A method for evaluating quality of variational mode decomposition based on six performance indexes

Abstract

The application discloses a kind of based on six performance indexes variational mode decomposition quality evaluation method, belong to signal processing and mode decomposition quality assessment technical field;Including the following steps: S1, the original signal to be evaluated is executed VMD decomposition, obtains an IMF component;S2, identify and eliminate false mode, determine effective mode number;S3, calculate residual energy proportion, assess signal fidelity;S4, calculate over-decomposition score, assess mode splitting number condition;S5, calculate under-decomposition score and under-decomposition proportion, assess whether mode separation is sufficient;S6, combine six performance indexes, complete the quality evaluation of original signal variational mode decomposition;The application uses the above method, the method for the quantitative evaluation of variational mode decomposition result by six indexes, suitable for the evaluation of equipment non-stationary signal decomposition quality and the horizontal comparison between different decomposition methods.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and mode decomposition quality assessment technology, and in particular relates to a variational mode decomposition quality assessment method based on six performance indicators. Background Technology

[0002] Variational Mode Decomposition (VMD), proposed by Dragomiretskiy et al. in 2014, is a non-recursive adaptive method for signal decomposition by constructing and solving variational problems. It has been widely applied in fields such as bearing fault diagnosis, hydropower unit vibration signal processing, and pressure pulsation analysis. The decomposition effect of VMD is highly dependent on the settings of two core parameters: the number of modes K and the penalty factor α. A mode number K that is too small will lead to under-decomposition, with different frequency components overlapping in the same intrinsic mode function; a K that is too large will cause over-decomposition, producing spurious modal components. The penalty factor α determines the bandwidth of the modal components and directly affects the decomposition accuracy.

[0003] In recent years, intelligent optimization algorithms such as particle swarm optimization, whale optimization, gray wolf optimization, and sparrow search have been introduced into VMD parameter optimization to adaptively determine the optimal parameter combination. However, different optimization algorithms yield different parameter combinations, resulting in significant differences in the decomposition results.

[0004] Meanwhile, existing technologies also have problems such as the inability of a single residual energy index to distinguish between "low residual due to a large number of modes" and "truly high-quality decomposition", which leads to result distortion; the lack of independent quantitative indicators for over-decomposition and under-decomposition; and the lack of a comprehensive evaluation framework from the number of modes and decomposition accuracy to signal fidelity. Summary of the Invention

[0005] The purpose of this invention is to provide a variational mode decomposition quality evaluation method based on six performance indicators. This method quantitatively evaluates the variational mode decomposition results using six indicators: number of modes, number of spurious modes, over-decomposition score, under-decomposition score, under-decomposition ratio, and residual energy ratio. It is applicable to the evaluation of the decomposition quality of non-stationary signals from equipment such as water turbines and rotating machinery, as well as the horizontal comparison between different decomposition methods.

[0006] To achieve the above objectives, this invention provides a variational mode decomposition quality evaluation method based on six performance indicators, comprising the following steps: S1. Perform VMD decomposition on the original signal to be evaluated to obtain... One IMF component; S2. Calculate the energy percentage of each IMF component, identify and eliminate spurious modes, and determine the number of valid modes; S3. Calculate the residual energy ratio of the effective mode number and evaluate the signal fidelity; S4. Calculate the over-decomposition score of the effective modal number and evaluate the modal splitting situation; S5. Calculate the under-decomposition score and under-decomposition ratio of the effective modal number to evaluate whether the modal separation is sufficient; S6. Combining the six performance indicators in S2-S5, complete the variational mode decomposition quality evaluation of the original signal.

[0007] Preferably, the process of S2 is as follows: S21. The optimal number of modes is obtained by using the decomposition order finally adopted in S1 and combining it with the physical components of the water bucket impeller signal. ; S22, Calculate the first The energy proportion of each IMF component is determined as follows: ; in Indicates the first One IMF component, Represents the original signal; S23. Perform the main judgment; if... If the value is less than the false mode detection threshold, the MF component is initially determined to be a false mode candidate component; otherwise, the MF component is considered to be a valid mode. S24. Perform auxiliary judgment. Further examine the spectrum of the spurious mode candidate component that meets the main criterion. If there is no obvious narrowband spectral peak in the frequency domain, the MF component is confirmed as a spurious mode. S25. Count all spurious modes to obtain the total number of spurious modes. ; S26. Calculate the effective modes. The process is as follows: .

[0008] Preferably, the process of S3 is as follows: S31. After completing the VMD decomposition of the original signal, calculate the residual signal that was not captured by each mode. ; S32. Calculate the proportion of residual energy in the original signal using the residual signal. The process is as follows: ; in This represents the original signal and completes the evaluation of signal fidelity.

[0009] Preferably, the calculation process of the residual signal in S31 is as follows: ; in Indicates the first One IMF component.

[0010] Preferably, in S4, over-decomposition is determined by the modal separation index, which combines the center frequency difference between adjacent modes with the individual values ​​of each adjacent mode. The degree of spectral overlap quantized by dB bandwidth.

[0011] Preferably, the process of S4 is as follows: S41. Perform bandwidth calculations and locate the spectral peak of each IMF component in the frequency domain. and its corresponding frequency , decreasing from peak The difference between the left and right frequency points at dB is used as dB bandwidth The calculation process is as follows: ; ; in and These represent the frequencies to the left and right of the spectral peak that first fall below the half-power point, respectively, calculated accurately through linear interpolation; S42. Calculate modal separation degree And determine whether there is over-decomposition among the effective modes; S43, The scoring was decomposed and quantified.

[0012] Preferably, the process of S42 is as follows: S421. Perform spectral analysis on the original signal to be evaluated, and extract the dominant frequency corresponding to the maximum amplitude of the spectrum. Set the percentage threshold of the original signal based on the main frequency corresponding to the maximum amplitude of the spectrum. ; S422. Sort the effective modes in ascending order of their center frequencies; S423. Calculate any first mode within the effective modes. The and the first Relative frequency separation of each mode The process is as follows: ; in , They represent the first The and the first The center frequency of each mode and They represent the first The and the first In each mode bandwidth in dB; S424, when Explanation of the first The and the first The frequency spacing of each mode is sufficient, and there is no over-decomposition; like Explanation of the first The and the first If the frequencies of two modes are close together, it is determined to be an over-decomposition event.

[0013] Preferably, the process of S43 is as follows: Over-decomposition quantification scoring is performed using a deduction system, with the initial over-decomposition score set to... One point is deducted for each over-decomposition event, and the final score for over-decomposition is recorded as follows: The process is as follows: ; in Indicates satisfaction The total number of modes, It is a positive integer; according to The degree of decomposition is determined by the value. The higher the value, the less over-decomposition is achieved, which is an assessment of the number of modal splits completed.

[0014] Preferably, the process of S5 is as follows: S51. For each valid mode, perform a quadratic VMD decomposition to obtain a fixed number of sub-modes. ; S52. Calculate the penalty factor for quadratic VMD decomposition. The calculation process is as follows: ; S53. Set the percentage threshold for the original IMF spectrum. Take the maximum amplitude value of the original IMF spectrum. of A multiple is used as the threshold for amplitude determination; S54. If the maximum amplitude of the spectra of the two sub-modes in the quadratic decomposition of each effective mode is greater than... This indicates that the original effective mode still contains two separable independent components, and it is determined that the effective mode is under-decomposed. S55. Quantify and score under-scoring using a deduction system, setting the initial under-scoring score to... One point is deducted for each under-decomposition event, and the final under-decomposition score is recorded as follows: The calculation process is as follows: ; in This indicates the number of under-decomposed modes. Represents positive integers. The higher the value, the less under-decomposition. S56. Calculate the under-decomposition ratio, the process is as follows: .

[0015] Preferably, the six performance indicators mentioned in S6 are the number of modes. and Number of spurious modes Over-decomposition scoring Under-decomposition score Under-decomposition ratio ; and residual energy ratio ; The six performance indicators are divided into three judgment levels: modality quantity layer, decomposition accuracy layer, and signal fidelity layer; The modality count layer includes the optimal number of modes. Number of spurious modes and effective mode number This is used to reflect the rationality of the decomposition structure; The decomposition precision layer includes over-decomposition scores. Under-decomposition score and under-decomposition ratio This is used to reflect the directional deviation of the decomposition; Signal fidelity layer includes under-decomposition ratio This is used to reflect the completeness of the decomposition.

[0016] Therefore, the variational mode decomposition quality evaluation method based on six performance indicators described above, as used in this invention, has the following advantages: 1. The decomposition quality is evaluated simultaneously from three levels: modality number, decomposition accuracy, and signal fidelity, using six indicators. This overcomes the problem of the one-sided evaluation by a single residual energy indicator and avoids the misjudgment that "low residual means high quality". 2. Through an automatic spurious mode identification mechanism, it can distinguish between valid modes and redundant modes, and the number of valid modes... It provides a comparable benchmark for comparing different methods; 3. Over-decomposition score and under-decomposition score quantify the decomposition deviation from two opposite directions, namely "too many modal splits" and "incomplete modal separation", respectively, which can accurately identify the specific type of decomposition defect; 4. The under-decomposition ratio eliminates the impact of differences in the number of effective modes, allowing for fair comparison between decomposition results with different numbers of modes; 5. The six indicators are independent yet complementary, forming a complete evaluation loop, which is suitable for horizontal comparison between different decomposition methods and algorithm selection.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is an overall flowchart of the variational mode decomposition quality evaluation method based on six performance indicators of the present invention; Figure 2 This is a flowchart illustrating the process of identifying and eliminating spurious modes and determining the number of effective modes in a variational mode decomposition quality evaluation method based on six performance indicators according to the present invention. Figure 3 This is a flowchart of the over-decomposition score for calculating the number of effective modes in a variational mode decomposition quality evaluation method based on six performance indicators according to the present invention. Figure 4 This is a flowchart illustrating the calculation of the under-decomposition score and under-decomposition ratio of the effective modes in a variational mode decomposition quality evaluation method based on six performance indicators according to the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.

[0020] Example like Figures 1-4 As shown, this invention provides a variational mode decomposition quality evaluation method based on six performance indicators, comprising the following steps: S1. Perform VMD decomposition on the original signal to be evaluated to obtain... One IMF component; S2. Calculate the energy percentage of each IMF component, identify and eliminate spurious modes, and determine the number of valid modes; Over-decomposition and under-decomposition are evaluated using an independent deduction system. All modal rationality judgments are carried out after eliminating spurious modalities to avoid meaningless components interfering with the evaluation results.

[0021] S21. The optimal number of modes is obtained by using the decomposition order finally adopted in S1 and combining it with the physical components of the water bucket impeller signal. ; In the IMF components obtained from the decomposition, some low-energy components have no clear physical meaning and are mostly redundant components or noise generated by over-decomposition. This application uses the component energy ratio as the main criterion for judging spurious modes, supplemented by frequency domain spectral peak verification.

[0022] S22, Calculate the first The energy proportion of each IMF component is determined as follows: ; in Indicates the first One IMF component, Represents the original signal; S23. Perform the main judgment; if... If the value is less than the false mode determination threshold, the MF component is initially determined to be a false mode candidate component. The selection criteria for the false mode determination threshold are as follows: after performing multiple VMD over-decomposition experiments on the water bucket wheel signal, the energy distribution of each redundant component is statistically analyzed. 0.3% is the upper bound empirical value of the redundant component energy. If the value is lower than this threshold, the component has no identifiable physical characteristics in both the time domain and the frequency domain. Otherwise, the MF component is considered to be a valid mode. S24. Perform auxiliary judgment. Further examine the spectrum of the spurious mode candidate component that meets the main criterion. If there is no obvious narrowband spectral peak in the frequency domain, the MF component is confirmed as a spurious mode. S25. Count all spurious modes to obtain the total number of spurious modes. ; S26. Calculate the effective modes. The process is as follows: .

[0023] S3. Calculate the residual energy ratio of the effective mode number and evaluate the signal fidelity; S31. After completing the VMD decomposition of the original signal, calculate the residual signal that was not captured by each mode. ; The calculation process for the residual signal is as follows: ; in Indicates the first One IMF component.

[0024] S32. Calculate the proportion of residual energy in the original signal using the residual signal. The process is as follows: ; in This represents the original signal and completes the evaluation of signal fidelity.

[0025] S4. Calculate the over-decomposition score of the effective modal number and evaluate the modal splitting situation; Over-decomposition refers to the phenomenon where the number of modes is too large, splitting the same physical component into multiple spectrally adjacent modes. This application uses a mode separation index to determine over-decomposition, which combines the center frequency difference between adjacent modes with their respective 3dB bandwidths to quantify the degree of spectral overlap.

[0026] Over-decomposition is determined by the modal separation index, which combines the center frequency difference between adjacent modes with the spectral overlap quantized by the 3dB bandwidth of each adjacent mode.

[0027] S41. Perform bandwidth calculations and locate the spectral peak of each IMF component in the frequency domain. and its corresponding frequency , decreasing from peak dB (i.e., amplitude drops to) The difference between the left and right frequency points at point ) is taken as the 3dB bandwidth. The calculation process is as follows: ; ; in and These represent the frequencies to the left and right of the spectral peak that first fall below the half-power point, respectively, calculated accurately through linear interpolation; S42. Calculate modal separation degree And determine whether there is over-decomposition among the effective modes; S421. Perform spectral analysis on the original signal to be evaluated, and extract the dominant frequency corresponding to the maximum amplitude of the spectrum. Set the percentage threshold of the original signal based on the main frequency corresponding to the maximum amplitude of the spectrum. With the main frequency Using a multiple as the critical interval for over-decomposition, based on the preprocessing experimental results, this application takes... (That is, 25% of the main frequency); S422. Sort the effective modes in ascending order of their center frequencies; S423. Calculate any number of modes within the effective IMF (i.e., the effective modes) after removing spurious modes. The and the first Relative frequency separation of each mode This does not involve comparisons with residuals or out-of-band components; the process is as follows: ; in , They represent the first The and the first The center frequency of each mode and They represent the first The and the first In each mode bandwidth in dB; S424, when Explanation of the first The and the first The frequency spacing of each mode is sufficient, and there is no over-decomposition; like Explanation of the first The and the first If the frequencies of two modes are close together, it is determined to be an over-decomposition event.

[0028] S43, The scoring was decomposed and quantified.

[0029] Over-decomposition quantification scoring is performed using a deduction system, with the initial over-decomposition score set to... One point is deducted for each over-decomposition event, and the final score for over-decomposition is recorded as follows: The process is as follows: ; in Indicates satisfaction The total number of modes, It is a positive integer; according to The degree of decomposition is determined by the value. The higher the value, the less over-decomposition is achieved, which is an assessment of the number of modal splits completed.

[0030] S5. Calculate the under-decomposition score and under-decomposition ratio of the effective modal number to evaluate whether the modal separation is sufficient; Under-decomposition refers to the phenomenon where the number of modes is too small, resulting in multiple independent physical components being mixed within the same mode. This application uses a forced quadratic decomposition method to determine under-decomposition. S51. For each valid mode, perform a quadratic VMD decomposition to obtain a fixed number of sub-modes. ; S52. Calculate the penalty factor for quadratic VMD decomposition. Take the optimal value of the first decomposition 1.2 times, the calculation process is as follows: ; The remaining control parameters are set using the same parameters as in the first decomposition to ensure the consistency of the decomposition bandwidth constraint and the reproducibility of the experiment.

[0031] S53. Set the percentage threshold for the original IMF spectrum. Take the maximum amplitude value of the original IMF spectrum. of The amplitude threshold is set at 1 / 2; based on the preprocessing experimental results, this paper takes 1 / 2 as the amplitude determination threshold. (i.e., 35% of the peak value of the spectrum), this threshold can effectively distinguish between real physical components and decomposed noise; S54. If the maximum amplitude of the spectra of the two sub-modes in the quadratic decomposition of each effective mode is greater than... This indicates that the original effective mode still contains two separable independent components, and it is determined that the effective mode is under-decomposed. S55. Quantify and score under-scoring using a deduction system, setting the initial under-scoring score to... One point is deducted for each under-decomposition event, and the final under-decomposition score is recorded as follows: The calculation process is as follows: ; in This indicates the number of under-decomposed modes. Represents positive integers. The higher the value, the less under-decomposition. S56. Calculate the under-decomposition ratio, the process is as follows: .

[0032] S6. Combining the six performance indicators in S2-S5, complete the variational mode decomposition quality evaluation of the original signal.

[0033] The six performance indicators are: number of modes and Number of spurious modes Over-decomposition scoring Under-decomposition score Under-decomposition ratio ; and residual energy ratio ; The six performance indicators are divided into three judgment levels: modality quantity layer, decomposition accuracy layer, and signal fidelity layer; The modality count layer includes the optimal number of modes. Number of spurious modes and effective mode number This is used to reflect the rationality of the decomposition structure; The decomposition precision layer includes over-decomposition scores. Under-decomposition score and under-decomposition ratio This is used to reflect the directional deviation of the decomposition; Signal fidelity layer includes under-decomposition ratio This is used to reflect the completeness of the decomposition.

[0034] The six indicators are independent yet complementary, forming a complete evaluation loop. Low residual energy does not necessarily indicate high-quality decomposition, and a high score for over-decomposition does not necessarily mean there are no problems. Only by comprehensively considering all six indicators can the quality of decomposition be fully evaluated.

[0035] The evaluation method of this application is applicable to the following scenarios: 1. Horizontal comparison of different optimization algorithms; Different optimization algorithms were used to optimize parameters and perform VMD decomposition on the same signal. Six performance indicators were calculated, and the decomposition quality of each algorithm was compared horizontally to provide a quantitative basis for algorithm selection.

[0036] 2. Comparison of optimization methods and empirical parameters; The decomposition results obtained by the intelligent optimization algorithm are compared with the decomposition results of the human empirical parameter VMD to verify the effectiveness of the optimization.

[0037] 3. Quality assessment of decomposition of different signals; The decomposition results of the same method on different signals are evaluated to determine the adaptability of the method to different signal characteristics.

[0038] Therefore, this invention employs a variational mode decomposition quality evaluation method based on six performance indicators, which has the following advantages: 1. The decomposition quality is evaluated simultaneously from three levels: modality number, decomposition accuracy, and signal fidelity, using six indicators. This overcomes the problem of the one-sided evaluation by a single residual energy indicator and avoids the misjudgment that "low residual means high quality". 2. Through an automatic spurious mode identification mechanism, it can distinguish between valid modes and redundant modes, and the number of valid modes... It provides a comparable benchmark for comparing different methods; 3. Over-decomposition score and under-decomposition score quantify the decomposition deviation from two opposite directions, namely "too many modal splits" and "incomplete modal separation", respectively, which can accurately identify the specific type of decomposition defect; 4. The under-decomposition ratio eliminates the impact of differences in the number of effective modes, allowing for fair comparison between decomposition results with different numbers of modes; 5. The six indicators are independent yet complementary, forming a complete evaluation loop, which is suitable for horizontal comparison between different decomposition methods and algorithm selection.

[0039] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A variational mode decomposition quality evaluation method based on six performance indicators, characterized in that, Includes the following steps: S1. Perform VMD decomposition on the original signal to be evaluated to obtain... One IMF component; S2. Calculate the energy percentage of each IMF component, identify and eliminate spurious modes, and determine the number of valid modes; S3. Calculate the residual energy ratio of the effective mode number and evaluate the signal fidelity; S4. Calculate the over-decomposition score of the effective modal number and evaluate the modal splitting situation; S5. Calculate the under-decomposition score and under-decomposition ratio of the effective modal number to evaluate whether the modal separation is sufficient; S6. Combining the six performance indicators in S2-S5, complete the variational mode decomposition quality evaluation of the original signal.

2. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 1, characterized in that, The process of S2 is as follows: S21. The optimal mode number is obtained by using the decomposition order finally adopted in S1 and combining it with the physical components of the water bucket impeller signal. ; S22, Calculate the first The energy proportion of each IMF component is determined as follows: ； in Indicates the first One IMF component, Represents the original signal; S23. Perform the main judgment; if... If the value is less than the false mode detection threshold, the MF component is initially determined to be a false mode candidate component; otherwise, the MF component is considered to be a valid mode. S24. Perform auxiliary judgment. Further examine the spectrum of the spurious mode candidate component that meets the main criterion. If there is no obvious narrowband spectral peak in the frequency domain, the MF component is confirmed as a spurious mode. S25. Count all spurious modes to obtain the total number of spurious modes. ; S26. Calculate the effective modes. The process is as follows: 。 3. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 2, characterized in that, The process of S3 is as follows: S31. After completing the VMD decomposition of the original signal, calculate the residual signal that was not captured by each mode. ; S32. Calculate the proportion of residual energy in the original signal using the residual signal. The process is as follows: ； in This represents the original signal and completes the evaluation of signal fidelity.

4. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 3, characterized in that, The calculation process of the residual signal in S31 is as follows: ； in Indicates the first One IMF component.

5. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 4, characterized in that: In S4, over-decomposition is determined by the modal separation index, which combines the center frequency difference between adjacent modes with the individual values ​​of each adjacent mode. The degree of spectral overlap quantized by dB bandwidth.

6. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 5, characterized in that, The process of S4 is as follows: S41. Perform bandwidth calculations and locate the spectral peak of each IMF component in the frequency domain. and its corresponding frequency , decreasing from peak The difference between the left and right frequency points at dB is used as dB bandwidth The calculation process is as follows: ； ； in and These represent the frequencies to the left and right of the spectral peak that first fall below the half-power point, respectively, calculated accurately through linear interpolation; S42. Calculate modal separation degree And determine whether there is over-decomposition among the effective modes; S43, The score was decomposed and quantified.

7. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 6, characterized in that, The process of S42 is as follows: S421. Perform spectral analysis on the original signal to be evaluated, and extract the dominant frequency corresponding to the maximum amplitude of the spectrum. Set the percentage threshold of the original signal based on the main frequency corresponding to the maximum amplitude of the spectrum. ; S422. Sort the effective modes in ascending order of their center frequencies; S423. Calculate any first mode within the effective modes. The and the first Relative frequency separation of each mode The process is as follows: ； in , They represent the first The and the first The center frequency of each mode and They represent the first The and the first In each mode bandwidth in dB; S424, when Explanation of the first The and the first The frequency spacing of each mode is sufficient, and there is no over-decomposition; like Explanation of the first The and the first If the frequencies of two modes are close together, it is determined to be an over-decomposition event.

8. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 7, characterized in that, The process of S43 is as follows: Over-decomposition quantification scoring is performed using a deduction system, with the initial over-decomposition score set to... One point is deducted for each over-decomposition event, and the final score for over-decomposition is recorded as follows: The process is as follows: ； in Indicates satisfaction The total number of modes, It is a positive integer; according to The degree of decomposition is determined by the value. The higher the value, the less over-decomposition is achieved, which is used to assess the number of modal splits completed.

9. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 8, characterized in that, The process of S5 is as follows: S51. For each valid mode, perform a quadratic VMD decomposition to obtain a fixed number of sub-modes. ; S52. Calculate the penalty factor for quadratic VMD decomposition. The calculation process is as follows: ； S53. Set the percentage threshold for the original IMF spectrum. Take the maximum amplitude value of the original IMF spectrum. of A multiple is used as the threshold for amplitude determination; S54. If the maximum amplitude of the spectra of the two sub-modes in the quadratic decomposition of each effective mode is greater than... This indicates that the original effective mode still contains two separable independent components, and it is determined that the effective mode is under-decomposed. S55. Quantify and score under-scoring using a deduction system, setting the initial under-scoring score to... One point is deducted for each under-decomposition event, and the final under-decomposition score is recorded as follows: The calculation process is as follows: ； in This indicates the number of under-decomposed modes. Represents positive integers. The higher the value, the less under-decomposition. S56. Calculate the under-decomposition ratio, the process is as follows: 。 10. The variational mode decomposition quality evaluation method based on six performance indicators according to claim 9, characterized in that: The six performance indicators mentioned in S6 are: modal number and Number of spurious modes Over-decomposition scoring Under-decomposition score Under-decomposition ratio ; and residual energy ratio ; The six performance indicators are divided into three judgment levels: modality quantity layer, decomposition accuracy layer, and signal fidelity layer; The modality count layer includes the optimal number of modes. Number of spurious modes and effective mode number This is used to reflect the rationality of the decomposition structure; The decomposition precision layer includes over-decomposition scores. Under-decomposition score and under-decomposition ratio This is used to reflect the directional deviation of the decomposition; Signal fidelity layer includes under-decomposition ratio This is used to reflect the completeness of the decomposition.

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