Signal processing method combining adaptive spectrum enhancement signal extension and focused learnable wavelet packet transformation
By combining adaptive spectral enhancement signal extension and focused learnable wavelet packet transform, the problem of handling sudden impulse noise in complex industrial signals is solved, achieving adaptive signal filling and efficient denoising, and ensuring the consistency of the signal's time-frequency characteristics and the effectiveness of the model.
Patent Information
- Application Number
- CN202511743234.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-25
- Publication Date
- 2026-03-06
AI Technical Summary
Existing technologies struggle to effectively handle sudden impulse noise in complex industrial signals, especially in unsupervised learning scenarios. Signal filling methods introduce boundary discontinuities or spectral distortion, affecting the accuracy of subsequent signal analysis. Furthermore, learnable wavelet packet transforms are sensitive to the quality and length of input data, leading to learning artifacts in the filling model.
By combining Adaptive Spectral Enhancement Signal Spreading (ASE-SE) with Focused Learnable Wavelet Packet Transform (LWPT-Focus), a consistent spread sequence is generated through adaptive analysis of signal end features, boundary smoothing, and spectral information constraints. During training, the filled regions are masked to ensure the model optimizes denoising performance and avoids learning filled artifacts.
It achieves accurate and adaptive denoising of signals of arbitrary length in complex impulse noise environments, eliminating boundary abrupt changes and spectral distortion caused by traditional padding, and improving the accuracy of signal analysis and the denoising effect of the model.
Smart Images
Figure CN121614843A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing technology, and specifically relates to a signal processing method that combines adaptive spectral enhancement signal expansion and focused learnable wavelet packet transform. Background Technology
[0002] Currently, in the field of industrial process monitoring and equipment health management, especially for core components such as the power and lubrication systems of ocean-going vessels, the acquisition and analysis of operating signals through sensors is a key means to ensure safety and efficiency. However, these actually acquired industrial signals generally have significant non-stationary characteristics, and due to factors such as the sensors themselves, transmission links, and harsh ship operating environments (such as strong vibrations, high temperatures, and high humidity), the signals are often mixed with sudden, high-amplitude impulse noise. This complex signal characteristic poses a severe challenge to subsequent accurate analysis, condition assessment, and predictive maintenance, and existing technologies have shown significant shortcomings in processing such signals. Traditional analysis methods based on Fourier transform or standard wavelet transform are often based on the assumption that the signal is stationary or locally stationary, making it difficult to effectively capture and process the non-stationary dynamic characteristics of the signal, which may lead to problems such as spectral aliasing, loss of low-frequency trend information, or the introduction of high-frequency processing artifacts. While researchers have proposed adaptive signal decomposition techniques such as Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) to better handle non-stationary signals, in practical applications, the forward decomposition process of these methods may lead to partial leakage of future information, thereby compromising the causal relationships and prediction accuracy of time series analysis. Wavelet Packet Transform (WPT) offers more flexible time-frequency localization analysis capabilities, but its denoising performance is highly dependent on the selection of the threshold function and the precise setting of the threshold. This process often requires tedious manual adjustments and is difficult to adaptively handle complex and variable real-world noise environments. In recent years, data-driven methods such as Learnable Wavelet Packet Transform (LWPT) have emerged, using neural networks to learn transform parameters or thresholds, improving the ability to handle non-stationary signals to some extent. However, these methods are usually sensitive to the quality of the input data, and their design goals often focus more on sparse signal representation than simple denoising. More importantly, methods such as LWPT typically have strict limitations on the length of the input signal (e.g., requiring a signal length of...). The requirement that signals must be an integer multiple of their length makes them unsuitable for directly processing variable-length signals commonly encountered in practical engineering. To overcome this signal length limitation, the original signal must be padded or extended before applying techniques such as LWPT. However, existing signal padding techniques also have significant drawbacks and cannot adequately meet the needs of subsequent precise analysis. For example, simple zero-padding or nearest-value padding introduces artificial abrupt changes at signal splicing points, causing boundary discontinuities and severely damaging the signal's inherent spectral structure and statistical properties. While symmetric padding can ensure a smooth boundary transition to some extent, the repetitive data patterns it introduces may mislead subsequent adaptive or learning models (especially in unsupervised learning scenarios lacking label information), causing them to incorrectly learn the noise characteristics or periodic artifacts of the padded portion, rather than the true dynamics of the original signal. Related research has also clearly pointed out that inappropriate signal extension can produce significant edge effects on subsequent processing such as wavelet analysis. Therefore, the existing technical system lacks a method that can effectively maintain the temporal continuity and frequency domain consistency of non-stationary, noisy signals (especially signals with burst impulse noise) during the padding and extension process. The shortcomings of this padding technique, combined with the sensitivity of the aforementioned advanced denoising techniques (such as LWPT) to the quality and length of input data, form a technical bottleneck. Especially in the context of unsupervised learning, how to coordinate the signal padding fidelity with the effectiveness of subsequent denoising model training (ensuring that the model focuses on the real signal rather than padding artifacts) is a key technical challenge that urgently needs to be solved for complex industrial signal processing applications. Summary of the Invention
[0003] Existing methods struggle to effectively remove the common, sudden, high-amplitude impulse noise found in industrial non-stationary time series signals. This type of noise (such as noise in marine lubrication system signals) poses challenges to signal analysis and subsequent applications (such as predictive maintenance). Signal padding or expansion is necessary before applying certain signal processing techniques (such as wavelet packet transform), but traditional padding methods suffer from problems like discontinuous entry boundaries or spectral distortion. These issues can interfere with the accuracy of subsequent signal analysis (such as denoising), especially in unsupervised scenarios where a clean signal is lacking as a reference. When using padded data to train unsupervised denoising models (such as LWPT), there is a risk that the model will learn the noise or artifacts introduced by the padding, failing to fully focus on the true characteristics of the original signal.
[0004] To address the aforementioned technical problems, this invention provides a signal processing method combining adaptive spectral enhancement signal spreading and focused learnable wavelet packet transform, comprising the following steps:
[0005] Step 1: Fill or expand the non-stationary noisy time series, i.e. the original time series signal. By adaptively analyzing the signal end features and combining spectral information constraints and boundary smoothing techniques, the splicing region between the end of the original signal and the generated expanded sequence is smoothed to generate an expanded sequence with the same time-frequency characteristics as the original signal and natural boundaries, thus realizing adaptive spectral enhancement signal expansion ASE-SE.
[0006] Step 2: The extended sequence is used as input and normalized first. The learnable wavelet packet transform (LWPT) model is then trained. A focused training mechanism is introduced during the training process. This mechanism ensures that the model optimization focuses on the denoising of the original signal by shielding the filled region when calculating the loss function, thereby avoiding learning the filled artifact and obtaining the trained learnable wavelet packet transform (LWPT) model.
[0007] Step 3: After processing the non-stationary noisy time series to be processed (i.e., the new signal or the original signal) using the extended method in Step 1, input it into the trained learnable wavelet packet transform (LWPT) model (i.e., the denoising model) for decomposition, thresholding, and reconstruction to obtain the final denoised signal, thus completing the signal processing.
[0008] Furthermore, the specific method for filling or expanding the non-stationary noisy time series in step 1 is as follows:
[0009] First, feature detection and analysis are performed on the end segments of the original time-series signal that need to be expanded, including calculating the local mean. First, calculate the local standard deviation; then, calculate the variance of the terminal stability window, evaluate the stability of the endpoints based on variance analysis, and then, based on the stability determination results, use a conditional expansion strategy to obtain the expanded sequence. Specifically:
[0010] 1) If a significant trend is detected, then an exponentially decaying linear extrapolation method is applied for expansion, with the expansion point... value It can be calculated by the following formula (1):
[0011]
[0012] in , The coefficients are obtained from linear regression of the original signal. It is the attenuation factor. It is the mean of the last segment of the original signal. and These are weighting factors that collectively ensure that the extrapolated value converges to the mean at infinity. ;
[0013] 2) If no significant trend is detected, an autoregressive AR model is fitted and used to predict the extended sequence. At the same time, the predicted values are constrained by spectral characteristics and the noise level is adjusted. The order of the AR model can be automatically determined by the information criterion AIC.
[0014] Furthermore, in step 1, the splicing region between the end of the original signal and the generated extended sequence is smoothed. Specifically,
[0015] Determining the length of the transition region using the autocorrelation function and overlap length Furthermore, a weighted fusion method based on sine function and cosine window is applied to ensure smooth boundary transition; transition region points value It can be calculated using the following formula (2):
[0016]
[0017] in, It is the value of the last point in the overlapping portion of the original signal. It is the value of the first point in the extended sequence. It is the value of the i-th point in the transition region;
[0018] As a further enhancement of the spectral information constraint and boundary smoothing techniques, a mean filter can be selectively applied to the spliced signal to remove possible outliers, and a low-pass filter (such as a Butterworth filter) with a cutoff frequency adaptively determined according to the centroid of the signal power spectral density (PSD) can be applied to further smooth the signal and suppress high-frequency disturbances, ultimately obtaining an extended signal with the required length and highly consistent characteristics with the original signal.
[0019] Furthermore, in step 2, the learnable wavelet packet transform (LWPT) model is trained, specifically as follows:
[0020] The signal after ASE-SE expansion is used as input;
[0021] First, a reversible normalization process is applied to the input signal to transform the signal... At the point of time raw value Standardized to As shown in equation (3):
[0022] in and It is a signal The mean and standard deviation are calculated from the valid (unfilled) region. This is a small constant added to prevent division by zero; the normalization operation can be reversed after processing to restore the original scale;
[0023] Then, the learnable wavelet packet transform (LWPT) is used to perform multi-scale decomposition on the normalized extended signal to obtain a series of sub-band coefficients of different frequency bands. LWPT uses a trainable filter bank for decomposition.
[0024] For the sub-band coefficients obtained from the decomposition An adaptive threshold function is applied to obtain the processed coefficients. The threshold function has learnable parameters (such as bias terms). The threshold function is optimized through training to suppress noise components while preserving the main features of the signal. The threshold function is shown in equation (4).
[0025] in, (⋅) is the Sigmoid activation function. These are hyperparameters that control the slope (e.g.) =10), usually can be set to = Use the sub-band coefficients after thresholding. The signal is reconstructed through the inverse transform of LWPT.
[0026] Furthermore, the training strategy involves employing a slicing masking mechanism (i.e., the focused training mechanism described in step 2) during unsupervised training (e.g., based on minimizing reconstruction error). While the forward and backward propagation calculations utilize the complete extended signal, a slicing masking mechanism is used when calculating the loss function. This mechanism considers only the reconstruction error of the corresponding part of the original signal, ignoring the error of the padded part. This ensures that the optimization of model parameters focuses on improving the denoising performance of the real signal, avoiding performance degradation due to learning artifacts in the padded part.
[0027] The advantages of this invention are:
[0028] This solution effectively addresses a core challenge in non-stationary signal processing by combining Adaptive Spectral Enhancement Signal Spreading (ASE-SE) with Focused Learnable Wavelet Packet Transform (LWPT-Focus). First, ASE-SE utilizes an autoregressive model and boundary smoothing strategies to overcome the strict limitations of traditional wavelet transforms on signal length and eliminate boundary abrupt changes and spectral distortion caused by conventional padding, ensuring the physical consistency of the extended signal's time-frequency characteristics. Building upon this, a focused training mechanism (slice masking mechanism) is introduced. This method forces the model to ignore padding regions during unsupervised training, fundamentally avoiding the risk of the model "mislearning" artificially synthesized artifacts. Combined with LWPT's adaptive threshold learning capability, it achieves accurate and adaptive denoising of signals of arbitrary length in complex impulse noise environments, overcoming the limitations of existing technologies where manual parameter tuning is cumbersome and denoising performance is easily affected by padding noise. Attached Figure Description
[0029] Figure 1 This is a schematic diagram of the signal filling process combining ASE-SE filling and LWPT-Focus denoising provided in the embodiments disclosed in this invention;
[0030] Figure 2 This is a schematic diagram of the learnable wavelet packet transform (LWPT-Focus) framework that incorporates slice loss calculation. Detailed Implementation
[0031] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.
[0032] refer to Figure 1 This invention provides a signal processing method combining adaptive spectral enhancement signal spreading and focused learnable wavelet packet transform, comprising the following steps:
[0033] Step 1: Fill or expand the non-stationary noisy time series, i.e. the original time series signal. By adaptively analyzing the characteristics of the signal end, and combining spectral information constraints and boundary smoothing techniques, the splicing region between the end of the original signal and the generated expanded sequence is smoothed to generate an expanded sequence that is highly consistent with the time-frequency characteristics of the original signal and has natural boundaries, thus realizing adaptive spectral enhancement signal expansion ASE-SE.
[0034] In this embodiment, the specific method for filling or expanding the non-stationary noisy time series is as follows:
[0035] First, feature analysis is performed on the end segments of the original time-series signal that need to be expanded, including calculating the local mean. First, calculate the local standard deviation; then, calculate the variance of the terminal stability window, evaluate the endpoint stability based on variance analysis, and obtain the expanded sequence using a conditional expansion strategy based on the stability determination results.
[0036] 1) If a significant trend is detected, then an exponentially decaying linear extrapolation method is applied for expansion, with the expansion point... value It can be calculated by the following formula (1):
[0037]
[0038] in , The coefficients are obtained from linear regression of the original signal. It is the attenuation factor. It is the mean of the last segment of the original signal;
[0039] 2) If no significant trend is detected, an autoregressive AR model is fitted and used to predict the extended sequence. At the same time, the predicted values are constrained by spectral characteristics and the noise level is adjusted. The order of the AR model can be automatically determined by the information criterion AIC.
[0040] As an improvement to the scheme, step 1 involves smoothing the splicing region between the end of the original signal and the generated extended sequence. Specifically:
[0041] Determining the length of the transition region using the autocorrelation function and overlap length Furthermore, a weighted fusion method based on sine function and cosine window is applied to ensure smooth boundary transition; transition region points value It can be calculated using the following formula (2):
[0042]
[0043] in, It is the value of the last point in the overlapping portion of the original signal. It is the value of the first point in the extended sequence;
[0044] As a further enhancement of the spectral information constraint and boundary smoothing techniques, a mean filter can be selectively applied to the spliced signal to remove possible outliers, and a low-pass filter (such as a Butterworth filter) with a cutoff frequency adaptively determined according to the centroid of the signal power spectral density (PSD) can be applied to further smooth the signal and suppress high-frequency disturbances, ultimately obtaining an extended signal with the required length and highly consistent characteristics with the original signal.
[0045] Table 1 shows the effectiveness of the ASE-SE signal padding method in maintaining signal consistency.
[0046]
[0047] Step 2: The extended sequence is used as input and normalized first. The learnable wavelet packet transform (LWPT) model is then trained. A focused training mechanism is introduced during the training process. This mechanism ensures that the model optimization focuses on the denoising of the original signal by shielding the filled region when calculating the loss function, thereby avoiding learning the filled artifact and obtaining the trained learnable wavelet packet transform (LWPT) model.
[0048] Specifically, the trainable wavelet packet transform (LWPT) model is performed as follows:
[0049] The signal after ASE-SE expansion is used as input;
[0050] First, a reversible normalization process is applied to the input signal to transform the signal... At the point of time raw value Standardized to As shown in equation (3):
[0051] in and It is a signal The mean and standard deviation are calculated from the valid (unfilled) region. This is a small constant added to prevent division by zero; the normalization operation can be reversed after processing to restore the original scale;
[0052] Then, the normalized extended signal is decomposed into multiple scales using Learnable Wavelet Packet Transform (LWPT) to obtain a series of sub-band coefficients of different frequency bands. LWPT uses a trainable filter bank for decomposition.
[0053] For the sub-band coefficients obtained from the decomposition An adaptive threshold function is applied to obtain the processed coefficients. The threshold function has learnable parameters (such as bias terms). The threshold function is optimized through training to suppress noise components while preserving the main features of the signal. The threshold function is shown in equation (4).
[0054] in, (⋅) is the Sigmoid activation function. These are hyperparameters that control the slope (e.g.) =10), usually can be set to = Use the subband coefficients after thresholding. The signal is reconstructed through the inverse transform of LWPT.
[0055] The training strategy involves employing a slicing and masking mechanism (i.e., the focused training mechanism described in step 2) during unsupervised training (e.g., based on minimizing reconstruction error). While the forward and backward propagation calculations utilize the complete extended signal, a slicing and masking mechanism is used when calculating the loss function. This mechanism considers only the reconstruction error of the corresponding part of the original signal, ignoring the error of the padded part. This ensures that the optimization of model parameters focuses on improving the denoising performance of the real signal, avoiding performance degradation due to learning artifacts in the padded part.
[0056] Step 3: After processing the non-stationary noisy time series (i.e., the new signal or the original signal) using the extended method in Step 1, input it into the trained denoising model for decomposition, thresholding, and reconstruction to obtain the final denoised signal, thus completing the signal processing. Table 2 shows the denoising performance metrics obtained on the three datasets.
[0057]
[0058] Table 2: LWPT-Focus noise reduction performance metrics.
[0059] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A signal processing method combining adaptive spectral enhancement signal expansion and focused learnable wavelet packet transform, characterized by: The method comprises the following steps: Step 1: filling or extending a non-stationary noise-containing time series, i.e. an original time series signal, smoothing a splicing area between an end of the original signal and a generated extended sequence by adaptively analyzing signal end characteristics and combining spectrum information constraints and boundary smoothing techniques, generating an extended sequence with consistent time-frequency characteristics and natural boundaries, and realizing adaptive spectrum enhancement signal extension ASE-SE; Step 2: taking the extended sequence as input, first performing normalization processing, and training a learnable wavelet packet transform LWPT model; A focused training mechanism is introduced in the training process to obtain the trained learnable wavelet packet transform LWPT model; Step 3: after the non-stationary noise-containing time series to be processed is processed by the above-mentioned extension method, the trained learnable wavelet packet transform LWPT model is input for decomposition, threshold processing and reconstruction to obtain a final denoising signal, and signal processing is completed.
2. The signal processing method of claim 1, wherein the adaptive spectral enhancement signal expansion and focusing learning wavelet packet transform is combined. The specific way of filling or extending the non-stationary noise-containing time series in step 1 is: First, the end piece of the original time series signal to be extended is analyzed by feature detection, including calculating local mean and local standard deviation; then, the variance of the end stable window is calculated, the end point stability is evaluated according to the variance analysis, and then, according to the stability determination result, the extended sequence is obtained by using conditional extension strategy, specifically: 1) if a significant trend is detected, the linear extrapolation method with exponential decay is applied for extension, and the value of the extension point can be calculated by formula (1): （1） wherein , is a coefficient obtained by linear regression of the end of the original signal, is a decay factor, is the mean of the end segment of the original signal, and are weighting factors, which together ensure that the extrapolated value converges to the mean at infinity ; 2) If no significant trend is detected, an autoregressive AR model is fitted, and the model is used to predict the extended sequence, while the predicted value is subjected to spectrum characteristic constraints and noise level adjustment; the order of the AR model is automatically determined by the information criterion AIC.
3. The signal processing method of claim 1, wherein the adaptive spectral enhancement signal spreading and focusing learning wavelet packet transform is combined. In step 1, the splicing area between the end of the original signal and the generated extended sequence is smoothed, specifically, Determining the length of the transition region using the autocorrelation function and overlap length Furthermore, a weighted fusion method based on sine function and cosine window is applied to ensure smooth boundary transition; transition region points value It can be calculated using the following formula (2): （2） wherein is the value of the last point of the end overlap portion of the original signal, is the value of the first point of the extension sequence, is the value of the i-th point of the transition region; As a further enhancement of the spectrum information constraint and boundary smoothing technique, median filtering can be selectively applied to the spliced signal to remove possible outliers, and a low-pass filter with a cutoff frequency adaptively determined according to the signal power spectral density PSD centroid is applied to further smooth the signal and suppress high-frequency disturbances, so that an extended signal with a required length and highly consistent with the original signal characteristics is finally obtained.
4. The signal processing method combining adaptive spectral enhancement signal spreading and focused learnable wavelet packet transform as described in claim 1, characterized in that: In step 2, the learnable wavelet packet transform LWPT model is trained, specifically: The signal extended by ASE-SE is taken as input; First, a reversible normalization process is applied to the input signal, which transforms the signal at the time point to the original value normalized to as shown in equation (3): （3） where and is the signal The mean and standard deviation computed over the valid (non-padding) region is a small constant added to prevent division by zero; this normalization operation can be reversed at the end of processing to restore the original scale; Then, the normalized spread signal is decomposed by using a learnable wavelet packet transform (LWPT) to obtain a series of sub-band coefficients of different frequency bands ; LWPT uses a trainable filter bank for decomposition; The sub-band coefficients obtained by the decomposition The adaptive threshold function is applied to process the sub-band coefficients to obtain processed coefficients ; The threshold function has learnable parameters, such as a bias term and is optimized through training, the threshold function being as in equation (4): （4） wherein, (⋅) is a Sigmoid activation function, is a hyperparameter controlling the slope (e.g. = 10), which can be set = ; the signal is reconstructed by inverse transform of the subband coefficients , through the inverse transform of the LWPT.
5. The signal processing method of claim 1, wherein: The training strategy is that, when calculating the loss function, a slice shielding mechanism, i.e. a focused training mechanism, is adopted, which only considers the reconstruction error of the original signal corresponding part and ignores the error of the filling part.