more difficult it is to improve the accuracy of the simulation. The second evaluation value is normalized to have any numerical value in the range of, for example, 0 to 1.

[0081] [Calculation of Composite Evaluation Value (Step S5)] FIG. 13 is a diagram showing an example of the composite evaluation value calculated in step S5 of FIG. 2. The value of each grid point in FIG. 13 is the sum of the first evaluation value shown in FIG. 4 and the second evaluation value shown in FIG. 12. In the example of FIG. 4, the first evaluation value has any numerical value in the range of 0 to 1, and in the example of FIG. 12, the second evaluation value has any numerical value in the range of 0 to 1. Therefore, the composite evaluation value has any numerical value in the range of 0 to 2.

[0082] [Determination of Sensor Position (Steps S6, S7)] FIG. 14 is a diagram for explaining the determination of the sensor positions in step S6 of FIG. 2. First, the data processing unit 124 determines the lattice point P(4, 4) associated with the maximum composite evaluation value of 1.81 among the plurality of lattice points P(x, y) included in the simulation model as the first sensor position. Subsequently, the data processing unit 124 sets a first circle centered on the first sensor position and having a radius equal to the minimum value of the distances between the sensors 12 based on the minimum value of the distances between the sensors 12 included in the sensor information acquired in step S3. In the example of FIG. 14, the minimum value of the distances between the sensors 12 is set to "1". The lattice points P(4, 4), P(3, 4), and P(4, 3) inside the first circle are excluded from the candidates for the next sensor position, and the lattice points outside the first circle become the candidates for the next sensor position. Next, the data processing unit 124 determines the lattice point P(3, 2) associated with the maximum composite evaluation value of 1.61 among the lattice points excluding P(4, 4), P(3, 4), and P(4, 3) as the second sensor position. Subsequently, the data processing unit 124 sets a second circle centered on the second sensor position and having a radius equal to the minimum value of the distances between the sensors 12. The lattice points P(2, 2), P(3, 1), P(3, 3), and P(4, 2) inside the second circle are excluded from the candidates for the next sensor position, and the lattice points outside the first and second circles become the candidates for the next sensor position. Thereafter, the data processing unit 124 repeats the same process until there are no lattice points that are candidates for the sensor positions in the simulation model, and determines all the lattice points where the sensor 12 can be installed as the sensor positions.

[0083] As described above, actually, since the simulation model includes lattice points arranged three-dimensionally, a sphere is set instead of a circle centered on the determined sensor position and having a radius equal to the minimum value of the distances between the sensors 12. The lattice points inside this sphere are excluded from the candidates for the next sensor position, and the lattice points outside this sphere become the candidates for the next sensor position.

[0084] FIG. 15 is a diagram showing an example of the sensor positions determined in step S6 of FIG. 2. The data processing unit 124 may output the determined sensor positions together with numbers via the output device 140.

[0085] [Effects of Embodiment] According to the present embodiment, a sensor arrangement determination method for determining the arrangement of at least one sensor 12 in the heat treatment apparatus 10 is provided. This method includes generating a simulation model including a plurality of positions of the heat treatment apparatus 10. This method includes calculating a first evaluation value for each position of the heat treatment apparatus 10 based on the structure of the heat treatment apparatus 10. This method includes acquiring sensor information regarding the specifications of the sensor 12. This method includes performing data assimilation calculation based on the predicted value of the state of the heat treatment apparatus 10 estimated by simulation and the measured value estimated to be acquired by the sensor 12 at any of the plurality of positions, thereby calculating a second evaluation value for each position of the heat treatment apparatus 10. This method includes calculating a composite evaluation value for each position of the heat treatment apparatus 10 based on the first evaluation value and the second evaluation value. This method includes determining the sensor position where the sensor 12 is installed based on the sensor information and the composite evaluation value.

[0086] With this configuration, the arithmetic unit 100 can determine the arrangement of the sensor 12 in advance so as to realize a highly accurate simulation before actually installing the sensor 12 in the heat treatment apparatus 10 in order to perform simulation of the heat treatment apparatus 10 using data assimilation.

[0087] According to the present embodiment, the simulation model may include the positions of a plurality of lattice points of the heat treatment apparatus 10. The first evaluation value may include a numerical value representing the ease of installing the sensor 12 at each position of the heat treatment apparatus 10.

[0088] According to the present embodiment, the sensor information may include the type of physical quantity acquired by the sensor 12 and the minimum value of the distance between the sensors 12.

[0089] According to the present embodiment, calculating the second evaluation value may include evaluating the influence of the measured value on the accuracy of the predicted value by performing sequential data assimilation calculation.

[0090] According to this embodiment, the sequential data assimilation calculation may be based on EFSO.

[0091] According to this embodiment, the composite evaluation value may be the sum of the first evaluation value and the second evaluation value.

[0092] According to this embodiment, determining the sensor position includes determining, as the sensor position, the position associated with the maximum composite evaluation value among one or more positions of the heat treatment apparatus 10 where no other sensor 12 exists within a predetermined distance range.

[0093] According to this embodiment, the sensor arrangement determination device determines the arrangement of at least one sensor 12 in the heat treatment apparatus 10. The sensor arrangement determination device includes a storage device storing a program including machine-readable instructions, and a processor executing the machine-readable instructions. When executed by the processor, the instructions cause the processor to generate a simulation model including a plurality of positions of the heat treatment apparatus 10. When executed by the processor, the instructions cause the processor to calculate a first evaluation value for each position of the heat treatment apparatus 10 based on the structure of the heat treatment apparatus 10. When executed by the processor, the instructions cause the processor to acquire sensor information regarding the specifications of the sensor 12. When executed by the processor, the instructions cause the processor to perform data assimilation calculation based on the predicted value of the state of the heat treatment apparatus 10 estimated by simulation and the measured value estimated to be acquired by the sensor 12 at any of the plurality of positions, thereby calculating a second evaluation value for each position of the heat treatment apparatus 10. When executed by the processor, the instructions cause the processor to calculate a composite evaluation value for each position of the heat treatment apparatus 10 based on the first evaluation value and the second evaluation value. When executed by the processor, the instructions cause the processor to determine the sensor position where the sensor 12 is installed based on the sensor information and the composite evaluation value.

[0094] With this configuration, before actually installing the sensor 12 in the heat treatment apparatus 10 for the arithmetic unit 100 to perform the simulation of the heat treatment apparatus 10 using data assimilation, the arrangement of the sensor 12 can be determined in advance so as to achieve a highly accurate simulation.

[0095] By arranging the sensor 12 at the sensor position thus determined, the user can perform the simulation of the heat treatment apparatus 10 using data assimilation and appropriately set the simulation parameters without relying on the intuition and know-how of the simulation engineer. For this reason, it is not necessary to perform a large number of simulations with random settings as done by unskilled persons. Also, wasteful use of computer resources due to repeating a large number of simulations can be prevented, and the computer resources can be used efficiently. Based on the result of the performed simulation, the heat treatment apparatus 10 can be operated to perform the desired heat treatment, and the heat treatment apparatus 10 can be stably operated.

[0096] [Other Embodiments] The data assimilation calculation may include other sequential data assimilation calculations instead of the sequential data assimilation calculation using the ensemble Kalman filter.

[0097] The second evaluation value may be represented by other indexes for evaluating the influence of the measured value on the accuracy of the predicted value instead of the value Δe calculated based on EFSO. 2

[0098] The composite evaluation value may be a weighted sum of the first evaluation value and the second evaluation value.

[0099] [Summary of Embodiments] The sensor arrangement determination method and the sensor arrangement determination apparatus according to the aspect of the present disclosure may be expressed as follows.

[0100] The sensor arrangement determination method according to the first aspect of the present disclosure is ​A sensor placement determination method for determining the placement of at least one sensor in a heat treatment apparatus, comprising: generating a simulation model including a plurality of positions of the heat treatment apparatus; calculating a first evaluation value for each position of the heat treatment apparatus based on the structure of the heat treatment apparatus; acquiring sensor information regarding the specifications of the sensor; performing data assimilation calculation based on a predicted value of the state of the heat treatment apparatus estimated by simulation and a measured value estimated to be acquired by a sensor at any of the plurality of positions, thereby calculating a second evaluation value for each position of the heat treatment apparatus; calculating a composite evaluation value for each position of the heat treatment apparatus based on the first evaluation value and the second evaluation value; determining a sensor position where the sensor is to be installed based on the sensor information and the composite evaluation value.

[0101] According to the sensor placement determination method according to the second aspect of the present disclosure, in the sensor placement determination method according to the first aspect, the simulation model includes positions of a plurality of lattice points of the heat treatment apparatus. The first evaluation value includes a numerical value representing the ease of installing the sensor at each position of the heat treatment apparatus.

[0102] According to the sensor placement determination method according to the third aspect of the present disclosure, in the sensor placement determination method according to the first or second aspect, the sensor information includes the type of physical quantity acquired by the sensor and the minimum value of the distance between sensors.

[0103] According to the sensor placement determination method according to the fourth aspect of the present disclosure, in the sensor placement determination method according to any one of the first to third aspects, calculating the second evaluation value includes evaluating the influence of the measured value on the accuracy of the predicted value by performing sequential data assimilation calculation.

[0104] According to the sensor placement determination method according to the fifth aspect of the present disclosure, in the sensor placement determination method according to the fourth aspect, the sequential data assimilation calculation is based on EFSO (Ensemble Forecast Sensitivity to Observations).

[0105] According to the sensor placement determination method according to the sixth aspect of the present disclosure, in the sensor placement determination method according to one of the first to fifth aspects, the composite evaluation value is the sum of the first evaluation value and the second evaluation value.

[0106] According to the sensor placement determination method according to the seventh aspect of the present disclosure, in the sensor placement determination method according to one of the first to sixth aspects, determining the sensor position includes determining, as the sensor position, a position associated with the maximum composite evaluation value among one or more positions of the heat treatment apparatus where no other sensors exist within a predetermined distance range.

[0107] The sensor placement determination device according to the eighth aspect of the present disclosure is a sensor placement determination device for determining the placement of at least one sensor in a heat treatment apparatus, the sensor placement determination device includes a storage device storing a program including machine-readable instructions, and a processor that executes the machine-readable instructions, the machine-readable instructions, when executed by the processor, generate a simulation model including a plurality of positions of the heat treatment apparatus, calculate a first evaluation value for each position of the heat treatment apparatus based on the structure of the heat treatment apparatus, acquire sensor information regarding the specifications of the sensor, Performing data assimilation calculation based on the predicted value of the state of the heat treatment apparatus estimated by simulation and the measured value estimated to be acquired by a sensor at any one of the plurality of positions, to calculate a second evaluation value for each position of the heat treatment apparatus; Calculating a composite evaluation value for each position of the heat treatment apparatus based on the first evaluation value and the second evaluation value; Determining the sensor position where the sensor is installed based on the sensor information and the composite evaluation value; Causing the processor to execute.

Industrial Applicability

[0108] The sensor placement determination method and sensor placement determination device according to the aspects of the present disclosure are applicable to the simulation of a heat treatment apparatus using data assimilation.

Explanation of Signs

[0109] 10 Heat treatment apparatus 11 Heater 12 Sensor 100 Arithmetic unit 110 Storage device 111 Program 113 First evaluation value 114 Sensor information 112 Simulation model 120 Processor 121 Simulation model generation unit 122 Simulation unit 123 Data assimilation unit 124 Data processing unit 130 Input device 140 Output device

Claims

1. 1. A sensor placement determination method for determining a placement of at least one sensor in a thermal processing device, comprising: generating a simulation model including a plurality of locations of the thermal processing device; calculating a first evaluation value for each position of the heat treatment device based on a structure of the heat treatment device; obtaining sensor information relating to a specification of the sensor; Calculating a second evaluation value for each position of the heat treatment device by performing a data assimilation calculation based on a predicted value of the state of the heat treatment device estimated by a simulation and a measurement value estimated to be acquired by a sensor at any of the multiple positions; calculating a composite evaluation value for each position of the heat treatment device based on the first evaluation value and the second evaluation value; determining a sensor position at which the sensor is installed based on the sensor information and the composite evaluation value. Sensor placement determination method.

2. The simulation model includes a plurality of grid point positions of the thermal processing apparatus. the first evaluation value includes a numerical value representing ease of installation of the sensor at each position of the heat treatment device; The method for determining a sensor placement according to claim 1 .

3. The sensor information includes a type of a physical quantity acquired by the sensor and a minimum value of a distance between the sensors. The method for determining a sensor location according to claim 2 .

4. Calculating the second evaluation value includes evaluating an influence of the measurement value on accuracy of the forecast value by performing a sequential data assimilation calculation. The method for determining a sensor location according to claim 3 .

5. The sequential data assimilation calculation is based on EFSO (Ensemble Forecast Sensitivity to Observations), The method for determining a sensor arrangement according to claim 4 .

6. the composite evaluation value is the sum of the first evaluation value and the second evaluation value. The sensor arrangement determination method according to claim 4 or 5.

7. Determining the sensor position includes determining, as the sensor position, a position associated with a maximum composite evaluation value among one or more positions of the heat treatment device where no other sensor is present within a predetermined distance range. The method for determining a sensor location according to claim 6 .

8. A sensor placement determination device for determining a placement of at least one sensor in a thermal processing device, comprising: The sensor placement determination apparatus includes a storage device that stores a program including machine-readable instructions, and a processor that executes the machine-readable instructions; The machine-readable instructions, when executed by the processor, generating a simulation model including a plurality of locations of the thermal processing device; calculating a first evaluation value for each position of the heat treatment device based on a structure of the heat treatment device; obtaining sensor information relating to a specification of the sensor; Calculating a second evaluation value for each position of the heat treatment device by performing a data assimilation calculation based on a predicted value of the state of the heat treatment device estimated by a simulation and a measurement value estimated to be acquired by a sensor at any of the multiple positions; calculating a composite evaluation value for each position of the heat treatment device based on the first evaluation value and the second evaluation value; determining a sensor position at which the sensor is to be installed based on the sensor information and the composite evaluation value; causing the processor to execute: Sensor placement determination device.

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