Inverse analysis method

Abstract

Compared to cases where weights are not included in the inverse analysis, we obtain an inverse analysis method that can derive parameters with higher accuracy. [Solution] The inverse analysis method by the inverse analysis device 10 is an inverse analysis method that performs inverse analysis using an objective function that obtains the sum of the differences between observed values ​​of predetermined types of physical quantities at multiple locations and calculated values ​​obtained by forward calculation using a mathematical model that approximates the actual field using predetermined parameters corresponding to the observed values, with weights applied to each of the multiple locations, and the parameters and weights are the targets of the inverse analysis.

Description

Technical Field

[0001] The present invention relates to an inverse analysis method.

Background Art

[0002] Inverse analysis, which estimates unknown analysis conditions from analysis results, is performed in a wide range of fields such as the construction field, civil engineering field, medical field, etc., contrary to the flow of calculating results from known analysis conditions such as general numerical analysis.

[0003] Conventionally, the following techniques have existed as techniques using inverse analysis.

[0004] Patent Document 1 discloses a rockfall risk determination method aimed at automatically and objectively determining the risk of rockfall regarding pumice parts quantitatively.

[0005] This rockfall risk assessment method includes the steps of: acquiring measurement information for the vibration of the loose rock and the vibration of the base from multiple vibration measuring instruments separately installed on the loose rock and the surrounding base; determining the RMS velocity amplitude ratio, which represents the ratio of the amplitude of the loose rock to the amplitude of the base, based on the measurement information; obtaining the frequency spectra of the loose rock and the base by frequency analysis of the measurement information; obtaining the power spectra of the loose rock and the base, and the cross-spectrum between the loose rock and the base, from the frequency spectra; determining the frequency response function and coherence function from the power spectrum and cross-spectrum; and determining the dominant frequency and damping constant that give a predetermined theoretical response curve that best approximates the frequency response function by inverse analysis. The method comprises the steps of determining the risk of rockfall related to the loose rock section based on the obtained RMS velocity amplitude ratio, the dominant frequency, and the damping constant, wherein the step of determining the dominant frequency and damping constant by inverse analysis comprises repeatedly performing the steps of determining assumed values ​​for the dominant frequency and damping constant, and comparing the frequency response function with the theoretical response curve given by the determined assumed values, and determining the assumed values ​​when the difference between the frequency response function and the theoretical response curve is smallest to determine the dominant frequency and damping constant to give a predetermined theoretical response curve that best approximates the frequency response function, wherein when performing the comparison, the frequency response function and the theoretical response curve are weighted according to the coherence function.

[0006] Patent Document 2 discloses a construction management system for earth retention work aimed at safely and efficiently carrying out earth retention excavation work.

[0007] This construction management system measures the behavior of the retaining wall structure, performs inverse analysis based on the measured values ​​to estimate the back-side pressure and ground reaction coefficient acting on the retaining wall, and predicts the displacement and stress state of the retaining wall structure in the next stage based on the obtained analysis results to manage the retaining wall excavation work. The system includes a measuring device that measures the current behavior of the retaining wall structure, including at least the inclination angle of the retaining wall and the axial force of the bracing placed between the retaining wall, and uses these measurement data input from the measuring device to manage the excavation work. A current state analysis means for analyzing the current stress state of the retaining frame, a first analysis means that takes the analysis values ​​obtained by the current state analysis means, assumed values ​​of the back pressure and ground reaction coefficient acting on the retaining wall to be estimated, the covariance of the error to the assumed values, and the covariance of the noise included in the analysis values ​​as input data, and repeats an extended Kalman filter a predetermined number of times to analyze the estimated values ​​of the back pressure and ground reaction coefficient acting on the retaining wall and the covariance of the error, and the analysis values ​​obtained by the current state analysis means and the first analysis A second analysis means takes the estimated values ​​analyzed by the means and the error covariance value multiplied by a predetermined weight as initial values ​​and repeats the extended Kalman filter a predetermined number of times to analyze the estimated values ​​of the back pressure and ground reaction coefficient acting on the retaining wall and the covariance value of the error. The second analysis means compares the assumed values ​​of the back pressure and ground reaction coefficient acting on the retaining wall set initially with the estimated values ​​analyzed by the second analysis means, and if the two do not match within a predetermined error level, multiplies the error covariance value by a predetermined weight. The system is characterized by comprising: a determination means that, when the second analysis means is executed again and the two results match within a predetermined error level, the estimated value analyzed by the second analysis means is set as the optimal estimated value; a prediction analysis means that takes in input data that includes at least the optimal estimated values ​​of the back pressure acting on the retaining wall and the ground reaction coefficient obtained by the determination means, performs elastoplastic analysis to predict the deformation and stress state of the retaining frame in the next stage; and an output device that outputs the analysis results obtained by the current state analysis means, determination means, and prediction analysis means.

[0008] Patent Document 3 discloses an inverse analysis method for earth retention work aimed at simultaneously estimating the back-side pressure and ground reaction coefficient acting on the earth retention wall with high accuracy and efficiency.

[0009] This inverse analysis method is an inverse analysis method for earth retaining construction in which the behavior of the earth retaining frame is measured and the obtained measured values ​​are used as input data to simultaneously estimate the values ​​of the back pressure and ground reaction coefficient acting on the earth retaining wall erected in the ground. The method involves taking in the measured values ​​obtained from measuring the behavior of the earth retaining frame, the value of the back pressure set to the design value of the back pressure, the initial values ​​of the back pressure and ground reaction coefficient acting on the earth retaining wall to be estimated, the covariance of the error, and an assumed value of the covariance of the noise included in the measured values, and repeating an extended Kalman filter a predetermined number of times to analyze the estimated values ​​of the back pressure and ground reaction coefficient and the covariance of the error, and the back pressure analyzed in the first analysis step The method is characterized by comprising: a second analysis step in which estimated values ​​of lateral pressure and ground reaction coefficient and the error covariance value obtained by multiplying them by a predetermined weight are taken as initial values, and the extended Kalman filter is repeated a predetermined number of times to analyze the estimated values ​​of back lateral pressure and ground reaction coefficient and the covariance value of their error; and a determination step in which the estimated values ​​of back lateral pressure and ground reaction coefficient analyzed in the first and second analysis steps are compared, and if the two do not match within a predetermined error level, the error covariance value is multiplied by a predetermined weight and the second analysis step is performed again, and if the two match within a predetermined error level, the estimated values ​​of back lateral pressure and ground reaction coefficient analyzed in the second analysis step are determined to be the optimal estimates. [Prior art documents] [Patent Documents]

[0010] [Patent Document 1] Japanese Patent Publication No. 2011-252865 [Patent Document 2] Japanese Patent Application Publication No. 8-151633 [Patent Document 3] Japanese Patent Application Publication No. 8-184046 [Overview of the Initiative] [Problems that the invention aims to solve]

[0011] Conventional inverse analysis methods, including those described in Patent Documents 1 to 3, limit the target of the inverse analysis to only the parameters to be identified, and the weights used in the identification process (hereinafter simply referred to as "weights") are predetermined.

[0012] However, the weights represent the importance of the actual observed values ​​and significantly influence the identification of the above parameters. Therefore, there was a problem in that applying pre-set values ​​as weights did not necessarily guarantee that the parameters derived by inverse analysis could be obtained with high accuracy.

[0013] This disclosure is made in view of the above circumstances and aims to provide an inverse analysis method that can derive parameters by inverse analysis with higher accuracy compared to cases where weights are not included in the inverse analysis. [Means for solving the problem]

[0014] The inverse analysis method according to claim 1 is an inverse analysis method that performs inverse analysis using an objective function that obtains the sum of the differences between observed values ​​of predetermined types of physical quantities at a plurality of locations and calculated values ​​obtained by forward calculation using a mathematical model that approximates the actual field using predetermined parameters corresponding to the observed values, with weights applied to each of the plurality of locations, wherein the parameters and weights are the targets of the inverse analysis, and the process is performed by a computer.

[0015] The inverse analysis method according to claim 1 of the present invention is an inverse analysis method that performs inverse analysis using an objective function that obtains the sum of the differences between observed values ​​of predetermined types of physical quantities at multiple locations and calculated values ​​obtained by forward calculation using a mathematical model that approximates the actual field using predetermined parameters corresponding to the observed values, with weights applied to each of the multiple locations. By making the above parameters and weights the subject of the inverse analysis, the parameters obtained by the inverse analysis can be derived with higher accuracy compared to the case in which the weights are not the subject of the inverse analysis.

[0016] The inverse analysis method according to claim 2 is the inverse analysis method according to claim 1, wherein initial values ​​for each of the parameters and weights are set in advance, a perturbation calculation is performed using the parameters and weights to derive the degree of influence of the parameters and weights on the objective function, the parameters and weights are updated using the derived degree of influence, the forward calculation is performed using the updated parameters, the value of the objective function is calculated using the updated weights and the calculated values ​​obtained in the forward calculation, and the process from the perturbation calculation onward is repeated until the calculated value of the objective function is less than a predetermined tolerance to obtain the final values ​​of the parameters and weights.

[0017] According to the inverse analysis method of the present invention described in claim 2, initial values ​​for each parameter and weight are set in advance, perturbation calculations are performed using the parameters and weights to derive the degree of influence of the parameters and weights on the objective function, the parameters and weights are updated using the derived degree of influence, forward calculations are performed using the updated parameters, the value of the objective function is calculated using the updated weights and the calculated values ​​obtained in the forward calculations, and the process from perturbation calculation onwards is repeated until the calculated value of the objective function is less than a predetermined tolerance error, thereby obtaining the final values ​​of the parameters and weights, and the weights can be identified by the same process as in conventional inverse analysis methods.

[0018] The inverse analysis method according to claim 3 is the inverse analysis method according to claim 1 or claim 2, wherein the physical quantity is a physical quantity relating to the ground.

[0019] According to the inverse analysis method of the present invention described in claim 3, by using physical quantities relating to the ground, when observing physical quantities relating to the ground, the parameters obtained by inverse analysis can be derived with higher accuracy.

[0020] The inverse analysis method according to claim 4 is the inverse analysis method according to claim 3, wherein the physical quantity relating to the ground is at least one of pressure and temperature in the ground.

[0021] According to the inverse analysis method of the present invention described in claim 4, by making the physical quantity relating to the ground at least one of pressure and temperature in the ground, the parameters obtained by inverse analysis can be derived with higher accuracy when at least one of pressure and temperature is used as the physical quantity relating to the ground.

[0022] The inverse analysis method according to claim 5 is the inverse analysis method according to claim 3 or claim 4, wherein the parameter is a physical quantity indicating the permeability of the ground.

[0023] According to the inverse analysis method of the present invention described in claim 5, by using a physical quantity indicating the permeability of the ground as the parameter, the physical quantity indicating the permeability of the ground can be derived with higher accuracy.

[0024] The inverse analysis method according to claim 6 is the inverse analysis method according to claim 2, wherein at least one of the update method and the update frequency is changed by the parameters and the weights.

[0025] According to the inverse analysis method of the present invention described in claim 6, by changing at least one of the update method and the update frequency for the parameters and weights, it is possible to suppress adverse effects on the parameter derivation accuracy caused by differences in the characteristics of the parameters and weights. [Effects of the Invention]

[0026] As explained above, according to the present invention, parameters can be derived with higher accuracy by inverse analysis compared to cases where weights are not subject to inverse analysis. [Brief explanation of the drawing]

[0027] [Figure 1] This is a block diagram showing an example of the hardware configuration of the inverse analysis device according to the embodiment. [Figure 2] This block diagram shows an example of the functional configuration of an inverse analysis device according to an embodiment. [Figure 3] This is a schematic diagram showing an example of the configuration of the initial information database according to the embodiment. [Figure 4] This is a schematic diagram showing an example of the configuration of the observation data database according to the embodiment. [Figure 5] This is a flowchart showing an example of the inverse analysis process according to the embodiment. [Figure 6] This is a perspective view showing the configuration of the artificial ground in an embodiment according to the present invention. [Figure 7] This is a perspective view illustrating the subject of the inverse analysis in the embodiment of the example. [Figure 8] This is a perspective view illustrating the measurement conditions of the observed values ​​of the artificial ground in an embodiment of the present invention. [Figure 9] This graph shows an example of observed values ​​(pressure) in an embodiment according to the specified pattern. [Figure 10] This graph shows an example of observed values ​​(temperature) in an embodiment according to the specified pattern. [Figure 11] This graph shows the average value and error bars (99% confidence interval) of the physical quantity indicating the permeability of the artificial ground in an embodiment of the example. [Figure 12] This graph shows the distribution of physical quantities indicating water permeability identified in the inverse analysis, both when the weights in the embodiment are not included in the inverse analysis and when the weights are included in the inverse analysis. [Figure 13] This graph shows the distribution of physical quantities indicating water permeability identified by inverse analysis when the weights in the embodiment are not subject to inverse analysis. [Figure 14] This graph shows the distribution of physical quantities indicating water permeability, identified by inverse analysis when the weights in the embodiment are also included in the inverse analysis. [Figure 15] This graph shows the distribution of weights identified by inverse analysis when the weights in the embodiment are also included in the inverse analysis. [Figure 16] This graph shows the results of the forward calculation of pressure (-10m layer) using the parameters identified by the inverse analysis in the embodiment of the example. [Figure 17] This graph shows the results of the forward calculation of pressure (-13m layer) using the parameters identified by the inverse analysis in the embodiment of the example. [Figure 18] This graph shows the results of the forward calculation of pressure (-16m layer) using the parameters identified by the inverse analysis in the embodiment of the example. [Figure 19] This graph shows the results of the forward temperature calculation (-10m layer) using the parameters identified by the inverse analysis in the embodiment. [Figure 20] This graph shows the results of the forward temperature calculation (-13m layer) using the parameters identified by the inverse analysis in the embodiment of the example. [Figure 21] This graph shows the results of the forward temperature calculation (-16m layer) using the parameters identified by the inverse analysis in the embodiment of the example. [Modes for carrying out the invention]

[0028] Hereinafter, embodiments for carrying out the present invention will be described in detail with reference to the drawings. In this embodiment, the case in which the inverse analysis method of the present disclosure is applied to an inverse analysis device will be described.

[0029] First, the configuration of the inverse analysis device 10 according to this embodiment will be described with reference to Figure 1. Figure 1 is a block diagram showing an example of the hardware configuration of the inverse analysis device 10 according to this embodiment. Examples of the inverse analysis device 10 include information processing devices such as personal computers and server computers.

[0030] As shown in Figure 1, the inverse analysis device 10 according to this embodiment includes a CPU (Central Processing Unit) 11 as a computer of the technology of this disclosure, a memory 12 as a temporary storage area, a non-volatile storage unit 13, an input unit 14 such as a keyboard and mouse, a display unit 15 such as a liquid crystal display, a media read / write device (R / W) 16, and a communication interface (I / F) unit 18. The CPU 11, memory 12, storage unit 13, input unit 14, display unit 15, media read / write device 16, and communication I / F unit 18 are connected to each other via bus B. The media read / write device 16 reads information written to the recording medium 17 and writes information to the recording medium 17.

[0031] The storage unit 13 is implemented by an HDD (Hard Disk Drive), SSD (Solid State Drive), flash memory, etc. The storage unit 13, as a storage medium, stores the reverse analysis program 13A. The reverse analysis program 13A is stored (installed) in the storage unit 13 when the recording medium 17 on which the program 13A is written is set in the media read / write device 16, and the media read / write device 16 reads the program 13A from the recording medium 17. The CPU 11 reads the reverse analysis program 13A from the storage unit 13 as appropriate, expands it into memory 12, and sequentially executes the processes contained in the reverse analysis program 13A.

[0032] Furthermore, the memory unit 13 stores the initial information database 13B and the observed value database 13C. Details of these databases will be described later.

[0033] Next, the functional configuration of the inverse analysis device 10 according to this embodiment will be described with reference to Figure 2. Figure 2 is a block diagram showing an example of the functional configuration of the inverse analysis device 10 according to this embodiment.

[0034] The inverse analysis method by the inverse analysis device 10 according to this embodiment calculates the difference between observed values ​​of predetermined types of physical quantities at multiple locations and calculated values ​​obtained by forward calculation using a mathematical model (hereinafter simply referred to as the "mathematical model") that approximates the actual field using predetermined parameters (hereinafter simply referred to as the "parameters") corresponding to the observed values. Furthermore, the inverse analysis method by the inverse analysis device 10 according to this embodiment performs inverse analysis using an objective function (hereinafter simply referred to as the "objective function") that obtains the sum of the calculated differences after reflecting a weight (hereinafter simply referred to as the "weight") for each of the multiple locations.

[0035] In the inverse analysis method using the inverse analysis device 10 according to this embodiment, in addition to the parameters that are targeted for identification by inverse analysis in conventional inverse analysis methods, weights are also targeted for identification by inverse analysis. Thus, in the inverse analysis method according to this embodiment, since the target for identification includes not only parameters but also weights, the computational load for identifying the weights will increase compared to conventional techniques. However, since the identification of weights can be performed using substantially the same algorithm as the identification of parameters in conventional techniques, the burden for developing the algorithm related to weight identification can be kept to a minimum.

[0036] In the inverse analysis device 10 according to this embodiment, the model shown in equation (1) below is applied as the mathematical model. Note that x in equation (1) cal The expression represents the calculation formula for the mathematical model using forward computation, P represents the parameter, and x0 represents the initial value of the parameter.

[0037]

number

[0038] As shown in equation (1), the mathematical model according to this embodiment is schematically represented as a function having a parameter P to be identified and an initial value x0 of the parameter P. Note that multiple types of parameters P are often applied, in which case the initial value x0 will also be provided for each parameter P.

[0039] Equation (1) shows only the minimum necessary to explain the inverse analysis method according to this embodiment, but the actual mathematical model approximates the actual field using parameter P. Note that in equation (1), parameter P is not a variable, so the way it is written could be considered incorrect, but the expression in equation (1) is used to represent the idea that parameter P becomes a variable in the inverse analysis, that is, that parameter P changes.

[0040] Furthermore, in the inverse analysis device 10 according to this embodiment, the following equation (2) is applied as the objective function. Note that in equation (2), J represents the objective function, and x obs_i This represents the i-th observation, and x cal_i This represents the calculated value of the sequential calculation corresponding to the i-th observed value according to equation (1), and W i This represents the weight for the i-th observation.

[0041]

number

[0042] In the inverse analysis method according to this embodiment, the observed values ​​are physical quantities at multiple locations. When there are multiple observed values, the objective function J is often calculated using the sum of squared residuals between the observed and calculated values, as shown in equation (2). In deriving the objective function J, relative weights W are used according to the importance and reliability of each observed value. iIt is often set. Therefore, in the inverse analysis method according to the present embodiment, the formula (2) is also applied as the objective function J.

[0043] On the other hand, the influence of the parameter P to be obtained by inverse analysis, that is, how much the observed value is affected (how important it is), varies depending on the type of the observed value, the observation time, etc. Considering the degree of influence, it is considered necessary to determine the weight W i However, it is not actually easy to take the degree of influence into account in advance.

[0044] Therefore, in the inverse analysis method according to the present embodiment, as described above, in addition to the parameter P, the weight W i is also the object of identification in the inverse analysis.

[0045] The observed values are affected by various parameters P, and depending on the type and time of the observed values, etc., which parameter P has a large influence degree (importance) changes. Even for an observed quantity whose influence degree of the parameter is unknown, by performing inverse analysis with the importance degree (weight W i ) itself as the object of inverse analysis, it becomes possible to identify the parameter P close to the true value.

[0046] In addition, according to the inverse analysis method according to the present embodiment, it is not necessary to carefully extract the observed values in which the influence degree of the parameter P is strongly manifested, which also leads to shortening of the working process.

[0047] That is, in the conventional inverse analysis method, as a method for setting the weight W i , a method of setting according to the importance degree and reliability of the observed value was often adopted. In this case, the importance degree was often arbitrarily determined based on reasons such as whether the observed value is the one for the point that is particularly desired, and whether it is considered to be strongly affected by the parameter P to be obtained, etc. Also, in the conventional inverse analysis method, there was an example of devising the setting of the weight W i , but it was only a method that did not take into account the mathematical model.

[0048] In contrast, in the inverse analysis method according to this embodiment, one of the parameters P of the mathematical model, which represents the influence of some influence on the observed values ​​that cannot be expressed in the mathematical model, and the influence of the parameter P to be identified, is weighted W. i It is understood that, in addition to the parameter P, the weight W i This is also included as a target for identification in the inverse analysis method.

[0049] To specifically implement this inverse analysis method, the inverse analysis device 10 according to this embodiment includes, as an example shown in Figure 2, a setting unit 11A, a derivation unit 11B, an update unit 11C, a forward calculation unit 11D, a calculation unit 11E, and an acceptance determination unit 11F. When the CPU 11 of the inverse analysis device 10 executes the inverse analysis program 13A, the CPU 11 functions as the setting unit 11A, the derivation unit 11B, the update unit 11C, the forward calculation unit 11D, the calculation unit 11E, and the acceptance determination unit 11F.

[0050] The setting unit 11A according to this embodiment sets the parameter P and the weight W i Initial values ​​for each of these are set in advance. In this embodiment, the parameter P and the weight W are set in advance. i The initial values ​​for each of these are set by reading them from a database pre-registered in the storage unit 13, but this is not the only way. For example, the initial values ​​may be set by having the user of the inverse analysis device 10 input them via the input unit 14, or by receiving them from an external device such as a server.

[0051] Furthermore, the derivation unit 11B according to this embodiment uses the parameter P and weight W set by the setting unit 11A. i By performing perturbation calculations using the parameter P and the weight W, i The degree of influence of on the objective function J is derived. Furthermore, the update unit 11C according to this embodiment uses the degree of influence derived by the derivation unit 11B to determine the parameter P and the weight W i Update.

[0052] Furthermore, the forward calculation unit 11D according to this embodiment performs forward calculations using the updated parameters P by the update unit 11C. Also, the calculation unit 11E according to this embodiment uses the updated weights W by the update unit 11C. i Then, using the calculated values ​​obtained from the above forward calculation, the value of the objective function J is calculated.

[0053] Then, the tolerance determination unit 11F in this embodiment repeats the processing after the perturbation calculation until the value of the objective function J calculated by the calculation unit 11E becomes less than a predetermined tolerance error ε, thereby determining the parameter P and weight W i The final value is obtained. The tolerance determination unit 11F uses the parameter P and weight W obtained here to determine the final value. i The final value is registered in the storage unit 13.

[0054] In this embodiment, the inverse analysis device 10 uses physical quantities related to the ground as the above-mentioned physical quantities, but it is not limited to this. For example, physical quantities related to buildings and structures, or physical quantities related to medical care, may also be used as the above-mentioned physical quantities.

[0055] Furthermore, in the inverse analysis device 10 according to this embodiment, pressure and temperature in the ground are applied as physical quantities relating to the ground, but this is not limited to this. For example, only one of the pressure and temperature may be applied as a physical quantity relating to the ground.

[0056] Furthermore, in the inverse analysis device 10 according to this embodiment, a physical quantity indicating the permeability of the ground is applied as the parameter, but it is not limited to this. For example, the water resistance or bearing capacity of the ground may be applied as the parameter.

[0057] Figures 3 and 4 show schematic diagrams illustrating examples of the configurations of the initial information database 13B and the observed data database 13C, respectively.

[0058] As shown in Figure 3, the initial information database 13B according to this embodiment stores information such as type, identifier, and initial value in association with each other.

[0059] The above types are based on the parameter P and the weight W. i This information indicates the distinction between the two, and the above identifier corresponds to the type (parameter P or weight W). i This is information for individually identifying the corresponding initial value of ), and the above initial value is information that indicates the initial value itself.

[0060] Furthermore, as shown in Figure 4, the observation database 13C according to this embodiment stores identifiers and observation data in association with each other.

[0061] The above identifier corresponds to the weight W in the initial information database 13B. i This is the same information as the identifier, and the above observation value corresponds to the weight W corresponding to the corresponding identifier. i This information indicates the observed value itself that corresponds to the value.

[0062] Next, the operation of the inverse analysis device 10 according to this embodiment will be explained with reference to Figure 5. Figure 5 is a flowchart showing an example of the flow of the inverse analysis process according to this embodiment. The inverse analysis process according to this embodiment is executed when the user of the inverse analysis device 10 gives an instruction to execute it via the input unit 14 after the initial information database 13B and the observed value database 13C have been constructed.

[0063] In step 100 shown in Figure 5, the CPU 11 calculates the weight W for each observation. i All initial values ​​W 0 i This is set by reading it from the initial information database 13B. In step 102, the CPU 11 sets all initial values ​​P for parameter P. 0 This is set by reading it from the initial information database 13B.

[0064] In step 104, the CPU 11 sets the initial value of the parameter P. 0 And the set weight Wi Initial value W 0 i Using the parameters P and weights W, i By performing perturbation calculations on the parameters P and weights W, i The degree of influence on the objective function J and the change information described later are derived. The method for deriving the degree of influence and change information according to this embodiment is described below.

[0065] In the perturbation calculation according to this embodiment, the initial value of parameter P is P 0 It is assumed that the initial value P immediately before the change is changed by a predetermined amount. In the perturbation calculation according to this embodiment, the initial value P immediately before the change is changed. 0 Apply the value of to the mathematical model's calculation formula x cal While performing forward calculations using the method described above, the initial value P immediately before the change is used. 0 Apply the value of to the mathematical model's calculation formula x cal A sequential calculation is performed using the following method. In the following, the value obtained from the former sequential calculation will be called the "first sequential calculation value," and the value obtained from the latter sequential calculation will be called the "second sequential calculation value."

[0066] In the perturbation calculation according to this embodiment, the difference between the first sequential calculation value and the second sequential calculation value is derived as the influence degree E.

[0067] For example, the first parameter P in parameter P A Regarding the parameter P A Initial value P 0 When changing from 1.0 to 1.1, if the first sequential calculation value is 0.2 and the second sequential calculation value is 0.25, the influence E is 0.05 (=|0.2-0.25|). Also, the parameter P A A second parameter P that is different from the first parameter. B Regarding the parameter P B Initial value P 0 parameter P A Similarly, when changing from 1.0 to 1.1, if the first sequential calculation value is 0.2 and the second sequential calculation value is 0.19, the influence E is 0.01 (=|0.2-0.19|). Therefore, the influence E in this case is equal to the parameter P AThe parameter P B It will be larger.

[0068] Furthermore, when performing this perturbation calculation, the CPU 11 determines whether the change in value from the first sequential calculation value to the second sequential calculation value is an increase or a decrease, based on the relative magnitudes of the first sequential calculation value and the second sequential calculation value, except when the derived influence E is 0 (zero). Hereafter, an increase will be referred to as a "positive change," and a decrease will be referred to as a "negative change." Also below, information indicating whether a change is positive or negative will be referred to as "change information."

[0069] The above describes the method for deriving the influence and change information regarding parameter P, but the weight W i Similarly, we derive impact and change information for this as well.

[0070] In step 106, the CPU 11 processes the influence and change information of the parameter P derived from the above process, and the weight W. i Using the influence and change information, the parameter P and weight W i The CPU 11 updates each of the values ​​of the parameters P and weights W. i Based on the influence and change information of each, the updated parameters P and weights W are determined using the conventionally known minimum norm method. i Derive the value of .

[0071] Thus, in this embodiment, the parameter P and the weight W i The updated values ​​of each are derived using the minimum norm method, but this is not the only method. For example, the parameters P and weights W can be derived using the steepest descent method. i It may also be expressed in a form that derives the updated values ​​of each of them.

[0072] In step 108, the CPU 11 performs a sequential calculation using equation (1) with the updated parameter P to obtain the calculated value x corresponding to the updated parameter P. cal_i Calculate.

[0073] In step 110, CPU 11 calculates the calculated value x cal_i And the calculated value x cal_i The corresponding observed value x obs_i And the updated weight W i The value of the objective function J is calculated using these methods.

[0074] In step 112, the CPU 11 determines whether the calculated value of the objective function J is less than a predetermined tolerance ε. If the determination is negative, the CPU 11 returns to step 104; if the determination is positive, it then checks the parameters P and weights W. i The identification is considered complete, and the process proceeds to step 114. When the processes from steps 104 to 112 are repeatedly executed, the CPU 11, in step 104, updates the parameter P and weight W that were updated by the process in the previous step 106 (the process in step 106 of the previous processing loop). i Each of these values ​​will be included in the perturbation calculation.

[0075] In step 114, the CPU 11 registers the value of parameter P at this point in the storage unit 13 as the identified value, and then terminates the inverse analysis process.

[0076] (Examples)

[0077] Next, in order to verify the effectiveness of the inverse analysis method according to this embodiment, the verification tests conducted by the inventors of the technology of this disclosure will be described with reference to Figures 6 to 8. Figure 6 is a perspective view showing the configuration of the artificial ground in an embodiment according to this embodiment. Figure 7 is a perspective view used to explain the target of the inverse analysis in an embodiment according to this embodiment. Furthermore, Figure 8 is a perspective view used to explain the measurement conditions of the observed values ​​of the artificial ground in an embodiment according to this embodiment.

[0078] The inventors of the technology disclosed herein created an artificial ground 50 as shown in Figure 6. The artificial ground 50 had dimensions of 40m × 33m × 25m, and its permeability was set with a resolution of 0.5m. Numerical hydraulic tests were conducted using this artificial ground 50.

[0079] In this test, as shown in Figure 6, observed values ​​obtained from a numerical hydraulic test targeting a 20m × 13m × 11m area 52 in the middle of the artificial ground 50 are used. In this test, as shown in Figure 7, the physical quantity indicating the permeability of each block 54 in the block group 56 corresponding to area 52, which is composed of 36 (4 × 3 × 3) rectangular blocks 54, each enclosed by a white line, is determined by the inverse analysis method according to this embodiment. Note that each point in the diagram shown in Figure 7 indicates the distribution of the physical quantity indicating the permeability of the artificial ground 50. Hereafter, based on the positional relationship in the depth direction, the uppermost layer of the 36 blocks 54 will be referred to as the -10m layer, the middle layer as the -13m layer, and the lowermost layer as the -16m layer.

[0080] In this test, as shown in Figure 8, channels 58 were provided from the top surface of the artificial ground 50 at positions a-1, a-5, c-1, and c-5, which are the four corners of the block group 56 in a plan view. In this test, 33°C hot water was injected at a rate of 10 L / min through the channels 58 at positions a-1 and c-1, and pumped out at a rate of 10 L / min through the channels 58 at positions a-5 and c-5, and this was continued for 70 days.

[0081] Specifically, as shown in Figure 8, the layer thicknesses of each layer in block group 56 are h1, h2, and h3, and the -10m layer at position c-1 (i.e., block 54 01 Hot water was injected into the ) at a flow rate of Q1 = 10 × h1 / (h1 + h2 + h3). Similarly, in the -13m layer at position c-1 (i.e., block 54 13 Hot water is injected into the -16m layer at position c-1 (i.e., block 54) at a flow rate of Q2 = 10 × h2 / (h1 + h2 + h3), and 25 Hot water was injected into the ) at a flow rate of Q3 = 10 × h3 / (h1 + h2 + h3). In the example shown in Figure 8, h1 = 6.5 m (-6 to -12.5 m), h2 = 3 m (-12.5 to -15.5 m), and h3 = 1.5 m (-15.5 to -17 m).

[0082] Similarly, for position a-1, the -10m layer (i.e., block 54) 09 Hot water is injected into the -13m layer (i.e., block 54) at the flow rate of Q1.21 Hot water is injected into the -16m layer (i.e., block 54) at the flow rate of Q2. 33 Hot water was injected into the container at the flow rate of Q3.

[0083] On the other hand, regarding pumping at position a-5, the -10m layer (i.e., block 54) 12 Pump water from ) at the flow rate of Q1, and -13m layer (i.e., block 54 24 Pumping is performed from ) at the flow rate of Q2, and the -16m layer (i.e., block 54 36 ) was pumped at the flow rate of Q3. Similarly, for pumping at position c-5, the -10m layer (i.e., block 54 04 Pump water from ) at the flow rate of Q1, and -13m layer (i.e., block 54 16 Pumping is performed from ) at the flow rate of Q2, and the -16m layer (i.e., block 54 28 Water was pumped from ) at a flow rate of Q3.

[0084] Under the conditions described above, pressure and temperature will be observed during the hydraulic test at a total of 10 locations at depths of 10m, 13m, and 16m (3 depths) at positions c-2, c-3, c-4, c-5, b-2, b-3, b-4, b-5, a-3, and a-5 as shown in Figure 8.

[0085] Figure 9 shows a graph illustrating an example of observed pressure (total head) values ​​in an embodiment of this embodiment. Figure 10 shows a graph illustrating an example of observed temperature values ​​in an embodiment of this embodiment. The examples shown in Figures 9 and 10 are all observed values ​​at a depth of 10 m. Here, "Head" on the vertical axis in Figure 9 represents total head. Total head represents the sum of pressure head, velocity head, and potential head. However, in the case of slow flows such as groundwater flow, the velocity head is very small and is almost always ignored, so in this example as well, it is calculated as the sum of pressure head and potential head.

[0086] In this verification test, as an example, we will perform an inverse analysis using the inverse analysis method according to this embodiment, using the observed values ​​of pressure and temperature at one time point each (the time points indicated by vertical lines in Figures 9 and 10). For pressure, the time point at which the change has largely stopped was used as the time point, and this time point was the same for all observation points (15 days after the start of the test). For temperature, we tried to use the time point at the midpoint between when the temperature started to rise and when the change became negligible, as much as possible. As a result, the time points for temperature are almost different at each observation point. The reason for adopting the midpoint time for temperature is that it is expected that the effect of permeability is greatest at that time, or in other words, that other effects are small.

[0087] The 60 observational values ​​described above—10 locations × 3 depths (10m, 13m, 16m) × 2 types (pressure, temperature) × 1 time point—will be used for the inverse analysis.

[0088] Weight W corresponding to each of the 60 observed values ​​above i Since we set the weight W i The number of blocks is 60. Also, the number of parameters P identified by inverse analysis is 36 blocks of 54. 01 ~54 36 These are 36 physical quantities that indicate the water permeability. In the inverse analysis method according to this embodiment, there are 36 parameters P and weights W. i Since all 60 of these will be subjected to inverse analysis, the total number of items to be identified will be 96.

[0089] In this test, since the permeability of each block 54 in the artificial ground 50 is known, the average value and confidence interval of the physical quantity indicating the permeability of each block 54 can be calculated in advance. Figure 11 shows a graph showing the average value (black dots in Figure 11) and error bars (99% confidence interval) of the physical quantity indicating the permeability of the artificial ground 50 in the embodiment of this example (in this embodiment, seepage rate). If the physical quantity indicating the permeability of each identified block 54 can be identified within the range of the error bars in the graph shown in Figure 11, it can be said that a highly accurate result has been obtained.

[0090] Figure 12 shows graphs illustrating the distribution of physical quantities indicating permeability identified in the inverse analysis of the embodiment according to this model, both when the weights are not included in the inverse analysis and when the weights are included in the inverse analysis. In Figure 12, the black triangles represent physical quantities indicating permeability when the weights are not included in the inverse analysis, and the black squares represent physical quantities indicating permeability when the weights are included in the inverse analysis. To clarify the distribution of each physical quantity indicating permeability, Figure 13 shows a graph only for the case where the weights are not included in the inverse analysis, and Figure 14 shows a graph only for the case where the weights are included in the inverse analysis.

[0091] As shown in Figures 12 to 14, when weights are not included in the inverse analysis, i.e., in the conventional inverse analysis method, there are many blocks 54 where the physical quantity indicating permeability cannot be identified. In contrast, when weights are also included in the inverse analysis, i.e., in the inverse analysis method according to this embodiment, identification is generally possible within or close to the 99% confidence interval, indicating a significant improvement in identification accuracy compared to the conventional inverse analysis method. Note that in the inverse analysis that yielded the results shown in Figures 12 to 14, the number of iterations of steps 104 to 112 in the inverse analysis process shown in Figure 5 was terminated after 40 iterations, and these results are obtained when the process is terminated before the value of the objective function J falls below the allowable error ε. Therefore, it is thought that the identification accuracy can be further improved by actually repeating the process until the value of the objective function J falls below the allowable error ε.

[0092] For reference, Table 1 and Figure 15 show the weights W identified in this verification test. i The value is shown. Note that the black line in Figure 15 represents the weight W for pressure. i The gray line represents the weight W for temperature. i That is the case.

[0093] [Table 1]

[0094] Figures 16 to 21 show graphs illustrating the results of forward calculations of pressure and temperature using the parameter P identified by the inverse analysis in the embodiment of this model. Figures 16 to 18 are graphs relating to pressure in the -10m, -13m, and -16m layers, respectively, while Figures 19 to 21 are graphs relating to temperature in the -10m, -13m, and -16m layers, respectively. In each graph, the high-concentration line represents the actual observed value, the medium-concentration line represents the result of forward calculations using the parameter P identified by the inverse analysis method of this model, and the low-concentration line represents the result of forward calculations when the initial value x0 is applied as the parameter P.

[0095] As shown in Figures 16 to 21, the results of forward calculations using the parameter P identified by the inverse analysis method according to this embodiment are extremely close to the actual observed values, confirming that a highly accurate mathematical model can be obtained using the inverse analysis method according to this embodiment.

[0096] As described above, according to this embodiment, in an inverse analysis method that performs inverse analysis using an objective function that obtains the sum of the differences between observed values ​​of predetermined types of physical quantities at multiple locations and calculated values ​​obtained by forward calculation using a mathematical model that approximates the actual field using predetermined parameters corresponding to the observed values, with weights applied to each of the multiple locations, the parameters and weights are the targets of the inverse analysis. Therefore, compared to the case where the weights are not the targets of the inverse analysis, the parameters obtained by the inverse analysis can be derived with higher accuracy.

[0097] Furthermore, according to this embodiment, initial values ​​for each parameter and weight are set in advance, and perturbation calculations are performed using the parameters and weights to derive the degree of influence of the parameters and weights on the objective function. The parameters and weights are updated using the derived degree of influence, forward calculations are performed using the updated parameters, and the value of the objective function is calculated using the updated weights and the calculated values ​​obtained from the forward calculations. The process from perturbation calculation onwards is repeated until the calculated value of the objective function is less than a predetermined tolerance error, thereby obtaining the final values ​​of the parameters and weights. Therefore, the weights can be identified by the same process as in conventional inverse analysis methods.

[0098] Furthermore, according to this embodiment, the physical quantities are physical quantities related to the ground. Therefore, when the physical quantities related to the ground are observed values, the parameters can be derived with higher accuracy through inverse analysis.

[0099] Furthermore, according to this embodiment, the physical quantity relating to the ground is defined as at least one of the pressure and temperature in the ground. Therefore, when at least one of pressure and temperature is defined as the physical quantity relating to the ground, the parameters obtained by inverse analysis can be derived with greater accuracy.

[0100] Furthermore, according to this embodiment, the parameters are physical quantities that represent the permeability of the ground. Therefore, the physical quantities that represent the permeability of the ground can be derived with higher accuracy.

[0101] In the inverse analysis device 10 according to the above embodiment, the parameter P and the weight W i While the above-mentioned update method and frequency of updates are described in relation to each other, the system is not limited to this. For example, at least one of the above-mentioned update method and frequency of updates may be changed.

[0102] For example, parameter P and weight W i As a form of changing the update method, the above-mentioned method of deriving the degree of influence is used with parameters P and weights W. iExamples of such forms include changing to... In this form, the parameter P and the weight W i Examples of forms include performing a predetermined increase (such as multiplying by a value greater than 1 with respect to the influence degree) on only the influence degree of either one of them. Also, for example, as a form of changing the update frequency with the parameter P and the weight W i Examples of forms of changing the update frequency with them include performing a predetermined increase (such as multiplying by a value greater than 1 with respect to the update frequency) on only the update frequency of either one of the parameter P and the weight W i Examples of such forms can be given.

[0103] According to this form, it is possible to suppress the adverse effect on the derivation accuracy of the parameter P caused by the difference in characteristics between the parameter P and the weight W i

[0104] Also, in the above embodiment, the case where the technology of the present disclosure is applied to the inverse analysis for identifying physical quantities related to the ground has been described, but it is not limited thereto. For example, the technology of the present disclosure can be applied to any physical quantity as long as it is a physical quantity that has conventionally been an object of identification by inverse analysis, such as physical quantities in the medical field, physical quantities in non-destructive inspection, etc.

[0105] Also, the configuration of the various databases applied in the above embodiment is an example, and it is needless to say that it is not limited to what is exemplified.

[0106] ​Furthermore, in the above embodiment, for example, the hardware structure of the processing unit that executes the setting unit 11A, the derivation unit 11B, the update unit 11C, the sequential calculation unit 11D, the calculation unit 11E, and the tolerance determination unit 11F can be any of the following types of processors. As mentioned above, these types of processors include a CPU, which is a general-purpose processor that executes software (programs) and functions as a processing unit, as well as a programmable logic device (PLD), such as an FPGA (Field-Programmable Gate Array), which is a processor whose circuit configuration can be changed after manufacturing, and a dedicated electrical circuit, such as an ASIC (Application Specific Integrated Circuit), which is a processor with a circuit configuration specifically designed to execute a particular process.

[0107] The processing unit may consist of one of these various processors, or it may consist of a combination of two or more processors of the same or different types (for example, a combination of multiple FPGAs, or a combination of a CPU and an FPGA). Alternatively, the processing unit may consist of a single processor.

[0108] Examples of configuring a processing unit with a single processor include, firstly, a configuration where one or more CPUs and software combine to form a single processor, as is common in client and server computers, and this processor functions as the processing unit. Secondly, a configuration using a processor that realizes the functions of the entire system, including the processing unit, on a single IC (Integrated Circuit) chip, as is common in System-on-a-Chip (SoC) systems. Thus, the processing unit is configured, in terms of hardware structure, using one or more of the above-mentioned types of processors.

[0109] Furthermore, the hardware structure of these various processors can more specifically utilize electrical circuits, which are combinations of circuit elements such as semiconductor devices. [Explanation of symbols]

[0110] 10 Inverse analysis device 11 CPU 11A setting section 11B Derivation part 11C update section 11D forward calculation section 11E Calculation section 11F Acceptance Judgment Section 12 memory 13 Storage section 13A Inverse Analysis Program 13B Initial Information Database 13C Observation Database 14 Input section 15 Display 16. Media reading / writing device 17 Recording media 18 Communication I / F Section 50 Artificial ground 52 areas 54 blocks 56 block groups 58 channels

Claims

1. An inverse analysis method that performs inverse analysis using an objective function that obtains the sum of the differences between observed values ​​of predetermined types of physical quantities at multiple locations and calculated values ​​obtained by forward calculation using a mathematical model that approximates the actual field using predetermined parameters corresponding to the observed values, while reflecting a weight for each of the multiple locations, The aforementioned parameters and weights are subject to the inverse analysis. A reverse analysis method that uses a computer to perform the processing.

2. The initial values ​​of the aforementioned parameters and weights are set in advance. By performing a perturbation calculation using the aforementioned parameters and weights, the degree of influence of the parameters and weights on the objective function is derived. Using the derived influence, update the parameters and weights. Perform the forward calculation using the updated parameters, The value of the objective function is calculated using the updated weights and the calculated values ​​obtained in the forward calculation. The process after the perturbation calculation is repeated until the calculated value of the objective function falls below a predetermined tolerance, thereby obtaining the final values ​​of the parameters and weights. The inverse analysis method according to claim 1.

3. The aforementioned physical quantity is a physical quantity relating to the ground. The inverse analysis method according to claim 1 or claim 2.

4. The physical quantity relating to the ground is at least one of the pressure and temperature in the ground. The inverse analysis method according to claim 3.

5. The aforementioned parameter is a physical quantity that indicates the permeability of the ground. The inverse analysis method according to claim 3.

6. The parameters and weights are used to change at least one of the update method and the update frequency. The inverse analysis method according to claim 2.

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