Non-periodic signal denoising and reconstruction method based on synchronous compression continuous wavelet transform

Abstract

This invention describes a method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform, comprising: S1, decomposing the original aperiodic signal into IMF components; S2, denoising the IMF components and superimposing them to form a corrected signal; S3, performing continuous wavelet transform on the corrected signal to obtain the instantaneous frequency of the signal; compressing and rearranging the instantaneous frequency in the time-frequency domain through synchronous compressed transform to construct an EMD-AWT-WSST model to obtain the instantaneous rotational frequency of the gearbox's aperiodic vibration signal; S4, obtaining the time-frequency diagram through the EMD-AWT-WSST model and extracting the time-frequency ridge data; correcting the time-frequency ridge data and fitting to extract the complete rotational speed ridge; resampling the original aperiodic signal in the angle domain to obtain the resampled steady-state signal. By performing mode-oriented denoising on the original signal, combined with adaptive wavelet thresholding and empirical mode decomposition denoising methods, noise can be effectively removed in strong noise environments while preserving the weak fault impact signal of the gearbox.

Description

Technical Field

[0001] This invention relates to the field of aperiodic signal processing technology, and specifically to a method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform. Background Technology

[0002] In wind turbine generators, the actual rotational speed of the gearbox exhibits significant non-steady-state characteristics due to wind speed fluctuations, with typical fluctuations reaching ±35% of the rated speed. This time-varying speed signal causes the gearbox vibration signal meshing frequency to change in real time with the rotational speed, resulting in frequency modulation. Furthermore, the transient impact caused by a fault typically accounts for less than 2% of the energy in the time-frequency distribution and is easily submerged by noise, causing attenuation of the impact component. External interferences such as wind turbine aerodynamic loads and generator electromagnetic excitation, combined with the inherent vibration of the gearbox, form a broadband coupled signal, resulting in multi-source interference coupling. Based on these reasons, and statistical data showing that approximately 70% of gearbox faults go undetected due to vibration signal analysis failures, it is clear that there is a fundamental contradiction between non-periodic vibration signals under variable speed conditions and steady-state analysis methods.

[0003] Current signal processing methods have the following systematic limitations when dealing with aperiodic signals:

[0004] I. Failure of traditional noise reduction methods

[0005] Wavelet thresholding method: Relies on basis function selection, it generates modal aliasing when the gearbox speed changes abruptly, with an aliasing rate >45% and an impact component amplitude loss of 38%-52%;

[0006] Empirical Mode Decomposition: Endpoint effects cause phase shift in the reconstructed signal. Analysis shows that the phase accumulation error can reach 0.22π, which seriously disrupts the timing characteristics of the fault impact.

[0007] Blind source separation technology: requires a pre-set fault type dictionary, and the separation success rate for unknown faults, such as compound pitting and tooth breakage, is less than 55%.

[0008] II. Failure of Signal Reconstruction Technology

[0009] Order analysis relies on tachometers: Existing standard-recommended order tracking methods require the additional installation of a speed sensor. However, in practical applications, tachometer installation errors can lead to angle synchronization deviations and generate pseudo-order components when speed changes abruptly.

[0010] The contradiction between time and frequency resolution: The short-time Fourier transform is limited by the Heisenberg uncertainty principle, making it difficult to capture both transient impacts and frequency modulation details at the same time.

[0011] Due to the limitations of the above technologies, it is currently difficult to achieve effective instantaneous frequency extraction and obtain more accurate speed change curves, thus failing to effectively overcome the adverse effects on the accuracy of gearbox fault diagnosis under variable speed operating conditions. Summary of the Invention

[0012] This invention aims to at least partially address the problems existing in the prior art. Therefore, this invention provides a method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform, the technical solution of which is as follows:

[0013] A method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform includes the following steps:

[0014] S1, the original aperiodic signal of the gearbox is decomposed into multiple IMF components through empirical mode decomposition;

[0015] S2, the IMF components are denoised by an adaptive wavelet threshold function, and the denoised IMF components are superimposed to form a corrected signal.

[0016] S3. Perform continuous wavelet transform on the corrected signal to obtain the phase information of the corrected signal and take its partial derivative to obtain the instantaneous frequency of the corrected signal.

[0017] Based on steps S1 and S2, and by performing compression and rearrangement operations on the instantaneous frequency in the time-frequency domain through synchronous compression transformation, the EMD-AWT-WSST model is constructed to complete the instantaneous frequency conversion acquisition of the original aperiodic signal of the gearbox.

[0018] S4. The time-frequency diagram of the original aperiodic signal of the gearbox is obtained through the EMD-AWT-WSST model, and the time-frequency ridge data is extracted. The extracted time-frequency ridge data is corrected by a piecewise cubic spline interpolation algorithm. The corrected time-frequency ridge data is fitted with a sine function to extract the complete speed ridge. The original aperiodic signal of the gearbox is resampled in the angle domain to obtain the resampled steady-state signal.

[0019] Furthermore, in step S1, the IMF components include effective and ineffective components, and the ineffective IMF components are eliminated by using the Pearson correlation coefficient and variance contribution rate.

[0020] The formula for the Pearson correlation coefficient is as follows:

[0021]

[0022] The formula for the variance contribution rate is as follows:

[0023]

[0024] In the above formula, The Pearson correlation coefficient; Contribution to variance; The sequence number of the IMF component; M represents the number of data points; M represents the total number of IMF components. It is the original aperiodic signal; Original aperiodic signal The mean; For the i-th IMF component; For the i-th IMF component The mean.

[0025] Furthermore, in step S2, the expression for the adaptive wavelet threshold function is as follows:

[0026]

[0027] in, The adaptive threshold parameter is expressed as follows:

[0028]

[0029] In the above formula, This is the adaptive wavelet threshold function, i.e., the j-th estimated wavelet coefficient in the l-th layer; It is a step function; The coefficients are obtained after wavelet transform; k is the adjustment parameter; e is the imaginary unit. For adaptive threshold parameters; The standard deviation of the noise; The signal length; This is the decomposition scale.

[0030] Furthermore, the sampling signal-to-noise ratio and root mean square error are used as evaluation metrics for the adaptive wavelet threshold function denoising, as shown in the following expressions:

[0031]

[0032]

[0033] In the formula,

[0034] SNR (dB) is the sampling signal-to-noise ratio; RMSE is the root mean square error. The total power of the signal; This represents the total power of the noise. This is the a-th sample of the original aperiodic signal; These are the denoised signal samples; The index of the signal sample; This represents the number of signal samples.

[0035] Furthermore, step S3 includes the following specific steps:

[0036] S301, for a given correction signal In continuous wavelets The continuous wavelet transform of the given condition, expressed in the frequency domain, is as follows:

[0037]

[0038] In the formula, To correct the signal Continuous wavelet transform under the mother wavelet; For scale variables; It is a time variable; Original aperiodic signal Fourier transform; The sub-wavelet is obtained by translation and scaling transformation of the mother wavelet; For frequency variables; For continuous wavelets Fourier transform of; e is the imaginary unit; This represents the phase information in the frequency domain; π is the mathematical constant pi; d is the differential sign of the definite integral.

[0039] S302, Single-frequency signal The continuous wavelet transform is defined as:

[0040]

[0041] It can be seen that single-frequency signal The instantaneous frequency c can be defined as:

[0042]

[0043] Therefore, for single-frequency signals Its phase transformation It can be defined as:

[0044]

[0045] In the formula for this step,

[0046] It is a single-frequency signal; A is a constant; e is the imaginary unit; Phase information in the frequency domain; π is pi; c is a single-frequency signal. The instantaneous frequency of is a constant, and c > 0; Single-frequency signal Continuous wavelet transform; For scale variables; is the time variable; d is the differential symbol of the definite integral; Single-frequency signal Fourier transform; For frequency variables; For continuous wavelets Fourier transform; The degree of matching between the wavelet and the instantaneous frequency c under the scale variable u; Single-frequency signal Its phase transformation;

[0047] S303, in the time-frequency plane, uses Representing the synchronous compressed continuous wavelet transform, the WSST formula is obtained as follows:

[0048]

[0049] WSST passed The inverse transform is used to reconstruct the signal, resulting in the reconstructed signal. :

[0050]

[0051] In the formula for this step,

[0052] To synchronously compress continuous wavelet transform; u belongs to the set of positive real numbers; Single-frequency signal The continuous wavelet transform coefficients; δ is the Dirac function; For scale variables; It is a time variable; Single-frequency signal Its phase transformation; d represents the frequency variable; d is the differential symbol of the definite integral. For reconstructing the signal; Re is the operation of taking the real part; It is a scaling factor, and ; Instantaneous frequency; This is the frequency bandwidth threshold, and .

[0053] Based on the above technical solution, the method described in this invention has the following beneficial effects:

[0054] By employing modal-oriented denoising on the original aperiodic signal of the gearbox, combined with adaptive wavelet thresholding and empirical mode decomposition denoising methods, noise can be effectively removed in high-noise environments while preserving the gearbox's weak fault impact signals. Furthermore, the EMD-AWT-WSST model can eliminate the bandwidth spread effect of synchronous compressed time-frequency analysis, freeing it from hardware dependence on the tachometer. Attached Figure Description

[0055] Figure 1This is a schematic diagram of the EMD-AWT-WSST algorithm flow.

[0056] Figure 2 This is a schematic diagram of the time and frequency domains of the original aperiodic signal from the gearbox.

[0057] Figure 3 This is a schematic diagram of the time and frequency domains of the original aperiodic signal after noise reduction.

[0058] Figure 4 A time-frequency diagram showing the extraction of instantaneous frequencies before and after WSST;

[0059] Figure 5 Here are the corrected scatter plot and the schematic diagram of the fitted curve;

[0060] Figure 6 A schematic diagram of the time and frequency domains of the reconstructed signal at equal angles;

[0061] Figure 7 This is a schematic diagram illustrating the principle of equal-angle resampling. Detailed Implementation

[0062] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. Unless otherwise defined, the technical or scientific terms used in this disclosure should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains.

[0063] This embodiment describes a method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform. The overall algorithm flow is as follows: Figure 1 As shown, the specific steps include:

[0064] S1, the original aperiodic signal of the gearbox is decomposed into multiple IMF components by Empirical Mode Decomposition (EMD), and then denoised and corrected. The specific steps include:

[0065] S101, acquires the raw aperiodic vibration signal of the gearbox during operation. Figure 2 (a) shows a time-domain schematic of the original aperiodic signal from the gearbox. Figure 2 (b) shows a frequency domain diagram of the original aperiodic signal of the gearbox. Find all the local maxima and minima of the original aperiodic signal.

[0066] S102, the upper and lower envelopes of the original signal are fitted using a cubic spline function, and the mean envelope is obtained by averaging the upper and lower envelopes, i.e.:

[0067] ,

[0068] In the formula, The mean envelope, The upper envelope, This is the lower envelope.

[0069] S103, subtract the mean envelope from the original aperiodic signal sequence to obtain a new signal with low frequencies removed. Repeat this process multiple times until the definition of IMF is satisfied, thus obtaining the first-order IMF component of the original aperiodic signal, i.e.:

[0070] ,

[0071] In the formula, For first-order IMF components, The original aperiodic signal, This is the mean envelope.

[0072] S104, using the original aperiodic signal Subtracting the first-order IMF component yields a new signal with high frequencies removed, resulting in the second-order IMF component of the original aperiodic signal, i.e.:

[0073] ,

[0074] In the formula, For new signals, The original aperiodic signal, It is a first-order IMF component.

[0075] S105, Repeat the above process until the nth order IMF component of the original aperiodic signal is obtained. .

[0076] S2, the IMF component is divided into two parts: effective component and invalid component. In order to fully eliminate invalid component, the selection of IMF component is optimized by using Pearson correlation coefficient and variance contribution rate.

[0077] The formula for the Pearson correlation coefficient is as follows:

[0078]

[0079] The formula for the variance contribution rate is as follows:

[0080]

[0081] In the above formula,

[0082] The Pearson correlation coefficient;

[0083] Contribution to variance;

[0084] The sequence number of the IMF component;

[0085] The number of data points;

[0086] M is the total number of IMF components;

[0087] It is the original aperiodic signal;

[0088] Original aperiodic signal The mean;

[0089] For the i-th IMF component;

[0090] For the i-th IMF component The mean.

[0091] S3. Establish the adaptive wavelet threshold function (AWT), determine the wavelet basis function and the number of decomposition levels, adaptively select appropriate threshold parameters and threshold functions to denoise the optimized IMF components, and construct the denoised IMF components. Figure 3 (a) shows a time-domain schematic diagram of the original aperiodic signal after denoising. Figure 3 (b) shows a frequency domain diagram of the original aperiodic signal after denoising.

[0092] The expression for the adaptive wavelet threshold function is as follows:

[0093]

[0094] in, This is an improved method for selecting threshold parameters, designed to ensure optimal threshold parameter selection.

[0095] Adaptive threshold parameter The expression is:

[0096]

[0097] In the above formula,

[0098] This is the adaptive wavelet threshold function, i.e., the j-th estimated wavelet coefficient in the l-th layer;

[0099] It is a step function;

[0100] These are the coefficients after wavelet transform;

[0101] k is an adjustment parameter;

[0102] e is the imaginary unit;

[0103] For adaptive threshold parameters;

[0104] The standard deviation of the noise;

[0105] The signal length;

[0106] This is the decomposition scale.

[0107] As the value of m changes, the adaptive wavelet threshold function can flexibly vary between soft and hard threshold functions, combining the advantages of both and avoiding the large deviation of the soft threshold function and the discontinuity of the hard threshold function.

[0108] S4, the denoised IMF components are superimposed to form the corrected signal. To obtain the best denoising effect, the sampling signal-to-noise ratio and root mean square error are used as evaluation indicators for adaptive wavelet threshold function denoising, as shown in the following expressions:

[0109]

[0110]

[0111] In the formula,

[0112] SNR (dB) is the sampling signal-to-noise ratio;

[0113] RMSE stands for root mean square error.

[0114] The total power of the signal;

[0115] This represents the total power of the noise.

[0116] This is the a-th sample of the original aperiodic signal;

[0117] These are the denoised signal samples;

[0118] The index of the signal sample;

[0119] This represents the number of signal samples.

[0120] S5. Perform a continuous wavelet transform on the denoised and corrected signal to obtain the phase information of the signal, and take its partial derivative to obtain the instantaneous frequency of the signal. Figure 4(a) shows a time-frequency diagram of the instantaneous frequency extracted before WSST. Figure 4 (b) shows a time-frequency diagram of the instantaneous frequency extracted after WSST.

[0121] By using the Empirical Mode Decomposition (EMD) recorded in step S1, the Adaptive Wavelet Transform (AWT) recorded in step 3, and the synchronous compression transform to compress and rearrange the instantaneous frequency in the time-frequency domain, the EMD-AWT-WSST model is constructed to obtain the instantaneous frequency of the gearbox's non-periodic vibration signal.

[0122] The specific steps are as follows:

[0123] S501, for a given correction signal In continuous wavelets The continuous wavelet transform of the given condition, expressed in the frequency domain, is as follows:

[0124]

[0125] In the formula,

[0126] To correct the signal Continuous wavelet transform under the mother wavelet;

[0127] For scale variables;

[0128] It is a time variable;

[0129] Original aperiodic signal Fourier transform;

[0130] The sub-wavelet is obtained by translation and scaling transformation of the mother wavelet;

[0131] For frequency variables;

[0132] For continuous wavelets Fourier transform;

[0133] e is the imaginary unit;

[0134] This refers to phase information in the frequency domain.

[0135] π is the mathematical constant pi.

[0136] d is the differential symbol for the definite integral.

[0137] S502, In order to achieve a clearer time-frequency representation of the signal, the synchronous compression transform redistributes the scale variable u of the continuous wavelet transform as a frequency variable, including the following steps:

[0138] For single-frequency signals The continuous wavelet transform is defined as:

[0139]

[0140] It can be seen that single-frequency signal The instantaneous frequency c can be defined as:

[0141]

[0142] Therefore, for single-frequency signals Its phase transformation It can be defined as:

[0143]

[0144] In the formula for this step,

[0145] It is a single-frequency signal;

[0146] A is a constant;

[0147] e is the imaginary unit;

[0148] This refers to phase information in the frequency domain.

[0149] π is the mathematical constant pi.

[0150] c is a single-frequency signal The instantaneous frequency of is a constant, and c > 0;

[0151] Single-frequency signal Continuous wavelet transform;

[0152] For scale variables;

[0153] It is a time variable;

[0154] d is the differential symbol for the definite integral;

[0155] Single-frequency signal Fourier transform;

[0156] For frequency variables;

[0157] For continuous wavelets Fourier transform;

[0158] The degree of matching between the wavelet and the instantaneous frequency c under the scale variable u;

[0159] Single-frequency signal Its phase transformation.

[0160] In the time-frequency plane, using Representing the synchronous compressed continuous wavelet transform, the WSST formula is obtained as follows:

[0161]

[0162] WSST passed The inverse transform is used to reconstruct the signal, resulting in the reconstructed signal. :

[0163]

[0164] In the formula for this step,

[0165] To synchronously compress continuous wavelet transform;

[0166] u belongs to the set of positive real numbers;

[0167] Single-frequency signal Continuous wavelet transform coefficients;

[0168] δ is the Dirac function;

[0169] For scale variables;

[0170] It is a time variable;

[0171] Single-frequency signal Its phase transformation;

[0172] For frequency variables;

[0173] d is the differential symbol for the definite integral;

[0174] For reconstructing the signal;

[0175] Re is the operation of taking the real part;

[0176] It is a scaling factor, and ;

[0177] Instantaneous frequency;

[0178] This is the frequency bandwidth threshold, and .

[0179] S6. The time-frequency graph is obtained using the EMD-AWT-WSST model, and the curve with the highest energy in the graph is selected for extraction. The extracted time-frequency ridge data is corrected using a piecewise cubic spline interpolation algorithm. The entire data interval is divided into several sub-intervals, and a cubic polynomial is constructed on each sub-interval. Constraints are used to ensure a smooth transition between adjacent polynomials at connection points. Finally, a sine function is used as the curve fitting function. Figure 5 (a) shows a schematic diagram of the corrected scatter plot. Figure 5 (b) shows a schematic diagram of the corrected fitting curve; after the rotational speed ridge is extracted, the original aperiodic signal can be resampled at equal angles based on it. Figure 7 The diagram illustrates the principle of equal-angle resampling, specifically the conversion from equal-time sampling to equal-angle resampling. The specific steps are as follows:

[0180] S601: Given N+1 data points Where q = 0, 1, ..., N, and In each sub-interval Construct a cubic polynomial:

[0181]

[0182] In the formula, , , , These are coefficients to be determined.

[0183] To ensure the smoothness of the interpolation curve, the piecewise cubic spline interpolation algorithm needs to satisfy the following four conditions: establish a system of linear equations and solve for the coefficients. , , , Thus, the piecewise cubic spline interpolation function is obtained.

[0184] (1) Interpolation conditions: for each polynomial It must pass through the endpoints of the interval, i.e. , .

[0185] (2) Continuity of the first derivative: The first derivatives of adjacent polynomials at the junction points must be equal, i.e. .

[0186] (3) Continuity of the second derivative: The second derivatives of adjacent polynomials at the junction points must be equal, i.e. .

[0187] (4) Boundary conditions: Natural boundary conditions are usually adopted, that is, the second derivatives of the starting point and the ending point are zero. , .

[0188] Piecewise cubic spline interpolation can accurately and reasonably reflect the characteristics and trends of various data, maintain the smoothness and continuity of the data, and reduce the loss of information. Based on this, a sine function is used to fit the corrected time-frequency ridge data to extract the complete rotational speed ridge. Piecewise cubic spline interpolation is suitable for non-uniformly distributed data points and can adapt to the complex changes in energy curves in time-frequency graphs.

[0189] S602: After the rotational speed ridge is extracted, the original aperiodic signal can be resampled in the angle domain to obtain the resampled steady-state signal. Figure 6 (a) shows a time-domain schematic of the reconstructed signal at equal angles. Figure 6 (b) shows a frequency domain diagram of the reconstructed signal at equal angles.

[0190] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform, characterized in that, For gearbox fault diagnosis, the following steps are included: S1, the original aperiodic signal of the gearbox is decomposed into multiple IMF components through empirical mode decomposition. The original aperiodic signal of the gearbox is the original aperiodic vibration signal during the operation of the gearbox. S2, the IMF components are denoised by an adaptive wavelet threshold function, and the denoised IMF components are superimposed to form a corrected signal. S3. Perform continuous wavelet transform on the corrected signal to obtain the phase information of the corrected signal and take its partial derivative to obtain the instantaneous frequency of the corrected signal. Based on steps S1 and S2, and by performing compression and rearrangement operations on the instantaneous frequency in the time-frequency domain through synchronous compression transformation, the EMD-AWT-WSST model is constructed to complete the instantaneous frequency conversion acquisition of the original aperiodic signal of the gearbox. The specific steps include the following: S301, for a given correction signal In continuous wavelets The continuous wavelet transform of the given condition, expressed in the frequency domain, is as follows: ， In the formula, To correct the signal Continuous wavelet transform under the mother wavelet; For scale variables; It is a time variable; Original aperiodic signal Fourier transform; The sub-wavelet is obtained by translation and scaling transformation of the mother wavelet; For frequency variables; For continuous wavelets Fourier transform; e is the imaginary unit; This represents the phase information in the frequency domain; π is the mathematical constant pi; d is the differential sign of the definite integral. S302, Single-frequency signal The continuous wavelet transform is defined as: ， Single-frequency signal The instantaneous frequency c is defined as: ， For single-frequency signals Its phase transformation Defined as: ， In the formula for this step, It is a single-frequency signal; A is a constant; e is the imaginary unit; Phase information in the frequency domain; π is pi; c is a single-frequency signal. The instantaneous frequency of is a constant, and c > 0; Single-frequency signal Continuous wavelet transform; For scale variables; d represents the time variable; d is the differential symbol of the definite integral. Single-frequency signal Fourier transform; For frequency variables; For continuous wavelets Fourier transform; The degree of matching between the wavelet and the instantaneous frequency c under the scale variable u; Single-frequency signal Its phase transformation; S303, in the time-frequency plane, uses Representing the synchronous compressed continuous wavelet transform, the WSST formula is obtained as follows: ， WSST passed The inverse transform is used to reconstruct the signal, resulting in the reconstructed signal. : ， In the formula for this step, To synchronously compress continuous wavelet transform; u belongs to the set of positive real numbers; Single-frequency signal The continuous wavelet transform coefficients; δ is the Dirac function; For scale variables; It is a time variable; Single-frequency signal Its phase transformation; d represents the frequency variable; d is the differential symbol of the definite integral. For reconstructing the signal; Re is the operation of taking the real part; It is a scale factor, and ; Instantaneous frequency; This is the frequency bandwidth threshold, and ; S4. The time-frequency diagram of the original aperiodic signal of the gearbox is obtained through the EMD-AWT-WSST model, and the time-frequency ridge data is extracted. The extracted time-frequency ridge data is corrected by a piecewise cubic spline interpolation algorithm. The corrected time-frequency ridge data is fitted with a sine function to extract the complete speed ridge. The original aperiodic signal of the gearbox is resampled in the angle domain to obtain the resampled steady-state signal.

2. The method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform according to claim 1, characterized in that, In step S1, the IMF components include effective and ineffective components. Ineffective IMF components are eliminated by using the Pearson correlation coefficient and variance contribution rate. The formula for the Pearson correlation coefficient is as follows: ， The formula for the variance contribution rate is as follows: ， In the above formula, The Pearson correlation coefficient; Contribution to variance; The sequence number of the IMF component; M represents the number of data points; M represents the total number of IMF components. It is the original aperiodic signal; Original aperiodic signal The mean; For the i-th IMF component; For the i-th IMF component The mean.

3. The method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform according to claim 1, characterized in that, In step S2, the expression for the adaptive wavelet threshold function is as follows: ， in, The adaptive threshold parameter is expressed as follows: ， In the above formula, This is the adaptive wavelet threshold function, i.e., the j-th estimated wavelet coefficient in the l-th layer; It is a step function; These are the coefficients after wavelet transform; k is the adjustment parameter; e is the imaginary unit; For adaptive threshold parameters; The standard deviation of the noise; The signal length; This is the decomposition scale.

4. The method for denoising and reconstructing aperiodic signals based on synchronous compressed continuous wavelet transform according to claim 3, characterized in that, The sampling signal-to-noise ratio and root mean square error are used as evaluation metrics for denoising using the adaptive wavelet threshold function, as expressed below: ， ， In the formula, SNR (dB) is the sampling signal-to-noise ratio; RMSE is the root mean square error. The total power of the signal; This represents the total power of the noise. This is the a-th sample of the original aperiodic signal; These are the denoised signal samples; The index of the signal sample; This represents the number of signal samples.

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