A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD

Abstract

This invention discloses a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD, belonging to the field of signal processing technology. The method involves wavelet packet decomposition of the original noisy signal to obtain sub-signals in multiple frequency bands. For each high-frequency sub-signal, a threshold is calculated according to a locally dynamically adjusted adaptive threshold rule, and an improved threshold function is used for threshold processing. Then, all processed sub-signals are reconstructed to obtain a preliminary purified signal. The preliminary purified signal is then subjected to EMD decomposition to obtain several Intrinsic Mode Function (IMF) components. This invention employs a collaborative denoising mechanism combining wavelet packet decomposition, adaptive threshold processing, and empirical mode decomposition, which can accurately suppress high-frequency noise in strongly interfering and non-stationary high-frequency piezoelectric signals while completely preserving signal impulse characteristics and key waveform information. It effectively improves the signal distortion and feature loss problems that easily occur in traditional denoising methods and significantly alleviates the EMD mode aliasing phenomenon.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD. Background Technology

[0002] Piezoelectric sensors, due to their advantages of high sensitivity, fast response speed, and strong micro-damage detection capability, have been widely used in geotechnical engineering monitoring. Existing research has shown that this technology has demonstrated good application potential in various fields such as slope displacement monitoring, landslide early warning systems, geological crack detection, and seismic vibration monitoring. However, in actual engineering environments, due to the complexity of blasting environments and numerous interference factors, the acquired piezoelectric signals are usually accompanied by strong noise and exhibit non-stationary, high-frequency dominant characteristics. The amplitude of multi-source interference, including blasting impact noise, electromagnetic interference, and sensor noise, often far exceeds the weak useful signal reflecting rock mass damage, causing it to be completely obscured. Therefore, efficient and accurate denoising of the signal is a prerequisite for subsequent feature extraction and analysis, and its denoising effect directly affects the accuracy and reliability of the piezoelectric signal analysis results.

[0003] Traditional signal denoising methods, such as single wavelet thresholding, while effective in processing non-stationary signals, are highly dependent on the selection of wavelet basis, decomposition level, and threshold function, lacking adaptability and prone to over-smoothing or loss of signal features during denoising. Empirical Mode Decomposition (EMD), although adaptive, easily leads to mode aliasing when directly performing EMD on the original signal in a noisy environment, making it difficult to effectively separate noise from valid signals. Therefore, how to extract valid signals with high fidelity from a noisy background has become a technical bottleneck in improving the reliability of blasting damage monitoring data. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD. The following technical solution is adopted: A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD includes the following steps: Step 1: Perform wavelet packet decomposition on the original noisy signal to obtain sub-signals in multiple frequency bands; Step 2: For each high-frequency sub-signal, calculate the threshold according to the adaptive threshold rule of local dynamic adjustment, and perform threshold processing using an improved threshold function. Then, reconstruct all processed sub-signals to obtain the preliminary purified signal. Step 3: Perform EMD decomposition on the preliminary purification signal to obtain several intrinsic mode function (IMF) components; Step 4: Calculate the correlation coefficient between each Intrinsic Mode Function (IMF) component and the preliminary purified signal, and select IMF components with correlation coefficients greater than a preset threshold. Step 5: Reconstruct the selected Intrinsic Mode Function (IMF) components to obtain the final denoised signal.

[0005] Optionally, step 1 can be performed as follows: the original noisy signal is decomposed into two parts, high frequency and low frequency, by performing three-level wavelet packet decomposition; the decomposed signal is reconstructed by low-pass filter coefficients and high-pass filter coefficients, wherein the low-pass filter coefficients and high-pass filter coefficients satisfy an orthogonal relationship; the decomposed signals of different decomposition levels are calculated using a recursive formula.

[0006] Optionally, the signal after three-level wavelet packet decomposition can be reconstructed using the following formula: ; The original signal before decomposition; For the decomposition of the first Layer Each node signal; The high-pass and low-pass filter coefficients satisfy an orthogonal relationship: ; These are the low-pass filter coefficients. These are the high-pass filter coefficients; The recursive formulas for decomposing signals at different decomposition levels are as follows: ; .

[0007] Optionally, step 2 includes the following sub-steps: Step 21: For each sub-signal, extract wavelet coefficients and independently calculate the noise standard deviation of each sub-signal. And calculate the corresponding threshold. ; Step 22, based on the number of decomposition layers pass By adjusting the threshold, thresholds at different decomposition scales are finally obtained. for:

[0008]

[0009] when hour, ; Step 23, the improved threshold function is a threshold function that introduces an exponential function and a double adjustment factor, and its expression is: ; In the formula, The wavelet coefficients of the original signal, For the threshold, The wavelet estimation coefficients for the denoised signal are a and b, which are adjustment factors. When a and b are both equal to 0, the function degenerates into a soft threshold function. When a is 0 and the value of b gradually increases, the function gradually approaches the hard threshold function. By changing the adjustment parameters a and b, the threshold function is adaptively adjusted. Step 24: Reconstruct all processed sub-signals to obtain the preliminary purified signal.

[0010] Optionally, the first and second adjustment factors of the dual adjustment factors are optimized using a grid search method with the objective function of maximizing the signal-to-noise ratio. The first adjustment factor is set to 0.1 and the second adjustment factor is set to 0.3.

[0011] Optionally, step 3, which involves performing empirical mode decomposition on the preliminary purified signal, includes the following sub-steps: Step 31: Perform EMD decomposition on the preliminary purification signal: Obtain the original signal All the maxima and minima are fitted into two envelopes using cubic spline functions. The mean of these two envelopes is then calculated. The original signal was obtained. with the mean Differences between Result: ; Step 32, Repeat step 31 as the new original signal until the... The function obtained this time By satisfying the two conditions of the IMF, the first intrinsic mode IMF function component of the original signal is obtained; Step 33, the initial purification signal Subtract the intrinsic mode IMF function components Obtain the remaining components For the remaining components Continue decomposing until the remaining components are obtained. Until further decomposition is no longer possible, several intrinsic mode IMF function components and residual components are obtained.

[0012] Optionally, the correlation coefficient in step 4 is the Pearson correlation coefficient, with a preset threshold of 0.05.

[0013] Optionally, the screening rule in step 4 is: retain intrinsic mode IMF function components with a correlation coefficient greater than 0.05, and remove intrinsic mode IMF function components with a correlation coefficient less than or equal to 0.05.

[0014] Optionally, the reconstruction method in step 5 is to sum up all the selected intrinsic mode IMF function components.

[0015] Optionally, high-frequency piezoelectric signal denoising is used for piezoelectric sensors. The original noisy signal is a high-frequency non-stationary signal collected by the piezoelectric sensor in geotechnical engineering monitoring, blasting vibration or landslide early warning scenarios, with a signal length of 4096 points.

[0016] In summary, the present invention has at least one of the following beneficial technical effects: This invention provides a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD. It adopts a collaborative denoising mechanism that combines wavelet packet decomposition, adaptive threshold processing and empirical mode decomposition. This method can accurately suppress high-frequency noise in high-frequency piezoelectric signals with strong interference and non-stationary conditions, while completely preserving the signal impact characteristics and key waveform information.

[0017] This method effectively improves the problems of signal distortion and feature loss that are prone to occur in traditional denoising methods, and significantly alleviates the EMD mode mixing phenomenon.

[0018] The overall solution is highly adaptable, requires no manual intervention, and can be stably adapted to complex engineering scenarios such as geotechnical engineering, blasting monitoring, and landslide early warning.

[0019] Compared with traditional denoising methods, this invention has a higher signal-to-noise ratio and a smaller root mean square error, significantly improving denoising accuracy and signal fidelity, and providing high-quality data support for subsequent signal feature extraction, damage identification and safety monitoring. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to the present invention. Figure 2 This is a three-layer wavelet packet decomposition diagram of a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to the present invention; Figure 3 This is a measured signal waveform diagram of a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to the present invention; Figure 4 This is a graph showing the correlation coefficients of each IMF component of the measured signal in a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to the present invention. Figure 5This is a comparison of the measured signal denoising effects before and after denoising using a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to the present invention. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings.

[0022] This invention discloses a high-frequency piezoelectric signal denoising method based on WPD-AT-EMD.

[0023] Reference Figures 1-5 Example 1: A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD, comprising the following steps: Step 1: Perform wavelet packet decomposition on the original noisy signal to obtain sub-signals in multiple frequency bands; Step 2: For each high-frequency sub-signal, calculate the threshold according to the adaptive threshold rule of local dynamic adjustment, and perform threshold processing using an improved threshold function. Then, reconstruct all processed sub-signals to obtain the preliminary purified signal. Step 3: Perform EMD decomposition on the preliminary purification signal to obtain several intrinsic mode function (IMF) components; Step 4: Calculate the correlation coefficient between each Intrinsic Mode Function (IMF) component and the preliminary purified signal, and select IMF components with correlation coefficients greater than a preset threshold. Step 5: Reconstruct the selected Intrinsic Mode Function (IMF) components to obtain the final denoised signal.

[0024] By adopting the above technical solution, a two-stage collaborative denoising mechanism combining coarse frequency domain denoising and fine time domain denoising is constructed. First, wavelet packet decomposition is performed on the original noisy high-frequency piezoelectric signal, splitting the signal into multiple sub-signals according to frequency bands, achieving preliminary separation of noise and effective signal. For each high-frequency sub-signal, local dynamic adaptive thresholding and an improved threshold function are used to complete denoising processing. Then, all processed sub-signals are reconstructed to obtain a preliminary purified signal. Empirical mode decomposition is performed on the preliminary purified signal to obtain a series of intrinsic mode function components. Effective components are selected by calculating the correlation coefficient between each component and the preliminary purified signal. Finally, the effective components are reconstructed to obtain the final denoised signal, achieving efficient and accurate denoising of high-frequency piezoelectric signals under strong interference.

[0025] In Example 2, the method of step 1 is as follows: the original noisy signal is decomposed into three-level wavelet packet decomposition, which decomposes the original signal into two parts: high frequency and low frequency; the decomposed signal is reconstructed by low-pass filter coefficients and high-pass filter coefficients, which satisfy an orthogonal relationship; the decomposed signals of different decomposition levels are calculated using a recursive formula.

[0026] By adopting the above technical solution, a three-layer wavelet packet decomposition is used as the basis for frequency domain processing. The original noisy signal is decomposed layer by layer into high-frequency and low-frequency sub-signals, allowing signals of different frequency components to be independently separated. The decomposition process uses low-pass and high-pass filter coefficients that satisfy orthogonality to ensure that signal energy is not leaked and information is not lost during decomposition and reconstruction. A pre-set recursive formula is used to standardize the signals at different decomposition layers, ensuring the accuracy and consistency of each layer's sub-signals and providing stable and reliable basic data for subsequent threshold processing.

[0027] Example 3: The signal after three-layer wavelet packet decomposition can be reconstructed using the following formula: ; The original signal before decomposition; For the decomposition of the first Layer Each node signal; The high-pass and low-pass filter coefficients satisfy an orthogonal relationship: ; These are the low-pass filter coefficients. These are the high-pass filter coefficients; The recursive formulas for decomposing signals at different decomposition levels are as follows: ; .

[0028] By employing the above technical solution, a complete decomposition and reconstruction of the signal is achieved based on the mathematical formula of three-layer wavelet packet decomposition. Using the original signal before decomposition as input, sub-signals at each node of each layer are calculated layer by layer. The low-pass and high-pass filter coefficients strictly satisfy the orthogonal constraint condition, ensuring the stability of the decomposition algorithm and the reconstruction accuracy. Signals from different decomposition layers are derived sequentially according to the recursive formula, realizing a complete transformation from the original signal to multiple layers of sub-signals, providing a clear mathematical basis and calculation path for subsequent adaptive thresholding processing.

[0029] Example 4, step 2 includes the following sub-steps: Step 21: For each sub-signal, extract wavelet coefficients and independently calculate the noise standard deviation of each sub-signal. And calculate the corresponding threshold. ; Step 22, based on the number of decomposition layers pass By adjusting the threshold, thresholds at different decomposition scales are finally obtained. for:

[0030]

[0031] when hour, ; Step 23, the improved threshold function is a threshold function that introduces an exponential function and a double adjustment factor, and its expression is: ; In the formula, The wavelet coefficients of the original signal, For the threshold, The wavelet estimation coefficients for the denoised signal are a and b, which are adjustment factors. When a and b are both equal to 0, the function degenerates into a soft threshold function. When a is 0 and the value of b gradually increases, the function gradually approaches the hard threshold function. By changing the adjustment parameters a and b, the threshold function is adaptively adjusted. Step 24: Reconstruct all processed sub-signals to obtain the preliminary purified signal.

[0032] By employing the above technical solution, wavelet coefficients are extracted independently for each sub-signal. The noise standard deviation is calculated based on the wavelet coefficients, and this is used to determine the initial threshold, ensuring that the threshold closely matches the actual noise level of each sub-signal. The threshold is dynamically adjusted based on the number of decomposition layers, allowing the threshold at different scales to adapt to signal characteristics and improving the targeting of noise suppression. An improved threshold function incorporating an exponential function and dual adjustment factors is used to process the wavelet coefficients, overcoming the shortcomings of traditional soft and hard threshold functions. Finally, all processed sub-signals are reconstructed to obtain a preliminary cleaned signal with significantly suppressed noise and complete retention of effective information.

[0033] In Example 5, the first and second adjustment factors of the dual adjustment factors were optimized using a grid search method with the objective function of maximizing the signal-to-noise ratio. The first adjustment factor was set to 0.1 and the second adjustment factor was set to 0.3.

[0034] By adopting the above technical solution, with the goal of maximizing the signal-to-noise ratio (SNR), a grid search method is used to traverse all combinations of dual adjustment factors. The SNR values ​​after denoising are compared for different combinations to select the optimal parameter combination. The first adjustment factor is set to 0.1, and the second adjustment factor is set to 0.3, so that the improved threshold function achieves the best balance between noise suppression and signal feature preservation, avoiding excessive signal smoothing or feature loss, and improving the overall denoising effect.

[0035] Example 6, the empirical mode decomposition method for the preliminary purified signal in step 3 includes the following sub-steps: Step 31: Perform EMD decomposition on the preliminary purification signal: Obtain the original signal All the maxima and minima are fitted into two envelopes using cubic spline functions. The mean of these two envelopes is then calculated. The original signal was obtained. with the mean Differences between Result: ; Step 32, Repeat step 31 as the new original signal until the... The function obtained this time By satisfying the two conditions of the IMF, the first intrinsic mode IMF function component of the original signal is obtained; Step 33, the initial purification signal Subtract the intrinsic mode IMF function components Obtain the remaining components For the remaining components Continue decomposing until the remaining components are obtained. Until further decomposition is no longer possible, several intrinsic mode IMF function components and residual components are obtained.

[0036] By employing the above technical solution, empirical mode decomposition (EMD) is performed on the initially purified signal. First, all maximum and minimum points of the signal are extracted. The upper and lower envelopes are fitted using cubic spline functions, and the mean of the envelopes is calculated, yielding the difference between the signal and the mean. This difference is used as a new signal for repeated iterative operations until the criterion for intrinsic mode functions (IMFs) is met, resulting in the first effective component. The obtained IMF components are then subtracted from the initially purified signal to obtain the remaining components. The decomposition operation continues on the remaining components until they become a monotonic sequence and cannot be further decomposed. Finally, all IMF components and residual components are obtained, completing the adaptive time-domain decomposition of the signal.

[0037] In Example 7, the correlation coefficient in step 4 is the Pearson correlation coefficient, and the preset threshold is 0.05.

[0038] By adopting the above technical solution, the Pearson correlation coefficient is used as a quantitative indicator to measure the degree of linear correlation between each intrinsic mode function component and the preliminary purified signal. The higher the correlation coefficient, the more effective signal information the component contains. A preset threshold of 0.05 is set as the correlation judgment threshold to distinguish effective signal components from noise-dominant components, thereby standardizing and quantifying the screening process and avoiding errors caused by human experience judgment.

[0039] In Example 8, the screening rule in step 4 is: retain the intrinsic mode IMF function components with a correlation coefficient greater than 0.05, and remove the intrinsic mode IMF function components with a correlation coefficient less than or equal to 0.05.

[0040] By employing the above technical solution, component screening is performed according to preset correlation screening rules. Intrinsic mode function components with a correlation coefficient greater than 0.05 with the initially purified signal are retained; these components contain a large number of valid signal features. Components with a correlation coefficient less than or equal to 0.05 are removed, as these components mainly contain invalid information such as noise and baseline drift. Through precise screening to remove residual interference, signal purity is further improved, providing high-quality components for final reconstruction.

[0041] In Example 9, the reconstruction method in step 5 is to sum up all the selected intrinsic mode IMF function components.

[0042] By employing the above technical solution, the final signal reconstruction is completed using a linear superposition method. All selected and retained effective intrinsic mode function components are sequentially superimposed to reconstruct the complete time-domain signal. The superposition process fully preserves the amplitude, phase, and waveform characteristics of each effective component. While effectively suppressing noise, it maximizes the preservation of the impact characteristics and key information of the high-frequency piezoelectric signal, resulting in a final denoised signal that meets the requirements of engineering analysis.

[0043] Example 10: High-frequency piezoelectric signal denoising for piezoelectric sensors. The original noisy signal is a high-frequency non-stationary signal collected by the piezoelectric sensor in geotechnical engineering monitoring, blasting vibration, or landslide early warning scenarios, with a signal length of 4096 points.

[0044] By adopting the above technical solution, and targeting highly interference-prone engineering scenarios such as geotechnical engineering monitoring, blasting vibration monitoring, and landslide early warning, this solution adapts to high-frequency non-stationary piezoelectric signals collected by piezoelectric sensors. The signal length is fixed at 4096 points to match the parameters of conventional acquisition equipment. Addressing the characteristics of this type of signal—high noise, non-stationarity, and weak effective signal—a two-stage collaborative denoising method is applied to achieve high-fidelity extraction of weak damage signals in complex environments, providing reliable data support for subsequent signal feature analysis, structural damage identification, and safety early warning.

[0045] The following specific embodiments illustrate the implementation principle of the present invention: This application is used in blasting monitoring scenarios in geotechnical engineering. A piezoelectric sensor acquires signals at a sampling frequency of 2MHz, with a signal length of 4096 points. The original signal amplitude ranges from -0.02 to 0.03. Follow the steps below to implement the process completely and provide specific calculated values. Figure 3 This is a waveform of the original noisy high-frequency piezoelectric signal acquired by a piezoelectric sensor. The horizontal axis represents time in seconds, and the vertical axis represents the signal amplitude. The signal sampling frequency is 2MHz, the length is 4096 points, and the amplitude range is between -0.02 and 0.03. The signal exhibits obvious non-stationary characteristics, accompanied by a large number of high-frequency noise spikes. The effective signal characteristics are covered by noise interference, intuitively reflecting the original state of the piezoelectric signal under strong interference engineering scenarios.

[0046] Step 1, three-layer wavelet packet decomposition; The original noisy signal is decomposed into high-frequency and low-frequency components layer by layer, and finally 8 frequency band sub-signals are obtained.

[0047] The decomposition uses orthogonal low-pass and high-pass filter coefficients to satisfy the orthogonal constraint condition.

[0048] The signals of each node in the third layer are calculated using the recursive formula, and the signals of the eight nodes in the third layer are denoted as X3.0, X3.1, X3.2, X3.3, X3.4, X3.5, X3.6, and X3.7.

[0049] X3.1, X3.2, X3.3, X3.5, X3.6, and X3.7 are high-frequency sub-signals, while X3.0 and X3.4 are low-frequency sub-signals.

[0050] Figure 2 This diagram illustrates the three-layer wavelet packet decomposition structure used in this method. The original signal is used as input and sequentially decomposed layer by layer through low-pass and high-pass filtering. The first layer yields two node signals, the second layer yields four node signals, and the third layer yields eight node signals. The node signals at each layer are recursively calculated using the corresponding low-pass and high-pass filter coefficients. The filter coefficients satisfy orthogonal constraints. This decomposition structure can uniformly divide the original high-frequency piezoelectric signal into different frequency bands, obtaining high-frequency and low-frequency sub-signals, providing a frequency domain partitioning basis for subsequent adaptive threshold denoising.

[0051] Step 2, Adaptive threshold processing and preliminary reconstruction; Step 21: Calculate the noise standard deviation and the initial threshold; Extract the wavelet coefficients of each high-frequency sub-signal and calculate the noise standard deviation independently.

[0052] Taking the X3.1 sub-signal as an example, the maximum value of the wavelet coefficients is 0.012, the minimum value is -0.011, and the calculated noise standard deviation is 0.0021.

[0053] The initial threshold was calculated as three times the noise standard deviation, resulting in an initial threshold of 0.0063.

[0054] Step 22: Adjust the threshold according to the number of decomposition layers; With the decomposition layer number i set to 3, and substituting it into the scaling formula, the final threshold is 0.0051.

[0055] The remaining high-frequency sub-signals were calculated using the same method, yielding thresholds of 0.0048, 0.0053, 0.0049, 0.0050, and 0.0052, respectively.

[0056] Step 23, improve threshold function processing; The improved threshold function uses two adjustment factors, a=0.1 and b=0.3.

[0057] Taking wavelet coefficients of 0.010 and threshold of 0.0051 as an example, substituting them into the function yields an estimated coefficient of 0.0072.

[0058] With wavelet coefficients of -0.009 and threshold of 0.0051, the estimated coefficient is -0.0065.

[0059] All wavelet coefficients of high-frequency sub-signals are corrected using this method.

[0060] Step 24, initial reconstruction; The processed high-frequency sub-signal is reconstructed together with the original low-frequency sub-signal to obtain the preliminary purified signal.

[0061] The initial purification signal amplitude ranges from -0.018 to 0.025, and noise spikes are significantly reduced.

[0062] Step 3: EMD decomposition yields IMF components; EMD decomposition is performed on the preliminary purification signal, extreme points are extracted sequentially, and the upper and lower envelopes are fitted with cubic spline functions and the mean is calculated.

[0063] The iteration yielded nine IMF components, namely IMF1 to IMF9, and one residual component r.

[0064] The amplitudes of each IMF component decrease sequentially, with IMF1 ranging from -0.008 to 0.009 and IMF9 ranging from -0.001 to 0.0012.

[0065] Step 4: Correlation coefficient calculation and component selection; The Pearson correlation coefficients between each IMF component and the preliminary purified signal were calculated, and the results are as follows: IMF1:0.72,IMF2:0.65,IMF3:0.58,IMF4:0.43,IMF5:0.31,IMF6:0.04,IMF7:0.03,IMF8:0.02,IMF9:0.08.

[0066] The preset threshold is 0.05. IMF1, IMF2, IMF3, IMF4, IMF5, and IMF9 are retained, while IMF6, IMF7, and IMF8 are removed.

[0067] Step 5, final reconstruction and result values; The six retained IMF components are linearly superimposed and summed to obtain the final denoised signal.

[0068] The final denoised signal amplitude ranges from -0.017 to 0.024, and the waveform is smooth and glitch-free.

[0069] The final signal-to-noise ratio (SNR) was calculated to be 18.15 dB, the root mean square error (RMSE) was 0.000934, the key impulse peaks of the signal were fully preserved, and the noise suppression effect was optimal.

[0070] Figure 4 This diagram illustrates the correlation coefficient distribution between the IMF components and the initial purified signal after EMD decomposition. The horizontal axis represents the IMF component number, and the vertical axis represents the correlation coefficient value. The dashed line in the diagram represents the preset correlation coefficient threshold of 0.05. IMF components with a correlation coefficient greater than 0.05 are marked as valid components, while IMF components with a correlation coefficient less than 0.05 are determined to be noise-dominant components. This visually demonstrates the selection criteria and distribution results for valid and invalid IMF components.

[0071] Figure 5 This image shows a waveform comparison between the original noisy signal and the denoised signal obtained using this method. The left side shows the original signal waveform, and the right side shows the denoised signal waveform processed by this method. The horizontal axis represents time, and the vertical axis represents signal amplitude. The comparison clearly shows that the high-frequency noise spikes in the denoised signal are completely removed, resulting in a smoother and more regular waveform. At the same time, key features of the original signal, such as peak values ​​and waveform morphology, are fully preserved, visually demonstrating the technical effectiveness of this method in suppressing high-frequency noise while faithfully preserving the effective signal.

[0072] The SNR and RMSE comparison results of the high-frequency piezoelectric signal denoising method based on WPD-AT-EMD of this invention with different denoising methods are shown in Table 1: Table 1

[0073] The SNR of the method of this invention reaches 18.15dB, which is the highest among all methods, indicating that the purity and effective information retention of the signal after denoising are optimal.

[0074] The RMSE corresponding to the method of this invention is as low as 0.000934, which is the lowest among all methods, indicating that the deviation between the denoised signal and the ideal signal is the smallest and the signal fidelity is the highest.

[0075] As the number of wavelet packet decomposition layers increases, the SNR gradually decreases while the RMSE gradually increases, indicating that 3 layers is the optimal number of decomposition layers.

[0076] The adaptive thresholding method used in this invention significantly outperforms the general thresholding method and traditional soft and hard thresholding wavelet denoising methods, fully validating WPD. AT The technical advantages of the EMD combination solution in high-frequency piezoelectric signal denoising scenarios.

[0077] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD, characterized in that, Includes the following steps: Step 1: Perform wavelet packet decomposition on the original noisy signal to obtain sub-signals in multiple frequency bands; Step 2: For each high-frequency sub-signal, calculate the threshold according to the adaptive threshold rule of local dynamic adjustment, and perform threshold processing using an improved threshold function. Then, reconstruct all processed sub-signals to obtain the preliminary purified signal. Step 3: Perform EMD decomposition on the preliminary purification signal to obtain several intrinsic mode function (IMF) components; Step 4: Calculate the correlation coefficient between each Intrinsic Mode Function (IMF) component and the preliminary purified signal, and select IMF components with correlation coefficients greater than a preset threshold. Step 5: Reconstruct the selected Intrinsic Mode Function (IMF) components to obtain the final denoised signal.

2. The high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 1, characterized in that: Step 1 involves performing a 3-level wavelet packet decomposition on the original noisy signal, dividing it into high-frequency and low-frequency components. The decomposed signal is then reconstructed using low-pass and high-pass filter coefficients, which are orthogonal. The decomposed signals at different decomposition levels are calculated using a recursive formula.

3. The high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 2, characterized in that: The signal after three-level wavelet packet decomposition can be reconstructed using the following formula: ； The original signal before decomposition; For the decomposition of the first Layer Each node signal; The high-pass and low-pass filter coefficients satisfy an orthogonal relationship: ； These are the low-pass filter coefficients. These are the high-pass filter coefficients; The recursive formulas for decomposing signals at different decomposition levels are as follows: ； 。 4. The high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 3, characterized in that: Step 2 includes the following sub-steps: Step 21: For each sub-signal, extract wavelet coefficients and independently calculate the noise standard deviation of each sub-signal. And calculate the corresponding threshold. ; Step 22, based on the number of decomposition layers pass By adjusting the threshold, thresholds at different decomposition scales are finally obtained. for: ； ； when hour, ; Step 23, the improved threshold function is a threshold function that introduces an exponential function and a double adjustment factor, and its expression is: ； In the formula, The wavelet coefficients of the original signal, For the threshold, The wavelet estimation coefficients for the denoised signal are a and b, which are adjustment factors. When a and b are both equal to 0, the function degenerates into a soft threshold function. When a is 0 and the value of b gradually increases, the function gradually approaches the hard threshold function. By changing the adjustment parameters a and b, the threshold function is adaptively adjusted. Step 24: Reconstruct all processed sub-signals to obtain the preliminary purified signal.

5. A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 4, characterized in that: The first and second adjustment factors of the dual adjustment factors were optimized using a grid search method with the objective function of maximizing the signal-to-noise ratio. The first adjustment factor was set to 0.1 and the second adjustment factor was set to 0.

3.

6. The high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 5, characterized in that: Step 3, which involves performing empirical mode decomposition on the preliminary purified signal, includes the following sub-steps: Step 31: Perform EMD decomposition on the preliminary purification signal: Obtain the original signal All the maxima and minima are fitted into two envelopes using cubic spline functions. The mean of these two envelopes is then calculated. The original signal was obtained. with the mean Differences between Result: ; Step 32, will Repeat step 31 as the new original signal until the... The function obtained this time By satisfying the two conditions of the IMF, the first intrinsic mode IMF function component of the original signal is obtained; Step 33, the initial purification signal Subtract the intrinsic mode IMF function components Obtain the remaining components For the remaining components Continue decomposing until the remaining components are obtained. Until further decomposition is no longer possible, several intrinsic mode IMF function components and residual components are obtained.

7. A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 6, characterized in that: In step 4, the correlation coefficient is the Pearson correlation coefficient, and the preset threshold is 0.

05.

8. A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 7, characterized in that: The screening rule in step 4 is: retain intrinsic mode IMF function components with a correlation coefficient greater than 0.05, and remove intrinsic mode IMF function components with a correlation coefficient less than or equal to 0.

05.

9. A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 8, characterized in that: The reconstruction method in step 5 is to sum up all the selected intrinsic mode IMF function components.

10. A high-frequency piezoelectric signal denoising method based on WPD-AT-EMD according to claim 9, characterized in that: High-frequency piezoelectric signal denoising for piezoelectric sensors: The original noisy signal is a high-frequency non-stationary signal collected by the piezoelectric sensor in geotechnical engineering monitoring, blasting vibration or landslide early warning scenarios, with a signal length of 4096 points.

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