JP6988050B2 - Data estimation method - Google Patents

Description

The present invention relates to a data estimation method.

Conventionally, a structure damage estimation system that can estimate the damage status of a structure due to an earthquake after the occurrence of an earthquake is known (see, for example, Patent Document 1). In the technique described in Patent Document 1, a plurality of simulated seismic waves having different characteristics and a dynamic response of the structure to each of the plurality of simulated seismic waves are stored in association with each other, and the vicinity of the structure is stored among the plurality of simulated seismic waves. Searches for simulated seismic waves that are similar to the actual seismic waves observed in, and displays the dynamic response of the structure to the searched simulated seismic waves.

Further, a dynamic response analysis method for applying an equivalent linear analysis method to a phenomenon in which physical properties change rapidly is known (see, for example, Patent Document 2). In the technique described in Patent Document 2, the input seismic motion is divided into a first group before liquefaction and a second group after liquefaction. In the first group, equivalent linear analysis using the dynamic deformation characteristics before liquefaction is performed. The second group uses the dynamic deformation characteristics after liquefaction, and performs an equivalent linear analysis in which the input seismic motion is from the liquefaction occurrence time t to the end. Then, when the solutions of the equivalent linear analysis of the first and second groups are obtained, the analysis results (response waveforms) are superposed and the procedure is completed.

Japanese Unexamined Patent Publication No. 2004-069598 Japanese Unexamined Patent Publication No. 2001-116651

However, in the techniques described in Patent Document 1 and Patent Document 2, input data cannot be appropriately estimated from observation data when a nonlinear input / output system having sequential nonlinearity is targeted for analysis.

For example, when the analysis model corresponding to the nonlinear input / output system is the ground model, the behavior of the ground at the time of an earthquake shows sequential nonlinearity, and the physical property values of the ground change from moment to moment.

In the technique described in Patent Document 2, equivalent linear analysis is performed before and after liquefaction, but since the physical property values of the ground change from moment to moment regardless of before and after liquefaction, a ground model is used. The input seismic motion, which is the input data, cannot be estimated properly.

In consideration of the above facts, an object of the present invention is to estimate the input data of the nonlinear input / output system from the observed data when the nonlinear input / output system having the sequential nonlinearity is targeted for analysis.

In order to achieve the above object, the data estimation method of the present invention obtains the input vector when an arbitrary output vector is observed in a nonlinear input / output system that outputs an output vector when the input vector is input. An arbitrary data estimation method for estimation, in which an input candidate vector representing a candidate for the input vector is calculated and an output candidate vector representing the output vector output when the input candidate vector is input to the nonlinear input / output system is calculated and observed. Using the output vector of the above as a target vector, a difference vector representing the difference between the target vector and the output candidate vector was calculated, and the elements were changed for each of the plurality of elements included in the input candidate vector. The input candidate change vector which is a vector is calculated, and for each of the plurality of input candidate change vectors, the output candidate change vector representing the output vector when the input candidate change vector is input to the nonlinear input / output system is calculated. For each of the plurality of output candidate change vectors, a coefficient vector representing the rate of change obtained from the difference between the output candidate change vector and the output candidate vector is calculated, and a matrix having the plurality of coefficient vectors as a column vector is calculated. A generalized inverse matrix of the response matrix is generated by generating a response matrix to be represented, selecting a specific mode from a plurality of modes obtained from the matrix decomposition result of the response matrix, and using the submatrix corresponding to the selected mode. Is generated, a correction vector representing the correction amount for the input candidate vector is calculated based on the generalized inverse matrix and the difference vector, and the new input is based on the input candidate vector and the correction vector. A candidate vector is generated, and the output candidate vector is calculated, the difference vector is calculated, the input candidate change vector is calculated, and the output candidate change vector is calculated until the value corresponding to the difference vector becomes less than a predetermined threshold. When the value corresponding to the difference vector becomes less than the threshold value by repeating each process of the calculation of, the generation of the response matrix, the generation of the generalized inverse matrix, and the generation of the new input candidate vector. A computer is made to perform a process of acquiring the input candidate vector as the input vector corresponding to any observed output vector. As a result, when a nonlinear input / output system having sequential nonlinearity is targeted for analysis, the input data of the nonlinear input / output system can be estimated from the observed data.

In the data estimation method of the present invention, when a specific mode is selected from a plurality of modes obtained from the matrix factorization result of the response matrix, the value representing the contribution of the mode is equal to or more than the threshold value for the preset mode. The mode may be selected and the submatrix corresponding to the selected mode may be used to generate a generalized inverse matrix of the response matrix. This makes it possible to shorten the convergence time of the iterative calculation when estimating the input data of the nonlinear input / output system from the observation data.

In the data estimation method of the present invention, when a specific mode is selected from a plurality of modes obtained from the matrix factorization result of the response matrix, the number of presets is set from the one with the larger value representing the contribution of the mode. A mode may be selected and the submatrix corresponding to the selected mode may be used to generate a generalized inverse matrix of the response matrix. This makes it possible to shorten the convergence time of the iterative calculation when estimating the input data of the nonlinear input / output system from the observation data.

In the data estimation method of the present invention, the nonlinear input / output system outputs an output vector at different observation points when an input vector is input, and any plurality of data observed at different observation points. With the output vector of the above as a plurality of target vectors, the input vector may be estimated when any plurality of the output vectors are observed at different observation points. Thereby, when the input data of the nonlinear input / output system is estimated from the observation data, the input data of the nonlinear input / output system can be estimated from a plurality of different observation data.

Further, in the data estimation method of the present invention, the input vector may include a plurality of types of vectors. This makes it possible to estimate a plurality of different types of input data when estimating the input data of the nonlinear input / output system from the observation data.

The nonlinear input / output system in the data estimation method of the present invention is a neural network in which the number of neurons is preset, the input vector is a parameter of the neural network, and the output vector is the output of the neural network. The difference vector is the difference between the output vector when the input data for training is input to the neural network and the target vector representing the output vector having a correct answer to the input data for training. May be. This makes it possible to estimate the parameters of a neural network, which is an example of a nonlinear input / output system.

Further, the data estimation method of the present invention may increase the number of selected modes by reducing the threshold value for the mode when each of the processes is repeated. This makes it possible to shorten the convergence time of the iterative calculation when estimating the input data of the nonlinear input / output system from the observation data.

Further, in the data estimation method of the present invention, the number of selected modes may be increased by increasing the preset number when each of the processes is repeated. This makes it possible to shorten the convergence time of the iterative calculation when estimating the input data of the nonlinear input / output system from the observation data.

Further, in the data estimation method of the present invention, when a new input candidate vector is generated based on the input candidate vector and the correction vector, the new input candidate vector and the correction vector are obtained. When it is determined whether or not the value of each element of the input candidate vector is within the preset range, and each element of the new input candidate vector has the element which is not within the preset range. In addition, the value of the element of the correction vector corresponding to the element is adjusted to correct the correction vector, and a new input candidate vector is obtained based on the input candidate vector and the corrected correction vector. May be generated. This makes it possible to appropriately estimate the input data of the nonlinear input / output system when the value of each element of the input vector of the nonlinear input / output system is limited.

According to the present invention, when a nonlinear input / output system having sequential nonlinearity is targeted for analysis, the effect that the input data of the nonlinear input / output system can be estimated from the observation data can be obtained.

It is a block diagram which shows an example of the structure of the data estimation apparatus which concerns on this embodiment. It is explanatory drawing for demonstrating the nonlinear input / output system F which consists of a building and the ground. It is explanatory drawing for demonstrating the tangential gradient of an arithmetic matrix. It is explanatory drawing for demonstrating the difference vector. It is explanatory drawing for demonstrating the output candidate change vector obtained by the minute perturbation. It is explanatory drawing for demonstrating the selection of a mode. It is a figure which shows an example of the data estimation processing routine which concerns on 1st Embodiment. It is a figure which shows an example of the data estimation processing routine which concerns on 2nd Embodiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the content of a simulation experiment. It is explanatory drawing for demonstrating the modification of this Embodiment. It is explanatory drawing for demonstrating the modification of this Embodiment. It is explanatory drawing for demonstrating the modification of this Embodiment.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Structure of the data estimation device according to the first embodiment of the present invention>

FIG. 1 shows an example of the configuration of the data estimation device 100 according to the first embodiment of the present invention. Functionally, as shown in FIG. 1, the data estimation device 100 can be represented by a configuration including a data reception unit 10, a computer 20, and an output unit 50. The data estimation device 100 of the present embodiment estimates the input vector when an arbitrary output vector is observed in the nonlinear input / output system F that outputs the output vector when the input vector is input.

An example of the nonlinear input / output system F is a nonlinear ground model. For example, consider the case where seismic motion is observed at an arbitrary observation point of a nonlinear ground model. In this case, there is a problem of estimating the input vector which is the input seismic motion for reproducing the output vector based on the output vector representing the seismic motion at the observation point. There are various methods for estimating such an input vector.

For example, in the soundness evaluation of a building after an earthquake, the simulation analysis of seismic motion is used when evaluating the foundation structure of the target building. When using seismic motion simulation analysis, it is necessary to reproduce the input vector representing the waveform of the input seismic motion.

FIG. 2 shows an explanatory diagram for explaining a nonlinear input / output system F composed of a building and the ground. As shown in FIG. 2, the nonlinear input / output system F includes a building, a pile, and a ground. In this case, at the observation point S shown in FIG. 2, an output waveform (Output Wave) representing the observation data of the seismic motion is obtained. At this time, the input waveform (Input Wave) representing the input seismic motion is estimated by inversion from the obtained output waveform. In this case, the input waveform representing the input seismic motion to be used in the simulation analysis needs to be estimated so that the output waveform is reproduced at the observation point S on the non-linear ground model.

Examples of the method for setting the input seismic motion include a method in the frequency domain of the signal. However, the frequency domain method is applicable only when the physical property value of the ground under analysis is constant. In general, the behavior of the ground during an earthquake shows sequential non-linearity, and the physical characteristics of the ground change from moment to moment. Therefore, it is difficult to use the frequency domain method for general purposes.

Therefore, when setting the input seismic motion used for the simulation analysis of the seismic motion, it is necessary to adopt the method based on the time domain. In the prior art regarding the method of setting the input seismic motion in the time domain, the target system is often a linear system. As an example considering non-linearity, a method of back-calculating the input seismic motion with the base input seismic motion as an unknown is known, but there is a problem that many high vibration components are generated in the input wave.

Therefore, there is no known general-purpose method for appropriately estimating the input vector, which is the input data, based on the output vector, which is the observation data, when the behavior of the analysis target shows sequential non-linearity. Therefore, when the data estimation device 100 of the present embodiment targets a non-linear input / output system having sequential non-linearity, the output vector which is the observation data and the input vector which is the input data of the non-linear input / output system are appropriately selected. presume.

The relationship between the output vector {a _o }, the nonlinear input / output system F, and the input vector { _ai } is expressed by the following equation (1).

（１）

(1)

The inversion shown in FIG. 2 corresponds to the inverse operation of the above equation (1), that is, the calculation of the input vector { _ai } _{from the output vector {a o}.} There are two problems in performing this inverse operation. The first problem is that the operation of the above equation (1) is an injective transformation in the forward direction, but is not an injective transformation in the reverse direction. The second problem is that the target system F is not a linear system, but a nonlinear system in which the output vector {a _o } changes in a complicated manner _{according to the input vector {ai}.}

When the input vector {a _i } is N-dimensional and the output vector {a _o } is N-dimensional, the nonlinear input / output system F can be regarded as an NxN arithmetic matrix. Therefore, in the present embodiment, the input vector {a _i } is estimated _{from the output vector {a o} } by using the tangential gradient of the arithmetic matrix represented by the nonlinear input / output system F.

FIG. 3 shows an explanatory diagram for explaining the tangential gradient of the calculation matrix. As shown in FIG. 3, the change of _{the output vector {a o} } from the change _{{Δa i } (Incremental Input Wave Vector) of the input vector {a i} } and the matrix [K] representing the tangential gradient of the arithmetic matrix. Minutes {Δa _o } (Incremental Output Wave Vector) are calculated. In the present embodiment, given the variation {.DELTA.a _i} for the input vector _{{a i},} to generate a matrix [K]. Therefore, in this embodiment, the matrix [K] is referred to as a perturbation impulse response matrix.

Further, in this embodiment, the singular value decomposition of the perturbation impulse response matrix [K], and select the significant mode for the estimation of the input vector from the result of singular value decomposition {a _i}, the estimated input vector {a _i } Iteratively corrects the estimation error.

Hereinafter, a specific description will be given.

The data receiving unit 10 receives an observed arbitrary output vector. The data receiving unit 10 is realized by, for example, a keyboard, a mouse, an input / output device that receives input from an external device, or the like. The output vector is, for example, observation data of seismic motion at each time obtained by sensors installed at predetermined locations around the building.

The computer 20 includes a CPU (Central Processing Unit), a ROM (Read Only Memory) that stores programs for realizing each processing routine, a RAM (Random Access Memory) that temporarily stores data, and a memory as a storage means. , Network interface, etc. are included. As shown in FIG. 1, the computer 20 functionally includes a data storage unit 21, an input candidate vector calculation unit 22, an output candidate vector calculation unit 24, a difference vector calculation unit 26, and a determination unit 27. , Input candidate change vector calculation unit 28, output candidate change vector calculation unit 30, response matrix calculation unit 32, generalized inverse matrix calculation unit 34, correction vector calculation unit 36, update unit 38, and result acquisition unit. It is equipped with 40.

The data storage unit 21 stores the output vector received by the data reception unit 10. The output vector stored in the data storage unit 21 is used as a target vector.

The input candidate vector calculation unit 22 sets an input candidate vector { _ai } representing an input vector candidate. For example, the input candidate vector calculation unit 22 sets an initial vector {a _{dom } for the input candidate vector {ai} as shown in the following equation (2).}

（２）

(2)

When the observed data is seismic motion data, the initial vector {a _dum } can set the input seismic motion obtained by the method of the frequency region using, for example, the initial rigidity of the ground. Alternatively, the input may be a ground motion of completely 0. In order to reduce the number of repetitions of the iterative calculation described later, it is preferable to use a highly accurate initial prediction solution.

_{The output candidate vector calculation unit 24 calculates an output candidate vector {a o} }, _{which is an output vector output when the input candidate vector {ai} } is input to the nonlinear input / output system F, according to the following equation (3). do.

（３）

(3)

The difference vector calculation unit 26 sets the output vector stored in the data storage unit 21 as the target vector {a _tar }. Then, the difference vector calculation unit 26 represents a difference vector between the _{target vector {a tar } and the output candidate vector {a o} } calculated by the output candidate vector calculation unit 24 according to the following equation (4). Calculate {r}.

（４）

(4)

FIG. 4 shows an explanatory diagram for explaining the difference vector. As shown in FIG. 4, each element (value at each time) of the difference vector {r} (Residual wave vector) is combined with each element (value at each time) of the target vector {a _tar } (Target wave vector). It is a difference between each element (value at each time) of the output candidate vector {a _{o} (Calculated wave vector By predicted input wave).} Therefore, if the value of each component of this difference vector is sufficiently small, the estimated input candidate vector { _ai } can secure sufficient accuracy.

The determination unit 27 determines whether or not the value corresponding to the difference vector calculated by the difference vector calculation unit 26 is less than a predetermined threshold value ε. _{In the present embodiment, the determination unit 27 extracts the maximum value | {r} max} | of each element of the difference vector {r} _{, and the maximum value | {r} max} | is set according to the following equation (5). It is determined whether or not it is less than the threshold value ε. The threshold value ε is appropriately set according to the model to be analyzed, the application, and the unit system (for example, 0.01 [cm / s2]).

（５）

(5)

When the maximum value | {r} _max | is less than the threshold value ε, the input candidate change vector calculation unit 28, the output candidate change vector calculation unit 30, the response matrix calculation unit 32, and the generalized inverse matrix calculation unit, which will be described later, are used. 34, the iterative calculation by the correction vector calculation unit 36 and the update unit 38 is completed, and the processing by the result acquisition unit 40, which will be described later, is started. On the other hand, when the maximum value | {r} _max | is equal to or greater than the threshold value ε, the input candidate change vector calculation unit 28, the output candidate change vector calculation unit 30, the response matrix calculation unit 32, and the generalized inverse matrix calculation unit, which will be described later, are used. 34, the correction vector calculation unit 36, and the update unit 38 continue the iterative calculation.

In the present embodiment, it is determined whether or not to end the iterative calculation depending on whether or not _{the maximum value | {r} max} | of each element of the difference vector {r} is less than the threshold value ε. As will be described as an example, the determination unit 27 may determine in any way. For example, the determination unit 27 may determine the end of the iterative calculation when the norm of the difference vector {r} is less than a predetermined threshold value. Further, the determination unit 27 may determine the end of the iterative calculation when the average of each element of the difference vector {r} is less than a predetermined threshold value.

The input candidate change vector calculation unit 28 executes the process when the determination unit 27 determines that the maximum value | {r} _max | of the difference vector is equal to or greater than the threshold value ε. When the determination unit 27 determines that the maximum value | {r} _max | of the difference vector is equal to or greater than the threshold value ε, the input candidate change vector calculation unit 28 is an input candidate set by the input candidate vector calculation unit 22. For each of the plurality of elements included in the vector {a _{i }, the input candidate change vector ({ai} } + {Δa _i ^j }), which is a vector obtained by changing the element, is calculated.

Then, the output candidate change vector calculation unit 30 determines the input candidate change vector ({{ _ai } + {Δa _i ^j }) for each of the plurality of input candidate change vectors ({ai} + {Δa i j}) calculated by the input candidate change vector calculation unit 28. The _{output candidate change vector {a o} ^j _{}, which is the output vector when a i} } + {Δa _i ^j }) is input to the nonlinear input / output system F, is calculated.

Specifically, when the output candidate change vector calculation unit 30 adds a minute perturbation {Δa _i ^j _{} to each element of the input candidate vector {ai} } according to the following equations (6) and (7). The response analysis of is performed to obtain the output candidate change vector {a _o ^j } _{when the perturbation {Δa i} ^{j} is added.}

（６）

（７）

(6)

(7)

Here, the minute perturbation amount Δ is set according to the estimation accuracy of the input vector to be estimated. For example, when the input vector is an input seismic motion, it is preferable to set the same value if accuracy in ^{0.1 [cm / s 2] units is required.} If the value of the perturbation amount Δ is large, there is a high possibility that vibration will occur under the assumption of convergence and a convergent solution cannot be obtained. On the other hand, when the value of the perturbation amount Δ is small, it takes a lot of time for convergence.

FIG. 5 shows an explanatory diagram for explaining an output candidate change vector {a _o ^j } obtained in response to a minute perturbation {Δa _i ^j}. As shown in FIG. 5, N output candidates are obtained by performing a response analysis in which a _{perturbation {Δa i} ^j } is given to the j-th element of the input candidate vector {a _{i} for all the elements.} The change vector {a _o ^j } is obtained. The difference between this output candidate change vector {a _o ^j } and the output candidate vector {a _o } obtained in the above equation (3) is given to the output by the perturbation in each element of the input candidate vector {a _i}. Shows the impact.

Response matrix calculator 32 according to the following equation (8), for each of a plurality of output candidate change vector calculated by the output candidate change vector calculating section 30 {a o ^_j}, the output candidate change vector {a _o ^{j } And the effect coefficient vector {k j} } representing the rate of change obtained from the difference between the output candidate vector {a _o}. The influence coefficient vector {k ^j } is an example of the coefficient vector of the present invention.

（８）

(8)

As shown in FIG. 5, ^{each element of the influence coefficient vector {k j} } changes the output candidate when the _{perturbation {Δa i} ^j } is given to the j-th element of the input candidate vector {a _i}. It is a rate of change obtained from the difference between each element of the vector {a _o ^j } and each element of the output candidate vector {a _o}.

Then, the response matrix calculation unit 32 generates a perturbation impulse response matrix [K] representing a matrix having a ^{plurality of influence coefficient vectors {k j} as column vectors.} The perturbation impulse response matrix [K] is an example of the response matrix of the present invention.

Specifically, the response matrix calculation unit 32 uses the calculated plurality of influence coefficient vectors {k ^j } as column vectors, and all the influence coefficient vectors {k ^j } as shown in the following equation (9). By arranging the above, a perturbation impulse response matrix [K] (square matrix N × N) is generated.

（９）

(9)

In the perturbation impulse response matrix [K], as shown in the following equation (10), when a change {Δa _i } is given to the _{input candidate vector {ai} which is a candidate at the present time.} It is a matrix for calculating the change {Δa _o } of the output vector {a _{o} of.}

（１０）

(10)

Therefore, the perturbation impulse response matrix [K] is a tangential gradient of the arithmetic matrix represented by the nonlinear input / output system F, and as shown in FIG. 3 above, the minute variation of the output vector is calculated from the minute variation of the input vector. It is a matrix.

Each column of the perturbation impulse response matrix [K] is a perturbation of an element of the output vector when a perturbation is given to an element of the input vector. Therefore, the upper triangular portion of this perturbation impulse response matrix [K] becomes 0, and in some cases, the diagonal portion also becomes 0. In the present embodiment, the inverse matrix of the perturbation impulse response matrix [K] is used to back-calculate the change {Δa _{i } with respect to the input candidate vector {a i} that eliminates the difference, and gradually correct it.} Approximately obtain an impulse solution.

Even when the perturbation impulse response matrix [K] is used, the problems of "the inverse matrix is not uniquely determined" and "the matrix changes from moment to moment" remain. Therefore, in the present embodiment, the former is modified by using a generalized inverse matrix instead of the usual inverse matrix and using only its main mode. The latter is solved by finding the perturbation impulse response matrix [K] for each iterative calculation. In this embodiment, singular value decomposition is used when calculating the generalized inverse matrix. Singular value decomposition is an example of a matrix factorization method.

The generalized inverse matrix calculation unit 34 matrix-decomposes the perturbation impulse response matrix [K] generated by the response matrix calculation unit 32 by using the singular value decomposition which is an example of the matrix factorization method. When the singular value decomposition of the perturbation impulse response matrix [K] is performed, the perturbation impulse response matrix [K] is decomposed as shown in the following equation (11).

（１１）

(11)

Here, [U] in the above equation (11) is a unitary matrix, and each column is composed of an orthonormal basis of the output. Further, [V] in the above equation (11) is also a unitary matrix, and each column thereof indicates an orthonormal basis of the input. [Σ] in the above equation (11) is a singular value matrix having singular values as diagonal terms. Note that this singular value is obtained by the number of ranks of the matrix before decomposition, and the magnitude of the singular value represents the magnitude of the contribution of each mode.

Next, the generalized inverse matrix calculation unit 34 selects a specific mode from a plurality of modes obtained from the matrix factorization result of the perturbation impulse response matrix [K]. Specifically, the generalized inverse matrix calculation unit 34 has a singular value representing the contribution of the mode when selecting a specific mode from a plurality of modes obtained from the matrix factorization result of the perturbation impulse response matrix [K]. Select a mode that is equal to or greater than the threshold TH for the preset mode. Therefore, the generalized inverse matrix calculation unit 34 degenerates each submatrix by excluding the mode in which the singular value is 0 or relatively small and considering the mode up to the N'order. Although the submatrix is degenerated, the dimension of the influence coefficient matrix as a whole does not change. The perturbation impulse response matrix [K'] obtained by selecting the mode by the generalized inverse matrix calculation unit 34 is expressed by the following equation (12).

（１２）

(12)

FIG. 6 shows an explanatory diagram for explaining the mode selection. As shown in FIG. 6, the generalized inverse matrix calculation unit 34 selects a mode in which the singular value is equal to or higher than the threshold value TH for the mode from the singular value matrix [Σ], and a new singular value matrix [Σ']. To generate.

In this way, ignoring the mode with a small singular value is the mode with a small singular value (that is, the degree of influence) on the identified input vector when the inverse matrix is calculated in the state where the singular value is 0 or the mode with a small value is taken into consideration. This is because it contains a large amount of the components of. In addition, there is also the meaning of avoiding a large number of numerical errors due to division by a value close to 0 in numerical calculation.

Since the data estimation method of the present embodiment is an approximate solution method in which the error is reduced by repetition, a minute mode is ignored and a significant mode is selected for correction. It should be noted that the boundary value of the singular value to be selected needs to be appropriately set according to the target problem. It should be noted that there is a possibility that the correction by a minute mode alone does not fall within the required margin of error. In such a case, it is necessary to gradually lower the threshold value according to the number of repetitions and make corrections using more modes.

Next, the generalized inverse matrix calculation unit 34 generates a ^{generalized inverse matrix [K'] +} of the perturbation impulse response matrix [K'] using the submatrix corresponding to the selected mode.

Specifically, the generalized inverse matrix calculation unit 34 utilizes the unitarity and diagonality of each matrix from the above equation (12) to generalize the inverse matrix [K'] of the perturbation impulse response matrix [K']. '] ⁺ Is calculated by the following equation (13).

（１３）

(13)

The correction vector calculation unit 36 is based on the generalized inverse matrix [K'] ⁺ generated by the generalized inverse matrix calculation unit 34 and the difference vector {r} calculated by the difference vector calculation unit 26 as follows. according to equation (14), calculates the correction vector {.DELTA.a _i} representative of the amount of correction for the input candidate vector _{{a i}.}

（１４）

(14)

The update unit 38 has a new input candidate vector {a _{i } based on the input candidate vector {ai} set by the input candidate vector calculation unit 22 and the correction vector {Δa i} } calculated by the correction vector calculation unit 36. _i } is generated.

Specifically, the update unit 38, as shown in equation (15) below, the adding to the set input candidate vectors {a _i} by the input candidate vector calculating unit 22 the correction vector {.DELTA.a _i}, Let it be a new input candidate vector { _ai }.

（１５）

(15)

_{Then, until the maximum value | {r} max} | of each element of the difference vector {r} becomes less than the threshold value ε, the output candidate vector {a _o } is calculated, the difference vector {r} is calculated, and the input candidate changes. ({A _i } + {Δa _i ^j }) Vector calculation, output candidate change vector {a _o ^j } calculation, perturbation impulse response matrix [K] generation, generalized inverse matrix [K'] ⁺ generation, And each process of generating a new input candidate vector { _{ai} is repeated.}

The result acquisition unit 40 is generated by the update unit 38 when _{the maximum value | {r} max} | of each element of the difference vector {r} calculated by the difference vector calculation unit 26 is less than the threshold value ε. The input candidate vector { _ai } is acquired as an input vector corresponding to the target vector stored in the data storage unit 21.

The output unit 50 outputs the input vector acquired by the result acquisition unit 40 as a result. For example, the output unit 50 is realized by a display.

<Action of data estimation device 100>

Next, the operation of the data estimation device 100 will be described. When the data receiving unit 10 of the data estimation device 100 receives the input of the observed arbitrary output vector, it stores it in the data storage unit 21. Then, when the computer 20 of the data estimation device 100 receives the instruction signal for processing execution, the computer 20 executes the data estimation processing routine shown in FIG. 7A. In the following processing, a case where a specific mode is selected from the singular value matrix [Σ] after generating the ^{generalized inverse matrix [K] +} for the perturbation impulse response matrix [K] will be described as an example.

In step S100, the input candidate vector calculation unit 22 sets an input candidate vector { _ai } representing an input vector candidate according to the above equation (2).

In step S102, the output candidate vector calculation unit 24 is _{an output vector output when the input candidate vector {ai} } set in step S100 is input to the nonlinear input / output system F according to the above equation (3). Compute a certain output candidate vector {a _o }.

In step S104, the difference vector calculation unit 26 sets the output vector stored in the data storage unit 21 as the target vector {a _tar }. _{Then, the difference vector calculation unit 26 creates} a difference vector {r} representing the difference between the target vector {a tar} and the output candidate vector {a _o } calculated in step S102 according to the above equation (4). calculate.

_{In step S106, the determination unit 27 extracts the maximum value | {r} max} | of each element of the difference vector {r} calculated in step S104, and according to the above equation (5), the maximum value | { It is determined whether or not r} _max | is less than the threshold value ε. Then, when the maximum value | {r} _max | is less than the threshold value ε, the data estimation processing routine is terminated. On the other hand, if the maximum value | {r} _max | is equal to or greater than the threshold value ε, the process proceeds to step S108.

In step S108, the input candidate change vector calculation unit 28 changes _{each of the plurality of elements included in the input candidate vector {ai} } set in step S100 according to the above equation (7). The input candidate change vector ({ _ai } + {Δa _i ^j }) which is a vector is calculated.

Then, in step S108, the output candidate change vector calculation unit 30 uses the above equation for each of _{the plurality of input candidate change vectors ({ai} } + {Δa _i ^{j}) calculated by the input candidate change vector calculation unit 28.} According to (6), _{the output candidate change vector {a o} ^j _{} when the input candidate change vector ({ai} } + {Δa _i ^j }) is input to the nonlinear input / output system F is calculated.

In step S110, response matrix calculator 32 according to the above formula (8), for each of a plurality of output candidate change vector calculated in step S108 _{a ^{o j},} the output candidate change vector ^{_{a o} j} ^{The influence coefficient vector {k j} } obtained from the difference between the _{output candidate vector {a o} } calculated in step S102 is calculated.

In step S112, the response matrix calculation unit 32 uses the plurality of influence coefficient vectors { ^kj } calculated in step S110 as column vectors as shown in the above equation (9), and the perturbation impulse response matrix [K]. To generate.

In step S114, the generalized inverse matrix calculation unit 34 decomposes the perturbation impulse response matrix [K] generated in step S112 into a singular value, and generalizes the perturbation impulse response matrix [K] according to the singular value decomposition result. Generates the inverse matrix [K] ^+.

In step S116, the generalized inverse matrix calculation unit 34 selects a mode in which the singular value is equal to or higher than the threshold value TH for the mode from the singular value matrix [Σ] constituting the ^{generalized inverse matrix [K] +, and a new mode is selected.} Generate a singular value matrix [Σ']. Further, the generalized inverse matrix calculation unit 34 generates a new matrix [U'] and a new matrix [V'] according to the selected singular value. Then, the generalized inverse matrix calculation unit 34 uses a new generalized inverse matrix [K'] based on the new singular value matrix [Σ'], the new matrix [U'], and the new matrix [V']. ] Generate ^+.

In step S118, the correction vector calculation unit 36 uses ^{the above equation (14) based on the generalized inverse matrix [K'] +} generated in step S116 and the difference vector {r} calculated in step S104. ) according to calculate the correction vector {.DELTA.a _i} for the input candidate vector _{{a i}.}

In step S120, the updating unit 38, and the updated input candidate vectors _{{a i}} by the input candidate vector _{{a i}} or the previous step S120 that has been set in the step S100, it is calculated in step S118 correction vector Based on {Δa _i }, a new input candidate vector {a _i } is generated according to the above equation (15).

_{In the data estimation processing routine, the output candidate vector {a o} } is calculated and the difference vector {r} is calculated _{until the maximum value | {r} max} | of each element of the difference vector {r} becomes less than the threshold value ε. , Input candidate change ({ _ai } + {Δa _i ^j }) vector calculation, output candidate change vector {a _o ^j } calculation, perturbation impulse response matrix [K] generation, generalized inverse matrix [K'] ^{Each process of generating +} and generating a new input candidate vector { _ai } is repeated.

_{The result acquisition unit 40 inputs the input candidate vector {ai} } _{generated by the update unit 38 when the maximum value | {r} max} | of each element of the difference vector {r} is less than the threshold value ε. , Acquired as an input vector corresponding to the target vector stored in the data storage unit 21.

The output unit 50 outputs the input vector acquired by the result acquisition unit 40 as a result.

As described in detail above, the data estimation device 100 of the present embodiment _{calculates an output candidate vector {a o} } that _{is output when the input candidate vector {ai} } is input to the nonlinear input / output system F. Using any observed output vector as the target vector {a _tar }, the difference vector {r} representing the difference between the target vector {a _tar } and the output candidate vector {a _{o} is calculated.} Then, data estimation device 100, for each of a plurality of elements included in the input candidate vector {a _i}, the input candidate change vector is a vector obtained by changing the element _{({a i} + {Δa} i j}) was calculated for each of the plurality of input candidates change vector _{({a i} + {Δa} i j}) , input candidate change vectors _{({a i} + {Δa} i j}) to the nonlinear input-output system F The output candidate change vector {a _o ^j } is calculated. Then, the data estimation device 100 calculates the influence coefficient vector {k} for each of the plurality of output candidate change vectors {a _o ^j }, and generates a perturbation impulse response matrix [K]. Then, the data estimation device 100 selects a specific mode from a plurality of modes obtained from the matrix factorization result of the perturbation impulse response matrix [K], and uses the submatrix corresponding to the selected mode to perform the perturbation impulse response matrix. Generate a generalized inverse matrix [K'] ^{+ of [K].} Then, the data estimation device 100 calculates a correction vector {Δa _{i } for the input candidate vector {ai} ^{} based on the generalized inverse matrix [K'] +} and the difference vector {r}. Then, the data estimation device 100 generates a new input candidate vector { _{ai } based on the input candidate vector {ai} } and the correction vector {Δa _{i}. Further, the data estimation device 100 calculates the output candidate vector {a o } until the maximum value | {r} max} | of each element of the difference vector {r} becomes less than the threshold value ε, and the difference vector {r}. Calculation, input candidate change ({ _ai } + {Δa _i ^j }) vector calculation, output candidate change vector {a _o ^j } calculation, perturbation impulse response matrix [K] generation, generalized inverse matrix [K] '] ^{The generation of + and} the generation of the new input candidate vector { _ai } are repeated. Then, the data estimation device 100 observes _{the input candidate vector {ai } when the maximum value | {r} max} | of each element of the difference vector {r} is less than the threshold value ε. Get as an input vector corresponding to the output vector of. As a result, when a nonlinear input / output system having sequential nonlinearity is targeted for analysis, the input data of the nonlinear input / output system can be estimated from the observed data.

<Structure of the data estimation device according to the second embodiment of the present invention>

Next, a second embodiment of the present invention will be described. The data estimation device of the second embodiment is used to calculate the correction vector {Δa _{i } for the input candidate vector {ai} }, and the value of each element of the new input candidate vector obtained from the input candidate vector and the correction vector. Is within a preset range. Then, when the data estimation device of the second embodiment has an element that is not within the preset range in each element of the new input candidate vector, the value of the element in the correction vector is adjusted and corrected. Modify the vector. Since the configuration of the data estimation device according to the second embodiment has the same configuration as that of the first embodiment, the same reference numerals are given and the description thereof will be omitted.

Correction vector calculation portion 36 of the second embodiment, according to the above formula (15), the equation correction vector {.DELTA.a _i} which are calculated according to (14), the input candidate vectors set by the input candidate vector computing section 22 { based on the a _i}, once calculated the new input candidate vectors _{{a i}.}

Next, the correction vector calculation unit 36 presets the values of each element of the new input candidate vector { _{ai } once obtained from the input candidate vector {ai} } and the correction vector {Δa _i}. Determine if it is within range.

For example, when identification is performed using the data estimation device of the present embodiment _{, each element of the input candidate vector {ai} } includes a parameter that must not be negative (for example, Young's modulus or proof stress). In that case, a negative value may be searched for as a candidate as the value of each element, and the convergence of the calculation may stop.

Therefore, the data estimation device of the second embodiment modifies the _{correction vector {Δa i } so that each element of the input candidate vector {ai} } does not fall outside the preset range. This makes it possible to appropriately estimate the input data of the nonlinear input / output system when the value of each element of the input vector of the nonlinear input / output system is limited.

Of the elements of the input candidate vector { _ai }, it is not necessary to set a predetermined range for the elements without restrictions.

Then, the correction vector calculation unit 36 corrects according to the following equation (16) when each element of _{the new input candidate vector {ai} once calculated contains an element that is not within the preset range.} adjust the value of each element of the vector {.DELTA.a _i} modifies the correction vector {Δa _i}.

（１６）

(16)

Update unit 38 of the second embodiment, after the correction by the correction vector calculation unit 36 is performed, as shown in equation (15), is set by the input candidate vector calculating unit 22 the correction vector {.DELTA.a _i} Add to the input candidate vector { _ai } to make a new input candidate vector { _ai }.

<Action of data estimation device>

Next, the operation of the data estimation device of the second embodiment will be described. When the data receiving unit 10 of the data estimation device of the second embodiment receives the input of the observed arbitrary output vector, it stores it in the data storage unit 21. Then, when the computer 20 of the data estimation device of the second embodiment receives the instruction signal for processing execution, the computer 20 executes the data estimation processing routine shown in FIG. 7B.

In step S219, the correction vector calculation unit 36 of the second embodiment has the input candidate vector { _ai } set in step S100 or the input candidate vector {a updated in the previous step S120 according to the above equation (15). _A new input candidate vector {a _i } is once calculated _{based on i} } and the correction vector {Δa i} calculated in step S118.

Then, in step S219, the correction vector calculation unit 36 determines whether or not the value of each element of _{the new input candidate vector {ai} once obtained is within the preset range.} Thus, variation of the input candidate vector by the correction vector {a _i} {a _i} whether is acceptable is judged. Then, if the value of each element of the new input candidate vector { _ai } once obtained is out of the preset range, the process proceeds to step S220. On the other hand, if _{the value of each element of the new input candidate vector {ai} } once obtained is within the preset range, the process proceeds to step S120.

In step S220, the correction vector calculation unit 36, in accordance with the above equation (16), modifies the correction vector {.DELTA.a _i} by adjusting the value of each element of the correction vector {Δa _i}.

In step S120, the updating unit 38, and the updated input candidate vectors _{{a i}} by the input candidate vector _{{a i}} or the previous step S120 that has been set in the step S100, it is calculated in step S118 correction vector Based on {Δa _i } or the correction vector {Δa _{i } modified in step S220, a new input candidate vector {a i} } is generated according to the above equation (15).

As described in detail above, the data estimation device of the second embodiment is a new method obtained from the input candidate vector and the correction vector when calculating the correction vector {Δa _{i } for the input candidate vector {ai}.} It is determined whether or not the value of each element of the input candidate vector is within the preset range. Then, when each element of the new input candidate vector has an element that is not within the preset range, the data estimation device of the second embodiment adjusts the value of the element in the correction vector to correct the vector. To fix. This makes it possible to appropriately estimate the input data of the nonlinear input / output system when the value of each element of the input vector of the nonlinear input / output system is limited.

<Simulation experiment>

Next, a simulation experiment using an example will be described.

FIG. 8 shows the analysis model of the target. The analysis model is a columnar free ground model with a depth of 50 m. The ground is assumed to be soft sand, with a Vs value of 100 [m / s], a Poisson's ratio of 0.33, and a unit volume weight of 1.8 [t / m ³ ]. Ramberg-Osgood (RO) model for non-linear characteristics of the ground (eg, References (Jennnings, PC, "Periodic Response of General Yielding Structure", J. Eng. Mech. Div., ASCE, EM2, pp.131-163) , 1964)) is adopted. For the parameters of the RO model, refer to the sandy soil values described in the reference (Architectural Institute of Japan: "Seismic Response Analysis and Design of Buildings Considering Dynamic Soil-Structure Interaction", Maruzen, 2006 (in Japanese)). _{, Set so that the shear strain γ 0.5} = 0.10% and the maximum damping constant hmax = 0.21 when the shear modulus reduction rate (G / G0) is 50%.

In addition, the lower part of the ground has a viscous boundary, and a viscous damper corresponding to a Vs value of 300 m / s and a unit volume weight of 1.8 t / m3 is set. The Newmark-β method (β = 1/4) is used for time integration, and the analysis time step is 0.01 seconds. The analysis program includes MuDIAN (for example, References (Tadahiko Shiomi and 3 others, "Development of Structural Analysis System Considering Nonlinear Behavior of Ground", Takenaka Institute of Technology Report, No.54, pp.1-8, 1998). See).

By simulation, the Taft1952EW seismic motion (maximum acceleration 1.76 m / s ² , duration up to 10 seconds) shown in FIGS. 9 (a) and 9 (b) was multiplied by α (α = 1,2,3) for this analysis model. The response analysis is performed with the object as the input seismic motion (input vector), and the ground surface output (output vector) is calculated. The analysis time was about 3 seconds in the case of the largest triple input.

FIG. 10 shows a distribution map of the calculated maximum response acceleration (Max Acc), maximum displacement (Max Disp), and maximum shear strain (Max Shear Strain) of the ground. From FIG. 10, it can be seen that the maximum shear strain of the ground reaches 0.1% or more even in the case of 1x input, and non-linearity occurs. In addition, in the case of triple input, the strain further increases, and at a depth of -30 m or deeper, a shear strain of 1% or more is generated, so it is predicted that the strain has reached the strongly non-linear region. This can be judged from the fact that the acceleration distribution and the displacement distribution do not have a simple coefficient-folded response.

FIG. 11 shows a transfer function (ParzenWindow0.1Hz) of the acceleration time history of the input seismic motion and the ground surface response. From FIG. 11, it can be confirmed that the transfer function changes over the entire period due to the influence of the non-linearization as the input seismic motion increases.

It is confirmed whether the input seismic motion that reproduces the acceleration time history of the ground surface obtained from these analyzes can be calculated by the proposed method, and to what extent the calculated input seismic motion matches the seismic motion used in this analysis. do.

The margin of error set by the above formula (5) was 0.01 m / s ² , the perturbation amount set by the above formula (8) was also 0.01 m / s ² , and the number of repetitions was 100 times. Regarding the number of modes set by the above equation (12), the mode of "singular value 1 or more" is extracted in the initial iteration, and thereafter, the maximum value of the component of the acceleration correction vector of the above equation (14) is extracted. When becomes less than 0.5 m / s ² , the threshold value of the singular value is halved. As a result, corrections including higher-order modes are gradually made.

In FIG. 12, the input seismic motion (Calculated) identified from the target ground surface output is shown by a solid line, and the input seismic motion (Target) used in the simulation analysis is shown by a dotted line. Further, in FIG. 13, the acceleration time history (Calculated) of the ground surface output obtained by the input seismic motion shown in FIG. 12 is shown by a solid line, and the ground surface output (Target) obtained from the input seismic motion used in the simulation analysis is shown by a dotted line. Indicated by. These identification results extract cases where the RMS (Root Mean Square) error from the target ground surface output is approximately less than 1.0.

From FIGS. 12 and 13, it can be seen that the ground surface outputs match with good accuracy, although there are some differences in the identified input seismic motions at both input magnifications. While the ground surface outputs are generally consistent in this way, the reason for the large difference in the identified input seismic motions is that the inverse problem is not an injective problem as described above. In other words, since there are multiple input seismic motions that realize the target ground surface output and are not uniquely determined, the input seismic motion identified this time is one of the solutions, but it is completely the same as the seismic motion used as the input seismic motion in the previous section. It is probable that they did not match. However, at any input magnification, the waveforms of the input seismic motions match with good accuracy in the region where the initial input is small and can be regarded as substantially linear. It is considered that this can be calculated accurately because the input / output relationship in the linear state has a one-to-one correspondence.

Table 1 below shows the number of convergences and calculation time required to keep the RMS error below 1.0. Further, FIG. 14 shows how the RMS error is reduced due to convergence. The numerical values in Table 1 are the values at the “pick up point” in FIG. Convergence is fast in the case of 1x input with small non-linearity, but it takes a lot of times of convergence and convergence time in 2x input and 3x input where non-linearity progresses. It is considered that the response became complicated in the analysis with advanced non-linearity, and it became difficult for the error to converge.

As described above, the feature of the proposed method in the present embodiment is that the iterative modification is limited to the significant mode. However, as a way of thinking, a method of using all modes is naturally conceivable.

Therefore, with reference to FIG. 15, it is confirmed that there is a difference in convergence when the number of modes to be considered is changed in the case of 1x input. In the case of comparison, in addition to the case where the minimum value of the singular value is gradually reduced (Gradient Decrease), the case where ^{it is fixed at 1.0 (const) and 10 -6} (Min. Singular value) is added. .. The former corresponds to the case where the correction is always performed only in the lower-order mode, and the latter corresponds to the case where the correction is performed using almost all modes.

From FIG. 15, ^{in the case of fixing at 10-6} using all modes, it does not converge and diverges on the contrary. On the other hand, even if the correction is made only in the low-order mode in which the minimum value is fixed at 1.0, the error convergence is slow and the error does not become small even if the number of convergences is repeated. Therefore, it can be said that it is effective to make corrections in the low-order mode at first, and then gradually add higher-order modes to make corrections when the error does not become small.

The present invention is not limited to the above-described embodiment, and various modifications and applications can be made without departing from the gist of the present invention.

The data estimation method of the above embodiment can be applied regardless _{of the output vector {a o} }, the nonlinear input / output system F, and the input vector { _ai}.

For example, as shown in FIG. 16, the nonlinear input / output system is a neural network F in which the number of neurons is preset, and the input vector { _ai } is a neural network parameter {W1, W2, ..., W100}, and the output vector {a _o } can be set to be the output of the neural network. In this case, the difference vector {r} is an output vector when the input data for training (TestData) is input to the neural network F, and a target vector (target vector) representing the correct output vector for the input data for training (TestData). It is set to be the difference between Target Output {Test1, Test2, Test3, ...}).

Further, in the above embodiment, when a specific mode is selected from a plurality of modes obtained from the matrix factorization result of the perturbation impulse response matrix [K], the value representing the contribution of the mode is equal to or more than the threshold value x regarding the mode. Was selected and the submatrix corresponding to the selected mode was used ^{to generate the generalized inverse matrix [K'] +} of the perturbation impulse response matrix [K], but the case is limited to this. It's not a thing. For example, when selecting a specific mode from a plurality of modes obtained from the matrix factorization result of the perturbation impulse response matrix [K], a preset number of modes are selected from the one with the larger value representing the contribution of the mode. , The submatrix corresponding to the selected mode may be used to generate ^{the generalized inverse matrix [K'] + of the perturbation impulse response matrix [K].}

Further, as shown in FIG. 17, the nonlinear input / output system F may output the output vectors at different observation points when the input vectors are input. In this case, the data estimation device 100 uses any plurality of output vectors observed at different observation points as a plurality of target vectors (Target Output1 and Target Output2), and any plurality of output vectors at different observation points. Estimate the input vector (Input) when observed. In this case, the relationship between the change {Δa _i } of the input vector {a _i }, the perturbation impulse response matrix [K], and the change {Δa _{o } of the output vector {a o} } is as shown in FIG. becomes, the output variation of the vector _{{a o} {Δa o}} , include changes in the output vector of a plurality of different observation points _{{a o} {Δa o}} .

Further, the input vector may include a plurality of types of vectors. For example, as shown in FIG. 18, when it is desired to estimate the input seismic motion (Input) and the ground stiffness K0, the acceleration data Acc representing the input seismic motion and the ground stiffness K0 can be set as input vectors. In this case, the relationship between the change {Δa _i } of the input vector {a _i }, the perturbation impulse response matrix [K], and the change {Δa _{o } of the output vector {a o} } is as shown in FIG. Therefore, the change {Δa _i } of the input vector {a _i } includes a perturbation related to the ground stiffness K0.

Further, the number of selected modes may be increased when each process is repeated. In this case, for example, the number of selected modes can be increased by decreasing the threshold value x regarding the mode each time each process is repeated. Alternatively, the number of selected modes can be increased by increasing the number of selected modes each time each process is repeated. It can be said that the method of correcting in the low-order mode at the beginning and gradually adding and correcting the high-order mode is effective as shown in FIG. In this case, as shown in FIG. 15, when estimating the input data of the nonlinear input / output system from the observation data, the convergence time of the iterative calculation can be shortened.

Further, although the mode in which the program is stored (installed) in advance in the storage unit (not shown) has been described above, the program is recorded on any recording medium such as a CD-ROM, a DVD-ROM, or a micro SD card. It is also possible to provide it in the form in which it is used.

10 Data reception unit 20 Computer 21 Data storage unit 22 Input candidate vector calculation unit 24 Output candidate vector calculation unit 26 Difference vector calculation unit 27 Judgment unit 28 Input candidate change vector calculation unit 30 Output candidate change vector calculation unit 32 Response matrix calculation unit 34 Generalized inverse matrix calculation unit 36 Correction vector calculation unit 38 Update unit 40 Result acquisition unit 100 Data estimation device

Claims (7)

A data estimation method that estimates the input vector when any output vector is observed in a nonlinear input / output system that outputs the output vector when the input vector is input.
An output candidate vector representing the output vector output when the input candidate vector representing the input vector candidate is input to the nonlinear input / output system is calculated.
Using any of the observed output vectors as the target vector, a difference vector representing the difference between the target vector and the output candidate vector is calculated.
For each of the plurality of elements included in the input candidate vector, an input candidate change vector, which is a vector obtained by changing the elements, is calculated.
For each of the plurality of input candidate change vectors, an output candidate change vector representing the output vector when the input candidate change vector is input to the nonlinear input / output system is calculated.
For each of the plurality of output candidate change vectors, a coefficient vector representing the rate of change obtained from the difference between the output candidate change vector and the output candidate vector is calculated, and a matrix having the plurality of coefficient vectors as a column vector is represented. Generate a response matrix and
A specific mode is selected from a plurality of modes obtained from the matrix factorization result of the response matrix, and the submatrix corresponding to the selected mode is used to generate a generalized inverse matrix of the response matrix.
Based on the generalized inverse matrix and the difference vector, a correction vector representing the correction amount for the input candidate vector is calculated.
A new input candidate vector is generated based on the input candidate vector and the correction vector.
Calculation of the output candidate vector, calculation of the difference vector, calculation of the input candidate change vector, calculation of the output candidate change vector, and the response matrix until the value corresponding to the difference vector becomes less than a predetermined threshold value. , The generation of the generalized inverse matrix, and the generation of the new input candidate vector are repeated.
When the value corresponding to the difference vector is less than the threshold value, the input candidate vector is acquired as the input vector corresponding to any observed output vector.
A data estimation method that causes a computer to perform processing. When selecting a specific mode from a plurality of modes obtained from the matrix factorization result of the response matrix, the mode in which the value representing the contribution of the mode is equal to or larger than the threshold value for the preset mode is selected and selected. Using the submatrix corresponding to the mode, a generalized inverse matrix of the response matrix is generated.
The data estimation method according to claim 1. When selecting a specific mode from a plurality of modes obtained from the matrix factorization result of the response matrix, a preset number of the modes are selected and selected from the one having the larger value representing the contribution of the mode. Using the submatrix corresponding to the mode, a generalized inverse matrix of the response matrix is generated.
The data estimation method according to claim 1. The nonlinear input / output system outputs an output vector at different observation points when an input vector is input.
Using any plurality of the output vectors observed at different observation points as the plurality of target vectors, the input vector when any plurality of the output vectors are observed at different observation points is estimated.
The data estimation method according to any one of claims 1 to 3. The input vector includes a plurality of types of vectors.
The data estimation method according to any one of claims 1 to 3. When generating a new input candidate vector based on the input candidate vector and the correction vector,
It is determined whether or not the value of each element of the new input candidate vector obtained from the input candidate vector and the correction vector is within the preset range.
When each element of the new input candidate vector has the element that is not within the preset range, the value of the element of the correction vector corresponding to the element is adjusted to obtain the correction vector. correct,
A new input candidate vector is generated based on the input candidate vector and the corrected correction vector.
The data estimation method according to any one of claims 1 to 5. The nonlinear input / output system is a neural network in which the number of neurons is preset.
The input vector is a parameter of the neural network.
The output vector is the output of the neural network.
The difference vector is a difference between the output vector when the input data for learning is input to the neural network and the target vector representing the output vector having a correct answer to the input data for learning.
The data estimation method according to any one of claims 1 to 3.

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