A vibration signal denoising and feature extraction method based on wavelet adaptive thresholding

Abstract

This invention discloses a vibration signal denoising and feature extraction method based on wavelet adaptive thresholding, belonging to the field of vibration sensor signal processing technology. The method includes the following steps: Step 1, performing multi-level decomposition of the signal using a filter bank constructed based on discrete wavelet transform; Step 2, adaptively calculating the noise threshold; Step 3, implementing wavelet coefficient shrinkage denoising based on the SureShrink algorithm; Step 4, reconstructing the vibration signal based on quasi-discrete wavelet transform; Step 5, automatically extracting signal features based on a multi-layer recurrent neural network. This invention, through signal decomposition based on discrete wavelet transform and an adaptive thresholding denoising algorithm, reduces the error impact caused by the vibration sensor's own noise and environmental disturbances, retains most of the features of the original vibration signal, and establishes a multi-layer recurrent neural network for the denoised vibration signal to achieve automatic extraction of time features, providing an important foundation for the subsequent development of fault diagnosis and health monitoring algorithms.

Description

Technical Field

[0001] This invention relates to the field of vibration sensor signal processing technology, and in particular to a vibration signal denoising and feature extraction method based on wavelet adaptive threshold. Background Technology

[0002] With the continuous development of structural health monitoring and fault diagnosis, vibration sensors, as core monitoring tools, are becoming increasingly important. In a laboratory environment, vibration sensors, combined with digital filters, signal amplifiers, and other equipment, can achieve high-precision, high-frequency measurements of structural vibration responses, which can then be used for load inversion and health status assessment of structures. However, in recent years, the demand for structural fault diagnosis and health monitoring of aerospace equipment has been growing, posing new challenges to the application of vibration sensors. Unlike laboratory environments, vibration sensors need to monitor vibrations while the equipment is in operation, and the operating environment of the equipment may also change; therefore, traditional vibration signal preprocessing methods cannot accurately extract structural vibration information.

[0003] In recent years, with the rapid development of artificial intelligence technology, deep neural networks have enabled the automatic extraction of complex data features. The automatic extraction of vibration signal features based on deep neural network technology not only greatly facilitates the construction and deployment of algorithms such as fault diagnosis, but also lays a solid foundation for achieving efficient and accurate structural health monitoring. Summary of the Invention

[0004] The purpose of this invention is to propose a vibration signal denoising and feature extraction method based on wavelet adaptive thresholding, which reduces the error caused by the vibration sensor's own noise and environmental disturbances, and realizes the accurate extraction of structural vibration information and automatic extraction of signal features in complex environments, providing a basis for the deployment and optimization of structural health monitoring in complex environments.

[0005] To achieve the above objectives, this invention proposes a vibration signal denoising and feature extraction method based on wavelet adaptive thresholding, the specific steps of which are as follows:

[0006] S1. The collected vibration signal is decomposed into high and low frequency signals by a filter bank based on discrete wavelet transform, and finally the multi-level decomposition of the vibration signal is realized.

[0007] S2, Adaptive calculation of noise threshold;

[0008] S3. Wavelet coefficient shrinkage and denoising based on SureShrink algorithm, adaptive threshold determination of wavelet band coefficients with different vibration intensities and different frequency ranges;

[0009] S4. Construct a multi-layer filter bank based on inverse discrete wavelet transform to reconstruct the vibration signal;

[0010] S5. Automatic extraction of signal features based on multi-layer recurrent neural networks.

[0011] Preferably, in step S1, the vibration signal acquired by the vibration sensor is decomposed into high and low frequency signals by a filter bank composed of discrete wavelet transform; wherein, the filter bank consists of a high-pass filter and a low-pass filter, and the vibration signal is processed by the low-pass filter to obtain the wavelet coefficients c(n) of the low-frequency signal, and the calculation formula is as follows:

[0012]

[0013] The vibration signal is processed by a high-pass filter to obtain the wavelet coefficients d(n) of the high-frequency signal. The calculation formula is as follows:

[0014]

[0015] Where * represents convolution operation, h k For a low-pass filter, g l Let x(n) be a high-pass filter, x(n) be the vibration signal, k and l be the lengths of the filter coefficients, and n be the length of the discrete signal.

[0016] The wavelet coefficients c(n) of the low-frequency signal and d(n) of the high-frequency signal obtained from the decomposition are then processed again through high-pass and low-pass filters to obtain wavelet coefficients with finer frequency resolution. This process is repeated to achieve multi-level decomposition of the signal. The multi-level decomposition calculation formula is as follows:

[0017]

[0018]

[0019] in, For the next layer of low-frequency wavelet coefficients, denoted as the high-frequency wavelet coefficients of the next layer, and j represents the layer to be decomposed.

[0020] Preferably, the low-pass filter calculation formula is as follows:

[0021]

[0022]

[0023] The formula for calculating a high-pass filter is as follows:

[0024]

[0025]

[0026] Where φ(x) is the scaling function, ψ(x) is the wavelet function, and x is the independent variable of the function.

[0027] Preferably, in S2, the noise threshold is divided into a global threshold and a SURE threshold; the noise threshold considers all signal features, and its calculation formula is as follows:

[0028]

[0029] Among them, T univ σ is the global threshold. n Where N is the noise standard deviation and N is the signal length;

[0030] The SURE threshold only considers the wavelet coefficients of the current wavelet band, and its calculation formula is as follows:

[0031]

[0032] Among them, T sure The SURE threshold, Let N be the noise variance. sub Y represents the length of the wavelet zone coefficients, #{·} represents the number of elements that satisfy the conditions. t is the current wavelet band coefficient, T is the noise threshold to be optimized, and i is an integer.

[0033] Preferably, the noise standard deviation σ n The coefficients are estimated from the wavelet coefficients of the finest frequency, and the calculation formula is as follows:

[0034] σ n =median(|d N -median(d N )|) / 0.6745;

[0035] Where, d N These are the wavelet coefficients with the finest frequency.

[0036] Preferably, in S3, based on the SureShrink algorithm, an adaptive threshold determination is performed on the wavelet band coefficients for different vibration intensities and frequency ranges. The noise threshold determination calculation formula is as follows:

[0037]

[0038] η N =log2(N) sub ) 3 / 2 ;

[0039]

[0040] Where, η N , This is the noise threshold determination factor;

[0041] Once the threshold is determined, wavelet coefficient shrinkage and denoising are implemented based on the soft thresholding method. Coefficients with amplitudes less than or equal to the threshold are set to 0, and coefficients with amplitudes greater than the threshold are shrunk to the difference between the coefficient and the threshold. The calculation formula is as follows:

[0042]

[0043] Where T(x) are wavelet coefficients.

[0044] Preferably, in S4, based on the denoised wavelet coefficients of each layer obtained in S3, a multi-layer filter bank is constructed, and the signal is reconstructed layer by layer starting from the finest-scale wavelet coefficients. The calculation formula for wavelet reconstruction is as follows:

[0045]

[0046] in, These are the reconstructed wavelet coefficients.

[0047] Preferably, in S5, a sliding window algorithm is used to implement the sliding window input of long signals, and the time features of the signals are automatically extracted through a multi-layer recurrent neural network to obtain the output of signal feature data in sequence form.

[0048] Therefore, this invention proposes a vibration signal denoising and feature extraction method based on wavelet adaptive thresholding, the beneficial effects of which are as follows:

[0049] (1) The present invention provides a vibration signal denoising and feature extraction method based on wavelet adaptive threshold. By using signal decomposition based on discrete wavelet transform and adaptive threshold denoising algorithm, the error caused by the vibration sensor’s own noise and environmental disturbance is reduced, and most of the features of the original vibration signal are preserved.

[0050] (2) The present invention provides a vibration signal denoising and feature extraction method based on wavelet adaptive threshold. A multi-layer recurrent neural network is established for the denoised vibration signal to realize the automatic extraction of time features, which provides an important foundation for the construction of subsequent fault diagnosis and health monitoring algorithms.

[0051] 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

[0052] Figure 1 This is a schematic diagram of the overall process of a vibration signal denoising and feature extraction method based on wavelet adaptive threshold according to the present invention;

[0053] Figure 2 This is a flowchart of the automatic feature extraction process of a vibration signal denoising and feature extraction method based on wavelet adaptive thresholding according to the present invention. Detailed Implementation

[0054] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of this application.

[0055] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0056] like Figure 1 As shown, this invention provides a method for denoising and feature extraction of vibration signals based on wavelet adaptive thresholding, the specific steps of which are as follows:

[0057] Step 1: Multi-level decomposition of vibration signals based on discrete wavelet transform.

[0058] In practical applications, due to the influence of equipment operating conditions and environmental conditions, the measured signals of vibration sensors often contain a large amount of noise, and the collected signals cannot be directly used for vibration analysis and fault diagnosis. For the measured vibration signals, high and low frequency signals can be decomposed by passing them through a filter bank composed of discrete wavelet transform.

[0059] The filter bank consists of a high-pass filter and a low-pass filter. The vibration signal is processed by the low-pass filter to obtain the low-frequency wavelet coefficients c(n), and the calculation formula is as follows:

[0060]

[0061] The vibration signal is processed by a high-pass filter to obtain the wavelet coefficients d(n) of the high-frequency signal. The calculation formula is as follows:

[0062]

[0063] Where * represents convolution operation, h k For a low-pass filter, g l Let x(n) be a high-pass filter, x(n) be the vibration signal, k and l be the lengths of the filter coefficients, and n be the length of the discrete signal.

[0064] low-pass filter h k The calculation formula is as follows:

[0065]

[0066]

[0067] High-pass filter g l The calculation formula is as follows:

[0068]

[0069]

[0070] Where φ(x) is the scaling function and ψ(x) is the wavelet function.

[0071] The wavelet coefficients c(n) of the low-frequency signal and d(n) of the high-frequency signal obtained from the decomposition are then processed again through high-pass and low-pass filters to obtain wavelet coefficients with finer frequency resolution. This process is repeated to achieve multi-level decomposition of the signal. The multi-level decomposition calculation formula is as follows:

[0072]

[0073]

[0074] in, For the next layer of low-frequency wavelet coefficients, denoted as the high-frequency wavelet coefficients of the next layer, and j represents the layer to be decomposed.

[0075] Step 2: Adaptive calculation of noise threshold.

[0076] Based on the multi-level decomposition coefficients obtained in step one, the global signal-noise threshold is first calculated. The formula for calculating the global threshold is as follows:

[0077]

[0078] Among them, T univ σ is the global threshold. n Where N is the noise standard deviation and N is the signal length;

[0079] Since the global threshold takes into account the data characteristics of the entire signal acquisition process, the noise threshold is generally too large. Therefore, for the coefficient characteristics of each sub-band, a local adaptive threshold, the SURE threshold, is calculated. The calculation formula is as follows:

[0080]

[0081] Among them, T sure The SURE threshold, Let N be the noise variance. sub Y represents the length of the wavelet zone coefficients, #{·} represents the number of elements that satisfy the conditions. t is the current wavelet band coefficient, T is the noise threshold to be optimized, and i is an integer.

[0082] Noise standard deviation σ n The coefficients are estimated from the wavelet coefficients of the finest frequency, and the calculation formula is as follows:

[0083] σ n=median(|d N -median(d N )|) / 0.6745;

[0084] Where, d N These are the wavelet coefficients with the finest frequency.

[0085] Step 3: Wavelet coefficient shrinkage and denoising based on the SureShrink algorithm.

[0086] Based on the two noise thresholds calculated in step two, the wavelet band threshold is first determined. The noise threshold determination formula is as follows:

[0087]

[0088] η N =log2(N) 3 / 2 ;

[0089]

[0090] Once the threshold is determined, wavelet coefficient shrinkage and denoising are implemented using a soft thresholding method. Coefficients with amplitudes less than or equal to the threshold are set to 0, while coefficients with amplitudes greater than the threshold are shrunk to the difference between the coefficient and the threshold, as shown in the following formula:

[0091]

[0092] Where T(x) are wavelet coefficients.

[0093] Step 4: Vibration signal reconstruction based on inverse discrete wavelet transform.

[0094] Based on the denoised wavelet coefficients obtained in step three, a multi-layer filter bank is constructed. Using inverse discrete wavelet transform, the signal is reconstructed layer by layer, starting from the finest-scale wavelet coefficients. The wavelet reconstruction calculation formula is as follows:

[0095]

[0096] in, These are the reconstructed wavelet coefficients.

[0097] Step 5: Automatic extraction of signal features based on multi-layer recurrent neural networks.

[0098] like Figure 2 As shown, based on the denoised vibration signal obtained in step four, the characteristics of the measured signal data of the vibration sensor are automatically extracted through a multi-layer recurrent neural network. First, the input of the recurrent neural network is determined based on the sliding window algorithm, a multi-layer recurrent neural network is constructed, the time characteristics of the vibration signal are extracted, and finally the sequence characteristics of the vibration signal are output.

[0099] Therefore, this invention provides a vibration signal denoising and feature extraction method based on wavelet adaptive threshold. By using signal decomposition based on discrete wavelet transform and adaptive threshold denoising algorithm, the error caused by the vibration sensor's own noise and environmental disturbances is reduced, while retaining most of the features of the original vibration signal. At the same time, a multi-layer recurrent neural network is established on the denoised vibration signal to realize the automatic extraction of time features, providing an important foundation for the construction of subsequent fault diagnosis and health monitoring algorithms.

[0100] 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 vibration signal denoising and feature extraction method based on wavelet adaptive threshold, characterized in that, The specific steps are as follows: S1, decompose the collected vibration signal into high-frequency and low-frequency signals by a filter bank based on discrete wavelet transform, and finally realize multi-layer decomposition of the vibration signal; S2, adaptive calculation of noise threshold; S3, wavelet coefficient shrinkage denoising based on SureShrink algorithm, adaptive threshold determination of wavelet coefficient in different vibration intensity and different frequency interval; S4, multi-layer filter bank is constructed based on inverse discrete wavelet transform to realize the reconstruction of the vibration signal; S5, automatic extraction of signal features based on multi-layer recurrent neural network; In S2, the noise threshold is divided into global threshold and SURE threshold; the noise threshold considers all signal features, and its calculation formula is as follows: where T univ is the global threshold, σ n is the noise standard deviation, and N is the signal length. The SURE threshold only considers the current wavelet coefficient, and its calculation formula is as follows: where T sure is a SURE threshold, is a noise variance, N sub is a subband coefficient length, #{·} denotes the number of elements satisfying the condition, Y t is a current subband coefficient, T is a noise threshold to be optimized, and i is an integer; In S3, based on SureShrink algorithm, adaptive threshold determination of wavelet coefficient in different vibration intensity and different frequency interval, noise threshold determination formula is as follows: η N = log2(N sub ) 3 / 2 ; wherein η N , is a noise threshold decision factor; After the threshold is determined, the wavelet coefficient is shrunk and denoised based on the soft threshold method, the coefficient whose amplitude is less than or equal to the threshold is set to 0, and the coefficient whose amplitude is greater than the threshold is shrunk to the difference between the coefficient and the threshold, and its calculation formula is as follows: Wherein, T(x) is the wavelet coefficient; In S5, the sliding window algorithm is used to realize the sliding window input of long signal, and the time characteristics of the signal are automatically extracted by the multi-layer recurrent neural network to obtain the sequence form of the signal feature data output.

2. The vibration signal de-noising and feature extraction method based on wavelet adaptive threshold according to claim 1, characterized in that, In S1, the vibration signal collected by the vibration sensor is decomposed into high-frequency and low-frequency signals by a filter bank composed of discrete wavelet transform; wherein the filter bank is composed of a high-pass filter and a low-pass filter, and the vibration signal is calculated by the low-pass filter to obtain the low-frequency signal wavelet coefficient c(n), and the calculation formula is as follows: The vibration signal is calculated by the high-pass filter to obtain the high-frequency signal wavelet coefficient d(n), and the calculation formula is as follows: Wherein, * represents convolution operation, h k is a low-pass filter, g l is a high-pass filter, x(n) is a vibration signal, k and l are the length of filter coefficients, and n is the length of discrete signal. The low-frequency signal wavelet coefficient c(n) and the high-frequency signal wavelet coefficient d(n) obtained by decomposition are calculated by high-pass filter and low-pass filter again, and further wavelet coefficients with finer frequency resolution are obtained, and the multi-layer decomposition is realized by iteration, and the multi-layer decomposition calculation formula is as follows: wherein, is the next lower level low frequency wavelet coefficient, is the next lower level high frequency wavelet coefficient, and j is the level to be decomposed.

3. The vibration signal de-noising and feature extraction method based on wavelet adaptive threshold according to claim 2, characterized in that, The calculation formula of the low-pass filter is as follows: The calculation formula of the high-pass filter is as follows: Wherein, φ(x) is the scale function, ψ(x) is the wavelet function, and x is the function argument.

4. The vibration signal de-noising and feature extraction method based on wavelet adaptive threshold according to claim 1, characterized in that, The noise standard deviation σ n The noise standard deviation σ is estimated from the finest frequency wavelet coefficients, using the following formula: σ n = median(|d N -median(d N )|) / 0.6745; where d N is the finest frequency wavelet coefficient.

5. The vibration signal de-noising and feature extraction method based on wavelet adaptive threshold according to claim 1, characterized in that, In S4, based on the denoised wavelet coefficients of each layer obtained in S3, a multi-layer filter bank is constructed, and the signal is reconstructed layer by layer from the finest scale wavelet coefficient, and the calculation formula of wavelet reconstruction is as follows: wherein are the reconstructed wavelet coefficients.

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