Aluminum plate ultrasonic Lamb wave denoising method based on ICPO-VMD combined wavelet threshold improvement
By combining ICPO-VMD with an improved wavelet thresholding method, the problem of improper parameter selection in ultrasonic Lamb wave signal processing of aluminum plates was solved, achieving high-fidelity denoising and improving the accuracy and reliability of detection.
Patent Information
- Application Number
- CN202610172131.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-06
- Publication Date
- 2026-05-19
AI Technical Summary
In the current technology for processing ultrasonic Lamb wave signals in aluminum plates, the parameter selection of the signal decomposition method is not intelligent enough, and the traditional threshold processing strategy is difficult to achieve the best balance between noise suppression and signal fidelity, resulting in insufficient accuracy and reliability of the detection results.
A method based on ICPO-VMD joint improvement of wavelet thresholding is adopted. By improving the Crown Porcupine optimization algorithm, the VMD parameters are adaptively selected. Combined with fuzzy entropy as the fitness function, signal decomposition and wavelet thresholding are performed to achieve accurate signal separation and high-fidelity denoising.
It significantly improves the denoising effect of ultrasonic Lamb wave signals of aluminum plates, enhances the accuracy and robustness of signal detection, and ensures high fidelity and reliability of defect detection.
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Figure CN122063201A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing technology, and particularly relates to an ultrasonic Lamb wave denoising method for aluminum plates based on ICPO-VMD jointly improved wavelet threshold. Background Technology
[0002] Ultrasonic Lamb wave nondestructive testing technology, with its high sensitivity, excellent long-distance propagation capability, and ability to excite multiple modes, has become a core technology for health monitoring and defect localization of large plate structures such as aluminum plates and composite laminates in fields such as aerospace, rail transportation, automobile manufacturing, and new energy equipment. In the aerospace field, aluminum alloy components are widely used in critical load-bearing structures such as wing skins and cabin bulkheads; potential fatigue cracks, corrosion damage, or delamination defects within these components directly affect flight safety. In lightweight automotive manufacturing, the welding quality and forming defects of aluminum body panels and battery pack casings also urgently require strict control through reliable nondestructive testing methods. Therefore, achieving high-precision and high-reliability detection of defects in aluminum plate structures is of paramount importance for ensuring structural integrity and preventing major accidents.
[0003] However, in actual industrial testing environments, the acquired Lamb wave signals are inevitably interfered with by various complex noises. These noises mainly originate from environmental noise and electromagnetic interference generated by other equipment in the industrial environment, scattered waves and multipath effects caused by material inhomogeneities and structural boundaries, and instrument noise generated by the electronic components of the data acquisition system itself. These noise components often overlap with the effective signals caused by defects in both the time and frequency domains, leading to a decrease in the signal-to-noise ratio, waveform distortion, and unclear time-frequency characteristics. In severe cases, this can cause misjudgment of defects, increased location errors, or even missed detections, directly affecting the accuracy and reliability of the test results. Therefore, developing high-performance signal processing algorithms that can effectively suppress noise, clearly extract, and enhance defect features is key to improving the engineering practical value of Lamb wave nondestructive testing technology.
[0004] Currently, common techniques for denoising Lamb wave signals mainly include several traditional methods. Traditional wavelet thresholding denoising methods rely on fixed wavelet bases and preset threshold rules, making them ill-suited to the non-stationary, multimodal dynamic characteristics of Lamb wave signals. This can easily lead to the loss of effective signal or the introduction of distortion at signal abrupt changes during denoising. Adaptive signal decomposition methods, such as empirical mode decomposition (EMD), can decompose signals based on their inherent characteristics, but they generally suffer from mode aliasing. While improved algorithms offer some relief, they introduce additional parameters and impose a heavy computational burden, with parameter settings largely dependent on experience. Variational mode decomposition (VMD), as a non-recursive decomposition method, can effectively suppress mode aliasing, but its decomposition performance is highly dependent on the preset values of two key parameters: the number of modes and the penalty factor. Currently, parameter selection largely relies on user experience and lacks an adaptive mechanism that dynamically matches signal characteristics. This can lead to insufficient or excessive decomposition, or inaccurate mode center frequency positioning, thus affecting the accuracy of subsequent denoising. To optimize parameter selection, some studies have introduced swarm intelligence optimization algorithms for automatic optimization. However, when faced with complex non-convex optimization problems, these standard optimization algorithms often have limitations such as slow convergence speed, easy getting trapped in local optima, and fixed algorithm parameters lacking dynamic adjustment capabilities, which restrict their adaptability and robustness in dealing with real complex industrial noise scenarios.
[0005] In summary, existing technologies still face a series of challenges in practical applications: the parameter selection of signal decomposition methods is not intelligent enough and relies too much on prior experience; the introduced optimization algorithms themselves have bottlenecks in convergence efficiency and global exploration capabilities; and traditional thresholding strategies struggle to achieve the best balance between noise suppression and signal fidelity.
[0006] Therefore, there is an urgent need in the industry to develop a more intelligent, adaptive and robust noise reduction solution to meet the high-fidelity processing requirements of ultrasonic Lamb wave signals from aluminum plates in complex industrial environments. Summary of the Invention
[0007] To address the problem of excessive reliance on empirical parameter selection during VMD decomposition in signal processing, leading to highly subjective results, and the shortcomings of the traditional Caucus Porcupine Optimization (CPO) algorithm in terms of adaptability, this invention provides an ultrasonic Lamb wave denoising method for aluminum plates based on ICPO-VMD joint improved wavelet thresholding. By improving the Caucus Porcupine Optimization algorithm, the method achieves adaptive selection of VMD parameters, thereby improving the rationality of signal decomposition and the overall denoising effect.
[0008] This invention provides a method for ultrasonic Lamb wave denoising of aluminum plates based on ICPO-VMD jointly improved wavelet thresholding, comprising the following steps: The ultrasonic echo signal of the aluminum plate was collected, and the improved hog optimization algorithm was used with fuzzy entropy as the fitness function to adaptively optimize the number of modes and the penalty factor parameter of the variational mode decomposition to obtain the optimal parameter combination. The improved hog optimization algorithm introduced at least one of the following: parallel computing, dynamic parameter adjustment strategy and random perturbation strategy. The ultrasonic echo signal is subjected to variational mode decomposition using the optimal parameter combination to obtain multiple intrinsic mode function components; Calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, and divide all components into signal-dominant components, mixed components, and noise-dominant components according to the preset correlation coefficient threshold. The mixed components are denoised using an improved wavelet threshold function; The dominant component of the signal is reconstructed with the denoised mixed component to obtain the denoised Lamb wave signal.
[0009] Optionally, variational mode decomposition of the ultrasonic echo signal is performed using the optimal parameter combination, specifically including: An augmented Lagrangian function, including a quadratic penalty factor and Lagrange multipliers, is constructed to transform the constrained variational problem into an unconstrained problem. The alternating direction multiplier method is then used to iteratively update each modal component and its center frequency until the preset convergence condition is met.
[0010] Optionally, the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal is calculated, specifically including: Calculate the covariance between each intrinsic mode function component and the original ultrasonic echo signal; Calculate the standard deviation of each intrinsic mode function component; Calculate the standard deviation of the original ultrasonic echo signal; Dividing the covariance by the product of the standard deviation of the original ultrasonic echo signal and the standard deviation of the corresponding intrinsic mode function component yields the correlation coefficient of the corresponding intrinsic mode function component.
[0011] Optionally, based on a preset correlation coefficient threshold, all components are divided into signal-dominant components, mixed components, and noise-dominant components, specifically including: Components with a correlation coefficient greater than the first threshold are classified as dominant signal components; The components whose correlation coefficients fall between the second threshold and the first threshold are classified as mixed components; Components with correlation coefficients less than the second threshold are classified as noise-dominant components; where the first threshold is greater than the second threshold.
[0012] Optionally, the mixed components are denoised using an improved wavelet threshold function, specifically including: The mixed components are subjected to multi-level wavelet decomposition to obtain the approximation coefficients and detail coefficients at each decomposition scale; The noise standard deviation is estimated based on the first layer detail coefficients obtained from the decomposition, and the fixed threshold used for denoising is calculated in combination with the signal length. Each level of detail coefficients is processed using an improved threshold function to obtain the processed detail coefficients. The improved threshold function introduces a dynamic adjustment factor that decays exponentially based on the ratio of the absolute value of the detail coefficient to the median value of all absolute values of the detail coefficients, on the basis of the soft threshold function. The approximation coefficients and the processed detail coefficients of each layer are reconstructed using wavelet refactoring to obtain the denoised mixed components.
[0013] Optionally, the noise standard deviation is obtained by calculating the median of the absolute values of the first-level detail coefficients after wavelet decomposition and then dividing it by a standard normal distribution statistical constant.
[0014] This invention also proposes an ultrasonic Lamb wave denoising system for aluminum plates based on optimized variational mode decomposition and jointly improved wavelet thresholding, for implementing the method, comprising: The signal acquisition module is used to acquire the ultrasonic echo signal of the aluminum plate; The parameter optimization module, connected to the signal acquisition module, is used to adaptively optimize the number of modes and penalty factor parameters of variational mode decomposition using the improved hog cauda optimization algorithm with fuzzy entropy as the fitness function, to obtain the optimal parameter combination; wherein, the improved hog cauda optimization algorithm introduces parallel computing, dynamic parameter adjustment strategy and random perturbation strategy; The mode decomposition module, connected to the parameter optimization module, is used to perform variational mode decomposition on the ultrasonic echo signal using the optimal parameter combination to obtain multiple intrinsic mode function components. The modal classification module, connected to the modal decomposition module, is used to calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, and to divide all components into signal-dominant components, mixed components and noise-dominant components according to a preset correlation coefficient threshold. The wavelet denoising module is connected to the modality classification module and is used to denoise the mixed components using an improved wavelet threshold function. The signal reconstruction module, connected to the wavelet denoising module, is used to reconstruct the dominant component of the signal and the denoised mixed component to obtain the denoised Lamb wave signal.
[0015] The signal output module, connected to the signal reconstruction module, is used to output the denoised Lamb wave signal.
[0016] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.
[0017] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.
[0018] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.
[0019] Compared with the prior art, the present invention has the following advantages and technical effects: To address the problem that key parameters in variational mode decomposition rely on manual experience, leading to highly subjective and poorly adaptable decomposition results, this invention introduces an improved Crowned Pig optimization algorithm that integrates parallel computing, dynamic parameter adjustment, and random perturbation strategies. By employing fuzzy entropy as the fitness function, it achieves adaptive and intelligent optimization of the number of modes and penalty factor parameters. This technique effectively overcomes the blindness of traditional parameter selection methods, ensuring that variational mode decomposition can automatically match the optimal decomposition mode based on the characteristics of the input signal, thus laying a reasonable and reliable decomposition foundation for subsequent processing.
[0020] To address the problem of mixed modal components after decomposition, making it difficult to directly distinguish useful signals from noise, this invention calculates the correlation coefficients between each modal component and the original signal, and then precisely classifies them into three categories—signal-dominant, mixed, and noise-dominant—based on preset thresholds. This technique achieves accurate separation of signal and noise components, avoiding the erroneous removal of effective signals or the retention of noise, and providing clear and accurate input for subsequent targeted processing.
[0021] To address the challenges of signal-noise interweaving in mixed components and the tendency of traditional denoising methods to lead to signal distortion or noise residue, this invention employs an improved wavelet threshold function based on adaptive adjustment of the signal amplitude median. This technique dynamically adjusts the threshold intensity according to local signal features, effectively suppressing noise while better preserving signal details and edge features, significantly improving the fidelity of the denoising process.
[0022] This invention constructs a complete adaptive signal processing workflow through the aforementioned series of synergistic technical means. This workflow fundamentally solves key technical problems in ultrasonic Lamb wave detection of aluminum plates, such as signal distortion, difficulty in feature extraction, and low reliability of results caused by complex noise interference. Ultimately, it achieves high-fidelity and high-reliability noise reduction of Lamb wave signals, significantly improving the accuracy and robustness of subsequent defect detection and feature analysis. Attached Figure Description
[0023] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a range diagram of the four defense mechanisms of the CPO optimization algorithm in this embodiment of the invention; Figure 2 This is a comparison diagram of the improved wavelet thresholding function and the soft and hard thresholding functions according to an embodiment of the present invention; Figure 3 This is a flowchart of the ICPO-VMD optimization process according to an embodiment of the present invention; Figure 4 This is a flowchart of the ICPO-VMD joint improved wavelet thresholding denoising method according to an embodiment of the present invention; Figure 5 This is a comparison chart of the ICPO optimization algorithm and the CPO optimization algorithm in the simulation experiment of an embodiment of the present invention; Figure 6 The waveform and spectrum diagrams of the simulated signal decomposition in this embodiment of the invention are shown below. Figure 7 The following are waveforms of simulated signals after denoising using five methods according to embodiments of the present invention: (a) the original signal waveform; (b) the noisy signal waveform after adding Gaussian white noise; (c) the waveform after VMD denoising; (d) the waveform after ICPO-VMD denoising; (e) the waveform after ICPO-VMD combined with wavelet soft thresholding denoising; (f) the waveform after ICPO-VMD combined with wavelet hard thresholding denoising; and (g) the waveform after denoising using the method proposed in this invention (ICPO-VMD combined with improved wavelet thresholding). Figure 8 This is a comparison chart of the ICPO optimization algorithm and the CPO optimization algorithm in the actual test experiment of this invention embodiment; Figure 9 The waveform and spectrum diagrams of the measured signal decomposition in this embodiment of the invention are shown below. Figure 10 The following are waveforms of measured signals after denoising using five methods according to embodiments of the present invention: (a) is the waveform after VMD denoising; (b) is the waveform after ICPO-VMD denoising; (c) is the waveform after ICPO-VMD combined with wavelet soft thresholding denoising; (d) is the waveform after ICPO-VMD combined with wavelet hard thresholding denoising; and (e) is the waveform after denoising using the method proposed in this invention (ICPO-VMD combined with improved wavelet thresholding). Detailed Implementation
[0024] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0025] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0026] Example 1 This embodiment provides a method for ultrasonic Lamb wave denoising of aluminum plates based on ICPO-VMD jointly improved wavelet thresholding, including the following steps: The ultrasonic echo signal of the aluminum plate was collected, and the improved hog optimization algorithm was used with fuzzy entropy as the fitness function to adaptively optimize the number of modes and the penalty factor parameter of the variational mode decomposition to obtain the optimal parameter combination. The improved hog optimization algorithm introduced at least one of the following: parallel computing, dynamic parameter adjustment strategy and random perturbation strategy. The ultrasonic echo signal is subjected to variational mode decomposition using the optimal parameter combination to obtain multiple intrinsic mode function components; Calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, and divide all components into signal-dominant components, mixed components, and noise-dominant components according to the preset correlation coefficient threshold. The mixed components are denoised using an improved wavelet threshold function; The dominant component of the signal is reconstructed with the denoised mixed component to obtain the denoised Lamb wave signal.
[0027] One specific implementation method includes the following steps: Step 1: Select a 1mm thick aluminum plate and place the piezoelectric ultrasonic transducer at a specific position on the aluminum plate for transmitting and receiving ultrasonic signals. Step 2: The acquired ultrasonic echo signal is imported into the variational mode decomposition algorithm (VMD), the improved hog porcupine optimization algorithm (ICPO) is introduced into the VMD decomposition, and fuzzy entropy is selected as the fitness function to search for the optimal parameters K and α that are suitable for the signal characteristics. Step 3: Decompose the ultrasonic echo signal based on the optimized VMD optimal parameter combination; Step 4: The decomposed modes are divided into three parts: signal modes, mixed modes, and noise modes using the correlation coefficient method, and the mixed modes are subjected to improved wavelet thresholding. Step 5: Reconstruct the signal mode and the mixed mode after wavelet thresholding to obtain the denoised Lamb wave signal.
[0028] It is feasible to perform variational mode decomposition on the ultrasonic echo signal using the optimal parameter combination, specifically including: An augmented Lagrangian function, including a quadratic penalty factor and Lagrange multipliers, is constructed to transform the constrained variational problem into an unconstrained problem. The alternating direction multiplier method is then used to iteratively update each modal component and its center frequency until the preset convergence condition is met.
[0029] Specifically, the variational mode decomposition (VMD) in step 2 includes the following: VMD constructs a variational problem by setting constraints, and in solving this problem, decomposes the original signal into several IMF components with finite bandwidth. Each intrinsic mode function is defined as an amplitude modulation and frequency modulation function, which can be expressed in the form of equation (1): in For modal components, The envelope amplitude of the IMF. This represents the instantaneous phase of the IMF.
[0030] First, the analytic signal of each modal component is obtained using the Hilbert transform, and then the corresponding one-sided spectral function is calculated. The frequency domain component and amplitude of the signal are described by equation (2): in Let be the impulse function.
[0031] Then Multiplying by the complex exponential factor of the predicted center frequency achieves a frequency shift operation on the single-sided spectrum of each mode, so that the center frequency of each IMF function is shifted to the baseband. The formula can be expressed by equation (3): in Let be the kth center frequency.
[0032] Then, the bandwidth of each modal signal is calculated using the square of the second norm of the signal gradient, and a constrained optimization variational problem is constructed, as shown in equation (4): To solve the above constrained variational problem, a quadratic penalty factor α and a Lagrange multiplier λ are introduced to transform the problem into an unconstrained variational problem for solution. The augmented Lagrange function is shown in equation (5). The alternating direction multiplier method (ADMM) is used to iteratively update the number of modes, center frequency, and Lagrange multipliers. The process ends when the termination condition is met, as shown in equations (6) to (9): in , ( ), f(t), respectively (t), Fourier transform of (t), For step size parameters, This is the termination threshold.
[0033] Furthermore, the improved Crowned Porcupine Optimization Algorithm (ICPO) in step 2 is detailed below: like Figure 1 As shown, the CPO optimization algorithm is designed from four aspects of defense mechanisms against porcupines: vision, sound, smell, and physical aggression, effectively balancing the exploration and development processes in the search space. Addressing the issues of computational efficiency, difficulty in selecting fixed parameters, and susceptibility to local optima in traditional CPO optimization algorithms, this embodiment proposes the following three improvements to enhance the optimization efficiency of the CPO algorithm and provide more suitable parameters for subsequent VMD.
[0034] (1) Using parallel computing: In the improved CPO algorithm, the serial for loop in the population fitness evaluation and iterative update stage of the original algorithm is rewritten into the parallel structure parfor, so that the parallel computing toolbox in MATLAB can start multiple working processes and distribute different computing tasks equally to these processes to be executed simultaneously, thereby shortening the computation time of the algorithm.
[0035] (2) Introduction of dynamically adjustable parameters: The improved CPO algorithm introduces dynamically adjustable α and α. The value, which decreases over time, is expressed mathematically in equations (10) and (11): in These represent the maximum and minimum convergence rates, respectively, which are taken as 0.9 and 0.2 in this embodiment. The maximum number of iterations, and These are the maximum and minimum values of the defense mechanism ratio, respectively, which are 0.8 and 0.5 in this embodiment.
[0036] (3) Introducing random perturbation: A slight random perturbation is introduced into the improved CPO optimization algorithm. In this embodiment, a random vector is added to the individual position with a 5% probability, so that it can jump out of the local optimum region and increase the search diversity. The specific formula is shown in Equation (12): in The disturbance amplitude is , Let represent a normal random vector of dimension 2, with a mean of 0 and a variance of 1.
[0037] By introducing the above three improvement strategies, the ICPO optimization algorithm can converge quickly and escape local optima in a timely manner when faced with more complex optimization problems, thus improving the algorithm's adaptability.
[0038] Furthermore, the fuzzy entropy in step 2 is specifically defined as follows: Fuzzy entropy is a nonlinear metric that reflects the complexity and regularity of time series data. It can be used as a fitness function in optimization algorithms, and its specific definition is as follows: (1) Let the N-point sampling sequence be The m-dimensional vectors of equation (13) are generated sequentially, and equation (14) is the mean of the vectors within the brackets.
[0039] (2) Definition and Distance between The maximum value of the difference between the two is shown in equation (15): (3) Introduce fuzzy membership function , where n is the gradient of the exponential function boundary and r is the width of the exponential function boundary.
[0040] (4) Define the average similarity function, as shown in equation (16): (5) The fuzzy entropy is shown in equation (17): It is feasible to calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, specifically including: Calculate the covariance between each intrinsic mode function component and the original ultrasonic echo signal; calculate the standard deviation of each intrinsic mode function component; calculate the standard deviation of the original ultrasonic echo signal; divide the covariance by the product of the standard deviation of the original ultrasonic echo signal and the standard deviation of the corresponding intrinsic mode function component to obtain the correlation coefficient of the corresponding intrinsic mode function component.
[0041] Furthermore, the correlation coefficient in step 4 is specifically defined as follows: The correlation coefficient measures the strength of the association between each component and the original data. A lower correlation coefficient indicates that the component contains fewer features of the overall data; a higher correlation coefficient indicates that the component contains more significant features of the original signal. The calculation process for the correlation coefficient is as follows: (1) Calculate the covariance: in, and These are the arithmetic mean of the original signal and the Kth IMF function, respectively.
[0042] (2) Calculate the standard deviation: in These are the standard deviations of the original signal and the IMF component, respectively.
[0043] (3) Calculate the correlation coefficient: Implementably, based on a preset correlation coefficient threshold, all components are divided into signal-dominant components, mixed components, and noise-dominant components, specifically including: Components with correlation coefficients greater than a first threshold are classified as signal-dominant components; components with correlation coefficients between a second threshold and a first threshold are classified as mixed components; and components with correlation coefficients less than a second threshold are classified as noise-dominant components; wherein the first threshold is greater than the second threshold.
[0044] Implementable denoising of the mixed components using an improved wavelet threshold function includes: The hybrid component is subjected to multi-level wavelet decomposition to obtain approximation coefficients and detail coefficients at each decomposition scale. The noise standard deviation is estimated based on the first-level detail coefficients obtained from the decomposition, and a fixed threshold for denoising is calculated in combination with the signal length. Each level of detail coefficients is processed using an improved threshold function to obtain processed detail coefficients. The improved threshold function introduces a dynamic adjustment factor that decays exponentially based on the ratio of the absolute value of the detail coefficient to the median value of all absolute values of the detail coefficients, on the basis of the soft threshold function. The approximation coefficients and the processed detail coefficients of each level are reconstructed using wavelet decomposition to obtain the denoised hybrid component.
[0045] Furthermore, the noise standard deviation is obtained by calculating the median of the absolute values of the first-level detail coefficients after wavelet decomposition and then dividing it by a standard normal distribution statistical constant.
[0046] Furthermore, such as Figure 2 As shown, the improved wavelet threshold in step 4 is specifically defined as follows: The basic principle of wavelet thresholding denoising is to utilize the multi-resolution characteristics of wavelet transform to decompose the noisy signal into components of different scales. An appropriate threshold is set based on the differences in coefficient amplitudes, and the wavelet coefficients are processed using a threshold function to retain and reconstruct the main signal components, thus achieving denoising. The specific process is as follows: (1)Wavelet decomposition: Wavelet decomposition uses high-pass and low-pass filters to separate noisy signals layer by layer into approximate coefficients representing trends and detail coefficients representing details. Through multi-level decomposition, the approximate coefficients are further decomposed into new approximate coefficients and detail coefficients, thereby better distinguishing between the overall trend and local details of the signal.
[0047] (2) Threshold processing: Thresholding is the core of wavelet thresholding denoising. A reasonable threshold selection can effectively remove noise while preserving signal features to the greatest extent. In this embodiment, a fixed threshold is selected for denoising, as shown in equation (21): in , Here are the detail coefficients for each decomposition, and 0.6745 is the median of the absolute values of the standard normal distribution. In the calculation, the absolute median estimate is converted into the standard deviation. N is the signal length.
[0048] After selecting the threshold, each approximate coefficient obtained from wavelet decomposition should be over-thresholded. To overcome the problems of traditional threshold functions, this embodiment proposes an improved threshold function. By introducing an adaptive factor, the threshold can be dynamically adjusted according to the changes in signal amplitude. The threshold design is based on the amplitude characteristics of the signal itself, where the median amplitude can reflect the central trend of the signal energy distribution and is not easily affected by extreme values. The mathematical formula of the threshold function is shown in equation (22): in The median of the amplitude. It is set to a minimum value to prevent the denominator from being 0.
[0049] Regarding the proposed threshold function, its asymptotic and bias properties are proven below: ① Gradualism: when hour, , when hour, , therefore Therefore, the threshold function proposed in this embodiment is based on It is an asymptote.
[0050] ② Deviation: Since this threshold function is an odd function, therefore when hour: , 0.
[0051] The above formula illustrates the threshold function proposed in this embodiment. and There is no constant deviation between them, which effectively alleviates the deviation caused by the soft threshold function in wavelet threshold denoising.
[0052] (3) Wavelet reconstruction: The essence of wavelet reconstruction is the inverse transform of wavelet decomposition, which uses the approximation coefficients of the deepest decomposition layer and the detail coefficients after thresholding of each layer to finally obtain the reconstructed signal.
[0053] Working principle: Parameter Adaptive Optimization: First, the noisy raw ultrasonic echo signal is input into the Variational Mode Decomposition (VMD) algorithm. To address the issue of empirically selecting the mode decomposition number K and penalty factor α in the VMD algorithm, an improved Crowned Hogs optimization algorithm is introduced to optimize the parameters, using fuzzy entropy as the fitness function to evaluate the solution quality. ICPO, through iterative search, can automatically find the optimal parameter combination that best matches the characteristics of the current input signal, thereby achieving better signal decomposition. The process is as follows: Figure 3 As shown.
[0054] Modality selection: The original signal is decomposed into VMD using the optimal parameters found by the ICPO optimization algorithm. Then, the correlation coefficient of each IMF component is calculated, and these components are classified into three categories: "signal mode" with effective signal as the main component, "mixed mode" with signal and noise mixed, and "noise mode" with noise as the main component.
[0055] Improved wavelet thresholding denoising: By introducing an adaptive factor into the soft thresholding function, the threshold can be dynamically adjusted according to the changes in signal amplitude. The improved wavelet thresholding function is used to denoise the "mixed modes".
[0056] Signal reconstruction: Finally, the retained “signal modes” are linearly superimposed with the “hybrid modes” that have undergone wavelet threshold denoising to reconstruct the signal. The final output is the denoised, high-fidelity Lamb wave signal.
[0057] The overall process is as follows Figure 4 As shown.
[0058] Algorithm verification: To verify the effectiveness of the algorithm proposed in this embodiment, this experiment first uses simulated signals for verification. Combining the physical characteristics of piezoelectric ultrasonic Lamb wave signals, the experiment uses a Gaussian envelope modulated sine wave to simulate the ultrasonic Lamb wave signal, and its mathematical expression is shown in equation (23): Where A is the amplitude, f is the center frequency, and N is the number of periods.
[0059] Based on the above expression, the pure simulation signal is designed as shown in equation (24): Since this signal was obtained through mathematical model simulation, it does not contain any noise components. However, real-world industrial signals are often affected by various noise sources, such as environmental noise and sensor noise. To more realistically simulate actual conditions, Gaussian white noise was added to the signal in this experiment, with a target signal-to-noise ratio of 10 dB. Figure 5 This is a comparison chart of the ICPO and CPO optimization algorithms in simulation experiments. Figure 6 These are waveforms and spectrum diagrams of the simulated signal decomposition.
[0060] The noisy signal was decomposed using CPO-VMD and ICPO-VMD respectively, and their fitness curves are shown below. Figure 5 As shown, the ICPO algorithm exhibits significant advantages: its convergence speed is extremely fast, approaching the optimal solution within the third iteration, and the final minimum fuzzy entropy obtained is approximately 0.497; while the CPO algorithm has a slower convergence path, only stabilizing after the 11th iteration, and the final minimum fuzzy entropy obtained is approximately 0.502, which is higher than that of ICPO. These phenomena all indicate that the ICPO algorithm can more effectively suppress mode aliasing and obtain modal components with higher purity. Therefore, this experiment adopts the optimization results of the ICPO algorithm (K=12, α=1882) for subsequent signal decomposition and denoising processing.
[0061] Table 1 according to Figure 6As can be seen from the spectrum and correlation coefficients of each IMF component in Table 1, no mode aliasing phenomenon occurred in the VMD decomposition. Table 1 shows the correlation coefficients of each IMF in the simulated signal. As can be seen from Table 1, the correlation coefficient of IMF2 reaches 0.8462, which meets the set threshold of 0.8 or higher, indicating that this part is dominated by useful information and can be directly retained. The correlation coefficients of IMF1 and IMF3 are 0.7001 and 0.6552, respectively, falling between the threshold of 0.1 and 0.8. To prevent the loss of effective signals or noise residue, this part of the component undergoes improved wavelet threshold denoising. The correlation coefficients of IMF4-IMF12 are all below 0.1, nearly two orders of magnitude smaller than the first two components. Therefore, these components are determined to be dominated by noise and are thus removed. Therefore, the denoised signal is reconstructed from IMF2 and the IMF1 and IMF3 components after wavelet threshold denoising.
[0062] To verify the denoising method proposed in this embodiment, this method is compared with the method described above. Using the same variable, the decomposition level of all wavelet threshold denoising in this experiment is set to 3 levels, and the wavelet basis function is selected as the 'db1' wavelet. Signal-to-noise ratio (SNR) and root mean square error (RMSE) are introduced to evaluate the denoised signal. SNR measures the relative strength of the useful signal to the noise component, while RMS measures the overall deviation between the denoised signal and the original signal. Their definitions can be expressed as equations (25) and (26), where... Represents the original signal. This represents the denoised signal, where N is the signal length.
[0063] Table 2 Table 2 shows the signal-to-noise ratio (SNR) and root mean square error (RMSE) of the simulated signal after denoising using five methods. As can be seen from Table 2, compared with VMD, the ICPO-VMD combined improved wavelet threshold denoising method improved the signal-to-noise ratio of the simulated signal by 79.7% and reduced the root mean square error by 64.4%, indicating that the method in this embodiment significantly improved the signal quality and reduced the interference of noise on the signal during the denoising process.
[0064] Figure 6 These are the waveform and spectrum diagrams of the measured signal decomposition. Figure 7 These are waveforms of measured signals after denoising using five methods, mainly including VMD, ICPO-VMD, and a combination of wavelet thresholding. Figure 7Figures (a) and (b) show the waveforms of the original signal and the noisy signal, respectively. Figure (c) shows the denoising effect of VMD, which removes some high-frequency noise, but the peak value restoration is slightly low and there are spurious oscillations. Figure (d) shows the denoising result of ICPO-VMD, which improves the signal restoration, but there are still many spikes in the waveform, indicating that there is still high-frequency noise residue in the signal. The denoising effect of ICPO-VMD combined with wavelet thresholding is shown in Figures (e) and (f), respectively. It can be seen that the wavelet soft thresholding method suppresses most of the high-frequency noise in the signal, but the main body of the signal shows excessive smoothing distortion. The wavelet hard thresholding method denoises the signal relatively smoothly overall, but there are jitter and pseudo-Gibbs phenomena in some areas. Figure (g) shows the denoising effect of the method proposed in this embodiment. The results show that the method can significantly suppress spikes and distortions in the waveform, and the reconstructed signal is closest to the original signal. Its overall performance is significantly better than the traditional soft and hard thresholding methods.
[0065] In summary, compared with the traditional VMD algorithm, the ICPO-VMD joint improved wavelet threshold denoising method improves the signal-to-noise ratio of the simulated signal by 79.7% and reduces the root mean square error by 64.4%. Furthermore, the comparison of the denoised waveforms shows that the simulated signal denoised by this embodiment is smoother overall and retains signal features better. These results verify the effectiveness and superiority of the algorithm proposed in this embodiment.
[0066] To further verify the practicality of the algorithm proposed in this embodiment, it was applied to an experiment involving piezoelectric ultrasonic nondestructive testing. The experimental apparatus included a 1mm thick aluminum plate, a function generator, a power amplifier, a preamplifier, an oscilloscope, probes, and several wires. First, a sinusoidal excitation signal with a center frequency of 200 kHz was generated by the function generator. After amplification by the power amplifier, the signal was input into the aluminum plate through the probe. Subsequently, other probes were used to receive the signal after it propagated through the medium. The received signal was first amplified by the preamplifier before being transmitted to the oscilloscope for visualization and acquisition.
[0067] The measured signal was denoised using ICPO-VMD combined improved wavelet thresholding, and the fitness function curve is shown below. Figure 8 As shown, due to the more complex waveform characteristics and background noise of the measured Lamb wave signal, the search difficulty of the VMD parameter optimization algorithm is significantly increased, while the ICPO optimization algorithm still demonstrates superior performance: compared to the CPO optimization algorithm, it has a faster search speed, converges with fewer iterations, and finds a lower final fuzzy entropy value. Therefore, the optimal parameters (K=6, α=2473) found by the ICPO optimization algorithm are still selected in this experiment. Table 3 shows the correlation coefficients of each IMF of the measured signal: Table 3 Depend on Figure 9 As shown in Table 3, the VMD optimized by the ICPO algorithm can reasonably separate the measured signal from low-frequency smooth components to high-frequency noise components. The correlation coefficients of IMF1 and IMF3 are between 0.1 and 0.8, therefore, improved wavelet threshold denoising is applied to these two IMF components. The correlation coefficient of IMF2 reaches 0.9094, so it can be directly retained. The denoised IMF1 and IMF3 components and the directly retained IMF2 component are then reconstructed to obtain the denoised signal. To verify the applicability of the method in the measured signal, a comparative experiment was conducted again. In the experiment, the number of decomposition layers for wavelet threshold denoising was still set to 3, and the wavelet basis functions were still all selected as 'db1' wavelets.
[0068] Since a clean signal cannot be obtained in reality, the signal-to-noise ratio (SNR) and root mean square error (RMSE) cannot be used as evaluation criteria. To comprehensively evaluate the denoising effect of the measured signal, this embodiment combines the signal energy ratio (SER), residual rate of change (RVR), and waveform diagram. The signal energy ratio represents the ratio of the total energy of the denoised signal to the total energy of the original signal, as shown in formula (27). The closer the SER is to 1, the better the signal energy is preserved during the denoising process. The residual rate of change is used to calculate the smoothness of the signal waveform and spectrum, as shown in formula (28). The closer the RVR is to 0, the higher the smoothness and stability of the signal. Clean and effective Lamb wave signals are relatively smooth. Therefore, through the comprehensive analysis of these three factors, the effect of the denoising algorithm can be comprehensively judged.
[0069] Table 4 Table 4 shows the signal energy ratio (SER) and residual rate of change (RVR) of the simulated signal after denoising by five methods. As can be seen from Table 4, compared with the traditional VMD algorithm, the signal energy ratio of the measured signal denoised by the method in this embodiment is improved by 6.3%, and the residual rate of change is reduced by 40.2%. This indicates that the method effectively removes high-frequency noise in the signal, retains the main information in the signal, and improves the smoothness of the signal.
[0070] Figure 10 The images show waveforms of the measured signals after denoising using five different methods, including VMD, ICPO-VMD combined wavelet soft and hard thresholding, and the measured signal denoised by the algorithm in this embodiment. Figure 10 As shown in (a), VMD preserves the main characteristics of the signal, but a large amount of high-frequency noise still exists in the signal; Figure 10As shown in (b), the VMD denoising effect is improved after ICPO optimization, but noise residue still remains in the signal; Figure 10 As shown in (c), the ICPO-VMD combined wavelet soft thresholding denoising removed most of the high-frequency noise, but the peak part of the signal still exhibited oscillation. Figure 10 In (d), the signal obtained by VMD combined with hard thresholding is significantly smoothed, but there is a piecewise constant phenomenon, with severe jitter in the latter half; Figure 10 As can be seen from (e) in this embodiment, the method effectively removes high-frequency noise from the signal, making the signal smoother and effectively preserving the details of the signal, which can provide a clean signal for subsequent operations.
[0071] In summary, compared with the traditional VMD algorithm, the ICPO-VMD joint improved wavelet threshold denoising method improved the signal-to-energy ratio of the measured signal by 6.3% and reduced the residual rate of change by 40.2%. Furthermore, the waveform comparison after denoising shows that the algorithm in this embodiment can effectively suppress high-frequency noise, making the time-domain waveform of the signal smoother while effectively preserving the signal's detailed features. This indicates that the method achieves a better balance between noise suppression and useful signal preservation, thus demonstrating superior signal processing performance.
[0072] On the other hand, this embodiment also proposes an ultrasonic Lamb wave denoising system for aluminum plates based on optimized variational mode decomposition and jointly improved wavelet thresholding, for implementing the method, including: The signal acquisition module is used to acquire the ultrasonic echo signal of the aluminum plate; The parameter optimization module, connected to the signal acquisition module, is used to adaptively optimize the number of modes and penalty factor parameters of variational mode decomposition using the improved hog cauda optimization algorithm with fuzzy entropy as the fitness function, to obtain the optimal parameter combination; wherein, the improved hog cauda optimization algorithm introduces parallel computing, dynamic parameter adjustment strategy and random perturbation strategy; The mode decomposition module, connected to the parameter optimization module, is used to perform variational mode decomposition on the ultrasonic echo signal using the optimal parameter combination to obtain multiple intrinsic mode function components. The modal classification module, connected to the modal decomposition module, is used to calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, and to divide all components into signal-dominant components, mixed components and noise-dominant components according to a preset correlation coefficient threshold. The wavelet denoising module is connected to the modality classification module and is used to denoise the mixed components using an improved wavelet threshold function. The signal reconstruction module, connected to the wavelet denoising module, is used to reconstruct the dominant component of the signal and the denoised mixed component to obtain the denoised Lamb wave signal.
[0073] The signal output module, connected to the signal reconstruction module, is used to output the denoised Lamb wave signal.
[0074] On the other hand, this embodiment also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.
[0075] On the other hand, this embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.
[0076] On the other hand, this embodiment also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.
[0077] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for ultrasonic Lamb wave denoising of aluminum plates based on ICPO-VMD jointly improved wavelet thresholding, characterized in that, Includes the following steps: The ultrasonic echo signal of the aluminum plate was collected, and the improved hog optimization algorithm was used with fuzzy entropy as the fitness function to adaptively optimize the number of modes and the penalty factor parameter of the variational mode decomposition to obtain the optimal parameter combination. The improved hog optimization algorithm introduced at least one of the following: parallel computing, dynamic parameter adjustment strategy and random perturbation strategy. The ultrasonic echo signal is subjected to variational mode decomposition using the optimal parameter combination to obtain multiple intrinsic mode function components; Calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, and divide all components into signal-dominant components, mixed components, and noise-dominant components according to the preset correlation coefficient threshold. The mixed components are denoised using an improved wavelet threshold function; The dominant component of the signal is reconstructed with the denoised mixed component to obtain the denoised Lamb wave signal.
2. The method according to claim 1, characterized in that, Variational mode decomposition of the ultrasonic echo signal using the optimal parameter combination specifically includes: An augmented Lagrangian function, including a quadratic penalty factor and Lagrange multipliers, is constructed to transform the constrained variational problem into an unconstrained problem. The alternating direction multiplier method is then used to iteratively update each modal component and its center frequency until the preset convergence condition is met.
3. The method according to claim 1, characterized in that, Calculate the correlation coefficient between each intrinsic mode function component and the original ultrasound echo signal, specifically including: Calculate the covariance between each intrinsic mode function component and the original ultrasonic echo signal; Calculate the standard deviation of each intrinsic mode function component; Calculate the standard deviation of the original ultrasonic echo signal; Dividing the covariance by the product of the standard deviation of the original ultrasonic echo signal and the standard deviation of the corresponding intrinsic mode function component yields the correlation coefficient of the corresponding intrinsic mode function component.
4. The method according to claim 1, characterized in that, Based on a preset correlation coefficient threshold, all components are divided into signal-dominant components, mixed components, and noise-dominant components, specifically including: Components with a correlation coefficient greater than the first threshold are classified as dominant signal components; The components whose correlation coefficients fall between the second threshold and the first threshold are classified as mixed components; Components with correlation coefficients less than the second threshold are classified as noise-dominant components; where the first threshold is greater than the second threshold.
5. The method according to claim 1, characterized in that, The mixed components are denoised using an improved wavelet threshold function, specifically including: The mixed components are subjected to multi-level wavelet decomposition to obtain the approximation coefficients and detail coefficients at each decomposition scale; The noise standard deviation is estimated based on the first layer detail coefficients obtained from the decomposition, and the fixed threshold used for denoising is calculated in combination with the signal length. Each level of detail coefficients is processed using an improved threshold function to obtain the processed detail coefficients. The improved threshold function introduces a dynamic adjustment factor that decays exponentially based on the ratio of the absolute value of the detail coefficient to the median value of all absolute values of the detail coefficients, on the basis of the soft threshold function. The approximation coefficients and the processed detail coefficients of each layer are reconstructed using wavelet refactoring to obtain the denoised mixed components.
6. The method according to claim 5, characterized in that, The noise standard deviation is obtained by calculating the median of the absolute values of the first-level detail coefficients after wavelet decomposition and then dividing it by a standard normal distribution statistical constant.
7. A system for ultrasonic Lamb wave denoising of aluminum plates based on optimized variational mode decomposition and improved wavelet threshold, characterized in that, For implementing the method of any one of claims 1-6, comprising: The signal acquisition module is used to acquire the ultrasonic echo signal of the aluminum plate; The parameter optimization module, connected to the signal acquisition module, is used to adaptively optimize the number of modes and penalty factor parameters of variational mode decomposition using the improved hog cauda optimization algorithm with fuzzy entropy as the fitness function, to obtain the optimal parameter combination; wherein, the improved hog cauda optimization algorithm introduces parallel computing, dynamic parameter adjustment strategy and random perturbation strategy; The mode decomposition module, connected to the parameter optimization module, is used to perform variational mode decomposition on the ultrasonic echo signal using the optimal parameter combination to obtain multiple intrinsic mode function components. The modal classification module, connected to the modal decomposition module, is used to calculate the correlation coefficient between each intrinsic mode function component and the original ultrasonic echo signal, and to divide all components into signal-dominant components, mixed components and noise-dominant components according to a preset correlation coefficient threshold. The wavelet denoising module is connected to the modality classification module and is used to denoise the mixed components using an improved wavelet threshold function. The signal reconstruction module, connected to the wavelet denoising module, is used to reconstruct the dominant component of the signal and the denoised mixed component to obtain the denoised Lamb wave signal. The signal output module, connected to the signal reconstruction module, is used to output the denoised Lamb wave signal.
8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-6.
10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-6.