Vehicle vibration signal denoising method based on wavelet decomposition

Abstract

The present invention discloses a vehicle vibration signal denoising method based on wavelet decomposition, which mainly solves the problems that when the current wavelet threshold denoising method is used to denoise the vehicle vibration signal, low-frequency noise is not filtered out, interfering with the effective signal, and the estimated wavelet coefficients deviate greatly from the original wavelet coefficients, resulting in the reduction of the amplitude of the effective signal in the reconstructed signal and signal distortion. The present invention performs five-layer wavelet decomposition on the vehicle vibration signal, then generates the threshold of each layer of wavelet coefficients, judges and estimates each layer of wavelet coefficients to obtain the estimated wavelet coefficients, and finally reconstructs the estimated wavelet coefficients to obtain the denoised vehicle vibration signal. Thereby, high- and low-frequency noises are simultaneously suppressed, signal distortion is reduced, and the characteristics of the original vehicle vibration signal are retained to a great extent.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and further relates to a method for denoising vehicle vibration signals based on wavelet decomposition in the field of intelligent transportation. The present invention can be used for denoising vehicle signals containing vibration signals in traffic scenarios. Background Art

[0002] When a vehicle travels on a road, it will generate a certain excitation on the road surface. This excitation causes the deformation of the earth medium and forms surface vibrations. Acceleration sensors deployed on both sides of the road can detect the vibration signals caused by the passing of vehicles and are used for vehicle detection, vehicle speed calculation, and vehicle classification research. In addition to the vibration signals caused by vehicles, the signals actually collected by acceleration sensors also contain a large number of interference signals, which cause great interference to the subsequent analysis of vehicle vibration signal characteristics such as frequency and amplitude. The existing traditional denoising methods mainly include IIR digital filtering, median filtering, frequency-domain filtering methods based on Fourier transform, etc. However, the prerequisite for using these methods is to accurately know the effective components of the signal. If the filtering range is set inappropriately, the denoising effect will not be ideal. To overcome the shortcomings of the above methods, a denoising method based on wavelet decomposition has been proposed, which can automatically adapt to the requirements of time-domain signal analysis and achieve a better denoising effect. However, the traditional wavelet threshold denoising method uses a single fixed threshold, and there are problems of constant deviation and discontinuity at the threshold for the hard and soft threshold functions respectively, resulting in distortion of the reconstructed signal.

[0003] Southwest University of Science and Technology disclosed a method for denoising microseismic signals based on an improved wavelet threshold function in its patent document "Method for Denoising Microseismic Signals Based on Improved Wavelet Threshold Function" (application number CN202110520815.2, publication number CN 113221746 A). The steps of this method are as follows: 1. Perform multi-layer wavelet decomposition on the noisy microseismic signal to obtain the approximate coefficients and detail coefficients after wavelet decomposition at each layer; 2. Perform threshold quantization processing on the obtained detail coefficients at each layer: first select a threshold rule and then shrink the detail coefficients at each layer through an improved threshold function with an adjustment factor; 3. Perform wavelet inverse transform on the approximate coefficients and the detail coefficients at each layer after threshold quantization processing to reconstruct the denoised microseismic signal. The disadvantage of this method is that when performing coefficient quantization processing on the wavelet decomposition of microseismic signals, a traditional single fixed threshold is used as the judgment threshold. Although it can filter out some high-frequency noises, it does not filter out low-frequency noises, and this part of low-frequency noises will interfere with the useful signals.

[0004] Nanjing University of Information Science and Technology discloses a wavelet denoising method based on an improved threshold function in its patent document "A Wavelet Denoising Method Based on an Improved Threshold Function" (Application No. CN202210275028.0, Publication No. CN 114581674 A). The steps of this method are as follows: 1. Decompose the noisy signal through a wavelet basis, select the VisuShrink threshold as the judgment threshold to improve the threshold function, and obtain an adjustable threshold function; 2. Filter the wavelet coefficients according to the improved adjustable threshold function to obtain the estimated wavelet coefficients; 3. Use the inverse wavelet transform to reconstruct the signal to obtain the denoised signal. The disadvantage of this method is that although the improved wavelet threshold function proposed by this method makes up for the problem of discontinuity of the traditional hard threshold function at the threshold, the deviation between the estimated wavelet coefficients and the original wavelet coefficients is relatively large, resulting in the reduction of the amplitude of some effective signals in the reconstructed signal and certain distortion. Summary of the Invention

[0005] The purpose of the present invention is to propose a wavelet decomposition-based vehicle vibration signal denoising method aiming at the deficiencies of the above-mentioned existing technologies, so as to solve the problems that when the wavelet threshold denoising method is used to denoise the vehicle vibration signal, the low-frequency noise is not filtered out, which interferes with the effective signal, the deviation between the estimated wavelet coefficients and the original wavelet coefficients is relatively large, resulting in the reduction of the amplitude of the effective signal in the reconstructed signal and distortion.

[0006] The technical idea for achieving the object of the present invention is that the present invention performs multi-layer wavelet decomposition on the collected vehicle vibration signal to obtain wavelet coefficients of each layer, then generates a threshold for each layer of wavelet coefficients, and then estimates the value of each layer of wavelet coefficients. The wavelet coefficients with absolute values less than the threshold are set to zero, and the wavelet coefficients with absolute values greater than the threshold are estimated by adding or subtracting an adjustable variable. Finally, the estimated wavelet coefficients of each layer are subjected to inverse wavelet transform to reconstruct the denoised vehicle vibration signal. Since the threshold used in the present invention introduces a natural logarithm function model in the denominator of the traditional threshold, and the variable of the model is the corresponding decomposition layer number plus one. Therefore, according to the different proportions of the effective signal and noise in each layer of coefficients obtained by decomposition, the threshold of each layer of wavelet coefficients can be obtained, so as to separate the wavelet coefficients corresponding to the noise signal and the effective signal at low frequencies, and it can solve the problem that the existing technology uses a single fixed threshold as the judgment threshold, resulting in the interference of the effective signal caused by the unfiltered low-frequency noise. The threshold function used in the present invention introduces an exponential function model as an adjustable variable, and the model contains an adjustment factor, which can change the change trend of the function in the interval outside the threshold break point, and can solve the problem that there is a large deviation between the wavelet coefficients estimated by the threshold function in the existing technology and the original wavelet coefficients, resulting in the reduction of the amplitude of some effective signals in the vehicle vibration signal reconstructed by inverse wavelet transform and the generation of distortion. Thus, the characteristics of the original vehicle vibration signal are retained to a great extent, and the influence on the subsequent processing and analysis of the vehicle vibration signal is reduced.

[0007] The specific steps for achieving the object of the present invention are as follows:

[0008] Step 1, convert the noisy vehicle vibration signal into a discrete digital signal;

[0009] Step 2, perform five-layer wavelet decomposition on the discrete digital signal to obtain wavelet coefficients of each layer;

[0010] Step 3, generate the threshold of each layer of wavelet coefficients according to the following formula:

[0011]

[0012] where λ j represents the threshold of the j-th layer of wavelet coefficients in the discrete digital signal, N j represents the length of the j-th layer of wavelet coefficients in the discrete digital signal, and δ j represents the standard variance of the noise of the j-th layer of wavelet coefficients in the discrete digital signal;

[0013] Step 4, estimate the value of each layer of wavelet coefficients:

[0014] Step 4.1, determine whether each layer of wavelet coefficients is greater than the threshold of this layer. If so, determine the value of this layer of wavelet coefficients as Otherwise, execute Step 4.2; where represents the value of the k-th wavelet coefficient at the j-th layer for estimating a discrete digital signal, w j,k represents the k-th wavelet coefficient at the j-th layer of a discrete digital signal, λ j represents the threshold of the wavelet coefficients at the j-th layer in a discrete digital signal. exp represents the exponential function with the natural constant e as the base, and β represents a shape adjustment factor used to adjust the deviation between the estimated wavelet coefficients and the original wavelet coefficients;

[0015] Step 4.2, determine whether each layer of wavelet coefficients is less than the negative value of the threshold of that layer. If so, determine the value of the wavelet coefficients of that layer as Otherwise, execute Step 4.3;

[0016] Step 4.3, determine the value of the wavelet coefficients of each layer except for Steps 4.1 and 4.2 as

[0017] Step 5, reconstruct the vehicle vibration signal:

[0018] Perform an inverse wavelet transform on the estimated value of the wavelet coefficients of each layer, and form the denoised vehicle vibration signal by combining the inverse-transformed values of the wavelet coefficients of each layer.

[0019] The present invention has the following advantages compared with the prior art:

[0020] First, since the threshold generated for each layer of wavelet coefficients in the present invention can be adaptively adjusted according to the decomposition level, it overcomes the deficiency in the prior art that the same threshold is used at different decomposition levels, resulting in the wavelet coefficients corresponding to the noise signal and the effective signal not being separated at low frequencies, leading to the failure to filter out low-frequency noise and further interfering with the effective signal. Therefore, the present invention can effectively filter out both high-frequency and low-frequency noises simultaneously when denoising the vehicle vibration signal, reducing the interference of noise on the effective signal.

[0021] Second, since the present invention uses a threshold function that is continuous at the threshold breakpoints and has no large deviation at non-breakpoints to estimate the wavelet coefficients of each layer, it overcomes the defect in the prior art that there is a large deviation between the wavelet coefficients estimated by the threshold function and the original wavelet coefficients, resulting in the reduction of the amplitude of some effective signals and distortion in the vehicle vibration signal reconstructed by the inverse wavelet transform. Therefore, when denoising the vehicle vibration signal, the present invention can filter out high-frequency and low-frequency noises while maximizing the retention of the characteristics of the original vehicle vibration signal. Description of the Drawings

[0022] Figure 1 is the implementation flowchart of the denoising method of the present invention.

[0023] Figure 2 is the comparison chart of the variation of the threshold function in the present invention and the traditional hard and soft threshold functions;

[0024] Figure 3 It is a comparison chart of the denoising effects of the method of the present invention and the existing wavelet threshold denoising method on the test signal;

[0025] Figure 4 It is a comparison chart of the denoising effects of the method of the present invention and the existing wavelet threshold denoising method on the simulated vehicle vibration signal;

[0026] Figure 5 It is a comparison chart of the denoising effects of the method of the present invention and the existing wavelet threshold denoising method on the vehicle vibration signal. Specific embodiments

[0027] The embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] Refer to Figure 1 , and further describe the implementation steps of the embodiments of the present invention.

[0029] Step 1, obtain the noisy vehicle vibration signal.

[0030] In the embodiment of the present invention, an acceleration sensor used to collect signals is an IEPE type acceleration sensor produced by Yangzhou Xiyuan Electronic Technology Co., Ltd., but it is not limited to other acceleration sensors on the market that can detect vehicle vibration signals. The test location indicates the inner section of the South Third Ring Road in Xi'an. The analog signal collected by this acceleration sensor from 10:22:50 on September 17, 2022 to 10:22:59 on September 17, 2022 is converted into a digital signal containing 45,000 discrete points through an analog-to-digital converter with a sampling rate Fs = 5000Hz.

[0031] Step 2, perform five-layer wavelet decomposition on the discrete digital signal to obtain wavelet coefficients of each layer.

[0032] Select the Sym8 wavelet basis and use the function in the MATLAB software to perform five-layer wavelet decomposition on the discrete digital signal, and output the wavelet coefficients of the first to fifth layers. The wavelet coefficients include approximation coefficients and detail coefficients.

[0033] The approximation coefficient represents the low-frequency component in the signal, and the detail coefficient represents the high-frequency component in the signal; due to the strong data decorrelation and sparsity of wavelet transform, it can concentrate the signal energy in the larger wavelet approximation coefficients, while the noise energy is mainly manifested as smaller wavelet detail coefficients. At the same time, as the decomposition level increases, the wavelet approximation coefficients of the original signal remain basically unchanged, while the noise wavelet detail coefficients gradually decay.

[0034] Step 3, generate the threshold of each layer of wavelet coefficients as follows.

[0035]

[0036] Among them, λ j represents the threshold of the wavelet coefficients of the j-th layer, δ j represents the standard variance of the noise in the wavelet coefficients of the j-th layer, δ j = median(|w j,k |) / 0.6745, median represents the median after arranging the sequence in ascending order, 0.6745 is the adjustment coefficient of the noise standard variance, w j,k represents the wavelet coefficients of the j-th layer, k represents the position index of each layer of wavelet coefficients, ln represents the natural logarithm with base e, N j represents the length of the wavelet coefficients of the j-th layer.

[0037] In this embodiment, the noise in the discrete digital signal is not only distributed at high frequencies but also at low frequencies. In order to separate the wavelet coefficients corresponding to the noise signal at low frequencies from the effective signal, the present invention introduces a natural logarithm function model on the basis of the traditional fixed threshold, and the variable of this model is the decomposition level plus one. Therefore, the threshold of each layer of wavelet coefficients can be obtained according to the different proportions of the effective signal and noise in each layer of coefficients obtained by decomposition, thus avoiding the problem that the use of a single fixed threshold as the judgment threshold causes interference to the effective signal due to the low-frequency noise not being filtered out.

[0038] The expression of the above-mentioned traditional fixed threshold is: δ represents the standard variance of the signal noise, δ = median(|w 1,k |) / 0.6745, median represents the median after arranging the sequence in ascending order, w 1,k represents the detail coefficients after the first wavelet decomposition, 0.6745 is the adjustment coefficient of the noise standard variance, N represents the signal length, and ln represents the natural logarithm with base e.

[0039] Step 4, estimate the value of each layer of wavelet coefficients.

[0040] Step 4.1, determine whether each layer of wavelet coefficients is greater than the threshold of that layer. If so, determine the value of that layer of wavelet coefficients as Otherwise, execute step 4.2; where represents the k-th wavelet coefficient value of the j-th layer for discrete digital signal estimation, w j,k represents the k-th wavelet coefficient of the j-th layer of the discrete digital signal, λ j represents the threshold of the wavelet coefficients of the j-th layer in the discrete digital signal, exp represents the exponential function with the natural constant e as the base, and β represents the shape adjustment factor, which is used to adjust the deviation between the estimated wavelet coefficients and the original wavelet coefficients.

[0041] Step 4.2, determine whether each layer of wavelet coefficients is less than the negative value of the threshold of that layer. If so, determine the value of the wavelet coefficients of that layer as Otherwise, execute step 4.3.

[0042] Step 4.3, determine the value of the wavelet coefficients of each layer except for step 4.1 and step 4.2 as

[0043] The above method for estimating the wavelet coefficients of each layer can be expressed as the following threshold function f(x):

[0044]

[0045] where x represents the wavelet coefficient, λ represents the threshold, exp represents the exponential function with the natural constant e as the base, and the shape adjustment factor β ∈ (0, ∞) is used to adjust the speed at which the function generally approaches the original wavelet coefficient. When β = 0, this expression is transformed into a soft threshold function. When β → ∞, this threshold function is transformed into a hard threshold function.

[0046] Refer to Figure 2 , draw the change graphs of the threshold function of the present invention and the traditional soft and hard threshold functions together, and compare the change trends of the threshold function of the present invention in the interval outside the threshold breakpoints. Among them, Figure 2 the abscissa in represents the wavelet coefficient, and the ordinate represents the estimated wavelet coefficient. Figure 2 In, the curve marked with a cross represents the change curve of the hard threshold function, the curve marked with a plus represents the change curve of the soft threshold function, the curve marked with a circle represents the change curve of the threshold function of the present invention when the parameter β takes 1, the curve marked with a star represents the change curve of the threshold function of the present invention when the parameter β takes 5, and the curve marked with a solid dot represents the change curve of the threshold function of the present invention when the parameter β takes 15. It can be seen from Figure 2 that as the adjustment factor β increases, the deviation between the wavelet coefficients estimated by the threshold function of the present invention and the original wavelet coefficients gradually decreases. When β is 10, the threshold function of the present invention only has a very small deviation in a very small interval outside the threshold breakpoints. Obviously, the threshold function of the present invention overcomes the deficiencies of the soft and hard threshold functions, such as having a constant deviation and being discontinuous at the threshold breakpoints.

[0047] Taking the left and right limits of the threshold function f(x) of the present invention at x = ±λ, the limits exist and are zero, indicating that the threshold function of the present invention is continuous in the entire real number domain, overcoming the defect that the existing hard threshold function has breakpoints at x = ±λ and will not generate additional oscillation points for the reconstructed signal.

[0048] Taking the limits of the threshold function f(x) of the present invention at positive and negative infinity, the limits exist and are x, indicating that the threshold function of the present invention has f(x) = x as an asymptote, which also shows that the adjustment factor β can be used to change its function shape, making the function approach the original wavelet coefficients in the intervals outside x = ±λ and improving the deficiency of the constant deviation existing in the soft threshold function.

[0049] Taking the derivative of the threshold function f(x) of the present invention at the threshold x = ±λ, the derivative result f'(x) is 1 + β, indicating that the threshold function is differentiable at the threshold x = ±λ and improving the denoising ability of the threshold function of the present invention.

[0050] The above-mentioned hard threshold function and soft threshold function are the two most commonly used functions in the current wavelet threshold denoising method. The definition of the hard threshold function is:

[0051]

[0052] The hard threshold function sets the coefficients in the signal that are less than the threshold to zero and retains the coefficients that are greater than or equal to the threshold. However, the threshold selection of the hard threshold function has a great impact on the reduction of the signal and noise, and the output of the hard threshold function is non-linear, which may cause distortion or distortion of some signals. The definition of the soft threshold function is:

[0053]

[0054] The soft threshold function sets the coefficients in the signal that are less than the threshold to zero and subtracts the threshold from the coefficients that are greater than or equal to the threshold. Although the output of the soft threshold function smooths the signal, due to subtracting the threshold, there is a constant deviation, which will cause a certain reduction of the signal.

[0055] The expression of the improved threshold function is as follows:

[0056]

[0057] Among them, a and b represent the adjustment parameters of the threshold function, a ∈ [0, 1], b > 0. Although the improved threshold function has improved the deficiencies of the hard and soft threshold functions in having a constant deviation and being discontinuous at the threshold breakpoints, in the intervals outside the threshold points, there is still a large deviation between the wavelet coefficients estimated by this function and the original wavelet coefficients, and even the adjustment parameters a and b cannot well reduce the deviation.

[0058] Step 5, reconstruct the vehicle vibration signal.

[0059] Use the function in MATLAB software to perform one-dimensional wavelet reconstruction on the estimated wavelet coefficients of each layer, complete the denoising process, and obtain the denoised discrete digital signal.

[0060] The effect of the present invention can be further demonstrated by the following simulation.

[0061] 1. Simulation experiment conditions.

[0062] The hardware platform for the simulation experiment of the present invention is: the processor is Intel(R) Core(TM) i5-10500 CPU@3.10GHz, the main frequency is 3.1GHz, and the memory is 16GB.

[0063] The software platform for the simulation experiment of the present invention is: Windows 10 operating system and MATLAB R2020b.

[0064] The test signal for the simulation experiment of the present invention is to use the sine function in MATLAB software to output a sine signal composed of 201 sample points for the numbers in the range of [0, 2] with a step value of 0.01, and use the function in MATLAB software to add Gaussian white noise to the test signal as the noise to be filtered, thereby obtaining a test signal containing Gaussian white noise.

[0065] The simulated vehicle vibration signal for the simulation experiment of the present invention is a vehicle vibration signal composed of 1356 sample points collected by an IEPE type acceleration sensor in a relatively quiet environment at night. Use MATLAB software to set all the noise in the non-effective signal segment of this signal to zero to simulate a pure vehicle vibration signal, and then use the noise addition function in MATLAB software to add Gaussian white noise to the simulated vehicle vibration signal as the noise to be filtered. Thus, a simulated vehicle vibration signal containing Gaussian white noise is obtained to illustrate that the method of the present invention is also effective for denoising real vehicle vibration signals.

[0066] The real vehicle vibration data for the simulation experiment of the present invention is an analog signal collected by an IEPE type acceleration sensor on the inner side of the South Third Ring Road in Xi'an from 10:22:50 on September 17, 2022 to 10:22:59 on September 17, 2022. After passing through an analog-to-digital converter with a sampling rate Fs = 5000Hz, a vehicle vibration signal composed of 45000 sample points is obtained.

[0067] The parameter settings of the simulation experiment of the present invention are as follows: The wavelet basis function for wavelet decomposition is Sym8, and the number of layers of wavelet decomposition is set to 5. The thresholds of the traditional hard threshold function, soft threshold function, and an improved threshold function disclosed in the prior art are where N represents the signal length, and w 1,k represents the detail coefficient after the first wavelet transform. The parameter settings of the improved threshold function are: a = 1, b = 5. The parameter settings of the threshold function adopted by the present invention are: β = 15, and the threshold is wherein, N j represents the length of the wavelet coefficients at the j-th layer, and w j,k represents the k-th wavelet coefficient at the j-th layer.

[0068] 2. Simulation content and result analysis.

[0069] In the simulation experiment of the present invention, the method of the present invention and two prior arts are used to perform wavelet threshold denoising on the test signal, simulated vehicle vibration signal, and real vehicle vibration data respectively, and three denoised signals are obtained.

[0070] To verify the simulation effect of the present invention, the signal-to-noise ratio (SNR) and root mean square error (RMSE) are used as the quality evaluation criteria for the denoised signal. The larger the SNR, the more thorough the noise removal. The smaller the RMSE, the smaller the error between the denoised signal and the original signal, and the better the denoising effect.

[0071] The signal-to-noise ratio and root mean square error are obtained by the following formula:

[0072]

[0073]

[0074] where SNR represents the signal-to-noise ratio, RMSE represents the root mean square error, s(i) represents the original pure signal, represents the denoised signal, N represents the signal length, and ∑ represents the summation operation.

[0075] In the simulation experiment of the present invention, the prior art adopted refers to:

[0076] Prior art 1 refers to the traditional soft threshold function and hard threshold function for the wavelet threshold function.

[0077] Prior art 2 refers to a microseismic signal denoising method based on an improved wavelet threshold function disclosed by Southwest University of Science and Technology in its patent document "Microseismic Signal Denoising Method Based on Improved Wavelet Threshold Function" (application number CN202110520815.2, publication number CN 113221746 A).

[0078] In order to verify the simulation effect of the present invention, the threshold function of the present invention is compared with the hard threshold function, the soft threshold function and the improved threshold function. The original signal of the test signal and its denoising effect diagram and evaluation index are shown in Figure 2. Figure 3 (a)-(f), as shown in Table 1.

[0079] Table 1 Comparison of SNR (dB) and RMSE of noisy test signals with different thresholds

[0080]

[0081] Figure 3 It is the signal graph after the test signal is denoised using different threshold functions. Figure 3 The horizontal axis represents the signal sampling point, and the vertical axis represents the amplitude of the signal. Figure 3 (a) represents the original test signal, Figure 3 (b) represents the noisy test signal after adding Gaussian white noise. Figure 3 (c) represents the test signal after denoising using the soft threshold function. Figure 3 (d) represents the test signal after denoising using the hard threshold function. Figure 3 (e) shows the test signal after denoising using the improved threshold function. Figure 3 (f) shows the test signal after denoising using the threshold function of the present invention. Figure 3 (c) and Figure 3 (d) It can be seen that the reconstructed signal after denoising by the soft and hard threshold functions produces offset and pseudo-Gibbs phenomenon. Figure 3 (e) and Figure 3 (f) It can be seen that the denoising effects of the two threshold functions are similar. The denoised signal is basically similar to the original signal, which is difficult to judge with the naked eye. Table 1 shows more detailed results. Table 1 shows a comparison table of SNR (dB) and RMSE of noisy test signals processed with different thresholds. The signal-to-noise ratio and root mean square error results calculated from Table 1 show that the threshold function used in the present invention has the highest signal-to-noise ratio SNR and the smallest root mean square error RMSE when processing the test signal, which reflects the practicality and more excellent denoising performance of the present invention.

[0082] In order to verify the simulation effect of the present invention, the threshold function of the present invention is compared with the hard threshold function, the soft threshold function and the improved threshold function, and the simulated vehicle vibration signal and its denoising effect diagram and evaluation index are shown in the following figure. Figure 4 (a)-(f), as shown in Table 2.

[0083] Table 2 Comparison of SNR (dB) and RMSE of simulated vehicle vibration signals with different thresholds

[0084]

[0085] Figure 4 These are signal graphs after denoising the simulated vehicle vibration signals using different threshold functions. Figure 4 In the figure, the abscissa represents the signal sampling points, and the ordinate represents the amplitude of the acceleration signal. Among them, Figure 4 (a) represents a section of simulated vehicle vibration signal. Figure 4 (b) represents the simulated vehicle vibration signal after adding Gaussian white noise. Figure 4 (c) represents the simulated vehicle vibration signal after denoising using the soft threshold function. Figure 4 (d) represents the simulated vehicle vibration signal after denoising using the hard threshold function. Figure 4 (e) represents the simulated vehicle vibration signal after denoising using the improved threshold function. Figure 4 (f) represents the simulated vehicle vibration signal after denoising using the threshold function of the present invention. It can be seen from Figure 4 that some effective signals are distorted after denoising with the soft threshold function. The denoising performance of the wavelet threshold function of the present invention is the best. This shows that the present invention also has good denoising ability for vehicle vibration signals. Table 2 shows more detailed results. Table 2 is a comparison table of the SNR (dB) and RMSE of the noisy simulated vehicle vibration signals processed by different thresholds. The calculated signal-to-noise ratio and root mean square error results in Table 2 show that when the threshold function adopted by the present invention is used to process the simulated vehicle vibration signals, the signal-to-noise ratio SNR is the highest and the root mean square error RMSE is the smallest, which reflects that the present invention also has good denoising ability for vehicle vibration signals.

[0086] To verify the simulation effect of the present invention, the threshold function of the present invention is compared with the hard threshold function, the soft threshold function, and the improved threshold function respectively. The real vehicle vibration signal and its denoising effect diagram are as shown in Figure 5 (a)-(e).

[0087] Figure 5 These are signal graphs after denoising the real vehicle vibration signals using different threshold functions. Figure 5 In the figure, the abscissa represents the signal time, and the ordinate represents the amplitude of the acceleration signal. Among them, Figure 5 (a) represents the original vehicle vibration signal. Figure 5 (b) represents the vehicle vibration signal after denoising using the hard threshold function. Figure 5 (c) represents the vehicle vibration signal after denoising using the soft threshold function. Figure 5 (d) represents the vehicle vibration signal after denoising using the improved threshold function. Figure 5 (e) represents the vehicle vibration signal after denoising using the threshold function of the present invention. Figure 5(b) It can be seen that the effective signal features are relatively completely retained, but the low-frequency noise in the non-signal section is not fully filtered out; from Figure 5 (c) It can be seen that the amplitudes of some effective signals are reduced and distorted, and the low-frequency noise in the non-signal section is not fully filtered out; from Figure 5 (d) It can be seen that the noise in the non-signal section is all filtered out, but the amplitudes of the effective signals are reduced and distorted; from Figure 5 (e) It can be seen that for the vehicle vibration signal denoised by using the threshold function of the present invention, the distortion of the effective signal is small, and the noise in the non-signal section is fully filtered out.

[0088] It can be seen therefrom that the threshold and threshold function adopted by the present invention have a good denoising effect when processing vehicle vibration signals, the distortion of the effective signal is small, the high and low frequency noises in the non-signal section can be fully filtered out, and the features of the effective signal in the vehicle vibration signal are well retained.

[0089] In summary, the present invention improves the denoising ability for vehicle vibration signals, and overcomes the problem that the reconstructed signal is distorted due to the constant deviation and breakpoints existing in the traditional hard and soft threshold functions. By denoising the noisy test signal, the simulated noisy vehicle vibration signal and the real vehicle vibration signal, the results show that the method of the present invention can further improve the signal-to-noise ratio of the denoised signal, reduce the root mean square error, and is very suitable for denoising vehicle vibration signals.

[0090] The above is only a preferred specific embodiment of the present invention, and does not constitute any limitation to the present invention. Obviously, for those skilled in the art, various modifications and changes can be made in terms of form and details under the idea and spirit of the present invention, but these modifications and changes based on the idea of the present invention are still within the protection scope of the claims of the present invention.

Claims

1. A vehicle vibration signal denoising method based on wavelet decomposition, characterized in that, Generate the threshold of each layer of wavelet coefficients and estimate the value of each layer of wavelet coefficients using the threshold. The steps of this denoising method are as follows: Step 1: Convert the noisy vehicle vibration signal into a discrete digital signal. Step 2: Perform five-layer wavelet decomposition on the discrete digital signal to obtain the wavelet coefficients of each layer. Step 3: Generate the threshold of each layer of wavelet coefficients according to the following formula: Among them, λ j represents the threshold of the j-th layer wavelet coefficient in the discrete digital signal, N j represents the length of the j-th layer wavelet coefficient in the discrete digital signal, δ j represents the standard variance of the noise of the j-th layer wavelet coefficient in the discrete digital signal; Step 4: Estimate the value of each layer of wavelet coefficients. Step 4.1: Determine whether each layer of wavelet coefficients is greater than the threshold of that layer. If so, determine the value of the wavelet coefficients of that layer as Otherwise, execute Step 4.2; where represents the value of the k-th wavelet coefficient of the j-th layer in the estimation of the discrete digital signal, w j,k represents the k-th wavelet coefficient of the j-th layer of the discrete digital signal, λ j represents the threshold of the wavelet coefficients of the j-th layer in the discrete digital signal. exp represents the exponential function with the natural constant e as the base, and β represents the shape adjustment factor, which is used to adjust the deviation between the estimated wavelet coefficients and the original wavelet coefficients; Step 4.2, determine whether each layer of wavelet coefficients is less than the negative value of the threshold of that layer. If so, determine the value of the wavelet coefficients of that layer as Otherwise, execute Step 4.3; Step 4.3, determine the value of each layer of wavelet coefficients except those in Step 4.1 and Step 4.2 as Step 5: Reconstruct the vehicle vibration signal: Perform inverse wavelet transform on the estimated value of each layer of wavelet coefficients, and form the denoised vehicle vibration signal by combining all the inverse-transformed values of each layer of wavelet coefficients.

2. The vehicle vibration signal denoising method based on wavelet decomposition according to claim 1, wherein, The standard deviation δ described in Step 3 j is obtained by the following formula: δ j = median(|w j,k |) / 0.6745 Among them, median represents the median value after the sequence is arranged in ascending order, and 0.6745 is the adjustment coefficient of the noise standard deviation.

3. The vehicle vibration signal denoising method based on wavelet decomposition according to claim 1, characterized in that The shape adjustment factor described in Step 4 is used to adjust the deviation between the estimated wavelet coefficients and the original wavelet coefficients. This factor is an integer within the range of [1, 30).

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