Method for removing noise and noise removal program

Abstract

To execute noise removal processing at high speed, in comparison with a case in which singular value decomposition is performed across the entire range.SOLUTION: A method for removing noise for removing noise included in an input vector includes the steps in which a computer: calculates an error vector on the basis of an output of an input / output system when a candidate of the input vector is input; generates a partial differential matrix of the error vector; performs singular value decomposition on the partial differential matrix while limiting the range to a part of all orders of the candidate of the input vector; extracts a low-order mode from the result of the singular value decomposition; calculates a low-order mode component; calculates a high-order mode component; and corrects the candidate of the input vector by removing the high-order mode component.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a noise removal method and a noise removal program. [Background technology]

[0002] Patent Document 1 states that "the noise removal device 100 calculates an output candidate vector {ao} that is output when an input candidate vector {ai} is input to an input / output system F, and calculates an error vector {r} between a target vector {atar} and the output candidate vector {ao}. The noise removal device 100 selects a high-order input mode matrix [VR] corresponding to a high-order mode from the matrix decomposition result of the partial differential matrix [K] of the error vector {r}, calculates a component vector {k}, and calculates a correction vector {Δai}. The noise removal device 100 subtracts the correction vector {Δai} from the input candidate vector {ai} to calculate a new input candidate vector {ai}new. The noise removal device 100 obtains the input candidate vector {ai} when the repetition condition is satisfied as the input vector from which noise has been removed."

[0003] Patent Document 2 states that "the estimation device (signal processing device 10) is a device that estimates an estimated signal of the same dimension as a teacher signal by multiplying an extracted signal, in which noise components (noise 91b) have been removed from an input physical quantity (near-engine sound 90), by a transfer function, and is equipped with a learning unit 21 and an estimated signal estimation unit (second estimation unit 31). The learning unit 21 uses a neural network to learn network weights and a transfer function that generate a mask for removing noise components from the input physical quantity and extracting the extracted signal, and performs learning by adding amplitude and phase components related to the input physical quantity to the mask and the transfer function. The estimated signal estimation unit uses the mask to obtain the extracted signal from which the noise components have been removed, and converts the extracted signal into an estimated signal by multiplying it by the transfer function."

[0004] Patent Document 3 states that "there is provided a noise removal device that removes noise components due to noise sources present in a transmission path of measurement light from distribution data of measurement light on a predetermined measurement surface, the noise removal device comprising: a first propagation calculation unit that calculates distribution data by propagating the distribution data of measurement light on the measurement surface up to a surface corresponding to the noise source; a noise removal unit that calculates distribution data by removing noise components due to the noise source from the distribution data calculated by the first propagation calculation unit; and a second propagation calculation unit that calculates distribution data by propagating the distribution data calculated by the noise removal unit up to the measurement surface." [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent Publication No. 2021-099241 [Patent Document 2] Japanese Patent Publication No. 2022-062453 [Patent Document 3] Japanese Patent Application Laid-Open No. 2010-281741 Summary of the Invention [Problem to be solved by the invention]

[0006] Patent Documents 1 to 3 relate to noise removal techniques. In particular, Patent Document 1 discloses a technique for removing unnecessary noise contained in an input vector when identifying the input vector of an input / output system, in which singular value infinitesimal modes of a partial differential matrix are extracted and unnecessary noise components are identified and removed. However, with conventional techniques, when the input vector has a large number of dimensions, the number of dimensions of the singular value infinitesimal modes to be extracted increases, resulting in a problem of requiring an excessively long calculation time.

[0007] Therefore, an object of the present disclosure is to provide a noise removal method and a noise removal program that can perform noise removal processing at high speed compared to when singular value decomposition is performed over the entire range. [Means for solving the problem]

[0008] A noise removal method according to a first aspect of the present disclosure is a noise removal method for removing noise contained in an input vector when an input / output system identifies an input vector for outputting a target output vector, the noise removal method including the steps of: calculating an error vector indicating an error with respect to the output vector based on an output of the input / output system when the input vector candidate is input; generating a partial differential matrix of the error vector with respect to the input vector candidate; performing singular value decomposition on the partial differential matrix within a limited range of a portion of all orders of the input vector candidate; extracting a low-order mode having a lower order among all orders from the result of the singular value decomposition; calculating a low-order mode component indicating a component of the low-order mode contained in the input vector candidate; excluding the low-order mode component from the input vector candidate; calculating a high-order mode component indicating a component of a high-order mode having a higher order among all orders; and removing the high-order mode component to correct the input vector candidate.

[0009] A noise removal method according to a second aspect of the present disclosure is the noise removal method according to the first aspect, wherein the range is determined by at least one of a lower limit of a singular value, an order, or a lower limit of a ratio to a first singular value.

[0010] A noise removal method according to a third aspect of the present disclosure is the noise removal method according to the first aspect, wherein extracting the low-order modes includes selecting a low-order input mode matrix corresponding to the low-order modes from input mode matrices obtained from the result of the singular value decomposition, and calculating the low-order mode components includes multiplying the low-order input mode matrix by the candidate input vector.

[0011] A noise removal method according to a fourth aspect of the present disclosure is the noise removal method according to the first aspect, wherein correcting the candidate input vector includes multiplying the higher-order mode component by a predetermined removal rate to calculate a correction vector, and subtracting the correction vector from the candidate input vector.

[0012] A noise removal method according to a fifth aspect of the present disclosure is the noise removal method according to any one of the first to fourth aspects, further including the computer repeatedly executing the steps of calculating the error vector, generating the partial differential matrix, performing singular value decomposition of the partial differential matrix, extracting the low-order modes, calculating the low-order mode components, calculating the high-order mode components, and modifying the candidate input vector until a predetermined condition is satisfied, and identifying the candidate input vector as the input vector when the condition is satisfied.

[0013] A noise removal program according to a sixth aspect of the present disclosure is a noise removal program that removes noise included in an input vector when an input / output system identifies an input vector for outputting a target output vector, and causes a computer to execute the following processes: calculating an error vector indicating an error with respect to the output vector based on the output of the input / output system when the input vector candidate is input; generating a partial differential matrix of the error vector for the input vector candidate; performing singular value decomposition on the partial differential matrix, limited to a partial range of all orders of the input vector candidate; extracting a low-order mode having a lower order among all orders from the result of the singular value decomposition; calculating a low-order mode component indicating a component of the low-order mode included in the input vector candidate; calculating a high-order mode component indicating a component of a high-order mode having a higher order among all orders by excluding the low-order mode component from the input vector candidate; and correcting the input vector candidate by removing the high-order mode component. [Effects of the Invention]

[0014] According to the present disclosure, it is possible to advantageously perform noise removal processing at high speed compared to when singular value decomposition is performed over the entire range. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a diagram illustrating an example of an input / output system 10 that is a target of noise removal processing by a noise removal device 100 according to the present embodiment. [Figure 2] 1 is a diagram illustrating an example of a hardware configuration of a noise removal device 100 according to an embodiment of the present invention. [Figure 3] FIG. 2 is a diagram illustrating an example of a functional configuration of a noise removal device according to the present embodiment. [Figure 4] FIG. 2 is a diagram showing a flow of a noise removal method according to the present embodiment. [Figure 5] FIG. 10 is a diagram showing an example of the flow of a noise removal method according to a conventional example. [Figure 6] FIG. 10 is a diagram illustrating an example of an analysis model used for verification. [Figure 7] FIG. 1 is a diagram showing input seismic motion from which noise is removed. [Figure 8] FIG. 10 is a diagram showing a ground surface response that is a target response. [Figure 9] FIG. 10 is a diagram showing input seismic motion when noise is removed by the noise removal method according to the present embodiment. [Figure 10] FIG. 10 is a diagram showing the ground surface response when noise is removed by the noise removal method according to the present embodiment. [Figure 11] FIG. 10 is a diagram showing input seismic motion when noise is removed by a noise removal method according to a conventional example. [Figure 12] FIG. 10 is a diagram showing the ground surface response when noise is removed by a noise removal method according to a conventional example. DETAILED DESCRIPTION OF THE INVENTION

[0016] An example of an embodiment of the disclosed technology will be described below with reference to the drawings. Note that the same or equivalent components and parts in each drawing are given the same reference numerals. Also, the dimensional proportions in the drawings may be exaggerated for the sake of explanation and may differ from the actual proportions.

[0017] FIG. 1 is a diagram showing an example of an input / output system 10 that is a target of noise removal processing by a noise removal device 100 according to this embodiment. The input / output system 10 receives an input vector {a i} is input, the output vector {a о}. The output vector {a о} is, for example, the input vector {a i}, that is, the solution of the function F with arguments F({a i}).

[0018] The noise removal device 100 according to this embodiment is configured to, for example, calculate the output vector {a tar} to output the input vector {a i}, the input vector {a i}. Note that "noise" here refers to unnecessary input components that have little effect on the output.

[0019] 2 is a diagram showing an example of the hardware configuration of a noise removal device 100 according to this embodiment. The noise removal device 100 includes a processor 101, a ROM (Read Only Memory) 102, a RAM (Random Access Memory) 103, a storage 104, a communication interface 105, and a user interface 106. These components are connected via a bus 109 so as to be able to communicate with each other.

[0020] The processor 101 executes various programs and controls each component. The ROM 102 stores various programs and various data. The RAM 103 temporarily stores programs or data as a working area. The storage 104 is configured with an HDD (Hard Disk Drive) or SSD (Solid State Drive) and stores various programs including the operating system and various data.

[0021] In the noise removal device 100 according to this embodiment, a noise removal program is stored in the ROM 102 or the storage 104. The processor 101 reads the noise removal program from the ROM 102 or the storage 104 and executes it using the RAM 103 as a working area, thereby controlling each component and performing various arithmetic processing in accordance with the noise removal program.

[0022] The communication interface 105 is an interface for the noise removal device 100 to communicate with other devices. The user interface 106 is an input / output interface for the noise removal device 100 to exchange information with a user.

[0023] 3 is a diagram showing an example of the functional configuration of a noise removal device 100 according to this embodiment. The noise removal device 100 includes a setting unit 110, an error vector calculation unit 120, a partial differential matrix generation unit 130, a decomposition unit 140, a low-order mode extraction unit 150, a low-order mode component calculation unit 160, a high-order mode component calculation unit 170, a correction unit 180, and an identification unit 190. These functional configurations are realized by the processor 101 reading out a noise removal program from the ROM 102 or the storage 104, loading the program into the RAM 103, and executing the program.

[0024] The setting unit 110 sets the target output vector {a tar} to output the input vector {a i}, the input vector {a i} Set the initial value of the candidate.

[0025] The error vector calculation unit 120 calculates the input vector {a i The output of the input / output system 10 when a candidate for {a о}, the target output vector {a tar}.

[0026] The partial differential matrix generator 130 calculates the input vector {a i}, generate a partial differential matrix [K] of the error vector {r} for the candidates.

[0027] The decomposition unit 140 decomposes the input vector {a i The partial differential matrix [K] is subjected to singular value decomposition within a limited range of all degrees in the candidates of {}.

[0028] The low-order mode extraction section 150 extracts a low-order mode having a low order among all the orders from the result of the singular value decomposition.

[0029] The low-order mode component calculation unit 160 calculates the input vector {a i The low-order mode components {k L}.

[0030] The high-order mode component calculation unit 170 calculates the input vector {a i}, the low-order mode component {k L}, the higher-order mode component {k H}.

[0031] The correction unit 180 calculates the higher order mode components {k H} and input vector {a i Correct the} suggestion.

[0032] The identification unit 190 performs calculation of the error vector {r}, generation of the partial differential matrix [K], singular value decomposition of the partial differential matrix [K], extraction of the low-order mode, and extraction of the low-order mode component {k L}, calculation of higher mode components {k H} and the input vector {a i}, and when the conditions are met, the input vector {a i} candidates into the input vector {a i}.

[0033] The noise removal method executed by the noise removal device 100 having such a functional configuration will be described in detail using a flow chart.

[0034] 4 is a diagram showing the flow of the noise removal method according to this embodiment. Each step in this flow may be executed by the computer when the processor 101 reads the noise removal program from the ROM 102 or the storage 104, loads it into the RAM 103, and executes it.

[0035] In step S200, the processor 101, as the setting unit 110, sets the target output vector {a tar} to output the input vector {a i}, the input vector {a i}, which is received via the user interface 106. tar} and the output vector {a tar}, the input vector {a i} may be stored. Then, the processor 101 may i} is the input vector {a i} may be set as the initial value of the candidate.

[0036] In step S210, the processor 101, as the error vector calculation unit 120, calculates the input vector {a i The output of the input / output system 10 when a candidate for {a о}, the target output vector {a tar}. More specifically, the processor 101 calculates an error vector {r} indicating the error with respect to the target output vector {a tar}, the output vector {a о}, the error vector {r} may be calculated.

[0037] In step S220, processor 101, functioning as identification unit 190, determines whether the number of times each step described below is repeatedly executed is equal to or greater than a predetermined threshold. If it is determined that the number is not equal to or greater than the threshold (No), processor 101 proceeds to step S230.

[0038] In step S230, the processor 101, functioning as the partial differential matrix generation unit 130, calculates the input vector {a i}, we generate a partial differential matrix [K] of the error vector {r} for the input vector {a i}, and is also called a Jacobian matrix. The partial differential may be calculated by analytical differentiation or numerical differentiation. The processes from steps S200 to S230 may be the same as those in the conventional noise removal method. Therefore, the contents of Patent Document 1 may be incorporated by reference.

[0039] In step S240, the processor 101, as the decomposition unit 140, i The partial differential matrix [K] is subjected to singular value decomposition within a limited range of all degrees in the candidates of {}. This will be explained in detail.

[0040] In general, when singular value decomposition of a partial differential matrix [K] is performed, the partial differential matrix [K] is decomposed as follows:

number

[0041] Here, [U] is a unitary matrix, and each column is composed of an orthonormal basis of the output. [V] is also a unitary matrix, and each column is composed of an orthonormal basis of the input. Here, [U] is called the output mode matrix, and [V] T is called the input mode matrix.

[0042] Furthermore, [Σ] is a singular value matrix with singular values ​​on the diagonal terms. Generally, the number of singular values ​​obtained is equal to the number of ranks of the matrix before decomposition, and the magnitude of the singular values ​​represents the magnitude of the contribution of each mode. Of the multiple modes of the singular value matrix [Σ], the mode with a relatively large singular value is a low-order mode, and the mode with a relatively small singular value is a high-order mode.

[0043] Here, the magnitude of the singular value represents the magnitude of the contribution of each mode, so low-order modes with large singular values ​​can be said to be necessary modes that have a large effect on the output, while high-order modes with small singular values ​​can be said to be unnecessary modes (also called "small singular value modes") that have a small effect on the output.

[0044] In the conventional technique, the partial differential matrix [K] is calculated by the input vector {a i}, the singular value decomposition was performed for all degrees in the candidates of the input vector {a i Even if the number of dimensions of {\displaystyle \mathbb {\displaystyle \mathbb {1}} is large (for example, about 10,000), the singular value decomposition is performed over the entire range. However, if the singular value small modes account for the majority (for example, about 9,970), most of the calculation time required for the singular value decomposition may be wasted.

[0045] Therefore, in this embodiment, the input vector {a iThe partial differential matrix [K] is subjected to partial singular value decomposition by limiting the range of all orders in the candidates for {}. In this case, the range of singular value decomposition may be determined by at least one of the lower limit of the singular value, the order, or the lower limit of the ratio to the first singular value. However, in general, it is often impossible to know up to what order is effective without performing an analysis. Therefore, in such cases, it is advisable to determine the range of singular value decomposition by the lower limit of the singular value or the lower limit of the ratio to the first singular value.

[0046] The partial singular value decomposition analysis itself may be performed using an existing method such as the DGEXVDX function implemented in LAPAK, a general-purpose numerical analysis software library, and therefore, detailed description of the singular value decomposition analysis itself will be omitted here.

[0047] In step S250, the processor 101, functioning as the low-order mode extraction unit 150, extracts a low-order mode having a low order among all orders from the result of the singular value decomposition. More specifically, the processor 101 extracts a low-order mode having a low order among all orders from the result of the singular value decomposition. T The low-order input mode matrix [V L For example, the processor 101 may select an input mode matrix [V] where m is the order in which singular value decomposition is performed and n is the order to extract as a lower order (where m and n are integers of 2 or more, and m≧n). T Each row vector {v1} T ~{v m} T From {v1} T ~{v n} T is the low-order input mode matrix [V L ] may be selected.

[0048] In step S260, the processor 101, as the low-order mode component calculation unit 160, calculates the input vector {a i The low-order mode components {k LIn this case, the processor 101 calculates the low-order input mode matrix [V L ] and the input vector {a i} and multiplying them, more specifically, the low-order input mode matrix [V L ] and the transpose of the low-order input mode matrix [V L ] T and the input vector {a i}, the lower mode components {k L} may be calculated.

[0049] In step S270, the processor 101, functioning as the high-order mode component calculation unit 170, calculates the input vector {a i}, the low-order mode components {k L}, the higher-order mode component {k H More specifically, the processor 101 calculates the input vector {a i}, the low-order mode components {k L}, the higher mode components {k H} may be calculated.

[0050] In step S280, the processor 101, functioning as the correction unit 180, calculates the high-order mode component {k H} and input vector {a i More specifically, the processor 101 modifies the candidates of the higher order modal components {k H} by a predetermined removal rate η to obtain the correction vector {Δa i}. Then, the processor 101 may calculate the input vector {a i}, the correction vector {Δa i} to obtain the input vector {a i You may modify the} candidate.

[0051] The processor 101 may repeatedly execute each of steps S210 to S280. If it is determined in step S220 that the number of repeated executions is equal to or greater than the threshold, the processor 101 advances the process to step S290.

[0052] In step S290, the processor 101, as the identification unit 190, determines the input vector {a i} candidates into the input vector {a i The processor 101 may perform the following steps in this manner, for example, until a predetermined condition is satisfied: calculation of the error vector {r}, generation of the partial differential matrix [K], singular value decomposition of the partial differential matrix [K], extraction of the low-order mode, and identification of the low-order mode component {k L}, calculation of higher mode components {k H} and the input vector {a i}, and when the conditions are met, the input vector {a i} candidates into the input vector {a i}.

[0053] Fig. 5 is a diagram showing an example of the flow of a noise removal method according to a conventional example. In this flow, the processes of steps S200 to S230 and S280 to S290 may be the same as those in the flow of Fig. 4, so detailed explanations will be omitted here. In this flow, steps S340 to S360 have been added instead of steps S240 to S270.

[0054] In step S340, unlike step S240, the singular value decomposition of the partial differential matrix [K] is performed over the entire range. Therefore, the input mode matrix [V] obtained from the result of the singular value decomposition is T Therefore, in step S350, the input mode matrix [V] is T from the high-order input mode matrix [V H ] can be directly extracted. Then, in step S360, the high-order input mode matrix [V H ] and the input vector {a i}, the higher mode components {k H} is calculated.

[0055] Thus, when comparing only the number of processing steps, the noise removal method according to the conventional example has one step less, but since the difference in calculation time between step S240 and step S340 is dominant, the noise removal method according to this embodiment ultimately has a shorter calculation time. Regarding this, the effect of this embodiment will be explained using as a verification example the identification of input seismic motion that reproduces the target ground surface output in a nonlinear ground model.

[0056] Figure 6 shows an example of the analytical model used for verification. The analytical model is a columnar free ground model with a depth of 50 m (element height 1 m × 50 elements). The surface layer is assumed to be soft sandy ground up to 40 m, with a Poisson's ratio of 0.33 and a unit mass of 1.8 Mg / m 3 The initial Vs value (S-wave velocity) is set to 150 m / s at a depth of -20 m, and is changed for each depth according to the square root of the average effective stress ratio. In other words, the initial shear stiffness G0 of each story is calculated using the following formula. Here, G ref is the shear stiffness equivalent to 150 m / s at a depth of -20 m, and σ´ m is the mean effective stress at the location, σ ref is the mean effective stress at a depth of -20 m.

number

[0057] The Vs value below -40m is 300m / s, the Poisson's ratio is 0.33, and the unit mass is 1.8Mg / m 3 The boundary at -50m is a viscous boundary, with a Vs value of 300m / s and a unit mass of 1.8Mg / m 3 The viscous damper C, which corresponds to the above, is set by the following equation: where ρ is the unit volume mass of the foundation and A is the cross-sectional area of ​​the soil column model.

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[0058] Regarding the nonlinear characteristics of the ground, we will consider a model (hereafter referred to as the YT model) that is an improved version of the Yoshida model to be able to express the behavior of liquefied ground. The nonlinear parameters are the HD model (h max =21%) and the liquefaction strength curve of Toyoura sand is used.

[0059] The analytical model is the same as the model used in the verification of Patent Document 1. However, in order to make the effect of the present disclosure more pronounced, only the analytical time step is changed to 1 / 1000 seconds.

[0060] Fig. 7 is a diagram showing the input earthquake motion from which noise is to be removed. Fig. 8 is a diagram showing the ground surface response that is the target response. The ground surface response obtained by inputting the TAFT earthquake motion shown in Fig. 7 into the model shown in Fig. 6 is the ground surface acceleration shown in Fig. 8. That is, the input earthquake motion shown in Fig. 7 is the target for noise removal in this verification, and the results of searching for earthquake motion from which input components unnecessary for reproducing the ground surface response shown in Fig. 8 have been removed are compared and verified between this embodiment and a conventional example.

[0061] Fig. 9 is a diagram showing input earthquake motion when noise has been removed by the noise removal method according to this embodiment. Fig. 10 is a diagram showing ground surface response when noise has been removed by the noise removal method according to this embodiment. That is, Fig. 10 shows ground surface response reproduced using input earthquake motion (input earthquake motion shown in Fig. 9) from which noise has been removed by the noise removal method according to this embodiment.

[0062] 9 and 10, it can be confirmed that the noise removal method according to this embodiment can remove unnecessary noise from the input seismic motion so as to ensure the reproduction accuracy of the target ground surface response.

[0063] Fig. 11 is a diagram showing input earthquake motion when noise is removed by a conventional noise removal method. Fig. 12 is a diagram showing ground surface response when noise is removed by a conventional noise removal method. That is, Fig. 12 shows ground surface response reproduced using input earthquake motion (input earthquake motion shown in Fig. 11) from which noise has been removed by a conventional noise removal method.

[0064] 11 and 12, it can be confirmed that the noise removal method according to the conventional example can also remove unnecessary noise from the input seismic motion so as to ensure the reproduction accuracy of the target ground surface response. In this way, it can be confirmed that the noise removal method according to this embodiment has the same noise removal effect as the noise removal method according to the conventional example.

[0065] Here, we focus on the calculation times of the noise removal method according to this embodiment and the conventional noise removal method. The noise removal method according to this embodiment required 14 hours and 22 minutes to obtain the results shown in Figures 9 and 10. On the other hand, the conventional noise removal method required 22 hours and 13 minutes to obtain the results shown in Figures 11 and 12.

[0066] As can be seen, the noise removal method according to the conventional example requires about 1.5 times the calculation time of the noise removal method according to this embodiment. In other words, the noise removal method according to this embodiment can reduce the calculation time to about two-thirds of that of the noise removal method according to the conventional example. Therefore, it can be said that the noise removal method according to this embodiment can perform noise removal processing at high speed compared to when singular value decomposition is performed over the entire range. Note that this difference in calculation time is expected to become even greater when the order of the input vector increases and the number of dimensions of the singular value infinitesimal modes to be extracted increases. Therefore, the noise removal method according to this embodiment requires about 1.5 times the calculation time of the input vector {a i} has many dimensions, and the input vector {a i This is particularly effective when the proportion of unnecessary modes included in {} is high.

[0067] In other words, in the conventional noise removal method, singular value decomposition is performed uniformly over the entire range, regardless of whether the mode is necessary or unnecessary, and unnecessary mode shapes are identified from the decomposition results and removed as noise. In contrast, in the noise removal method according to this embodiment, singular value decomposition is performed partially within a range that is likely to contain necessary modes, and necessary mode shapes are identified from the decomposition results, so that the remaining mode shapes are determined to be unnecessary modes without even needing to be analyzed, and are removed as noise. In this way, the noise removal method according to this embodiment removes unnecessary mode shapes as noise without identifying them in detail. Therefore, according to the noise removal method according to this embodiment, calculations required to identify unnecessary mode shapes can be omitted, thereby shortening calculation time. Furthermore, even if the calculation time is shortened by the noise removal method according to this embodiment, the input vector {a i} is sufficiently removed, and the target output vector {a tar This disclosure has revealed that the above-mentioned} can be accurately reproduced.

[0068] It should be noted that the present disclosure is not limited to the above-described embodiments, and various modifications and applications are possible without departing from the spirit and scope of the present disclosure. For example, in the above description, a process for removing noise based on a higher-order mode has been described, but a process for reducing error based on a lower-order mode may also be executed following or in parallel with the process.

[0069] In the above description, the case where the ground surface output is reproduced from the input earthquake motion has been described as an example. However, the noise removal method and the noise removal program according to the present embodiment can also be used to remove the output vector {a o} and input / output system 10 and input vector {a i} can be applied regardless of what kind of

[0070] Furthermore, although the above description describes a case where the noise removal program is pre-stored (installed) in ROM 102 or storage 104, the noise removal program can also be provided in a form recorded on various recording media such as a CD-ROM, DVD-ROM, and microSD card. [Explanation of symbols]

[0071] 10 Input / Output System 100 Noise Eliminator 101 processors 102 ROM 103 RAM 104 Storage 105 Communication Interface 106 User Interface 109 Bus 110 Setting section 120 Error vector calculation unit 130 Partial differential matrix generator 140 Disassembly section 150 Low-order mode extraction section 160 Low-order mode component calculation section 170 Higher-order mode component calculation section 180 Correction Department 190 Identification Section

Claims

1. A noise removal method for removing noise contained in an input vector when identifying an input vector for outputting a target output vector from an input / output system, comprising: The computer calculating an error vector indicating an error with respect to the output vector based on an output of the input / output system when the candidate input vector is input; generating a partial derivative matrix of the error vector with respect to the candidate input vector; performing singular value decomposition on the partial differential matrix within a limited range of all degrees of the candidate input vectors; extracting a low-order mode having a lowest order among all the orders from the result of the singular value decomposition; calculating a low-order modal component indicative of the low-order modal component contained in the candidate input vector; excluding the low-order mode components from the input vector candidates and calculating high-order mode components indicating high-order mode components having higher orders among all orders; removing the higher order modal components to modify the candidate input vectors; Including, Noise removal method.

2. The range is determined by at least one of a lower limit of a singular value, an order, or a lower limit of a ratio to a first singular value. The noise removal method according to claim 1 .

3. extracting the low-order modes includes selecting a low-order input mode matrix corresponding to the low-order modes from input mode matrices obtained from the result of the singular value decomposition; calculating the low-order modal components includes multiplying the low-order input mode matrix by the candidate input vectors; The noise removal method according to claim 1 .

4. modifying the candidate input vector includes: calculating a modification vector by multiplying the higher-order modal component by a predetermined cancellation rate; and subtracting the modification vector from the candidate input vector. The noise removal method according to claim 1 .

5. The computer the method further includes repeatedly executing steps of calculating the error vector, generating the partial differential matrix, performing singular value decomposition on the partial differential matrix, extracting the low-order modes, calculating the low-order mode components, calculating the high-order mode components, and correcting the candidate input vector until a predetermined condition is satisfied, and identifying the candidate input vector as the input vector when the condition is satisfied. The noise removal method according to claim 1 .

6. A noise removal program for removing noise contained in an input vector when identifying an input vector for outputting a target output vector from an input / output system, comprising: On the computer, a process of calculating an error vector indicating an error with respect to the output vector based on an output of the input / output system when the candidate input vector is input; generating a partial differential matrix of the error vector with respect to the candidate input vector; A process of performing singular value decomposition on the partial differential matrix within a limited range of all degrees of the candidate input vectors; a process of extracting a low-order mode having a lowest order among all the orders from the result of the singular value decomposition; calculating a low-order mode component indicative of the low-order mode component included in the candidate input vector; a process of excluding the low-order mode components from the candidates of the input vector and calculating high-order mode components indicating high-order mode components of the highest order among all the orders; removing the higher-order mode components to modify the candidate input vectors; Execute Noise removal program.

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