Sparse-augmented variational nonlinear signal decomposition method and system

Abstract

The application provides a sparse auxiliary variational nonlinear signal decomposition method and system, comprising: determining the number of sub-signals of an original signal and initial instantaneous frequencies of each sub-signal, calculating a preliminary demodulation signal of each sub-signal, calculating an optimized demodulation signal of each sub-signal, calculating an initial instantaneous frequency increment of each sub-signal, calculating an optimized instantaneous frequency increment of each sub-signal, calculating an initial optimized instantaneous frequency of each sub-signal, calculating a final optimized instantaneous frequency of each sub-signal, reconstructing each sub-signal x according to the optimized demodulation signal and the final optimized instantaneous frequency of each sub-signal i ; setting a termination iteration threshold value ε, and judging whether the reconstructed sub-signal satisfies the set termination iteration threshold value; if not, repeating the execution, and if yes, completing the decomposition of the original signal. The application realizes the decomposition of a complex multi-component signal, accurately estimates the instantaneous frequency of each sub-signal and reconstructs each sub-signal.

Description

Technical Field

[0001] This invention relates to the field of engineering signal processing, and more specifically, to a sparse-assisted variational nonlinear signal decomposition method and system. Background Technology

[0002] In practical industrial applications, there are numerous complex, multi-component nonlinear signals. The instantaneous frequency and amplitude of these signals vary over time and are also known as amplitude-frequency modulation (AM-FM) signals. Examples include vibration signals from mechanical systems operating under non-stationary conditions, radar detection signals, and voice signals. These signals typically contain multiple components, exhibit highly complex variation patterns, and are susceptible to noise interference.

[0003] Decomposing complex nonlinear signals in practical industrial fields can effectively estimate the variation characteristics of the instantaneous frequency (IF) and instantaneous amplitude (IA) of the signal, reveal the time-frequency variation law of the original signal, and thus effectively analyze the operating state characteristics of the corresponding object. However, existing frequency modulation signal decomposition methods cannot effectively handle AM-FM signals with very complex instantaneous frequency and amplitude variation laws, resulting in serious mode aliasing problems, and cannot accurately estimate the instantaneous frequency and reconstruct the sub-signals of the signal. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a sparse-assisted variational nonlinear signal decomposition method and system.

[0005] A sparse-assisted variational nonlinear signal decomposition method according to the present invention includes:

[0006] Step S1: Determine the number of sub-signals of the original signal and the initial instantaneous frequency IF of each sub-signal;

[0007] Step S2: Based on the initial instantaneous frequency IF, calculate the preliminary demodulated signal for each sub-signal. and ;

[0008] Step S3: Based on the preliminary demodulated signal and Calculate the optimized demodulated signal for each sub-signal. and ;

[0009] Step S4: Based on the optimized demodulated signal and Calculate the initial instantaneous frequency increment of each sub-signal.

[0010] Step S5: Based on the initial instantaneous frequency increment Calculate the optimized instantaneous frequency increment for each self-signal.

[0011] Step S6: Based on the optimized instantaneous frequency increment Calculate the initial optimized instantaneous frequency of each sub-signal.

[0012] Step S7: Based on the initial optimized instantaneous frequency Calculate the final optimized instantaneous frequency of each sub-signal.

[0013] Step S8: Reconstruct each sub-signal x based on the optimized demodulated signal and the final optimized instantaneous frequency of each sub-signal. i ;

[0014] Step S9: Set the termination iteration threshold ε and determine whether the reconstructed sub-signal meets the set termination iteration threshold; if it does not meet the threshold, continue to repeat steps S1 to S8; if it does meet the threshold, the decomposition of the original signal is completed.

[0015] Preferably, in step S1, when the original signal y has overlapping instantaneous frequencies, the number K of sub-signals in the original signal and the initial instantaneous frequency of each sub-signal are determined according to the time-frequency representation of the frequency-modulated wavelet transform of the local maximum synchronous compression of the original signal y. When the original signal y does not have intersecting instantaneous frequencies, the number K of sub-signals and the initial instantaneous frequency are determined based on the time-frequency representation of the short-time Fourier transform of the original signal y. Preferably, in step S2, the initial demodulated signal and The calculation formula is:

[0016]

[0017]

[0018] In the formula, α represents the penalty coefficient, Ω is the second derivative matrix, and A i and B i These are the cosine and sine phase matrices of the i-th sub-signal, respectively, and ρ1 is an auxiliary vector.

[0019] Preferably, in step S3, the demodulated signal is optimized. and The calculation formula is:

[0020] In the formula, β and γ represent penalty coefficients, and p, q, ρ2 and ρ3 are auxiliary vectors.

[0021] Preferably, in step S4, the initial instantaneous frequency increment The calculation formula is:

[0022]

[0023] In the formula, t is the instantaneous moment, and π is the mathematical constant pi.

[0024] Preferably, in step S5, the instantaneous frequency increment is optimized. The calculation formula is:

[0025]

[0026] In the formula, μ1 and μ2 are weighting coefficients, D is the first derivative matrix, I is the identity matrix, and Ω is the second derivative matrix.

[0027] Preferably, in step S6, the initial optimization instantaneous frequency... The calculation formula is:

[0028]

[0029] Preferably, in step S7, the instantaneous frequency is finally optimized. The calculation formula is:

[0030]

[0031] In the formula, μ3, μ4 and γ are weighting coefficients, r and ρ4 are auxiliary vectors, Ω is the second derivative matrix, I is the identity matrix, and κ is the regularization coefficient.

[0032] Preferably, in step S8, each sub-signal x i The corresponding calculation formula is:

[0033]

[0034] A i and B i These are the cosine and sine phase matrices of the i-th sub-signal, respectively. i and v i This is the demodulated signal.

[0035] A sparse-aided variational nonlinear signal decomposition system according to the present invention includes:

[0036] Module M1: Determines the number of sub-signals of the original signal and the initial instantaneous frequency IF of each sub-signal;

[0037] Module M2: Calculates the preliminary demodulated signal for each sub-signal based on the initial instantaneous frequency IF. and ;

[0038] Module M3: Based on the preliminary demodulated signal and Calculate the optimized demodulated signal for each sub-signal. and ;

[0039] Module M4: Based on the optimized demodulated signal and Calculate the initial instantaneous frequency increment of each sub-signal. ;

[0040] Module M5: Based on the initial instantaneous frequency increment Calculate the optimized instantaneous frequency increment for each self-signal. ;

[0041] Module M6: Based on optimized instantaneous frequency increment Calculate the initial optimized instantaneous frequency of each sub-signal. ;

[0042] Module M7: Based on the initial optimized instantaneous frequency Calculate the final optimized instantaneous frequency of each sub-signal. ;

[0043] Module M8: Reconstructs each sub-signal x based on the optimized demodulated signal of each sub-signal and the final optimized instantaneous frequency. i ;

[0044] Module M9: Sets the termination iteration threshold ε and determines whether the reconstructed sub-signal meets the set termination iteration threshold; if it does not meet the threshold, it continues to trigger modules M1 to M8 repeatedly; if it does meet the threshold, it completes the decomposition of the original signal.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. The invented sparse-assisted signal decomposition technique can estimate the IF of each sub-signal and reconstruct each sub-signal more accurately than existing signal decomposition methods, thereby extracting the variation patterns of complex AM-FM signals more effectively.

[0047] 2. The invented sparse-assisted signal decomposition technique optimizes the iterative optimization formula of the demodulated signal, improves the signal demodulation performance, and thus enables more accurate estimation of the signal's IF.

[0048] 3. The invented sparse-assisted signal decomposition technique optimizes the iterative optimization formula of IF, and can more effectively extract the variation law of complex IF. Attached Figure Description

[0049] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0050] Figure 1 The flowchart shows the sparse-aided variational nonlinear decomposition method of the present invention.

[0051] Figure 2a This is a time-domain curve of the simulation signal of the present invention.

[0052] Figure 2b This is a diagram showing the instantaneous frequency of the simulated signal in this invention.

[0053] Figure 2c and Figure 2d The above is a time-domain curve of each sub-signal of the simulated signal of this invention.

[0054] Figure 3a This is an instantaneous frequency diagram of the estimated values ​​of each sub-signal of the simulated signal according to the present invention.

[0055] Figure 3b and Figure 3c This is a time-domain curve of the reconstruction of each sub-signal of the simulated signal according to the present invention.

[0056] Figure 4a This is a time-frequency representation of the vibration signal of the variable speed fault bearing of the present invention.

[0057] Figure 4b This is a time-frequency representation diagram of the vibration signal of the bearing decomposed and reconstructed according to the present invention. Detailed Implementation

[0058] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0059] A sparse-aided variational nonlinear signal decomposition method includes the following steps:

[0060] Step S1: Determine the number of sub-signals and the initial instantaneous frequency (IF) in the original signal.

[0061] Step S2: Using the estimated initial instantaneous frequency, calculate the preliminary demodulated signal for each sub-signal. and .

[0062] Step S3: Calculate the optimized demodulated signal for each sub-signal. and .

[0063] Step S4: Calculate the initial instantaneous frequency increment of each sub-signal. .

[0064] Step S5: Calculate the optimized instantaneous frequency increment for each self-signal. .

[0065] Step S6: Calculate the initial optimized instantaneous frequency of each sub-signal. .

[0066] Step S7: Calculate the final optimized instantaneous frequency of each sub-signal .

[0067] Step S8: Reconstruct each sub-signal x based on the demodulated signal and instantaneous frequency of each optimized sub-signal. i .

[0068] Step S9: Set the termination iteration threshold ε and determine whether the reconstructed sub-signal meets the set termination iteration threshold. If it does not meet the threshold, continue repeating steps S1 to S8. If it does meet the threshold, the decomposition of the original signal is complete.

[0069] In step S1, the number of sub-signals of the original signal and their corresponding initial instantaneous frequencies are determined. For the original signal y, when it has overlapping instantaneous frequencies, the number K of sub-signals and the initial instantaneous frequency of each sub-signal are determined according to the time-frequency representation (TFR) of the synchronously compressed frequency-modulated wavelet transform (LMSSCT) of the signal's local maxima. When there is no crossover instantaneous frequency, the number K of sub-signals and the initial instantaneous frequency are determined according to the TFR of the short-time Fourier transform (STFT) of the signal. .

[0070] The initial demodulated signal in step S2 and The calculation formula is: In the formula, α represents the penalty coefficient, Ω is the second derivative matrix, and A i and B i These are the cosine and sine phase matrices of the i-th sub-signal, respectively, and ρ1 is an auxiliary vector.

[0071] Optimization of demodulated signal in step S3 and The calculation formula is: In the formula, β and γ represent penalty coefficients, and p, q, ρ2 and ρ3 are auxiliary vectors.

[0072] Initial instantaneous frequency increment in step S4 The calculation formula is:

[0073] In step S5, the instantaneous frequency increment is optimized. The calculation formula is: In the formula, μ1 and μ2 are weighting coefficients, D is the first derivative matrix, and I is the identity matrix.

[0074] Initial optimization of instantaneous frequency in step S6 The calculation formula is:

[0075] In step S7, the instantaneous frequency is finally optimized. The calculation formula is: In the formula, μ3, μ4 and γ are weighting coefficients, and r and ρ4 are auxiliary vectors.

[0076] Each sub-signal x in step S8 i The corresponding calculation formula is:

[0077] The range of the termination iteration threshold ε in step S9 is 10. -6 ~10 -8 The corresponding calculation formula is: In the formula, x i Let i be the i-th sub-signal.

[0078] In step S1, the number of sub-signals and the initial instantaneous frequency of each sub-signal are determined by extracting the IF ridge curve from the TFR.

[0079] The formula for calculating the auxiliary vector ρ1 in step S2 is as follows:

[0080] The formula for calculating the auxiliary vector p in step S3 is as follows: Where soft represents the soft threshold function.

[0081] The formula for calculating the auxiliary vector q in step S3 is as follows:

[0082] The formula for calculating the auxiliary vector ρ2 in step S3 is as follows:

[0083] The formula for calculating the auxiliary vector ρ3 in step S3 is as follows:

[0084] The method provided by this invention is used to decompose simulated signals and actual signals with complex variation patterns. Figures 2a to 2d These are the time-domain curves of the simulated signal, the IF of each sub-signal, and the time-domain curves of each sub-signal. Figures 3a to 3c The result is the result of decomposing the simulated signal using the method of the present invention. The results show that the present invention can accurately estimate the IF of each sub-signal and the reconstructed sub-signal. Figure 4a It is the TFR of the actual bearing vibration signal. Figure 4bThe TFR obtained by decomposing the bearing vibration signal using the method of this invention shows that the invention effectively filters out noise from the original actual signal and accurately estimates the IF and reconstructed sub-signals of each sub-signal, thereby obtaining a TFR with strong energy concentration.

[0085] The present invention also provides a sparse-assisted variational nonlinear signal decomposition system, which can be implemented by executing the process steps of the sparse-assisted variational nonlinear signal decomposition method. That is, those skilled in the art can understand the sparse-assisted variational nonlinear signal decomposition method as a preferred embodiment of the sparse-assisted variational nonlinear signal decomposition system.

[0086] A sparse-aided variational nonlinear signal decomposition system includes:

[0087] Module M1: Determines the number of sub-signals of the original signal and the initial instantaneous frequency IF of each sub-signal;

[0088] Module M2: Calculates the preliminary demodulated signal for each sub-signal based on the initial instantaneous frequency IF. and ;

[0089] Module M3: Based on the preliminary demodulated signal and Calculate the optimized demodulated signal for each sub-signal. and ;

[0090] Module M4: Based on the optimized demodulated signal and Calculate the initial instantaneous frequency increment of each sub-signal.

[0091] Module M5: Based on the initial instantaneous frequency increment Calculate the optimized instantaneous frequency increment for each self-signal.

[0092] Module M6: Based on optimized instantaneous frequency increment Calculate the initial optimized instantaneous frequency of each sub-signal.

[0093] Module M7: Based on the initial optimized instantaneous frequency Calculate the final optimized instantaneous frequency of each sub-signal.

[0094] Module M8: Reconstructs each sub-signal x based on the optimized demodulated signal of each sub-signal and the final optimized instantaneous frequency. i ;

[0095] Module M9: Sets the termination iteration threshold ε and determines whether the reconstructed sub-signal meets the set termination iteration threshold; if it does not meet the threshold, it continues to trigger modules M1 to M8 repeatedly; if it does meet the threshold, it completes the decomposition of the original signal.

[0096] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0097] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A sparsely assisted variational nonlinear signal decomposition method, characterized by, Comprising: Step S1: determining the number of sub-signals of the original signal and the initial instantaneous frequency IF of each sub-signal; Step S2: Calculate a preliminary demodulation signal of each sub-signal according to the initial instantaneous frequency IF of the sub-signal and ; Step S3: calculating an optimized demodulation signal for each sub-signal from the preliminary demodulation signals and ; calculating an optimized demodulation signal for each sub-signal from the preliminary demodulation signals and ; Step S4: calculating an initial instantaneous frequency increment of each sub-signal from the optimized demodulation signal and ;​ Step S5: Based on the initial instantaneous frequency increment Calculate the optimized instantaneous frequency increment for each sub-signal. ; Step S6: Based on the optimized instantaneous frequency increment Calculate the initial optimized instantaneous frequency of each sub-signal. ; Step S7: calculating the final optimized instantaneous frequency of each sub-signal according to the initial optimized instantaneous frequency ; and ; Step S8: reconstruct each sub-signal from the optimized demodulation signal and the final optimized instantaneous frequency of each sub-signal x i ; Step S9: setting a termination iteration threshold ε , and determining whether the reconstructed sub-signal meets the set termination iteration threshold; if not, repeating steps S1 to S8, and if yes, completing the decomposition of the original signal; In step S3, the demodulated signal is optimized. and The calculation formula is: , , where β and γ denote penalty coefficients, p , q , ρ 2 and ρ 3 are auxiliary vectors; In the step S5, the instantaneous frequency increment The calculation formula is: wherein μ 1 and μ 2 are weight coefficients, D is a first derivative matrix, I is an identity matrix, and Ω is a second derivative matrix; In the step S7, the final optimized instantaneous frequency The calculation formula is: wherein μ 3, μ 4 and γ are weight coefficients, r and ρ 4 is an auxiliary vector, Ω is a second derivative matrix, I is an identity matrix, is a regularization coefficient.

2. The sparsely assisted variational nonlinear signal decomposition method of claim 1, wherein, in step S1, the number of sub-signals and the initial instantaneous frequency of each sub-signal are determined from the time-frequency representation of the original signal y with crossing instantaneous frequencies y by synchronously compressing the time-frequency representation of the original signal K with crossing instantaneous frequencies by synchronously compressing the time-frequency representation of the original signal y without crossing instantaneous frequencies y by the short-time Fourier transform of the original signal K without crossing instantaneous frequencies .

3. The sparsely assisted variational nonlinear signal decomposition method of claim 1, wherein, In the step S2, the preliminary demodulation signal and The calculation formula is: wherein α denotes a penalty coefficient, Ω is a second derivative matrix, A i and B i are the cosine and sine phase matrices of the i ρ 1 is an auxiliary vector.​ 4. The sparsely assisted variational nonlinear signal decomposition method of claim 1, wherein, In the step S4, the initial instantaneous frequency increment is calculated by the formula: Wherein, t is the instantaneous time, and π is the circular constant.

5. The sparsely assisted variational nonlinear signal decomposition method of claim 1, wherein, In the step S6, the initial optimized instantaneous frequency The calculation formula is: 。 6. The sparsely assisted variational nonlinear signal decomposition method of claim 1, wherein, In the step S8, each sub-signal x i , and the corresponding calculation formula is: A i and B i They are the first i The cosine and sine phase matrices of each sub-signal and This is the demodulated signal.

7. A sparsity-augmented variational nonlinear signal decomposition system, characterized by, Comprising: Module M1: determining the number of sub-signals of the original signal and the initial instantaneous frequency IF of each sub-signal; Module M2: from the initial instantaneous frequency IF, compute a preliminary demodulated signal for each sub-signal and ; Module M3: calculating, from the preliminary demodulation signal and an optimized demodulation signal for each sub-signal and ; Module M4: computing an initial instantaneous frequency increment of each sub-signal from the optimized demodulation signal and ;​ Module M5: calculating an optimized instantaneous frequency increment for each sub-signal from the initial instantaneous frequency increment ;​ Module M6: Based on optimized instantaneous frequency increment Calculate the initial optimized instantaneous frequency of each sub-signal. ; Module M7: calculating the final optimized instantaneous frequency of each sub-signal from the initial optimized instantaneous frequency ;​ Module M8: reconstruct each sub-signal from the optimally demodulated signal and the final optimally instantaneous frequency of each sub-signal x i ; Module M9: setting a termination iteration threshold ε , and determining whether the reconstructed sub-signal meets the set termination iteration threshold; if not, continuing to repeat the work of modules M1 to M8, and if yes, completing the decomposition of the original signal; In said module M3, the demodulated signal is optimized and The calculation formula is: , , where β and γ denote penalty coefficients, p , q , ρ 2 and ρ 3 are auxiliary vectors; In said module M5, the calculation formula of the optimized instantaneous frequency increment is: wherein μ 1 and μ 2 are weight coefficients, D is a first derivative matrix, I is an identity matrix, and Ω is a second derivative matrix; In said module M7, the final optimization of the instantaneous frequency The calculation formula is: wherein μ 3, μ 4 and γ are weight coefficients, r and ρ 4 is an auxiliary vector, Ω is a second derivative matrix, I is an identity matrix, is a regularization coefficient.

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