A multi-modal adaptive classification weak impact signal denoising system

Abstract

This invention discloses a multimodal adaptive classification system for denoising weak impact signals, relating to the field of low-velocity impacts. The system includes: a parameter adaptive optimization module, which uses envelope entropy as the fitness function and employs an artificial lemming optimization algorithm to globally optimize the penalty factor of successive variational mode decomposition; a signal decomposition module, which performs continuous iterative decomposition of the impact response signal according to the optimal penalty factor to obtain several intrinsic mode components; a mode classification module, which constructs a multidimensional evaluation index based on sparse measures and correlation coefficients and adaptively divides the several intrinsic mode components using a clustering algorithm; a fine denoising module, which performs wavelet packet transform threshold quantization denoising processing on the noisy components; and a signal reconstruction module, which reconstructs the feature components and the denoised components to output a high-fidelity denoised signal. This invention can achieve high-fidelity extraction of transient features of weak impacts under strong noise backgrounds and effective noise suppression without the need for manually preset decomposition parameters.

Description

Technical Field

[0001] This invention relates to the field of low-speed impact, and in particular to a multimodal adaptive classification system for denoising weak impact signals. Background Technology

[0002] In the fields of composite material structural health monitoring and low-velocity impact load identification, effective extraction of impact response signals is a prerequisite for subsequent damage assessment and localization. Response signals under low-velocity impact are characterized by weak energy, short duration, and significant non-stationarity. Furthermore, the measured signals inevitably contain strong noise interference from various sources, including sensor noise, environmental vibration, and structural boundary reflections. These factors collectively result in a low signal-to-noise ratio for the original impact signal, often submerging the effective impact characteristics in the background noise. Therefore, it is necessary to perform denoising preprocessing on the acquired impact response signals to suppress noise components and retain the characteristic information reflecting the essence of the impact event. Existing denoising methods can be broadly categorized into four types based on the processing domain: time-domain methods, frequency-domain methods, transform-domain methods, and deep learning-based methods.

[0003] Time-domain methods (such as moving average filtering and median filtering) rely on the assumption of local continuity of the signal, which is insufficient to preserve the abrupt changes of non-stationary impact signals and can easily lead to excessive smoothing of edge details. Frequency-domain methods (such as low-pass / band-pass filtering and Wiener filtering) are suitable for stationary signals with concentrated frequency bands, but when the signal and noise spectra overlap, it is difficult to achieve a balance between preserving effective components and suppressing noise. Transform-domain methods (represented by wavelet transform and empirical mode decomposition) have the ability to perform time-frequency localization analysis, but their denoising effect is highly dependent on the manual pre-setting of decomposition parameters (such as wavelet basis functions, number of decomposition layers, number of modes, and penalty factors), and there is a lack of unified objective criteria for parameter selection. Deep learning-based methods can implicitly learn the mapping relationship between signals and noise from data, but their performance is heavily dependent on large-scale labeled training samples, and the determination of network structure and hyperparameters largely depends on empirical trial and error, which limits their generalization ability in low-speed impact scenarios where sample acquisition is difficult. In summary, existing methods lack a denoising scheme capable of adaptively determining decomposition parameters, accurately identifying signal modes, and effectively preserving weak impact characteristics for non-stationary, low-energy, low-speed impact response signals in noisy environments. Therefore, based on these challenges, this invention proposes a multi-modal adaptive classification system for denoising weak impact signals. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a multimodal adaptive classification system for weak impact signal denoising. Targeting the non-stationary, weak-energy, and easily obscured characteristics of low-speed impact response signals in strong noise environments, this invention provides a denoising scheme that eliminates the need for manually presetting key decomposition parameters, adaptively identifies and classifies signal modes based on the signal's own characteristics, and thus effectively suppresses strong noise components while accurately preserving the transient characteristics of weak impacts.

[0005] To achieve the above objectives, the present invention provides a multimodal adaptive classification system for weak impulse signal denoising. The system acquires the impact response signal from the strain sensor on the structure under test through a signal acquisition module. Using envelope entropy as the fitness function, the artificial lemming optimization algorithm is employed to globally optimize the penalty factor for each order during the successive variational mode decomposition (SMD) process of extracting intrinsic mode components. Based on the optimal penalty factor for each order, the SMD algorithm is used to continuously iteratively decompose the impact response signal. In each iteration, an intrinsic mode component is extracted based on the optimal penalty factor for the current order, and the residual signal is updated synchronously until the decomposition termination condition is met. A multidimensional evaluation index is constructed based on the sparsity measure characterizing the impact characteristics of the signal and the correlation coefficient characterizing the energy distribution correlation between the intrinsic mode components and the original signal. A clustering algorithm is used to adaptively classify all intrinsic mode components obtained from the decomposition into three categories: feature components, noisy components, and pure noise components. The noisy components are denoised by threshold quantization using wavelet packet transform, and the wavelet basis function and decomposition level are optimized based on the evaluation function of weighted fusion of multiple performance indicators. Finally, the feature components and the denoised noisy components are reconstructed to obtain the denoised impact response signal.

[0006] In a first aspect, the present invention provides a multimodal adaptive classification system for denoising weak impulse signals, comprising: The signal acquisition module is used to acquire the impact response signal of the strain sensor on the structure under test; The parameter adaptive optimization module is used to extract intrinsic mode components in the successive variational mode decomposition algorithm. It uses the envelope entropy as the fitness function and the artificial lemming optimization algorithm to perform global optimization on the penalty factor of the current order to obtain the optimal penalty factor that matches the current decomposition stage. The signal decomposition module is used to continuously iterate the impact response signal according to the optimal penalty factor corresponding to each order using the successive variational mode decomposition algorithm. Each iteration extracts an intrinsic mode component based on the optimal penalty factor of the current order and updates the residual signal synchronously until the decomposition termination condition is met, and several intrinsic mode components are obtained. The modal classification module is used to construct multidimensional evaluation indicators based on sparse measures that characterize the impulsive characteristics of the signal and correlation coefficients that characterize the degree of correlation between the energy distribution of the intrinsic modal components and the original signal. Through clustering algorithms, the intrinsic modal components are adaptively divided into three categories: feature intrinsic modal components, noisy intrinsic modal components, and pure noise intrinsic modal components. The fine denoising module is used to perform threshold quantization denoising on the noisy intrinsic mode components through wavelet packet transform, and to select the wavelet basis function and decomposition level based on the evaluation function of weighted fusion of multiple performance indicators. The signal reconstruction module is used to reconstruct the characteristic intrinsic mode components and the noisy intrinsic mode components after wavelet packet transform denoising to obtain the denoised impulse response signal.

[0007] Furthermore, the artificial lemming optimization algorithm achieves global exploration of the search space by simulating the long-distance migration and burrowing behavior of lemmings, achieves local development by simulating the foraging behavior and predator avoidance behavior of lemmings, and adaptively switches between the exploration and development stages based on the energy factor that decreases with the iteration process.

[0008] Furthermore, the envelope entropy is used to characterize the degree of order of signal energy in the envelope distribution. The energy of the impact signal is concentrated in a few moments in the time domain, thus corresponding to a smaller envelope entropy value. The energy of the noise signal is evenly distributed in the time domain, thus corresponding to a larger envelope entropy value. The artificial lemming optimization algorithm iteratively updates the position of individuals in the population with the minimization of the envelope entropy value as the optimization direction.

[0009] Furthermore, in the process of extracting the current order intrinsic mode components, the successive variational mode decomposition algorithm takes minimizing the bandwidth of the current order mode component around its center frequency, minimizing the spectral overlap between the current order mode component and the residual signal, and minimizing the energy of the current order mode component at the center frequencies of the extracted mode components as joint optimization objectives, constructs an augmented Lagrangian function and solves iteratively using the alternating direction multiplier method.

[0010] Furthermore, the sparsity measure includes a kurtosis index and a negative entropy index. The kurtosis index is used to quantify the impact pulse characteristics of the intrinsic mode component, and the negative entropy index is used to quantify the degree to which the intrinsic mode component deviates from the Gaussian distribution. The two together characterize the significance of the transient impact features contained in the intrinsic mode component.

[0011] Furthermore, the correlation coefficient is an energy distribution correlation coefficient, which measures the degree of linear correlation between the energy distribution of the intrinsic mode component and the energy distribution of the original impact response signal in terms of energy distribution by calculating the ratio of the covariance to the product of their respective variances.

[0012] Furthermore, the clustering algorithm is the K-means clustering algorithm, which uses the multidimensional evaluation index of each intrinsic modal component as the clustering feature vector to unsupervisedly aggregate all intrinsic modal components into three clusters, corresponding to the feature intrinsic modal component, the noisy intrinsic modal component, and the pure noise intrinsic modal component, respectively.

[0013] Furthermore, the threshold quantization denoising process of the wavelet packet transform includes: determining the optimal decomposition tree structure of the wavelet packet decomposition based on the logarithmic energy entropy criterion; selecting a threshold processing function between a hard threshold function and a soft threshold function based on the comparison result of the noise level of the noisy intrinsic mode component and the preset noise threshold; and calculating an adaptive threshold to quantize the wavelet packet coefficients of each layer based on the estimated values ​​of the signal length and the noise standard deviation; wherein, when the noise level indicates that the noise component is dominant, the hard threshold function is selected, otherwise the soft threshold function is selected.

[0014] Furthermore, the evaluation function of the weighted fusion of multiple performance indicators normalizes the three performance indicators of signal-to-noise ratio, root mean square error and correlation coefficient respectively, and then sums them by weight. The optimal combination of wavelet basis functions and decomposition levels is selected from multiple wavelet families and different decomposition levels based on the maximization of the comprehensive evaluation value.

[0015] Furthermore, the fitness function is a composite fitness function, which includes a first sub-term and a second sub-term. The first sub-term is a comprehensive measure of the envelope entropy of each intrinsic modal component obtained after decomposing the impulse response signal under the candidate penalty factor. The second sub-term is a measure of the energy concentration of the residual signal after decomposition. During the iterative optimization process, the artificial lemming optimization algorithm dynamically adjusts the weight ratio of the first sub-term and the second sub-term in the composite fitness function according to the current iteration number through a monotonically nonlinear decreasing function. The dynamic weight coefficient of the weight ratio decreases monotonically and nonlinearly from an initial value approaching 1 to approaching 0 as the iteration number increases. This ensures that the first sub-term dominates in the early stage of optimization and gradually shifts to the second sub-term in the later stage of optimization, so as to obtain the optimal penalty factor that matches the residual spectrum structure of the current decomposition stage.

[0016] Furthermore, in the fine denoising module, the feature intrinsic mode components are superimposed to construct a reference signal, and the cross-entropy value between each noisy intrinsic mode component and the reference signal is calculated. The cross-entropy value is used to measure the degree of difference between each noisy component and the reference signal at the probability distribution level. Based on the cross-entropy value, all noisy intrinsic mode components are divided into two or more denoising levels, and different combinations of wavelet packet denoising parameters are matched for components of different denoising levels. The hierarchical denoising processing is performed based on the actual noise level of each component.

[0017] Secondly, the present invention also provides a method for denoising weak impulse signals based on multimodal adaptive classification, the method being based on the system described in the first aspect above, comprising: Acquire the impact response signal of the strain sensor on the structure under test; Using envelope entropy as the fitness function, the artificial lemming optimization algorithm is used to perform global optimization for the penalty factor of the current order in the process of extracting intrinsic mode components by successive variational mode decomposition algorithm, so as to obtain the optimal penalty factor that matches the current decomposition stage. Based on the optimal penalty factor corresponding to each order, the impulse response signal is continuously iteratively decomposed using the successive variational mode decomposition algorithm. In each iteration, an intrinsic mode component is extracted based on the optimal penalty factor of the current order and the residual signal is updated synchronously until the decomposition termination condition is met, and several intrinsic mode components are obtained. A multidimensional evaluation index is constructed based on the sparsity measure characterizing the impulsive characteristics of the signal and the correlation coefficient characterizing the degree of correlation between the energy distribution of the intrinsic modal components and the original signal. The intrinsic modal components are adaptively divided into three categories: characteristic intrinsic modal components, noisy intrinsic modal components, and pure noise intrinsic modal components through a clustering algorithm. The noisy intrinsic mode components are denoised by threshold quantization using wavelet packet transform, and the wavelet basis function and decomposition level are selected based on an evaluation function that uses a weighted fusion of multiple performance indicators. The characteristic intrinsic mode components are reconstructed by combining them with the noisy intrinsic mode components denoised by wavelet packet transform, to obtain the denoised impulse response signal.

[0018] This invention utilizes a linkage mechanism between the artificial lemming optimization algorithm and successive variational mode decomposition to automatically match the decomposition parameters with the inherent oscillation modes of the impact signal, ensuring the intrinsic physical consistency of the decomposition results without relying on manually preset parameters. Furthermore, by constructing a multi-dimensional evaluation index jointly using sparse measures and correlation coefficients, combined with the unsupervised classification capability of clustering algorithms, each inherent mode component is precisely divided into feature components, noisy components, and pure noise components, enabling a clear distinction between effective impact components and noise components at the feature level. Further, targeted threshold quantization processing is applied to the noisy components using wavelet packet transform, and the transform parameters are adaptively optimized based on the fusion evaluation of multiple performance indicators, maintaining the local morphology and amplitude fidelity of the signal waveform while finely suppressing residual noise. Finally, through the reconstruction of feature components and denoised components, high-fidelity extraction and fully automatic, end-to-end denoising processing of weak impact transient features are achieved in a strong noise background.

[0019] Beneficial effects By implementing the multimodal adaptive classification weak impulse signal denoising system provided by the present invention, the following technical effects are achieved: (1) When extracting each intrinsic mode component, the joint optimization objectives are to minimize the bandwidth of the current mode component around its center frequency, minimize the spectral overlap between the current mode component and the residual signal, and minimize the energy of the current mode component at the center frequencies of the extracted modes. The solution is obtained iteratively using the augmented Lagrangian function and the alternating direction multiplier method. This multi-objective joint constraint mechanism implements multiple physical constraints on the extraction process of each mode component from a global frequency domain perspective, effectively suppressing mode aliasing and spectral leakage, improving the separation and physical interpretability of each mode component in the frequency domain, and enabling a one-to-one physical mapping relationship between the decomposition results and the multi-mode composition of the actual impact signal.

[0020] (2) The significance of transient impact characteristics in each intrinsic modal component is characterized by two high-order statistical indicators, kurtosis and negative entropy. Simultaneously, an energy distribution correlation coefficient is introduced to quantify the linear correlation between each component and the original signal at the energy distribution level. A clustering feature vector is constructed using three-dimensional evaluation indicators, and unsupervised adaptive classification of intrinsic modal components is achieved through the K-means clustering algorithm. This mechanism establishes a comprehensive classification basis in both time-domain waveform morphology and energy distribution dimensions through the complementary fusion of sparse measures and energy correlation criteria. This effectively avoids misjudging weak impacts and random noise under low signal-to-noise ratio conditions using a single indicator, enabling the classification results to adaptively match the energy distribution differences of different impact response signals, thus improving the accuracy and generalization performance of modal classification.

[0021] (3) By introducing a dynamic weight coefficient that decreases nonlinearly with the number of iterations into the fitness function of the artificial lemming optimization algorithm, the optimization direction of the penalty factor is adaptively shifted at different stages of successive variational mode decomposition. This mechanism ensures that each modal component obtains an optimal penalty factor that matches the current residual spectral structure at the time of extraction, effectively avoiding the mode extraction mismatch problem caused by changes in the residual signal spectral structure in the later stages of successive decomposition due to the fixed penalty factor, and improving the adaptability of the decomposition process at each stage and the overall quality of each modal component.

[0022] (4) By calculating the cross-entropy between each noisy intrinsic mode component and the reference signal constructed from the set of characteristic components, the degree of difference between each noisy component and the typical impulse component at the probability distribution level is quantified. Based on this, the noisy components are divided into differentiated denoising levels, and the wavelet basis function type, decomposition level, and threshold shrinkage intensity are automatically matched for different levels. This mechanism enables precise matching between the denoising intensity and the actual noise level of each component, avoiding excessive smoothing of low-noise components and insufficient denoising of high-noise components caused by uniform denoising parameters. While effectively suppressing residual noise in each frequency band, it preserves the weak impulse details in the noisy components to the maximum extent. Attached Figure Description

[0023] To make the above-described multimodal adaptive classification weak impulse signal denoising system of the present invention more obvious and understandable, the accompanying drawings used in the specific embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 This diagram illustrates the process flow of the method of the present invention. Figure 2 This diagram shows the experimental apparatus of the present invention. Figure 3 This is a schematic diagram illustrating the artificial lemming algorithm. Detailed Implementation

[0025] Example 1: This embodiment provides a multimodal adaptive classification system and method for denoising weak impulse signals. The method flow is as follows: Figure 1 As shown, it specifically includes: Step 1: Obtain the impact response signal from the strain sensor on the structure under test (e.g., a composite laminated structure specimen).

[0026] like Figure 2 As shown, a 400mm × 400mm square monitoring area was selected on a 650mm × 650mm × 3mm composite laminate specimen. Strain sensors were symmetrically attached to one corner of the monitoring area, with the axis of the strain sensor parallel to the diagonal of the square at that corner and forming a 45° angle with the side of the monitoring area. The signal acquisition device used a sampling frequency of 10kHz to collect the impact signals acquired by the strain sensors.

[0027] Step 2: Using the Artificial Lemming Algorithm (ALA), with envelope entropy as the fitness function, the SVMD algorithm is adaptively optimized to decompose the original impact signal from Step 1, obtaining the optimal penalty factor. .

[0028] Penalty coefficient in finding the optimal decomposition When selecting envelope entropy as the fitness function for the artificial lemming optimization algorithm, envelope entropy is chosen as a metric for signal complexity, reflecting the uncertainty of signal energy distribution within the envelope. Impact signals have energy concentrated in a few moments, resulting in a sparser and more ordered envelope distribution, exhibiting smaller envelope entropy values. Noise signals, on the other hand, have a uniform energy distribution and a disordered envelope distribution, resulting in larger envelope entropy values. Therefore, during optimization, the goal is to find functions that minimize envelope entropy. The envelope entropy value is calculated using the following formula:

[0029]

[0030] In the formula, for The normalized form; The envelope signal is obtained by applying the Hilbert transform to the intrinsic mode functions (IMFs). This represents the total number of sampling points for the envelope signal of the intrinsic mode function; For the first The calculated components corresponding to each sampling point.

[0031] It should be noted that the envelope entropy mentioned above is calculated for each of the intrinsic mode functions obtained by decomposition, and the arithmetic mean of the envelope entropy of each intrinsic mode function is used as the fitness function value. The artificial lemming optimization algorithm takes minimizing this mean as the optimization direction.

[0032] The Artificial Lemming Optimization Algorithm is a population-based algorithm that requires initializing the positions of all search agents before entering the iterative process. The set of all initial candidate solutions is a collection of... (Overall size) rows and The matrix composed of (number of dimensions) columns is expressed by the following formula:

[0033]

[0034] In the formula, A random number in the range of 0 to 1; For the first The upper limit of dimensions; For the first The lower limit of the dimension.

[0035] The artificial lemming optimization algorithm has five key stages, including long-distance migration, burrowing behavior, foraging behavior, predator avoidance, and the transition from exploration to development. The algorithm flow is as follows: Figure 3 As shown.

[0036] During long-distance migrations, lemmings explore their search space to find habitats, based on their current location and the locations of random individuals within the population. The direction and distance of lemming migration can be described as follows:

[0037]

[0038]

[0039]

[0040] In the formula, For the first The search agent in the 1st The position at the next iteration; This is the current optimal solution; For the first The current location of the search agent; For the search individual randomly selected from the population; for Integer indices between; A flag used to change the search direction, in order to avoid local optima; To characterize the random number vector of Brownian motion, a dynamically uniform step size can be used to explore some potential regions in the search space. The step size of standard Brownian motion is obtained from the probability density function of a normal distribution with variance of 1 and mean of 0. For size A vector whose elements are random numbers uniformly distributed in the interval [-1, 1] controls the movement of the current best individual and random individuals in the population and is used to represent the interaction between individuals during the migration process.

[0041] Lemmings will randomly dig new burrows based on their current location and the locations of random individuals within the population, in order to improve their survival. This burrowing behavior of lemmings falls under the exploration process in optimization algorithms, and can be described as follows:

[0042] In the formula, For the search individual randomly selected from the population; A random number related to the current iteration number; For the middle Random integer index values ​​between. and Used to characterize the interactions between individual lemmings when digging new burrows. The calculation method is as follows:

[0043] Lemmings typically establish a relatively small foraging area within their habitat, depending on the abundance and availability of food. To obtain as much food as possible, lemmings will randomly roam within their foraging area. The foraging behavior of lemmings falls under the development process in optimization algorithms. This stage of behavior is modeled using a spiral winding mechanism as follows:

[0044] In the formula, The spiral shape randomly searched during foraging is calculated using the following formula:

[0045]

[0046] In the formula, The radius of the foraging range is the Euclidean distance between the current position and the optimal solution.

[0047] The final stage involves the lemming's avoidance and protection behaviors when encountering danger. Upon spotting an enemy, the lemming uses its exceptional running ability to escape back to its burrow. Simultaneously, it employs deceptive maneuvers to evade predators. This behavior also falls under the development process within the optimization process and can be described as follows:

[0048]

[0049]

[0050] In the formula, denoted as the escape coefficient of lemmings, representing their escape ability, which decreases as the number of iterations increases; This represents the maximum number of iterations. for Flight function, used to simulate the deceptive behavior of lemmings during escape; and A random value within the range of 0 to 1; It is a constant with a value of 1.5.

[0051] The transition from exploration to exploitation in the artificial lemming optimization algorithm involves four search strategies closely related to the lemming's energy level. In the initial stage, lemmings frequently explore to locate promising areas, while in the later stages of the search, they tend to exploit local areas to obtain a better global optimum. To maintain a stable balance between exploration and exploitation, this embodiment designs an energy factor that decreases with iteration. When lemmings have sufficient energy, they selectively migrate or dig burrows; otherwise, they hunt or escape predators. The formula for calculating the energy factor is:

[0052] To avoid When the logarithmic terms approach 0, they diverge, leading to numerical instability. In actual calculations, this will... Constraints Within the interval, It is a very small positive number.

[0053] when If the activity is active, it will perform exploration behavior (migrating or digging); otherwise, it will perform development behavior (foraging or escaping).

[0054] Based on the population evolution and position update mechanism of the artificial lemming optimization algorithm, the position of individuals in the population is iteratively optimized and updated until the preset maximum number of iterations or the fitness value satisfies the convergence condition. Finally, the parameters corresponding to the globally optimal individual are output, which is the optimal penalty factor of SVMD. .

[0055] Step 3: Calculate the optimal penalty factor. It is applied to Sequential Variational Mode Decomposition (SVMD). A multi-parameter strategy is adopted, selecting sparse measure and correlation coefficient as the classification criteria to classify the decomposed modes. Based on the above evaluation indicators, through... After decomposition by mean clustering algorithm Classification as features Noise and pure noise .

[0056] Step three specifically includes: It is an adaptive signal decomposition method based on a variational optimization framework, compared to the variational mode decomposition (VMD) algorithm. It can adaptively and continuously extract all modes without pre-setting the number of modes. It possesses advantages such as strong adaptability, high decomposition accuracy, and good robustness. It is especially suitable for feature extraction under impact signals and complex noise environments.

[0057] use The method decomposes the target impact signal data as follows: Input the target composite impact signal to In the algorithm, the original composite impact signal It is decomposed into two signals, including First-order intrinsic mode component signal and residual signal Among them, residual signal Except Other signals include the sum of all previously obtained modes. Unprocessed portion of combined impact signals The expression is:

[0058]

[0059] The decomposition method is based on the following four criteria: First, to ensure that each modal component is compact around its center frequency, thus ensuring its energy concentration in the frequency domain, the second... The minimization criterion for the first modal components is as follows:

[0060] In the formula, This is an objective criterion for minimizing the bandwidth of modal components in the frequency domain. It is a unit impulse function; It is the imaginary unit in complex numbers; For the first The center frequency of the first-order natural mode component; It is a complex exponential function used to convert signals to the frequency domain.

[0061] Second, in order to minimize the residual signal and The spectral overlap between them should be addressed by using a suitable filter. Filter the filter and minimize its energy. The frequency response of the selected filter and the constraints to be established are as follows.

[0062]

[0063] In the formula, This is the frequency domain response of the filter described above; This is the impulse response of the filter described above; To minimize the residual signal and the first Constraint criteria for spectral overlap of an intrinsic mode component.

[0064] Third, to avoid minimizing only the two criteria mentioned above and Caused the First-order mode and the second-order mode When aliasing occurs, a suitable filter needs to be used to ensure... The energy is low near the center frequency of the extracted modes, so the frequency response of the filter and the constraints to be established can be defined as follows:

[0065] In the formula, This is the frequency domain response of the filter described above; For the first The center frequency of the first-order natural mode component; To ensure the current modal components The constraint criterion is to have minimum energy near the center frequency of the previously obtained intrinsic modal components; This is the impulse response of the filter described above.

[0066] Fourth, in order to ensure It can be extracted The first mode and the unprocessed portion of the signal are fully reconstructed to construct the final standard:

[0067] In the formula, This represents the unprocessed portion of the original composite impact signal; For the first The sum of all intrinsic modal components obtained before the first intrinsic modal component.

[0068] Therefore, currently When the first mode is known, solve for the second mode. The problem of first-order modes is equivalent to minimizing the sum of the first three constraints:

[0069] In the formula, for , and The balance coefficients are obtained by using the Lagrange multiplier method.

[0070] To improve convergence behavior and enhance fidelity reconstruction in the presence of noise, an augmented Lagrangian function is constructed by combining a quadratic penalty function and Lagrange multipliers, with the following specific form:

[0071] In the formula, It is a Lagrange multiplier.

[0072] According to Passevar's equation, the above formula can be rewritten as:

[0073] In the formula, quilt replace; and These are the initial input signals. and unprocessed parts Fourier transform; and Modal components and Fourier transform; Lagrange multipliers Fourier transform.

[0074] Finally, the alternating direction multiplier algorithm is used to solve the above minimization problem, yielding the result of the following step. The calculation equations for each parameter in the next iteration are expressed as follows:

[0075]

[0076]

[0077] In the formula, This is the step size for the iteration; The number of iterations; It is a variable parameter, and is the first... The first mode in the first In the next iteration, at the center frequency to The result of performing a Fourier transform; For the first Frequency domain representation of Lagrange multipliers in the next iteration.

[0078] To characterize the transient features of the impact signal, kurtosis (k) and negative entropy (NE) were chosen as sparsity measures to guide the analysis. middle The choice.

[0079] The definition of kurtosis is as follows:

[0080] In the formula, For raucousness; For signal; for The mean; for Standard deviation; For quantity The expected value.

[0081] The definition of negative entropy is as follows:

[0082] In the formula, It is the mean operator; The squared envelope spectrum is obtained by constructing an analytic signal from the original signal through Hilbert transform, taking the modulus, and then squaring it.

[0083] In addition to using kurtosis and negative entropy indices to capture impact characteristics, to distinguish between periodic impacts and random noise, an energy distribution correlation coefficient is further introduced as a component to achieve a more comprehensive and robust mode screening. Its expression is:

[0084]

[0085] In the formula, For signal sample points; The number of signal sample points; The correlation coefficient; for Energy distribution; The energy distribution of the original signal; For covariance; Let Variance be the variance.

[0086] For the decomposed The problem of lacking clear classification thresholds for pure noise components, noisy components, and feature components is addressed by introducing... Mean clustering algorithm. Means clustering is a commonly used unsupervised learning algorithm, mainly used for data clustering. Its basic idea is to divide the dataset into groups. Find clusters such that the sum of the distances between each data point and the centroid of its cluster is minimized. Given the target number of clusters, Mean clustering algorithm achieves fast automatic classification, overcoming the limitations of traditional fixed threshold methods, and can classify different impact signals. Perform adaptive classification.

[0087] In the aforementioned continuous iterative decomposition process, the decomposition termination condition is preferably set as follows: the energy of the residual signal is lower than a preset proportion threshold of the total energy of the original impulse response signal, or the envelope entropy of the residual signal is greater than a preset threshold, or a preset maximum decomposition order is reached. In this embodiment, both the residual energy proportion and the maximum decomposition order are used as the decomposition termination condition.

[0088] Step 4: Through the above steps, Divided into characteristics Noise and pure noise Remove pure noise Preserving features For noisy Fine-grained denoising is performed using wavelet packet transform. The retained features... Noise content after denoising Combined, the denoised signal is reconstructed.

[0089] Step four specifically includes: using wavelet packet transform to process noisy data. Perform fine noise reduction processing, retaining the noisy data. The effective signal components in the wavelet packet decomposition. The optimal tree for wavelet packet decomposition is generated by the logarithmic energy entropy criterion. The choice of hard and soft thresholding functions depends on the effective signal components after decomposition. The noise level threshold is calculated as follows:

[0090] In the formula, The standard deviation of the noise; The signal length; The original signal; Decomposition level; For median operations; The value is 0.6745, which is the median of the absolute values ​​of the standard normal distribution.

[0091] The key to wavelet packet transform lies in selecting appropriate wavelet basis functions and decomposition levels. For the Symlet (Sym1-10), Daubechies (Db1-10), and Coiflet (Coif1-5) wavelet families, a comprehensive evaluation function is constructed to select the optimal wavelet basis functions and corresponding wavelet packet decomposition levels. This function achieves a comprehensive evaluation of the denoising results by weightedly fusing three performance indicators: signal-to-noise ratio (SNR), root mean square error (RMSE), and correlation coefficient (CC). It is defined as follows:

[0092] In the formula, This is the overall score; Set to 1 / 3, Set to 1 / 3, Set to 1 / 3; For normalization ; For anti-normalization ; For normalization .

[0093] The weighting coefficients can be preset to fixed values ​​according to the actual application scenario, or they can be adaptively adjusted based on the importance of each performance indicator or the signal-to-noise ratio level. In this embodiment, equal weighting is used as an example to achieve a balanced consideration of signal-to-noise ratio, root mean square error and correlation coefficient.

[0094] The noise level of the noisy intrinsic mode component is quantified by estimating the signal-to-noise ratio or noise energy percentage of the component. When the quantization result indicates that the noise component is dominant, a hard threshold function is selected to aggressively suppress the strong noise component; when the quantization result indicates that the effective impulse signal component is dominant, a soft threshold function is selected to avoid excessive attenuation of the effective signal amplitude and maintain waveform continuity.

[0095] This method optimizes the parameter settings during wavelet packet transform and constructs a system evaluation framework to preserve the amplitude characteristics of the impulse signal while maintaining the original waveform shape, and ensures that important impulse components are fully preserved during the denoising process.

[0096] Example 2: In successive variational mode decomposition (SMD), the value of the penalty factor directly determines the bandwidth characteristics and spectral compactness of each intrinsic mode component. Existing methods typically employ a fixed optimization strategy to perform a one-time global optimization of the penalty factor. However, at different stages of successive decomposition, as the number of extracted modes increases, the spectral structure of the residual signal continuously changes, making it difficult for the same penalty factor value to maintain optimal decomposition performance at each stage. This embodiment proposes a dynamic weight adaptive adjustment mechanism. By introducing a dynamic weight coefficient that changes with the decomposition process into the fitness function of the artificial lemming algorithm, the optimization direction of the penalty factor focuses on minimizing the bandwidth of the mode components in the early stage of decomposition, while gradually shifting towards the energy concentration of the residual signal in the later stage, thus achieving adaptive dynamic adjustment of the penalty factor with the decomposition process. The core of this mechanism lies in constructing a weight function that changes nonlinearly with the number of iterations, allowing the optimization algorithm to assign differentiated attention to different objective items at different decomposition stages, ultimately ensuring that each mode component obtains an optimal penalty factor that matches the current residual spectral structure at the time of extraction.

[0097] In optimizing the SVMD penalty factor using the artificial lemming algorithm, the traditional approach is to use a fixed envelope entropy as a single fitness function for a one-time global optimization. This embodiment introduces a dynamic weight adaptive adjustment mechanism in this step, as follows: In the initialization phase of the artificial lemming algorithm, in addition to initializing the position vectors of the individuals in the population (each individual corresponds to a set of candidate penalty factor values), a dynamic weight coefficient is additionally initialized. This coefficient is the number of iterations of the artificial lemming algorithm. A changing function. The initial value of this weighting coefficient is set to be close to 1, and as the number of iterations increases, the coefficient gradually approaches 0 according to a non-linear decreasing law.

[0098] The nonlinear decreasing law refers to the monotonically decreasing dynamic weight coefficients as the number of iterations increases, with the decreasing rate gradually accelerating as the iteration progresses. This ensures a gradual decrease in weights in the early stages of optimization to guarantee sufficient exploration of the optimal solution for the envelope entropy, while in the later stages, the weights rapidly converge to zero to focus on optimizing the concentration of residual energy. This monotonically nonlinear decreasing law can be achieved through power function decreasing, exponential function decreasing, or cosine annealing decreasing methods.

[0099] Unlike existing methods that use only envelope entropy as the single fitness metric, this mechanism designs the fitness function as a combination of two sub-terms: the first sub-term is the mean envelope entropy of each modal component obtained after SVMD decomposition of the original signal under the current candidate penalty factor value, which is used to characterize the sparsity of the modal components and the significance of the impact characteristics; the second sub-term is the energy concentration index of the residual signal after decomposition, which is used to characterize the uniformity of the distribution of undecomposed energy in the residual signal.

[0100] Dynamic weighting coefficients A composite fitness function is introduced, and its mathematical expression is as follows:

[0101] In the formula, The composite fitness function value represents the value of the fitness function in the artificial lemming algorithm. In the next iteration, the candidate penalty factor The corresponding comprehensive evaluation value; These are dynamic weighting coefficients, which vary with the number of iterations. The function increases rather than decreases linearly. In the early stage of decomposition, the value is large, which makes the optimization focus on minimizing the envelope entropy. In the later stage of decomposition, the value approaches zero, which makes the optimization focus on the concentration of residual energy. The envelope entropy sub-term represents the candidate penalty factor. The arithmetic mean of the envelope entropy values ​​of all modal components obtained after SVMD decomposition of the original signal is the smaller the value, the more sparse and ordered the envelope distribution of each modal component is, and the more significant the impact characteristics are. The residual energy concentration sub-term represents the candidate penalty factor. After SVMD decomposition is completed, the ratio of the sum of the energies of the first few dominant frequency components in the residual signal spectrum to the total energy of the residual signal is the largest value. This indicates that the undecomposed energy in the residual signal is more concentrated, and the impact components that have not yet been extracted in the current decomposition still dominate.

[0102] In the initial stage of decomposition When the entropy is large, the optimization algorithm mainly searches based on the principle of minimizing the envelope entropy. Values ​​are set to ensure that the early extracted modal components have optimal sparsity and impact characteristics; as the decomposition process progresses... As the energy concentration of the residual signal gradually decreases, the optimization algorithm gradually takes into account the energy concentration of the residual signal, so that the modal components extracted later focus more on the effective capture of the remaining energy in the residual signal.

[0103] In each iteration of the artificial lemming algorithm, the fitness value of each individual in the population is calculated based on the aforementioned composite fitness function, and the optimal position and global optimal solution of the population are updated accordingly. Because... Dynamically changes with the number of iterations, the same candidate The fitness evaluation value obtained at different iteration stages is different, thereby guiding the individual population to dynamically adjust its optimization direction in the search space.

[0104] When the artificial lemming algorithm reaches its maximum number of iterations or meets the convergence condition, it outputs the parameters corresponding to the globally optimal individual as the optimal penalty factor for the current decomposition stage. .

[0105] The result of dynamic optimization The value is applied to the current mode extraction of SVMD. When extracting the next mode, the above steps are repeated, and the artificial lemming optimization process is restarted based on the new residual signal, thereby ensuring that the extraction of each mode uses the optimal penalty factor that matches the residual spectral structure at that time.

[0106] To verify the effectiveness of this mechanism, a fixed penalty factor (take) was used. Using successive variational mode decomposition as a benchmark, comparative experiments were conducted under the same input signal (a simulated low-speed impact response signal composed of single-frequency sinusoidal decaying oscillations superimposed with simulated transient impact components, and Gaussian white noise to achieve an input signal-to-noise ratio of 15 dB) and the same number of iterations of the artificial lemming algorithm (maximum 50 iterations). Both sets of experiments used envelope entropy as an evaluation index for decomposition quality. The results show that with a fixed penalty factor, the average envelope entropy of each decomposed mode component is approximately 0.52; however, after adopting the dynamic weight adaptive adjustment mechanism, the average envelope entropy of each mode component decreases to approximately 0.38, a reduction of approximately 27%. Simultaneously, the signal-to-noise ratio of the reconstructed signal after decomposition increases from approximately 22.5 dB under the fixed penalty factor condition to approximately 28.6 dB. These results demonstrate that the dynamic weight mechanism ensures that each mode receives a penalty factor matching the current residual spectral structure during extraction, effectively improving the sparsity of each mode component and the quality of impact feature representation.

[0107] Example 3: After the modality classification module divides the intrinsic modal components into feature components, noisy components, and pure noise components, existing methods typically apply uniform wavelet packet denoising parameters (such as the same wavelet basis function, the same decomposition level, and the same thresholding rule) to all noisy components. However, different noisy components exhibit significant differences in noise characteristics due to their different frequency band positions and the varying ratios of effective signal to noise. Some noisy components have a high proportion of effective impulse components, requiring only mild denoising; others have noise that is absolutely dominant, requiring deep denoising. This embodiment proposes an adaptive hierarchical denoising strategy for noisy components based on intermodal cross-entropy. By calculating the cross-entropy between each noisy component and the set of feature components as a similarity measure, the noisy components are divided into different denoising levels. Differentiated denoising parameter configurations are automatically matched for different levels of components, including differentiated combinations of wavelet basis function type, decomposition level, and threshold shrinkage intensity. This achieves precise matching between the denoising intensity and the actual noise level of each component, avoiding the loss of effective signal due to past noise or excessive residual noise due to insufficient past noise.

[0108] In the process of fine denoising using wavelet packet transform, this embodiment improves upon the original unified denoising strategy by introducing an adaptive hierarchical mechanism based on inter-modal cross-entropy, as detailed below: After completing modal classification, we obtain the sets of characteristic intrinsic modal components, the set of noisy intrinsic modal components, and the set of pure noise intrinsic modal components. We then superimpose all components from the characteristic component set to construct a reference signal, which represents the purest and most typical effective impact component in the original impact response signal.

[0109] For each noisy intrinsic mode component in the set of noisy components, calculate its cross-entropy with the reference signal. Cross-entropy is used here to measure the degree of difference between the two signals at the probability distribution level. The smaller the cross-entropy value, the closer the probability distribution of the noisy component is to that of the reference signal, that is, the higher the proportion of effective impulse components it contains, and the lower the required denoising intensity. The larger the cross-entropy value, the greater the difference in distribution between the noisy component and the reference signal, that is, the higher the proportion of noise components it contains, and the higher the required denoising intensity.

[0110] The mathematical expression for intermodal cross-entropy is:

[0111] In the formula, For the first The cross-entropy value between a noisy intrinsic mode component and a reference signal is used to quantify the degree of difference between the two signals at the probability distribution level. The smaller the cross-entropy value, the closer the distribution of the noisy component is to that of the reference signal, and the higher the proportion of effective impulse components it contains. This represents the total number of probability intervals. The larger this value is, the higher the accuracy of the probability distribution description. However, it is necessary to ensure that there are enough sample points in each interval to guarantee statistical stability. For the reference signal at the 1st The probability mass function value over the probability interval, i.e., the sampled value of the reference signal falling into the th probability interval. The proportion of samples in each interval; For the first The noisy intrinsic mode component in the first... The probability mass function value over the probability interval, i.e., the sampling point value of the noisy component falling into the probability interval. The proportion of samples in each interval; It is a very small positive constant used to ensure the numerical stability of logarithmic operations.

[0112] Based on the calculated cross-entropy values ​​of each noisy component, the natural discontinuity classification method or the equal frequency classification method are used to divide all noisy components into three denoising levels: low noise level (minimum cross-entropy value, corresponding to mild denoising), medium noise level (medium cross-entropy value, corresponding to moderate denoising) and high noise level (maximum cross-entropy value, corresponding to deep denoising).

[0113] Different combinations of denoising parameters are configured for components with different denoising levels. Specifically: for low-noise-level components, wavelet basis functions with good temporal locality preservation capabilities, lower decomposition levels, and milder soft thresholding functions are selected to preserve effective impulse details to the maximum extent; for medium-noise-level components, balanced wavelet basis functions, moderate decomposition levels, and conventional thresholding rules are selected; for high-noise-level components, wavelet basis functions with good frequency-domain energy compression capabilities, higher decomposition levels, and more aggressive hard thresholding functions or strong contraction strategies are selected to effectively suppress strong noise components.

[0114] After determining the denoising level and corresponding parameter configuration for each component, wavelet packet transform denoising is performed on each noisy component. After denoising, the components are arranged according to their original frequency band order.

[0115] The final denoised signal is obtained by reconstructing all noisy components after hierarchical denoising and the retained feature components. Because the hierarchical denoising strategy ensures that each noisy component receives a denoising intensity that matches its actual noise level, the reconstructed signal effectively suppresses noise while preserving the weak impulse characteristics in each frequency band to the greatest extent.

[0116] To verify the effectiveness of this strategy, a comparative experiment was conducted using the traditional uniform parameter wavelet packet denoising method (applying the same Db4 wavelet basis to all noisy components, fixing the decomposition level to 4 levels, and uniform soft thresholding) as a benchmark, under the same noisy component set and signal reconstruction conditions. Both sets of experiments used the signal-to-noise ratio (SNR) and root mean square error (RMSE) of the reconstructed signal as evaluation metrics. The results show that with uniform denoising parameters, the SNR of the reconstructed signal is approximately 26.3 dB, and the RMS error is approximately 0.047. However, after adopting the adaptive hierarchical denoising strategy based on cross-entropy, the SNR of the reconstructed signal increases to approximately 31.8 dB, and the RMS error decreases to approximately 0.031. The SNR is improved by approximately 5.5 dB, and the RMS error is reduced by approximately 34%. These results demonstrate that the hierarchical strategy based on cross-entropy achieves differentiated denoising intensity matching for components with different noise levels. While effectively suppressing residual noise in each frequency band, it avoids excessive smoothing of low-noise components by uniform parameters, thereby improving the overall fidelity of the reconstructed signal.

Claims

1. A multimodal adaptive classification system for denoising weak impulse signals, characterized in that, include: The signal acquisition module is used to acquire the impact response signal of the strain sensor on the structure under test; The parameter adaptive optimization module is used to extract intrinsic mode components in the successive variational mode decomposition algorithm. It uses the envelope entropy as the fitness function and the artificial lemming optimization algorithm to perform global optimization on the penalty factor of the current order to obtain the optimal penalty factor that matches the current decomposition stage. The signal decomposition module is used to continuously iterate the impact response signal according to the optimal penalty factor corresponding to each order using the successive variational mode decomposition algorithm. Each iteration extracts an intrinsic mode component based on the optimal penalty factor of the current order and updates the residual signal synchronously until the decomposition termination condition is met, and several intrinsic mode components are obtained. The modal classification module is used to construct multidimensional evaluation indicators based on sparse measures that characterize the impulsive characteristics of the signal and correlation coefficients that characterize the degree of correlation between the energy distribution of the intrinsic modal components and the original signal. Through clustering algorithms, the intrinsic modal components are adaptively divided into three categories: feature intrinsic modal components, noisy intrinsic modal components, and pure noise intrinsic modal components. The fine denoising module is used to perform threshold quantization denoising on the noisy intrinsic mode components through wavelet packet transform, and to select the wavelet basis function and decomposition level based on the evaluation function of weighted fusion of multiple performance indicators. The signal reconstruction module is used to reconstruct the characteristic intrinsic mode components and the noisy intrinsic mode components after wavelet packet transform denoising to obtain the denoised impulse response signal.

2. The system according to claim 1, characterized in that: The artificial lemming optimization algorithm achieves global exploration of the search space by simulating the long-distance migration and burrowing behavior of lemmings, and achieves local development by simulating the foraging behavior and predator avoidance behavior of lemmings. It also adaptively switches between the exploration and development phases based on the energy factor that decreases with the iteration process.

3. The system according to claim 1, characterized in that: The envelope entropy is used to characterize the degree of order of signal energy in the envelope distribution. The energy of the impact signal is concentrated in a few moments in the time domain, thus corresponding to a smaller envelope entropy value. The energy of the noise signal is evenly distributed in the time domain, thus corresponding to a larger envelope entropy value. The artificial lemming optimization algorithm iteratively updates the position of individuals in the population with the minimization of the envelope entropy value as the optimization direction.

4. The system according to claim 1, characterized in that: The successive variational mode decomposition algorithm, in the process of extracting the current order intrinsic mode components, takes minimizing the bandwidth of the current order mode component around its center frequency, minimizing the spectral overlap between the current order mode component and the residual signal, and minimizing the energy of the current order mode component at the center frequencies of the extracted mode components as joint optimization objectives. It constructs an augmented Lagrangian function and solves iteratively using the alternating direction multiplier method.

5. The system according to claim 1, characterized in that: The clustering algorithm is the K-means clustering algorithm, which uses the multidimensional evaluation index of each intrinsic mode component as the clustering feature vector to unsupervisedly aggregate all intrinsic mode components into three clusters, corresponding to the feature intrinsic mode component, the noisy intrinsic mode component, and the pure noise intrinsic mode component, respectively.

6. The system according to claim 1, characterized in that: The threshold quantization denoising process of the wavelet packet transform includes: determining the optimal decomposition tree structure of the wavelet packet decomposition based on the logarithmic energy entropy criterion; selecting a threshold processing function between a hard threshold function and a soft threshold function based on the comparison result of the noise level of the noisy intrinsic mode component and the preset noise threshold; and calculating an adaptive threshold based on the estimated values ​​of the signal length and the noise standard deviation to quantize the wavelet packet coefficients of each layer; wherein, when the noise level indicates that the noise component is dominant, the hard threshold function is selected, otherwise the soft threshold function is selected.

7. The system according to claim 1, characterized in that: The evaluation function, which weights and fuses multiple performance indicators, normalizes the three performance indicators—signal-to-noise ratio, root mean square error, and correlation coefficient—and then sums them by weight. Based on the maximization of the comprehensive evaluation value, it selects the optimal combination of wavelet basis functions and decomposition levels from multiple wavelet families and different decomposition levels.

8. The system according to claim 1, characterized in that: The fitness function is a composite fitness function, which includes a first sub-term and a second sub-term. The first sub-term is a comprehensive measure of the envelope entropy of each intrinsic mode component obtained after decomposing the impulse response signal under the candidate penalty factor. The second sub-term is a measure of the energy concentration of the residual signal after decomposition. During the iterative optimization process, the artificial lemming optimization algorithm dynamically adjusts the weight ratio of the first sub-term and the second sub-term in the composite fitness function according to the current iteration number through a monotonically nonlinear decreasing function. The dynamic weight coefficient of the weight ratio decreases monotonically and nonlinearly from an initial value approaching 1 to approaching 0 as the number of iterations increases, so that the first sub-term dominates in the early stage of optimization and gradually shifts to the second sub-term in the later stage of optimization, so as to obtain the optimal penalty factor that matches the residual spectrum structure of the current decomposition stage.

9. The system according to claim 1, characterized in that: In the fine denoising module, the feature intrinsic mode components are superimposed to construct a reference signal. The cross-entropy value between each noisy intrinsic mode component and the reference signal is calculated. The cross-entropy value is used to measure the degree of difference between each noisy component and the reference signal at the probability distribution level. Based on the cross-entropy value, all noisy intrinsic mode components are divided into two or more denoising levels, and different combinations of wavelet packet denoising parameters are matched for components of different denoising levels. The hierarchical denoising processing is performed based on the actual noise level of each component.

10. A method for denoising weak impulse signals using multimodal adaptive classification, characterized in that, The method is implemented based on the system described in any one of claims 1 to 9, and includes: Acquire the impact response signal of the strain sensor on the structure under test; Using envelope entropy as the fitness function, the artificial lemming optimization algorithm is used to perform global optimization for the penalty factor of the current order in the process of extracting intrinsic mode components by successive variational mode decomposition algorithm, so as to obtain the optimal penalty factor that matches the current decomposition stage. Based on the optimal penalty factor corresponding to each order, the impulse response signal is continuously iteratively decomposed using the successive variational mode decomposition algorithm. In each iteration, an intrinsic mode component is extracted based on the optimal penalty factor of the current order and the residual signal is updated synchronously until the decomposition termination condition is met, and several intrinsic mode components are obtained. A multidimensional evaluation index is constructed based on the sparsity measure characterizing the impulsive characteristics of the signal and the correlation coefficient characterizing the degree of correlation between the energy distribution of the intrinsic modal components and the original signal. The intrinsic modal components are adaptively divided into three categories: characteristic intrinsic modal components, noisy intrinsic modal components, and pure noise intrinsic modal components through a clustering algorithm. The noisy intrinsic mode components are denoised by threshold quantization using wavelet packet transform, and the wavelet basis function and decomposition level are selected based on an evaluation function that uses a weighted fusion of multiple performance indicators. The characteristic intrinsic mode components are reconstructed by combining them with the noisy intrinsic mode components denoised by wavelet packet transform, to obtain the denoised impulse response signal.

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