Arithmetic processing system

Abstract

To provide an arithmetic processing system for improving accuracy in constituting a model expression in a learning model.SOLUTION: An arithmetic processing system for applying mode decomposition for decomposing input data into a combination of a plurality of pieces of different waveform data and calculating a model expression by using a parameter obtained by the mode decomposition creates a plurality of pieces of waveform data by performing mode decomposition of the input data by a prescribed decomposition number, executes restoration of the input data by synthesizing the plurality of pieces of created waveform data by using a plurality of values of candidates for the decomposition number as the prescribed decomposition number, and specifies a decomposition number to be used for the model expression on the basis of evaluation of the restoration performed in the plurality of candidates for the decomposition number.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present disclosure relates to processing systems. [Background technology]

[0002] Mode decomposition is known, which decomposes predetermined data into a combination of a plurality of different waveform data.

[0003] Patent Document 1 discloses that a model formula can be constructed using parameters obtained by mode decomposition, even for time-series data that is discontinuous and appears to have no regularity at first glance. The model formula constructed in this way can be used as a prediction model for unknown data. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2022-185713 Summary of the Invention [Problem to be solved by the invention]

[0005] However, in the mode decomposition described in Patent Document 1, the accuracy of the obtained model can vary depending on the method of mode decomposition. Another example is a method that focuses on the over-decomposition problem and searches for the maximum number of decompositions. However, while this method can obtain the number of modes before the total energy of the intrinsic mode function suddenly increases, it does not solve the problem of partial decomposition, and there are cases where it is not possible to approximately restore the original signal, which is time-series data. Therefore, a new method was needed to achieve higher accuracy.

[0006] The present disclosure provides a processing system that improves accuracy when constructing a model formula in a learning model. [Means for solving the problem]

[0007] The arithmetic processing system according to the present disclosure applies mode decomposition to input data, which decomposes the input data into a combination of a plurality of different waveform data, and determines a model formula using parameters obtained by the mode decomposition. The system performs mode decomposition of the input data using a predetermined number of decompositions to create a plurality of waveform data, and combines the created plurality of waveform data to restore the input data, using a plurality of candidate decomposition numbers as the predetermined decomposition number, and identifies the number of decompositions to use in the model formula based on an evaluation of the restoration performed using the plurality of candidate decomposition numbers. This makes it possible to identify the number of decompositions that maximizes restoration accuracy from among a plurality of candidate numbers of decompositions in mode decomposition. [Effects of the Invention]

[0008] According to the present disclosure, it is possible to provide a calculation processing system that improves the accuracy when constructing a model formula in a learning model. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is a diagram illustrating a configuration of a processing system according to the present disclosure. [Figure 2] 1A and 1B are diagrams illustrating examples of an original signal and decomposed and restored signals according to the present disclosure. [Figure 3] FIG. 10 is a diagram illustrating a state in which a decomposition number is calculated from an original signal according to the present disclosure. [Figure 4] 4 is a flowchart of the operation of the arithmetic processing system according to the first embodiment. [Figure 5] 10 is a flowchart of the operation of the arithmetic processing system according to the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0010] Embodiment 1 The following describes the data processing system according to this embodiment with reference to the drawings. Figure 1 shows an example of the configuration of a data processing system 1.

[0011] The arithmetic processing system 1 includes an input unit 11, a setting unit 12, an implementation unit 13, an evaluation unit 14, a storage unit 15, a determination unit 16, and an output unit 17. The arithmetic processing system 1 can also be executed as a single arithmetic processing device.

[0012] Here, the arithmetic processing system 1 applies mode decomposition to time-series data, which decomposes the time-series data into a combination of multiple different waveform data, and obtains a model formula using parameters obtained by this mode decomposition. Figures 2(a) and 2(b) show examples of how the arithmetic processing system 1 decomposes an original signal using a predetermined number of decompositions and restores the signal based on the decomposed data. Note that the number of decompositions in Figure 2(a) is 5, and the number of decompositions in Figure 2(b) is 2. For example, as shown in Figure 2(b), a model formula obtained using an inappropriate number of decompositions will not produce a valid restoration result, whereas as shown in Figure 2(a), a model formula obtained using an appropriate number of decompositions will produce a restoration result that is nearly identical to the original waveform data.

[0013] 3, the processing system 1 decomposes the original signal and searches for the number of decompositions that minimizes the absolute difference between the restored signal and the original signal. This allows the processing system 1 to maximize the effect of variational mode decomposition.

[0014] Returning to Fig. 1, we will now explain each component of the arithmetic processing system 1. An input unit 11 inputs an original signal. Here, the original signal can be time-series data.

[0015] As an example, the time series data input to the input unit 11 is data of the sampling results at each predetermined sampling time as follows. [Table 1]

[0016] The setting unit 12 sets the number of decompositions. For example, the setting unit 12 allows the user to arbitrarily set the initial number of decompositions by inputting the number, but in this example, the initial number of decompositions is set to 1.

[0017] As will be described in detail later, when iterative processing is performed in the arithmetic processing system 1, the setting unit 12 can increment the set decomposition number by one for each iterative processing.

[0018] The implementation unit 13 implements variational mode decomposition of the data input by the input unit 11 based on the current number of decompositions set by the setting unit 12.

[0019] Specifically, when performing the variational mode decomposition, the implementation unit 13 solves the following unconstrained optimization problem:

number

[0020] The evaluation unit 14 evaluates the restoration effect when the variational mode decomposition is performed while changing the number of decompositions in the implementation unit 13. This allows the evaluation unit 14 to calculate the optimal number of decompositions.

[0021] Specifically, the evaluation unit 14 calculates the mean absolute difference ε for each sampling time using the following formula: K Calculate.

number

[0022] The determination unit 16 can determine whether or not to continue the repeated execution of the calculation by the execution unit 13 while changing the number of decompositions set in the setting unit 12.

[0023] For example, if the current number of iterations is equal to or greater than the maximum number of iterations set, the decision unit 16 determines to stop the iterations. In this case, if the current number of iterations is smaller than the maximum number of iterations, the decision unit 16 updates the decomposition number K to K+1 and determines to return to the variational mode decomposition.

[0024] As will be described later in the second embodiment, the determining unit 16 determines the convergence threshold E and the mean absolute difference ε K Based on this, it can be determined whether or not to continue the repeated execution of the calculations by the execution unit 13.

[0025] The output unit 17 outputs the optimal variational mode decomposition result. In other words, the output unit 17 outputs the mean absolute difference ε K The mode decomposition result μ that minimizes K ,k∈[1,K].

[0026] FIG. 4 is a diagram showing an example of the operation of the arithmetic processing system 1, in which the process is repeated while increasing the number of decompositions up to a preset maximum number of iterations.

[0027] First, an original signal is input to the input unit 11 (step S1).

[0028] The setting unit 12 sets the number of decompositions for the first time to 1 (step S2). In the following description, it is assumed that the number of decompositions for mode decomposition performed by the arithmetic processing system 1 is the same as the number of iterations.

[0029] The implementation unit 13 performs mode decomposition with the current number of decompositions set by the setting unit 12. The mode decomposition result at this time is μ K , k∈[1,K], and the maximum number of iterations is T (step S3).

[0030] The evaluation unit 14 calculates the mean absolute difference ε K is calculated (step S4).

[0031] Here, the storage unit 15 stores the mean absolute difference ε K and the mode decomposition result μ K , k∈[1,K] is stored (step S5).

[0032] The determination unit 16 determines whether the current number of iterations is equal to or greater than a preset maximum number of iterations (step S6). If the current number of iterations is equal to or greater than the maximum number of iterations (Yes in step S6), the output unit 17 outputs the mean absolute difference ε K The mode decomposition result μ that minimizes K , k∈[1,K] (step S7). After that, the data processing system 1 ends the process.

[0033] On the other hand, if the current number of iterations is smaller than the maximum number of iterations (No in step S6), the number of iterations is incremented by 1, and the number of decompositions is also incremented by 1 (step S8). After that, the process returns to step S3 with the changed number of decompositions and number of iterations, and repeats the process.

[0034] As a result, the calculation processing system 1 can calculate the mode decomposition result while increasing the number of decompositions until it reaches the maximum number of iterations, and can output the number of decompositions that maximizes the effect of variational mode decomposition.

[0035] In other words, the computation processing system 1 restores the input data by increasing the number of decompositions by one for each candidate number of decompositions until the number of iterations becomes equal to or greater than the maximum number of iterations, and can identify the number of decompositions that provides the best evaluation of the restoration.

[0036] The number of decompositions that optimizes the evaluation of the restoration is the mean absolute difference ε K can be calculated and the case with the smallest mean absolute value identified as the best evaluation of restoration.

[0037] Embodiment 2 Next, an embodiment will be described in which, in the arithmetic processing system 1, a convergence threshold E is set in advance when an input signal is input to the input unit 11, and processing is terminated when a predetermined mode decomposition result is obtained. Fig. 5 shows an example of the operation flow of the arithmetic processing system 1 according to the second embodiment.

[0038] First, the original signal is input to the input unit 11 (step S11).

[0039] The setting unit 12 sets the number of decompositions for the first time to 1 (step S12). In the following description, it is assumed that the number of decompositions for mode decomposition performed by the arithmetic processing system 1 is the same as the number of iterations.

[0040] The implementation unit 13 performs mode decomposition with the current number of decompositions set by the setting unit 12. The mode decomposition result at this time is μ K , k∈[1, K], and the maximum number of iterations is T (step S13). Note that the setting unit 12 sets a convergence threshold E.

[0041] The evaluation unit 14 calculates the mean absolute difference ε K is calculated (step S14). Here, the mean absolute difference ε K teeth,

number

[0042] Here, the storage unit 15 stores the current mean absolute difference ε K and the mode decomposition result μ K , k∈[1,K]. Furthermore, the memory unit 15 stores the mean absolute difference ε K-2 and the mode decomposition result μ K , k∈[1, K−2] is deleted (step S15). For example, when K=1 or 2, the storage unit 15 deletes the mean absolute difference ε K and the mode decomposition result μ K ,k∈[1,K] is only stored.

[0043] The determination unit 16 determines the rate of change ε ​​of the mean absolute difference as

number

[0044] On the other hand, if K is 2 or more and the rate of change ε ​​is not within the range of 0 or more and smaller than the convergence threshold E (No in step S16), the process proceeds to step S17.

[0045] The determination unit 16 determines whether the rate of change ε ​​is smaller than 0 (step S17). If the rate of change ε ​​is smaller than 0 (Yes in step S17), the output unit 17 outputs the mean absolute difference ε K The mode decomposition result μ that minimizes K , k∈[1,K] (step S20). After that, the data processing system 1 ends the process.

[0046] On the other hand, if the rate of change ε ​​is equal to or greater than 0 (No in step S17), the process proceeds to step S18.

[0047] The determination unit 16 determines whether the current number of iterations is equal to or greater than a preset maximum number of iterations (step S18). If the current number of iterations is equal to or greater than the maximum number of iterations (Yes in step S18), the output unit 17 outputs the mean absolute difference ε K The mode decomposition result μ that minimizes K , k∈[1,K] (step S20). After that, the data processing system 1 ends the process.

[0048] On the other hand, if the current number of iterations is smaller than the maximum number of iterations (No in step S18), the number of iterations is incremented by 1, and the number of decompositions is also incremented by 1 (step S19). After that, the process returns to step S13 with the changed number of decompositions and number of iterations, and repeats the process.

[0049] As a result, in the arithmetic processing system 1, when the rate of change ε ​​falls within a range smaller than a predetermined convergence threshold E, the decomposition number can be set as a number that decomposes the original signal so that it can be restored with sufficient accuracy.

[0050] Therefore, in the arithmetic processing system 1, mode decomposition is applied to input data, which decomposes the input data into a combination of multiple different waveform data, and when a model formula is obtained using parameters obtained by the mode decomposition, the mode decomposition of the input data is performed using a predetermined number of decompositions to create multiple waveform data, and the created multiple waveform data are combined to restore the input data, and this is performed using multiple candidate decomposition numbers as the predetermined decomposition number, and the decomposition number to be used in the model formula can be identified from the candidate decomposition numbers based on an evaluation of the restoration performed using the multiple candidate decomposition numbers.

[0051] As shown in the second embodiment, in the arithmetic processing system 1, a convergence threshold E is set in advance, and a mean absolute difference ε K and the mean absolute difference ε K-1 When the mean absolute difference change rate ε, which is the rate of change of the factor, is equal to or greater than 0 and smaller than E, the candidate for the predetermined decomposition number can be identified as the decomposition number to be used in the model formula.

[0052] Furthermore, in the calculation processing system 1, when the mean absolute difference change rate ε is smaller than 0, the candidate for the predetermined decomposition number can be identified as the decomposition number to be used in the model formula.

[0053] Therefore, in the arithmetic processing system 1, when different candidates for decomposition numbers are compared, the decomposition number to be adopted can be updated to the decomposition number with higher restoration accuracy.

[0054] The present invention is not limited to the above-described embodiment, and can be appropriately modified without departing from the spirit of the present invention. In other words, the above description has been omitted or simplified as appropriate for the sake of clarity, and a person skilled in the art can easily modify, add, or convert each element of the embodiment within the scope of the present invention.

[0055] For example, in steps S16 and S17 shown in the second embodiment, the criteria for determining whether to output and terminate the processing can be changed arbitrarily. [Explanation of symbols]

[0056] 1. Processing System 11 Input section 12 Setting section 13 Implementation Department 14 Evaluation Section 15 Storage section 16 Judgment section 17 Output section

Claims

1. A calculation processing system that applies mode decomposition to input data, which decomposes the input data into a combination of a plurality of different waveform data, and obtains a model formula using parameters obtained by the mode decomposition, performing modal decomposition of the input data by a predetermined number of decompositions to create a plurality of waveform data, and synthesizing the created plurality of waveform data to restore the input data, using a plurality of candidate values ​​for the predetermined number of decompositions; identifying a decomposition number to be used in the model formula based on an evaluation of the restoration performed on the plurality of candidate decomposition numbers; Processing system.

2. Set the maximum number of iterations in advance, for the candidate decomposition numbers to be used as the predetermined decomposition number, restoring the input data while increasing the decomposition number by one until the number of iterations becomes equal to or greater than the maximum number of iterations; Identifying the decomposition number that provides the best evaluation of restoration based on the evaluation of restoration using each of the candidate decomposition numbers.

2. The processing system according to claim 1.

3. For each candidate decomposition number, a mean absolute difference ε is calculated, which is the sum of the absolute values ​​of the differences between the input data and the restored data at each sampling point. K and determining the number of decompositions based on the fact that the mean absolute difference is the smallest, as the evaluation of the restoration is optimal.

3. The processing system according to claim 2.

4. A convergence threshold E is preset, A mean absolute difference ε is the sum of the absolute values ​​of the differences between the input data and the restored data for each sampling point in a predetermined number of decomposition candidates. K and the mean absolute difference ε K-1 and the mean absolute difference rate of change, which is the rate of change of [Equation 1] is greater than or equal to 0 and less than E, the candidate for the predetermined decomposition number is identified as the decomposition number to be used in the model formula.

2. The processing system according to claim 1.

5. If the mean absolute difference change rate ε is smaller than 0, the candidate for the predetermined decomposition number is identified as the decomposition number to be used in the model formula.

5. The processing system according to claim 4.

Images