Constant Identification Program

Abstract

To provide a constant identification program capable of defining constants of a model formula without spending effort and time.SOLUTION: A constant identification program makes a computer 31 execute an input acceptance process, an analysis value calculation process, a reading process, a score calculation process, and a selection process. In the input acceptance process, inputs of an upper limit value and a lower limit value of a constant are accepted. In the analysis value calculation process, a plurality of candidate values within a range between the upper limit value and the lower limit value are respectively substituted as the constants, and a model formula is used for each candidate value to calculate an analysis value which is a dam inflow based on a rainfall amount. In the reading process, an actual value of the dam inflow amount with respect to the rainfall amount stored in a storage portion 34 of the computer 31 is read. In the score calculation process, the analysis value and the actual value are used to calculate a score based on an error between the two for each candidate value. In the selection process, the candidate value suitable for use as the constant is selected among the plurality of candidate values based on the score calculated for each candidate value.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a constant identification program. [Background technology]

[0002] Given the roles of dams, such as flood control, water utilization, and hydroelectric power generation, it is desirable to maintain the dam's water storage capacity at an optimal value according to the situation. In other words, it is desirable to always maintain the dam's water level at an optimal value according to the situation. The water level of a dam changes depending on the inflow of water into the dam due to rainfall and the release of water from the dam downstream. Water inflow into a dam due to rainfall occurs when rain that falls in the dam's catchment area flows through the surface and underground into a river, and then flows from the river into the dam. Furthermore, the release of water from a dam must be carried out taking into account the impact on downstream areas of the dam.

[0003] During rainfall, the amount of water flowing into a dam changes significantly with changes in the amount of rainfall. Therefore, if the water discharge from the dam is not properly adjusted during rainfall, the dam's water level may exceed its upper limit, or the water discharge from the dam may have a significant impact on downstream areas. In order to properly adjust the water discharge from the dam, it is necessary to accurately predict the amount of water that flows into the dam due to rainfall and to discharge water from the dam based on that predicted inflow.

[0004] In order to predict the amount of water inflow into a dam, it is possible to use a model formula for calculating the inflow amount. For example, one such model formula uses a tank model as disclosed in Patent Document 1. Another such model formula uses a storage function method. By using these model formulas, it is possible to calculate an analytical value, which is the amount of water flowing into the dam from the ground via a river based on rainfall. However, in order to ensure that the amount of water inflow into the dam (analytical value) calculated using the model formula is accurate as the amount of water inflow into the dam due to rainfall, it is necessary to set multiple constants in the model formula to appropriate values. The constants are manually set by an operator, for example, using the following procedure.

[0005] During actual rainfall, the actual rainfall amount and the amount of water inflow into the dam are recorded. The analytical value is calculated using the model formula based on the rainfall amount while appropriately switching between the multiple constants in the model formula. The constants and their combinations that make the calculated analytical value closest to the actual value are selected, and these constants are adopted as the multiple constants in the model formula. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Patent Publication No. 2021-9150 Summary of the Invention [Problem to be solved by the invention]

[0007] However, in the above-described method of determining the constants in the model formula, an operator must manually change the constants while calculating analytical values using the model formula, and then search for constants that make the calculated analytical values closer to the actual values, which is a time-consuming and labor-intensive task. [Means for solving the problem]

[0008] The means for solving the above problems and their effects will be described below. A constant identification program for solving the above problem targets a model formula for calculating the amount of water inflow into a dam based on rainfall, and causes a computer to execute a process for determining constants in the model formula. The program causes the computer to execute the following processes: input acceptance process, analytical value calculation process, reading process, score calculation process, and selection process. The input acceptance process accepts input of upper and lower limit values of the constant. The analytical value calculation process sets multiple candidate values for the constant within the range between the upper and lower limit values, and calculates an analytical value, which is the amount of water inflow into the dam based on rainfall, for each candidate value using a model formula in which each candidate value is substituted as the constant. The reading process reads out actual values of the inflow for the rainfall stored in the computer. The score calculation process calculates a score for each candidate value based on the error between the analytical value calculated for each candidate value by the analytical value calculation process and the actual value read out by the reading process. The selection process selects an appropriate candidate value to be used as the constant from among multiple candidate values based on the score calculated for each candidate value.

[0009] According to the program, when an operator inputs upper and lower limit values for the constants in the model formula, a suitable candidate value to be used as the constant is selected from a plurality of candidate values that fall within the range between the upper and lower limit values, thereby enabling the constants in the model formula to be determined without requiring much time and effort.

[0010] The above model formula may be a model formula using a tank model or a model formula using a storage function method. In the constant identification program, the analytical value calculation process calculates the analytical value for each time interval for each of a plurality of candidate values based on the rainfall for each specified time interval. The reading process reads out the actual inflow value corresponding to the rainfall for each time interval stored in the computer. The score calculation process weights the error between the analytical value and the actual value for each time interval in accordance with the water inflow characteristics of the dam during rainfall, and calculates the score, which is the sum of the errors, for each of a plurality of candidate values. The selection process may select an appropriate candidate value to be used as the constant from among a plurality of candidate values based on the score calculated for each candidate value.

[0011] According to the program, when selecting a suitable candidate value to be used as a constant in the model formula based on the score, the error used in calculating the score is weighted according to the water inflow characteristics at the dam during rainfall. Therefore, the score can be calculated taking into account the water inflow characteristics at the dam during rainfall, and a suitable candidate value to be used as the constant can be selected based on the score calculated in this way.

[0012] In the constant identification program, the computer stores a plurality of inflow change patterns, with each pattern being defined as an inflow change pattern, and the actual inflow value for each time interval corresponding to the rainfall for each time interval. The analytical value calculation process calculates the analytical value for all of the plurality of inflow change patterns. The score calculation process calculates the scores for all of the plurality of inflow change patterns and weights the scores. The selection process may select a candidate value from among the plurality of candidate values that is appropriate for use as the constant for all of the plurality of inflow change patterns based on the total score of the plurality of inflow change patterns calculated for each candidate value.

[0013] According to the program, suitable candidate values for use as constants in the model formula are selected for all of the multiple inflow change patterns. Therefore, the analytical values calculated using the model formula are more accurate values for the amount of water inflow into the dam during rainfall. Furthermore, by weighting the scores calculated for each of the multiple inflow change patterns, it is possible to select candidate values that emphasize accuracy for some of the inflow change patterns.

[0014] In the above-mentioned constant identification program, the selection process may involve selecting an appropriate candidate value to be used as the constant, and then displaying on a computer display for each inflow change pattern the trend of the analytical value calculated based on a model formula into which the candidate value is substituted as the constant, superimposed on the trend of the actual value.

[0015] According to this program, after selecting an appropriate candidate value, the operator can make a final confirmation while looking at the display as to whether or not the selection is correct. In the constant identification program, the model formula is a model formula using a tank model, and the analytical value calculation process calculates the water outflow rate for each tank in the tank model when calculating the analytical values. Furthermore, the selection process can display the calculated water outflow rate for each tank overlaid on the analytical value and the actual value.

[0016] According to this program, when final confirmation is made as to whether the selected candidate values are acceptable, the display can show the trends in the outflow rate for each tank of the tank model, superimposed on the trends in the analysis value and the actual value. The outflow rate for each tank affects the rise and fall, etc., of the trends in the analysis value. Here, there are multiple constants in the model equation using the tank model, each corresponding to each tank in the tank model. Each constant in the model equation using the tank model affects the outflow rate of the corresponding tank. Therefore, if the selected candidate values are found to be inappropriate during final confirmation, it becomes easier to determine which of the constants is the cause of the inadequacy based on the trends in the outflow rate for each tank relative to the trends in the analysis value. Furthermore, when correcting the upper and lower limit values of the constants that caused the inadequacy, it becomes easier to determine the appropriate correction. [Brief explanation of the drawings]

[0017] [Figure 1] This is a schematic diagram showing the river connected to the dam and the surrounding ground. [Figure 2] 1 is a schematic diagram showing a tank model. [Figure 3] (a) is a graph showing the change in rainfall amount at a specified time interval, and (b) is a graph showing the change in the analytical value calculated using a model formula using a tank model based on the rainfall amount and the change in the actual value of the inflow amount of water flowing into the dam. [Figure 4] 1 is a schematic diagram showing a computer and its peripherals. [Figure 5] 1 is a table showing data on the amount of water entering a dam relative to rainfall. [Figure 6] FIG. 10 is a front view showing the display when the input reception process is performed. [Figure 7] (a) is a graph showing the change in rainfall amount at specified time intervals, and (b) is a graph showing the change in the analytical value calculated using a model formula using a tank model based on the rainfall amount and the change in the actual value of the inflow amount of water flowing into the dam. [Figure 8]10 is a table showing the error between the analytical value and the actual value at each predetermined time interval in a predetermined inflow change pattern. [Figure 9] 10 is a table showing the total value of error A, the total value of error B, and the total value of error C for each of a plurality of inflow change patterns. [Figure 10] FIG. 10 is a front view showing a display when the transition of analytical values and the transition of actual values are displayed for each of a plurality of inflow change patterns. [Figure 11] 10 is a flowchart showing the execution procedure of a series of processes in a constant identification program for a model equation using a tank model. [Figure 12] 10 is a graph showing the transition of analytical values calculated using a model formula that employs the storage function method based on rainfall. DETAILED DESCRIPTION OF THE INVENTION

[0018] [First embodiment] A first embodiment of the constant identification program will be described below with reference to FIGS.

[0019] As shown in Figure 1, water that has soaked into the ground 12 due to rainfall flows into a river 11 connected to a dam. This water flows into the dam through the river 11. The amount of water released downstream from the dam is adjusted based on the water level of the dam and the amount of water inflow into the dam. In order to appropriately adjust the amount of water released downstream from the dam, it is necessary to accurately predict the amount of water inflow into the dam due to rainfall, and to release water from the dam based on the predicted inflow. When predicting the amount of water inflow into a dam, a model formula is used to calculate the inflow amount as an analytical value. One such model formula is, for example, a model formula using a tank model.

[0020] The tank model is shown in Figure 2. In this tank model, the ground 12 around the dam is modeled as multiple levels of tanks 13 to 16 (four levels in this example) with holes.

[0021] The first-stage tank 13 in the tank model corresponds to the surface 17 of the ground 12 shown in Figure 1. The flow rate of water exiting the upper and lower holes 21 and 22 on the side of the tank 13 corresponds to the amount of water flowing into the dam from the surface 17 of the ground 12 via the river 11. The flow rate of water exiting the holes 21 and 22 is related to the area of the holes 21 and 22 and also to the height of the holes 21 and 22 from the bottom of the tank 13. Furthermore, the flow rate of water exiting the hole 23 on the bottom of the tank 13 corresponds to the flow rate of water seeping from the surface 17 of the ground 12 into the surface layer 18. The flow rate of water exiting the hole 23 is related to the area of the hole 23. The tank model includes constants QR1U and QR1L corresponding to the areas of the holes 21 and 22, constants L1U and L1L corresponding to the height of the holes 21 and 22 from the bottom of the tank 13, and a constant QF1 corresponding to the area of the hole 23.

[0022] The second tank 14 in the tank model corresponds to the surface layer 18 located below the surface 17 of the ground 12. The flow rate of water exiting a hole 24 on the side of the tank 14 corresponds to the amount of water flowing into the dam from the surface layer 18 of the ground 12 via the river 11. The flow rate of water exiting the hole 24 is related to the area of the hole 24 and also to the height of the hole 24 from the bottom of the tank 14. Furthermore, the flow rate of water exiting a hole 25 on the bottom of the tank 14 corresponds to the flow rate of water seeping from the surface layer 18 of the ground 12 into the intermediate layer 19. The flow rate of water exiting the hole 25 is related to the area of the hole 25. The tank model includes a constant QR2 corresponding to the area of the hole 24, a constant L2 corresponding to the height of the hole 24 from the bottom of the tank 14, and a constant QF2 corresponding to the area of the hole 25.

[0023] The third tank 15 in the tank model corresponds to the intermediate layer 19 located below the surface layer 18 of the ground 12. The flow rate of water exiting a hole 26 on the side of the tank 15 corresponds to the amount of water flowing into the dam from the intermediate layer 19 of the ground 12 via the river 11. The flow rate of water exiting the hole 26 is related to the area of the hole 26 and also to the height of the hole 26 from the bottom of the tank 15. Furthermore, the flow rate of water exiting a hole 27 on the bottom of the tank 15 corresponds to the flow rate of water seeping from the intermediate layer 19 of the ground 12 into the deep layer 20. The flow rate of water exiting the hole 27 is related to the area of the hole 27. The tank model includes a constant QR3 corresponding to the area of the hole 26, a constant L3 corresponding to the height of the hole 26 from the bottom of the tank 15, and a constant QF3 corresponding to the area of the hole 27.

[0024] The fourth tank 16 in the tank model corresponds to the deep layer 20 located below the intermediate layer 19 in the ground 12. The flow rate of water exiting a hole 28 on the side of the tank 16 corresponds to the amount of water flowing into the dam from the deep layer 20 of the ground 12 via the river 11. The flow rate of water exiting a hole 29 on the bottom of the tank 16 corresponds to the amount of water flowing out of the deep layer 20 of the ground 12 and becoming groundwater without flowing into the river 11. The flow rate of water exiting the hole 28 is related to the area of the hole 28 and also to the height of the hole 28 from the bottom of the tank 16. The flow rate of water exiting the hole 29 is related to the area of the hole 29. The tank model includes constants QR4 and QF4 corresponding to the areas of the holes 28 and 29, and a constant L4 corresponding to the height of the hole 28 from the bottom of the tank 16. The tank model also includes a constant RT corresponding to the delay time between water infiltrating into the ground 12 and flowing out into the dam via the river 11.

[0025] The amount of water (analytical value) flowing into the dam from the ground 12 via the river 11 due to rainfall can be calculated by a model formula using the tank model. Such a model formula is, for example, as shown in the following formulas (1) to (14).

[0026] Q1U = QR1U · (X1 - L1U) ... (1) Q1L=QR1L·(X1-L1L)…(2) Q2 = QR2 (X2 - L2) (3) Q3 = QR3 (X3 - L3) ... (4) Q4 = QR4 (X4 - L4) ... (5) S1=QF1·X1…(6) S2=QF2·X2…(7) S3=QF3·X3…(8) S4=QF4·X4…(9) X1 = previous X1 - previous Q1U - previous Q1L - previous S1 + R... (10) X2 = previous X2 - previous Q2 - previous S2 + previous S1... (11) X3 = last X3 - last Q3 - last S3 + last S2... (12) X4 = previous X4 - previous Q4 - previous S4 + previous S3... (13) R = f(RT)…(14) Q1U in equation (1) and Q1L in equation (2) represent the flow rate of water coming out of the holes 21 and 22 of the first-stage tank 13 in the tank model. S1 in equation (6) represents the flow rate of water coming out of the hole 23 of the tank 13. X1 in equations (1), (2), and (6) represents the height from the bottom of the tank 13 to the water surface.

[0027] Q2 in equation (3) represents the flow rate of water coming out of the hole 24 of the second-stage tank 14 in the tank model. Also, S2 in equation (7) represents the flow rate of water coming out of the hole 25 of the tank 14. X2 in equations (3) and (7) represents the height from the bottom of the tank 14 to the water surface.

[0028] Q3 in equation (4) represents the flow rate of water coming out of the hole 26 of the third tank 15 in the tank model. S3 in equation (8) represents the flow rate of water coming out of the hole 27 of the tank 15. X3 in equations (4) and (8) represents the height from the bottom of the tank 15 to the water surface.

[0029] Q4 in equation (5) represents the flow rate of water coming out of the hole 28 of the fourth tank 16 in the tank model. S4 in equation (9) represents the flow rate of water coming out of the hole 29 of the tank 16. X4 in equations (5) and (9) represents the height from the bottom of the tank 16 to the water surface.

[0030] The water surface heights X1 to X4 will be described in detail below. <Water surface height x1> The water surface height X1 is calculated using equation (10) based on the rainfall R at a predetermined time interval. Specifically, the water surface height X1 based on the rainfall R at a predetermined timing Ti is calculated using equation (10) based on the previous X1, previous Q1U, previous Q1L, previous S1, and the rainfall R.

[0031] The rainfall amount R in equation (10) is calculated using equation (14) based on the constant RT corresponding to the delay time described above. The rainfall amount R calculated from equation (14) is calculated as the rainfall amount from the delay time before described above. Therefore, the rainfall amount R used in equation (10) is the rainfall amount from the delay time before described above.

[0032] Furthermore, the previous X1 in equation (10) is the water surface height X1 calculated based on the rainfall R at the timing Ti-1 immediately before the specified time interval has elapsed, relative to the rainfall R in equation (10). Furthermore, the previous Q1U, previous Q1L, and previous S1 in equation (10) are the flow rates Q1U, Q1L, and S1 calculated using equations (1), (2), and (6) based on the previous X1, in other words, the flow rates Q1U, Q1L, and S1 at timing Ti-1.

[0033] <Water surface height x2> The water surface height X2 is calculated using equation (11) based on the previous X2, previous Q2, previous S2, and previous S1. This water surface height X2 is the water surface height X2 at the timing Ti. Furthermore, the previous X2, previous Q2, previous S2, and previous S1 in equation (11) are the water surface height X2, flow rate Q2, flow rate S2, and flow rate S1 at the timing Ti-1.

[0034] <Water surface height x3> The water surface height X3 is calculated using equation (12) based on the previous X3, previous Q3, previous S3, and previous S2. This water surface height X3 is the water surface height X3 at the timing Ti. Furthermore, the previous X3, previous Q3, previous S3, and previous S2 in equation (12) are the water surface height X3, flow rate Q3, flow rate S3, and flow rate S2 at the timing Ti-1.

[0035] <Water surface height x 4> The water surface height X4 is calculated using equation (13) based on the previous X4, Q4, S4, and S3. This water surface height X4 is the water surface height X4 at the timing Ti. Furthermore, the previous X4, Q4, S4, and S3 in equation (13) are the water surface height X4, flow rate Q4, flow rate S4, and flow rate S3 at the timing Ti-1.

[0036] Using the above model equations (1) to (14), an analytical value is calculated, which is the amount of water flowing into the dam from the ground 12 via the river 11 due to rainfall. That is, the total value of the flow rates of water coming out of the holes 21, 22, 24, 26, and 28 in the tank model, i.e., the total value of the flow rates Q1U, Q1L, Q2, Q3, and Q4 calculated by equations (1) to (5), is calculated as the analytical value. In order to make this analytical value an accurate value for the amount of water inflow into the dam due to rainfall, the multiple constants QR1U, QR1L, L1U, L1L, QF1, QR2, L2, QF2, QR3, L3, QF3, QR4, L4, QF4, and RT in the model equations (1) to (14) using the tank model must be set to appropriate values.

[0037] In Figure 3, (a) shows the change in rainfall amount at a predetermined time interval, and (b) shows the change in the analytical value (solid line) calculated using the model formula based on the rainfall amount and the change in the actual value of the inflow amount of water into the dam (dashed line). The change in the analytical value shown by the solid line in Figure 3(b) can be changed by appropriately changing the multiple constants mentioned above in the model formula. Therefore, it is preferable to determine the multiple constants in the model formula so that the change in the analytical value matches the change in the actual value as much as possible.

[0038] In the transition of the analytical value, the initial stage of the rise (region A1) is heavily influenced by the first tank 13 in the tank model, and the final stage of the rise (region A2) leading up to the peak is heavily influenced by the second tank 14. In addition, in the transition of the analytical value, the initial stage of the fall from the peak (region A3) is heavily influenced by the third tank 15, and the final stage of the fall (region A4) is heavily influenced by the fourth tank 16. It is possible to determine multiple constants in the above model formula taking into account the influence of each of the tanks 13 to 16 on the transition of the analytical value.

[0039] However, in order to determine appropriate values for the multiple constants in the model formula, it is necessary to calculate analytical values using the model formula while changing the constants, and then to search for constants that make the calculated analytical values closer to the actual values, which is a time-consuming and labor-intensive process.To address this issue, a computer is made to run a constant identification program.This constant identification program makes it possible to determine the constants in the model formula without spending time and effort.

[0040] 4, a computer 31 that executes the constant identification program is connected to an input device 32 and a display 33. The input device 32 may be a keyboard, a mouse, or a touch panel. The display 33 may incorporate a touch panel, which is one of the input devices 32.

[0041] The computer 31 is equipped with a storage unit 34. The storage unit 34 stores various data related to the amount of water inflow into the dam due to rainfall. For example, such data includes actual values of the amount of water inflow into the dam relative to the amount of rainfall, as shown in Fig. 5. More specifically, the actual value of the inflow for each time interval corresponding to the amount of rainfall for each predetermined time interval is defined as one inflow change pattern, and multiple inflow change patterns (10 patterns in this example) are stored as the data.

[0042] The constant identification program causes the computer 31 to execute the following input reception process, analytic value calculation process, read process, score calculation process, and selection process. Each of these processes will be described in detail below.

[0043] [Input reception processing] This process is carried out when the operator inputs upper and lower limit values of the multiple constants in the model equations (1) to (14) using the tank model.

[0044] 6 shows the display on the display 33 when this process is being performed. At this time, the operator inputs upper and lower limit values for each of the multiple constants in the model formula using the input device 32. As an input reception process, the computer 31 receives input of the upper and lower limit values for each of the multiple constants.

[0045] [Analysis value calculation process] In this process, for each of the multiple constants in the model formula, multiple candidate values are set within the range of the input upper and lower limit values. Furthermore, for all combinations of candidate values for each constant, an analytical value, which is the amount of water inflow into the dam based on rainfall, is calculated using the model formula in which the combined candidate values are substituted as constants. The analytical value is calculated as a value for each time interval based on the rainfall for each specified time interval. The rainfall for each time interval used here is the rainfall for multiple inflow change patterns stored in the memory unit 34 of the computer 31. Therefore, the analytical value is calculated for each of the multiple inflow change patterns.

[0046] Line LI1 in Figure 7 shows the transition of the above-mentioned analytical value calculated based on a predetermined combination of candidate values for each constant and rainfall under a predetermined inflow change pattern. Line LI2 in Figure 7 shows the transition of the actual value of water inflow into the dam based on changes in rainfall under the above-mentioned inflow change pattern. Lines LI3, LI4, LI5, and LI6 in Figure 7 respectively show the transition of water outflow from each of tanks 13 to 16 in the tank model based on changes in rainfall under the above-mentioned inflow change pattern.

[0047] [Read process] In this process, the actual values of the amount of water inflow into the dam in relation to the amount of rainfall at each time interval are read out for each of the multiple inflow change patterns stored in the memory unit 34. An example of the transition of the actual values thus read out is shown by line LI2 in Figure 7.

[0048] [Score calculation process] In this process, the analytical values calculated for each combination of candidate values by the analytical value calculation process and the actual values read out by the readout process are used to calculate a score based on the error between the two for each combination of candidate values for each constant. More specifically, for the multiple inflow change patterns stored in the memory unit 34, the error between the analytical value and the actual value for each time interval is weighted according to the water inflow characteristics of the dam during rainfall. The sum of the errors after this weighting is used as the score. This score is calculated for each combination of candidate values for each constant. The calculation of the error, the weighting, and the score can be performed, for example, as follows.

[0049] FIG. 8 shows a table of the errors between the analytical values and the actual values for each time interval in a predetermined inflow change pattern. As can be seen from FIG. 8, three types of errors are used as errors between the analytical values and the actual values: Error A, Error B, and Error C. In the "Weight" column in the table of FIG. 8, the magnitude of weighting for the error between the analytical value and the actual value is determined by an integer value, for example, from 1 to 10. The larger the integer value, the greater the weighting for the error. The integer value, i.e., the magnitude of weighting for the error, can be set arbitrarily by an operator within the range of 1 to 10, taking into consideration the water inflow characteristics of a dam during rainfall.

[0050] The error A is a value obtained by weighting the absolute error between the analytical value and the actual value based on the integer value in the "weight" column. The error B is a value obtained by dividing the absolute error between the analytical value and the actual value by the actual value, and then weighting the value based on the integer value in the "weight" column. The error C is a value obtained by weighting the square of the absolute error between the analytical value and the actual value based on the integer value in the "weight" column. Furthermore, the total value of error A, the total value of error B, and the total value of error C for a predetermined inflow change pattern are each calculated. These calculations are performed in the same way for other inflow change patterns.

[0051] FIG. 9 shows a table of the sum of errors A, B, and C for each of a plurality of (10 in this example) inflow change patterns. In the "Weight" column in the table of FIG. 9, the magnitude of weighting for the sum of errors A, B, and C is defined by an integer value of, for example, 1 to 5. The larger the integer value, the greater the weighting for the sum. The integer value, i.e., the magnitude of weighting for the sum, can be set by the operator within the range of 1 to 5.

[0052] Then, for a given inflow change pattern, the sum of the weighted sums of Error A, Error B, and Error C is taken as the score based on the error between the analytical value and the actual value for the inflow change pattern. This score is a weighted value based on the integer value in the "Weight" column of Figure 9. The score is calculated in the same manner for other inflow change patterns. Furthermore, the score is calculated for each combination of candidate values for each constant for multiple inflow change patterns.

[0053] [Selection Processing] In this process, for multiple inflow change patterns, a combination of candidate values for each constant is selected from the combinations of candidate values for each constant based on the score calculated for each combination of candidate values for each constant. Specifically, the total score shown in Figure 9 is calculated for each combination of candidate values for each constant. Then, the combination of candidate values corresponding to the smallest total score for each combination of candidate values is selected as the combination of candidate values suitable for use as the constant.

[0054] Furthermore, in this process, after selecting a combination of candidate values suitable for use as the constants, the computer 31 displays the trends in the analytical values calculated based on the model formula into which the combination of candidate values is substituted as the constants, for each inflow change pattern on the display 33. At this time, the computer 31 displays the trends in the analytical values on the display 33, superimposed on the trends in the actual values.

[0055] Figure 10 shows the screen of the display 33 at this time. As can be seen from Figure 10, the trends in the analytical values and the trends in the actual values for each individual inflow change pattern are displayed in display areas 35 to 44 on the display 33 at this time. In addition, the display area 45 of the display 33 displays a combination of candidate values selected as constants for the above model equation.

[0056] 7, the computer 31 can also display on the display 33 the transition of the analytical values superimposed on the transition of the actual values and the transition of the outflow rate for each of the tanks 13 to 16 of the tank model. The computer 31 can display on the display 33 the transition of the analytical values, the transition of the actual values, and the transition of the outflow rate for each of the tanks 13 to 16 for each of a plurality of inflow rate change patterns.

[0057] Next, the operation of the constant identification program will be described. 11 is a flowchart showing the execution procedure of a series of processes, such as input acceptance process, analytic value calculation process, readout process, score calculation process, and selection process, in the constant identification program. In this flowchart, the process of step 101 (S101) corresponds to the input acceptance process, and the processes of S102 and S103 correspond to the analytic value calculation process. Furthermore, S104 corresponds to the readout process, S105 corresponds to the score calculation process, and S106 to S108 correspond to the selection process.

[0058] 6, the operator inputs upper and lower limit values for the multiple constants in the model formula using the input device 32. The computer 31 accepts the input of the upper and lower limit values by the operator as the process of S101 in FIG.

[0059] In the process of S102, the computer 31 sets multiple candidate values for each of the multiple constants in the model formula within the range of the input upper and lower limit values. Furthermore, in the process here, the computer 31 prepares all combinations of candidate values for each constant.

[0060] In the process of S103, the computer 31 calculates an analytical value, which is the amount of water inflow into the dam based on the amount of rainfall, for all combinations of candidate values for each constant, using the model formula in which the combined candidate values are substituted as constants. The calculation of such an analytical value is performed for each of a plurality of inflow change patterns stored in the memory unit 34 of the computer 31.

[0061] For example, in the inflow change pattern of Figure 7, line LI2 shows the transition of the actual value of the water inflow into the dam in response to changes in rainfall for each predetermined time interval. Based on the rainfall for each predetermined time interval, computer 31 calculates an analytical value for each time interval using the model formula for each combination of candidate values for each constant. Line LI1 in Figure 7 shows the transition of the analytical value calculated using a predetermined combination of candidate values for each constant. Lines LI3 to LI6 in Figure 7 show the transition of the water outflow for each tank 13 to 16 of the tank model when calculating the analytical value.

[0062] In the process of S103, the calculation of the analytical value and the outflow rate of water from the tanks 13 to 16 are performed for each combination of candidate values of each constant. Then, the calculation of the analytical value and the outflow rate for each combination of candidate values is performed for each of a plurality of inflow rate change patterns.

[0063] 11, the computer 31 reads out the actual values of the amount of water inflow into the dam in relation to the amount of rainfall at each predetermined time interval for the plurality of inflow change patterns stored in the memory unit 34. For example, for the inflow change pattern of FIG. 7, the actual values thus read out progress as indicated by line LI2. The actual values are read out for each of the plurality of inflow change patterns.

[0064] As the process of S105 in Fig. 11, the computer 31 calculates a score based on the error between the analytical value calculated for each combination of candidate values of each constant and the read-out actual value for a plurality of inflow change patterns. More specifically, as shown in Fig. 8, the computer 31 calculates errors A, B, and C for each predetermined time interval using the analytical value and the actual value. Furthermore, as shown in Fig. 9, the computer 31 calculates the score by adding together the sum of errors A, B, and C. This score calculation is performed for each of a plurality of inflow change patterns. Furthermore, the computer 31 calculates the score for each combination of candidate values of each constant for each inflow change pattern.

[0065] In the process of S106 in Fig. 11, the computer 31 calculates the total score shown in Fig. 9 for each combination of candidate values for each constant. In the process of S107 in Fig. 11, the computer 31 selects the combination of candidate values corresponding to the smallest total score among the total scores for each combination of candidate values as the combination of candidate values appropriate for use as the constants in the model formula. In the process of S108, the computer 31 displays on the display 33 the trends in the analytical values calculated based on the model formula into which the selected combination of candidate values is substituted as constants, for each inflow change pattern.

[0066] FIG. 10 shows the screen of the display 33 at this time. The trends in the analytical values for each of the multiple inflow rate change patterns are displayed in display areas 35-44 of the display 33, respectively. Furthermore, the computer 31 displays the trends in the actual values of the water inflow into the dam for the inflow rate change pattern corresponding to the analytical values in the display areas 35-44, superimposed on the trends in the analytical values for each inflow rate change pattern. The computer 31 can also display the trends in the water outflow rate for each of the tanks 13-16 on the display 33, with the trends in the analytical values and the trends in the actual values superimposed. An example of the trends in the analytical values, the trends in the actual values, and the trends in the outflow rates when such a display is performed is shown in FIG. 7 by lines LI1-LI6.

[0067] In the process of S109 of FIG. 11, the computer 31 determines whether the operator has made a pass judgment regarding the combination of candidate values selected as described above. The operator visually checks the trends in the analytical values and the actual values displayed in the display areas 35-44 of the display 33, and if the operator determines that the selected combination of candidate values is appropriate, makes a pass judgment using the input device 32. At this time, the operator displays the trends in the water outflow rate for each of the tanks 13-16 on the display 33 so that they are superimposed on the trends in the analytical values and the actual values, and visually checks the display to use it as information for making the pass judgment. If the operator has made a pass judgment, it is determined in S109 that the operator has made a pass judgment, and the process proceeds to S110. In the process of S110, the computer 31 determines that the selected combination of candidate values will be used as a constant in the model formula.

[0068] On the other hand, if the operator visually checks the trends in the analytical values and the actual values displayed in the display areas 35-44 of the display 33 and determines that the selected combination of candidate values is inappropriate, the operator uses the input device 32 to make a rejection judgment. In this case, the operator also displays the trends in the water outflow rates for each of the tanks 13-16 on the display 33 so that they are superimposed on the trends in the analytical values and the actual values, and visually checks the display to use as information for the rejection judgment. If the operator makes a rejection judgment, it is determined in S109 that the operator did not make a pass judgment, and the process returns to S101. In this case, the computer 31 repeats the processes from S101 onward, and the operator re-enters the upper and lower limit values for the constants in the model formula. Furthermore, the operator re-sets the weighting for the error in the score calculation process, i.e., the integer value in the "weight" column in FIG. 8, and re-sets the weighting for the score in the score calculation process, i.e., the integer value in the "weight" column in FIG. 9.

[0069] According to the present embodiment described above in detail, the following effects can be obtained. (1) When an operator inputs upper and lower limit values for the constants in the model formula, a suitable candidate value to be used as the constant is selected from among multiple candidate values within the range between the upper and lower limit values. Therefore, the constants in the model formula can be determined without much time and effort.

[0070] (2) When selecting appropriate candidate values to be used as constants in the model formula based on the scores, weights are assigned to the errors A, B, and C used in calculating the scores according to the inflow characteristics of water into the dam during rainfall. Therefore, the scores can be calculated taking into account the inflow characteristics of water into the dam during rainfall, and appropriate candidate values can be selected as the constants based on the scores calculated in this way.

[0071] (3) According to the program, suitable candidate values for use as constants in the model formula are selected for all of the multiple inflow change patterns. Therefore, the analytical values calculated using the model formula are more accurate values for the amount of water inflow into the dam during rainfall. Furthermore, by weighting the scores calculated for each of the multiple inflow change patterns, it is possible to select candidate values that emphasize accuracy for some of the inflow change patterns.

[0072] (4) The transition of the analytical value calculated based on the above model formula, into which the selected candidate value is substituted as a constant, is displayed on the display 33 for each of a plurality of inflow change patterns, superimposed on the transition of the actual value. Therefore, after selecting a candidate value, the operator can make a final confirmation by looking at the display 33 as to whether or not the selection is correct.

[0073] (5) When making a final confirmation as to whether the selected candidate value is acceptable, the outflow rate trends for each of the tanks 13 to 16 in the tank model can be displayed on the display 33, superimposed on the trends in the analytical values and the actual values. The outflow rates for each of the tanks 13 to 16 affect the rise and fall, etc., of the trends in the analytical values.

[0074] Here, there are multiple constants in the model equation, each corresponding to one of the tanks 13 to 16 in the tank model. Each constant in the model equation affects the outflow amount of the tanks 13 to 16 corresponding to that constant. For example, in the example of FIG. 7, an abnormality can be confirmed in that the change in the water outflow amount in tank 13 (line LI3) is on the increasing side compared to the change in the actual value (line LI2). As a result, it can be seen that the constants QR1U, QR1L, L1U, L1L, and QF1 corresponding to tank 13 are abnormal.

[0075] In this way, if the selected candidate value is found to be inappropriate in the final confirmation, it becomes easy to determine which of the constants is the cause of the inadequacy from the transition of the outflow rate of each tank 13 to 16 relative to the transition of the analysis value. Furthermore, when correcting the upper and lower limit values of the constant that caused the inadequacy, it becomes easy to determine the guideline for the correction.

[0076] [Second embodiment] Next, a second embodiment of the constant identification program will be described with reference to FIG. In this embodiment, the amount of water (analytical value) flowing into the dam from the ground 12 via the river 11 due to rainfall is calculated by a model formula using the storage function method. Such a model formula is, for example, as shown in the following formulas (15) to (17).

[0077] g(t)=Q(t+TL)·f…(15) Re(t)-Q(t)=dS(t) / dt…(16) S(t)=k·Q(t)^p…(17) In equation (15), g(t) is the flow rate of water flowing from ground 12 into river 11 due to rainfall, and corresponds to the inflow amount (analytical value) of water flowing into the dam from ground 12 via river 11 due to rainfall. In equations (15) to (17), Re(t) is the amount of rainfall, S(t) is the storage height representing the amount of water that accumulates in ground 12 due to rainfall, and Q(t) is the runoff height representing the amount of water that flows out of ground 12 due to rainfall.

[0078] Q(t+TL) in equation (15) represents the runoff height taking into account the delay time TL after rainfall until water runs off from the ground 12. This runoff height Q(t+TL) is the runoff height at the point when the delay time TL has elapsed for the rainfall Re(t) used in equation (16). f in equation (15) represents the runoff rate, which is the proportion of the amount of water that flows out into the river 11 out of the total amount of water that runs off from the ground 12.

[0079] This runoff rate f is switched between a primary runoff rate f1 and a secondary runoff rate f2 depending on whether the rainfall R(t) is equal to or greater than the saturated rainfall Rsa. That is, when the rainfall R(t) is less than the saturated rainfall Rsa, the primary runoff rate f1 is used as the runoff rate f, and when the rainfall R(t) is equal to or greater than the saturated rainfall Rsa, the secondary runoff rate f2 is used as the runoff rate f.

[0080] The term "dS(t) / dt" in equation (16) is the time derivative of the storage height S(t). Also, the term "Q(t)^p" in equation (17) is the pth power of the outflow height Q(t). In equation (17), the storage height S(t) is calculated by multiplying the term "Q(t)^p" by the coefficient k.

[0081] The analytical value is calculated using the model equations shown in equations (15) to (17) based on the rainfall Re(t). That is, the flow rate g(t) in equation (15) is calculated as the analytical value. To accurately represent the amount of water inflow into the dam due to rainfall, several constants in the model equations using the storage function method, such as equations (15) to (17), must be set to appropriate values. The constants used here include a total of six constants: delay time TL, saturated rainfall Rsa, primary runoff rate f1, secondary runoff rate f2, coefficient k, and power p.

[0082] Figure 12 shows the analytical value calculated using the model formula based on the amount of rainfall, i.e., the trend in the amount of water inflow into the dam due to rainfall, and the effect on the trend of the inflow (analytical value) when the above multiple constants are changed.

[0083] Among the multiple constants, the coefficient k affects the maximum value of the inflow (analysis value), the delay time TL affects the timing of the entire waveform showing the transition of the analysis value, and the power p affects the period during which the analysis value is greater than "0." Furthermore, among the multiple constants, the primary runoff rate f1 affects the rate of increase of the analysis value when rainfall R(t) is less than the saturated rainfall Rsa, and the secondary runoff rate f2 affects the rate of increase of the analysis value when rainfall R(t) is equal to or greater than the saturated rainfall Rsa. Furthermore, among the multiple constants, the saturated rainfall Rsa affects the timing of the rise of the analysis value, i.e., the timing of the sudden increase in the rate of increase of the analysis value.

[0084] As in the first embodiment, the above-mentioned multiple (six) constants can be determined without much time and effort by having a computer execute a constant identification program. Therefore, according to this embodiment, the same effects as those (1) to (4) of the first embodiment can be obtained.

[0085] [Other embodiments] The above-described embodiments can be modified, for example, as follows: The above-described embodiments and the following modifications can be combined with each other within the scope of technical compatibility.

[0086] In the first embodiment, after selecting the most appropriate combination of candidate values to be used as constants, an analytical value is calculated using the model formula in which the combination of candidate values is substituted as a constant, and the transition of the analytical value can be displayed as follows: That is, the transition of the analytical value can be displayed superimposed on the transition of the water outflow rate for each of the tanks 13-16 of the tank model. However, it is not necessarily necessary to be able to display the transition of the water outflow rate for each of the tanks 13-16 in this way.

[0087] After selecting the most appropriate combination of candidate values to be used as constants, the transition of the analytical values calculated using the model formula with the combination of candidate values substituted as constants is displayed on the display 33. However, such display is not necessarily required. In this case, after selecting the most appropriate combination of candidate values to be used as constants, it is immediately decided to use the combination of candidate values as constants.

[0088] The calculation of the error, weighting, and score in the score calculation process may be performed by methods other than those described above. For example, instead of using the three errors A, B, and C, one or two of them may be used to calculate the error.

[0089] Weighting in the score calculation process is not necessarily required. Only one inflow change pattern may be stored in the storage unit 34, and the constants of the model formula may be determined using only this inflow change pattern.

[0090] Instead of storing the inflow change pattern in the memory unit 34, the current rainfall amount and the actual values of the water inflow amount into the dam are continuously input into the computer 31 at predetermined time intervals.Then, the constants of the model formula may be redefined at regular intervals using the rainfall amount and the inflow amount. [Explanation of symbols]

[0091] 11...Rivers 12…Ground 13~16...Tank 17…Surface 18…Surface layer 19...Middle class 20…Deep layer 21~29...holes 31...Computer 32...Input device 33...Display 34...Storage section 35~45…display area

Claims

1. A constant identification program for causing a computer to execute a process for determining constants of a model formula for calculating the amount of water inflow into a dam based on rainfall, an input reception process for receiving an input of an upper limit value and a lower limit value of the constant; an analytical value calculation process in which a plurality of candidate values for the constant are set within a range between the upper limit value and the lower limit value, and an analytical value, which is the amount of water inflow into the dam based on the amount of rainfall, is calculated for each candidate value using the model formula into which the candidate values are respectively substituted as the constants; a reading process for reading the actual value of the inflow amount relative to the rainfall amount stored in the computer; a score calculation process that calculates a score for each candidate value based on an error between the analytical value calculated for each candidate value by the analytical value calculation process and the actual value read out by the readout process; a selection process of selecting an appropriate candidate value to be used as the constant from among the plurality of candidate values based on the score calculated for each candidate value; the analytical value calculation process calculates the analytical value for each of the plurality of candidate values for each predetermined time interval based on the amount of rainfall for each predetermined time interval; the reading process is to read out the actual value of the inflow corresponding to the rainfall amount for each time interval stored in the computer, the score calculation process weights the error between the analytical value and the actual value for each time interval in accordance with the inflow characteristics of water at the dam during rainfall, and calculates the score, which is the sum of the errors, for each of the plurality of candidate values; the selection process selects a candidate value appropriate for use as the constant from among a plurality of the candidate values based on the score calculated for each of the candidate values; the errors for the time intervals used in the score calculation process are error A, error B, and error C, The error A is a weighted value of the absolute error between the analytical value and the actual value, The error B is a weighted value obtained by dividing the absolute error between the analytical value and the actual value by the actual value, The error C is a weighted value obtained by squaring the absolute error between the analytical value and the actual value, The score calculation process is a constant identification program in which the sum of the total value of the errors A, the total value of the errors B, and the total value of the errors C is used as the score.

2. 2. The constant identification program according to claim 1, wherein the model formula is a model formula using a tank model.

3. 2. The constant identification program according to claim 1, wherein the model formula is a model formula using a storage function method.

4. the computer stores a plurality of inflow change patterns, each of which is an actual value of the inflow for each time interval corresponding to the amount of rainfall for each time interval; the analytical value calculation process calculates the analytical value for all of the plurality of inflow change patterns, the score calculation process calculates the scores for all of the plurality of inflow change patterns and weights the scores; The constant identification program described in any one of claims 1 to 3, wherein the selection process selects a candidate value from among the plurality of candidate values that is suitable for use as the constant in all of the plurality of inflow change patterns based on the sum of the scores of the plurality of inflow change patterns calculated for each candidate value.

5. The constant identification program according to claim 4, wherein the selection process selects an appropriate candidate value to be used as the constant, and then displays on the computer display for each of the inflow change patterns the trend of the analytical value calculated based on a model formula into which the candidate value is substituted as the constant, superimposed on the trend of the actual value.

6. the model formula is a model formula using a tank model, The analytical value calculation process calculates the amount of water outflow for each tank in the tank model when calculating the analytical value, The constant identification program according to claim 5, wherein the selection process is capable of displaying on the display the calculated trends in outflow volume for each tank, superimposed on the trends in the analytical value and the trends in the actual value.

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