Honeycomb sandwich structure air coupling ultrasonic signal processing method based on COA-VMD combined wavelet threshold improvement

Abstract

The invention relates to an air coupling ultrasonic signal processing method based on a COA-VMD combined improvement wavelet threshold, and the method specifically comprises the following steps: 1, employing a meta-heuristic algorithm Coati, and introducing a minimum envelope entropy as a fitness function of the algorithm, and taking the minimum envelope entropy as an evaluation criterion of an optimal solution; 2, decomposing a noisy part in the air coupling ultrasonic signal into a plurality of intrinsic mode function components by using the optimized VMD decomposition parameters; and 3, on the basis of the step 2, distinguishing an effective ultrasonic signal component f1 and a noise component f2 in the detected IMF components by adopting a correlation coefficient method. And step 4, processing the noise component f2 by adopting an improved wavelet threshold function algorithm to obtain a noise-reduced air coupling ultrasonic signal. According to the method, COA-VMD and an improved wavelet threshold noise reduction method are combined, the signal-to-noise ratio is effectively improved, and a technical basis is provided for high-precision detection of defects in the honeycomb sandwich structure.

Description

Technical Field

[0001] The invention relates to a signal processing method, in particular to an air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold, and belongs to the technical field of ultrasonic detection. Background Art

[0002] Honeycomb sandwich structures are widely used in aerospace, automotive manufacturing and construction industries due to their light weight, high strength and excellent rigidity. The integrity of these structures is critical, which is directly related to the performance and safety of the structures. However, the complex porous nature of honeycomb sandwich structures poses challenges to conventional contact ultrasonic testing methods, such as poor coupling, low detection efficiency and potential damage to the material being tested. Therefore, it is particularly important to choose a non-contact detection technology. The non-contact air-coupled ultrasonic testing method uses air as the transmission medium, overcoming the complexity and material damage risk brought by the liquid coupling agent in the conventional method. This technology does not require physical contact with the object being tested, and can achieve fast and flexible detection, thereby improving the detection efficiency. However, the signal-to-noise ratio of air-coupled ultrasonic testing is low, which will affect the detection accuracy of defects in honeycomb sandwich structures. Therefore, there is an urgent need for a new solution to solve the above technical problems. Summary of the invention

[0003] The present invention aims at the technical problems existing in the prior art and provides an air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold. The technical invention can effectively enhance the signal-to-noise ratio by adopting a noise reduction method combining VMD parameters optimized by COA algorithm with improved wavelet threshold, which can provide a basis for further realizing high-precision detection of defects in honeycomb sandwich structures.

[0004] In order to achieve the above object, the technical solution of the present invention is as follows: a method for processing air-coupled ultrasonic signals based on COA-VMD combined with improved wavelet threshold, the method comprising the following steps:

[0005] The method comprises the following steps:

[0006] Step 1: First, the meta-heuristic algorithm Coati (COA) is used, and the minimum envelope entropy is introduced as the fitness function of the algorithm as the evaluation criterion for the optimal solution. For the air-coupled ultrasonic signal in the honeycomb sandwich structure, the COA algorithm is used to adaptively optimize the variational mode decomposition (VMD) to obtain the best combination of decomposition parameters. Step 2: Using the optimized VMD decomposition parameters, the noisy part of the air-coupled ultrasonic signal is decomposed into multiple intrinsic mode function (IMF) components.

[0007] Step 3: Based on step 2, the correlation coefficient method is used to distinguish the effective ultrasonic signal component f1 and the noise component f2 in the detected IMF component.

[0008] Step 4: Use the improved wavelet threshold function algorithm to process the noise component f2 to obtain the IMF component f22 after noise reduction. Then superimpose and reconstruct f22 and f1 to obtain the air-coupled ultrasonic signal after noise reduction.

[0009] In the invention, the variational mode decomposition (VMD) method is a non-recursive method that can decompose the hypersignal into band-limited intrinsic mode functions (BIMFs). Unlike empirical mode decomposition, VMD does not produce residuals and reduces modal aliasing, thereby effectively improving the ability to distinguish between signals and noise. However, in the process of VMD decomposition, the parameters α and K are usually selected based on empirical judgment, and too large or too small α and K counts will cause the decomposition results to fail to accurately represent the true characteristics and information of the signal. In order to solve this problem, the present invention proposes to use the meta-heuristic algorithm COA, with the minimum envelope entropy as the fitness function, to find the optimal solution of VMD parameters. Then, the improved VMD is used to decompose the air-coupled ultrasonic detection signal of the actual test into multiple IMF components, and the correlation coefficient method is used to distinguish the effective ultrasonic signal component from the noise signal component. In the post-processing process, the improved wavelet threshold function algorithm is used to process the noise signal component, and the noise component after denoising is superimposed and reconstructed with the effective ultrasonic signal component to obtain the air-coupled ultrasonic signal after denoising, which can provide a basis for further realizing high-precision detection of defects in honeycomb sandwich structures.

[0010] Variational Mode Decomposition Algorithm

[0011] VMD is an adaptive, non-recursive decomposition method that achieves signal decomposition through variational optimization without the need for preset basis functions or wavelet functions. VMD decomposes a complex signal into several modal components (IMFs) with different center frequencies and limited bandwidths through variational optimization. Each IMF is equivalent to a frequency modulated and amplitude modulated signal, expressed as:

[0012] u k (t) = A k (t)cos(φ k (t)) (8)

[0013] Where k is the number of IMFs, k = 1, 2, ... k. k (t) is the kth IMF; Ak (t) is the instantaneous amplitude of the kth IMF; φ k (t) is the phase function of the Kth modal component, which usually contains frequency modulation information and indicates that the phase of the signal changes with time.

[0014] The core idea of ​​VMD decomposition is to construct and solve a variational problem. The goal is to find k modal functions u k (t), so that the total bandwidth of all decomposed IMFs is minimized, and their sum is equal to the input source signal. The specific steps are as follows:

[0015] (1) Constructing a variational problem:

[0016]

[0017] in, represents the partial derivative with respect to time t; ω k Corresponding to u k The center frequency of; δ(t) is the Dirac function; is the Hilbert transform.

[0018] (2) Introduce the penalty factor α and the multiplicative operator λ, and use the Lagrangian method to transform equation (10) into an equivalent unconstrained variational problem. The value of α ensures the decomposition accuracy of the signal, and the value of λ ensures the strictness of the constraint conditions. The augmented Lagrangian function is:

[0019]

[0020] Among them, [] is the inner product operation.

[0021] Coati optimizes VMD algorithm

[0022] The Coati Optimization Algorithm (COA) is a new population-based intelligent optimization algorithm proposed by Mohammad Dehghani et al. in January 2023 to optimize the parameter settings of VMD. The algorithm imitates the natural behavior of raccoons preying on lizards and avoiding predators to find the optimal solution. Unlike classic intelligent optimization algorithms such as genetic algorithms and particle swarm optimization algorithms, COA constructs a mathematical model by simulating the natural behavior of raccoons. Its search mechanism is divided into two stages: predation and avoidance. It has the ability of global search and local optimization, and there is no need to set complex parameters. The specific steps for COA to optimize VMD parameters are as follows:

[0023] Step (1-1): Problem definition and parameter initialization. First, define the parameters of the COA algorithm to optimize VMD decomposition as the penalty factor and the number of decomposition modes. Then, initialize the parameters of the COA algorithm, including the number of raccoons (each raccoon represents a set of candidate solutions), the maximum number of iterations, the range of parameter changes, etc. Assume that there are M raccoons, and the location information of the raccoons is represented by X i (i=1, 2, ..., M), the position of the raccoon is randomly generated, the maximum number of iterations is T, and the definition is expressed by formula (1).

[0024] Step (1-2): Definition of fitness function,

[0025] Fitness function is a core concept in evolutionary algorithms, genetic algorithms, genetic programming and other heuristic search algorithms. It is used to evaluate the quality of candidate solutions, that is, the fitness or quality of the solution. The fitness function usually maps the solution to the problem to a real number or vector. This value can be used to compare the performance of different solutions and guide the selection, crossover and mutation operations in the search process. In air-coupled ultrasonic signal processing, this function can be constructed based on factors such as the quality of signal reconstruction after VMD decomposition, the degree of reduction of background noise, and the fidelity of the signal. The goal of the fitness function is to maximize the quality of the signal or minimize the error. As a fitness function, the average envelope entropy can effectively reflect the sparsity of the signal. When the original signal is decomposed into K IMFs through the VMD algorithm, the fewer the noise components contained in the IMF, the stronger the correlation with the original signal, and the smaller the average envelope entropy. Therefore, this scheme selects the minimum average envelope entropy as the fitness function of COA.

[0026] Then, before the first iteration of the COA algorithm, the initial fitness value f(X i ), as an indicator for evaluating the parameters of VMD decomposition. In metaheuristic algorithms such as COA, the criterion for measuring the quality of candidate solutions is the value of the objective fitness function. Therefore, the population member that leads to the best value evaluation of the objective function is called the best member of the population. Since the candidate solutions are continuously updated during the algorithm iterations, the best member of the population is also updated in each iteration.

[0027] Steps (1-3): Simulating raccoon predation behavior for air-coupled ultrasonic signal processing

[0028] 1. Grouping and target setting: When the algorithm is initialized, all raccoons (representing different VMD parameter combinations) are divided into two groups. One group remains stationary and does not change the current parameter settings, simulating raccoons "resting in a tree". The other group actively explores new parameter combinations, simulating raccoons "looking for prey on the ground".

[0029] 2. Fitness evaluation and update: The fitness of each raccoon is evaluated based on its impact on the ultrasonic signal processing results, such as the quality of signal reconstruction or the effect of noise suppression. The optimal solution (prey) is considered to be the best parameter combination found so far. The raccoons on the ground will update their parameter settings based on this optimal solution, that is, move towards a better parameter combination. The mathematical model for the raccoons in the trees is expressed by equation (2).

[0030] When the lizard falls from the tree, the best position is randomly updated, and the raccoon position is also updated accordingly, and the fitness of the individual is calculated again. The strategy in the predation phase causes the raccoon to move to different positions in the search space, reflecting the exploration ability of the COA algorithm to conduct global search in the problem-solving space.

[0031] For the positions of the raccoon waiting for prey on the ground and the fallen lizard, the mathematical expressions are expressed by equations (3) and (4).

[0032] Step (1-4): During the parameter optimization process of ultrasonic signal processing, the parameter combination may cause the result to fall into a local optimum. The present invention can be improved as follows.

[0033] 1. Escape strategy: When some raccoon parameter combinations show stagnant or degraded improvements, these solutions will simulate the behavior of escaping from predators, i.e. randomly changing their parameter settings to escape possible local optimal traps. This helps explore new parameter spaces and may discover better global solutions.

[0034] When a predator attacks a raccoon, the raccoon will flee from its location. The mathematical formula is expressed by equation (5).

[0035] 2. Maintain exploration capability: Through this escape mechanism, the algorithm can continue to explore uncovered parameter areas, enhance global search capabilities, and avoid premature convergence.

[0036] Step (1-5): Perform greedy selection on the population to obtain the global optimal solution, and store and output the optimal solution. Greedy selection is represented by formula (6).

[0037] Improved wavelet threshold denoising

[0038] The calculation of wavelet coefficients needs to be determined by a threshold. If the threshold is too large, part of the useful signal will be mistakenly filtered out as noise. Otherwise, there will be residual noise. In this scheme, the threshold is selected as shown in equation (16).

[0039]

[0040] Where N is the length of the signal, σ is the root mean square error of the noise, and λ is the threshold.

[0041] The conventional hard threshold function is able to retain more of the true signal spike features, but due to poor continuity, oscillations will occur during the reconstruction process. There is a continuous difference between the estimated value and the true value, which results in some errors in the reconstructed signal even though the soft threshold function has greater continuity and the reconstructed signal is smoother. The expressions for hard and soft thresholds are shown below:

[0042] Hard threshold function:

[0043]

[0044] Soft threshold function:

[0045]

[0046] where ω j,k is the wavelet coefficient, w j, k is the thresholded wavelet coefficient and sgn is the sign function.

[0047] The present invention adopts an improved threshold function. Formula (14) is the mathematical formula of the function:

[0048]

[0049] Where a and β are adjustment parameters of the threshold function. When 0<a<1, β is a constant with a positive sign. By adjusting the a and β parameters, the threshold function can be adjusted between the soft threshold and the hard threshold, so as to achieve better noise reduction effect and reduce errors. The present invention uses an improved wavelet threshold function algorithm to perform noise reduction on the noise component, and on this basis, the IMF component after noise reduction is superimposed and reconstructed with the effective ultrasonic signal component to obtain the air-coupled ultrasonic signal after noise reduction.

[0050] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for processing air-coupled ultrasonic signals of a honeycomb sandwich structure based on improved variational mode decomposition and combined with improved wavelet threshold is implemented.

[0051] A computer-readable storage medium stores computer instructions, which, when executed by a processor, implement the air-coupled ultrasonic signal processing method of a honeycomb sandwich structure based on improved variational mode decomposition and combined with improved wavelet threshold.

[0052] Compared with the prior art, the present invention has the following advantages: 1) Improved variational mode decomposition technology: an improved VMD technology is proposed, which improves the signal-to-noise ratio of air-coupled ultrasonic signals by optimizing the mode decomposition parameters based on the COA algorithm and jointly improving the wavelet threshold. Compared with the traditional VMD method, it effectively solves the problem that the two parameters of the penalty factor and the number of decomposed modes in the traditional VMD algorithm need to be manually set. This improved algorithm can more effectively separate and extract the complex signal components in the honeycomb sandwich structure, including signal changes caused by noise and defects. This improvement improves the signal-to-noise ratio of the signal, which can provide a basis for further realizing high-precision detection of defects in honeycomb sandwich structures. 2) Integrated application of air-coupled ultrasonic detection: the air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold can effectively detect internal defects of honeycomb sandwich structures without physical contact. This non-contact detection method not only reduces the potential damage to the sample, but also enhances the flexibility and safety of the detection process. The application of air coupling technology makes the algorithm particularly suitable for evaluating materials and structures that are sensitive to or difficult to contact, further expanding the application scope of ultrasonic detection technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is the wavelet threshold function graph,

[0054] Figure 2 It is a schematic diagram of the overall process of the present invention,

[0055] Figure 3 This is a schematic diagram of the actual collected air-coupled ultrasonic signal of the honeycomb sandwich structure.

[0056] Figure 4 is a schematic diagram of the fitness function curve,

[0057] Figure 5 Schematic diagram of IMF components decomposed by VMD.

[0058] Figure 6 This is a comparison chart of the original signal and the noise-reduced signal. DETAILED DESCRIPTION

[0059] Example 1: See Figure 1-Figure 6 A method for processing air-coupled ultrasonic signals of a honeycomb sandwich structure based on improved variational mode decomposition combined with improved wavelet threshold and improved wavelet threshold is characterized in that the method comprises the following steps:

[0060] Step 1: First, the metaheuristic algorithm Coati (COA) is used, and the minimum envelope entropy is introduced as the fitness function of the algorithm as the evaluation criterion for the optimal solution. For the air-coupled ultrasonic signal in the honeycomb sandwich structure, the COA algorithm is used to adaptively optimize the variational mode decomposition (VMD) to obtain the best combination of decomposition parameters. Variational mode decomposition (VMD) is an adaptive and completely non-recursive signal processing method suitable for complex non-stationary signals, which aims to decompose the signal into several intrinsic mode functions (IMFs) with different center frequencies and limited bandwidths. The COA optimization algorithm is a population-based intelligent optimization algorithm used to optimize the parameter settings of VMD. The algorithm imitates the natural behavior of raccoons preying on lizards and avoiding predators to find the optimal solution. Unlike classic intelligent optimization algorithms such as genetic algorithms and particle swarm optimization algorithms, COA constructs a mathematical model by simulating the natural behavior of raccoons. Its search mechanism is divided into two stages: predation and avoidance. It has the ability of global search and local optimization, and does not require the setting of complex parameters. In response to the challenge that air-coupled ultrasonic signals are often masked by noise, the present invention adopts a signal processing method based on COA-VMD. The advantage of the COA algorithm is that it can effectively solve the problem that the two parameters of the penalty factor and the number of decomposed modes in the traditional VMD algorithm need to be manually set. Through the introduction of the COA algorithm, the performance of VMD has been significantly improved, which provides a basis for the subsequent improved wavelet threshold processing of the noise component, making the noise suppression and feature extraction of ultrasonic echo signals more accurate and convenient.

[0061] Step 2: Using the optimized VMD decomposition parameters, the noisy part of the air-coupled ultrasonic signal is decomposed into multiple intrinsic mode function (IMF) components.

[0062] Step 3: Based on step 2, the correlation coefficient method is used to distinguish the effective ultrasonic signal component f1 and the noise component f2 in the detected IMF component.

[0063] Step 4: Use the improved wavelet threshold function algorithm to process the noise component f2 to obtain the IMF component f22 after noise reduction. Then superimpose and reconstruct f22 and f1 to obtain the air-coupled ultrasonic signal after noise reduction. The present invention combines COA-VMD and the improved wavelet threshold noise reduction method to effectively improve the signal-to-noise ratio and provide a technical basis for high-precision detection of defects in honeycomb sandwich structures.

[0064] The specific implementation process of step 1 is as follows:

[0065] (1-1) Problem definition and parameter initialization. First, define the parameters of the COA algorithm to optimize VMD decomposition as the penalty factor and the number of decomposition modes. Then, initialize the parameters of the COA algorithm, including the number of raccoons (each raccoon represents a set of candidate solutions), the maximum number of iterations, and the range of parameter changes. Assume that there are M raccoons, and the location information of the raccoons is represented by X i (i=1, 2, ..., M), the position of the raccoon is randomly generated, the maximum number of iterations is T, and the definition is expressed by formula (1):

[0066] (1-2) Definition of fitness function, fitness function is a core concept in evolutionary algorithms, genetic algorithms, genetic programming and other heuristic search algorithms. It is used to evaluate the quality of candidate solutions, that is, the fitness or quality of the solution. The fitness function usually maps the solution to a real number or vector. This value can be used to compare the performance of different solutions and guide the selection, crossover and mutation operations in the search process. In air-coupled ultrasonic signal processing, this function is constructed based on factors such as the quality of signal reconstruction after VMD decomposition, the degree of background noise reduction, and signal fidelity. The goal of the fitness function is to maximize the quality of the signal or minimize the error. The average envelope entropy, as a fitness function, can effectively reflect the sparsity of the signal. When the original signal is decomposed into K IMFs through the VMD algorithm, the fewer noise components contained in the IMF, the stronger the correlation with the original signal, and the smaller the average envelope entropy. Therefore, this scheme selects the minimum average envelope entropy as the fitness function of COA. Then, before the first round of iteration of the COA algorithm, the initial fitness value f(xi) of the individual is calculated as an indicator for evaluating the VMD decomposition parameters. In metaheuristic algorithms (such as COA), the criterion for measuring the quality of candidate solutions is the value of the target fitness function. Therefore, the group member that leads to the optimal value evaluation of the objective function is called the best member of the group. Since the candidate solution is continuously updated during the algorithm iteration, the best member of the population will also be updated in each iteration.

[0067] (1-3) The simulated raccoon predation behavior is applied to air-coupled ultrasonic signal processing, as follows:

[0068] (1) Grouping and target setting: When the algorithm is initialized, all raccoons (representing different VMD parameter combinations) are divided into two groups. One group remains stationary and does not change the current parameter settings, simulating raccoons "resting in a tree". The other group actively explores new parameter combinations, simulating raccoons "looking for prey on the ground".

[0069] (2) Fitness evaluation and update: The fitness of each raccoon is evaluated based on its impact on the ultrasonic signal processing results, such as the quality of signal reconstruction or the effect of noise suppression. The optimal solution (prey) is considered to be the best parameter combination currently found. The raccoons on the ground will update their parameter settings based on this optimal solution, that is, move towards a better parameter combination. The mathematical model for the raccoons in the trees is expressed by formula (2).

[0070] When the lizard falls from the tree, the best position is randomly updated, and the raccoon's position is also updated accordingly. The fitness of the individual at this time is calculated. The strategy in the predation stage causes the raccoon to move to different positions in the search space, which reflects the exploration ability of the COA algorithm to conduct global search in the problem-solving space.

[0071] For the positions of the raccoon waiting for prey on the ground and the fallen lizard, the mathematical models are expressed by equations (3) and (4), respectively.

[0072] (1-4) In the process of parameter optimization of ultrasonic signal processing, if the parameter combination causes the result to fall into a local optimum, further processing is performed, and the specific processing is as follows:

[0073] (1) Escape strategy: When some raccoon parameter combinations show stagnation or degradation, these solutions will simulate the behavior of escaping from predators, that is, randomly changing their parameter settings to escape possible local optimal traps. This helps explore new parameter spaces and may discover better global solutions.

[0074] When a predator attacks a raccoon, the raccoon will flee from its location. The mathematical model is expressed as formula (5).

[0075] (2) Maintaining exploration capability: Through this escape mechanism, the algorithm can continue to explore uncovered parameter areas, enhance global search capabilities, and avoid premature convergence.

[0076] (1-5) Finally, greedy selection is performed on the population to obtain the global optimal solution, and the optimal solution is stored and output, which is the penalty factor of VMD and the variational mode decomposition number; the greedy selection is expressed by formula (6).

[0077] The specific implementation process of step 2 is as follows: based on step 1, the VMD algorithm is used to select the penalty factor α and the variational mode decomposition number K obtained in step 1, and the air-coupled ultrasonic signal in the honeycomb sandwich structure is decomposed by VMD to obtain multiple IMF components.

[0078] The specific implementation process of step 3 is as follows: after VMD decomposition of the original air-coupled ultrasonic signal, the correlation coefficient method is introduced to select the IMF components obtained by decomposition, and the correlation coefficient threshold is set to 0.5. For the IMF components with correlation coefficients less than the threshold, improved wavelet threshold processing is performed, and for the IMF components with correlation coefficients greater than the threshold, no processing is performed. This method uses the correlation coefficient method to effectively divide the IMF components after VMD decomposition into effective ultrasonic signal components and noise components, laying the foundation for the subsequent improved wavelet threshold processing.

[0079] The specific implementation process of step 4 is as follows: using the improved wavelet threshold function, represented by formula (14).

[0080] When a and β take different values, the comparison between hard threshold and soft threshold function is as follows Figure 1 As shown by Figure 1 It can be seen that the improved threshold function has the flexibility of parameter adjustment, and can be adjusted between the soft and hard threshold functions according to the signal, so as to achieve better noise reduction effect and reduce errors. The present invention uses an improved wavelet threshold function algorithm to perform noise reduction on the noise component, and on this basis, the noise-reduced IMF component is superimposed and reconstructed with the effective ultrasonic signal component to obtain the noise-reduced air-coupled ultrasonic signal.

[0081] The present invention performs noise reduction processing on the actually collected air-coupled ultrasonic signals of the honeycomb sandwich structure. Figure 3 is the actual collected air-coupled ultrasonic signal. The following Coati algorithm is executed to optimize the VMD decomposition signal. The raccoon population is set to 20 and the maximum number of iterations is set to 10. The optimization range of the penalty factor is [100, 3500], the iteration range of the decomposition mode number is [2, 12], and the minimum value of the minimum envelope entropy is taken as the optimal strategy for this example. Figure 4 Display the fitness function curve. When the number of iterations is 4, the fitness function reaches the minimum value of 6.45.

[0082] For the Coati algorithm to optimize VMD parameters, the optimal solution obtained in the example is: the number of decomposed modes is 11, and the penalty factor is 2105. Figure 5 As shown, the VMD algorithm is used to decompose the original signal into 11 IMF components.

[0083] like Figure 6 As shown in the figure, the IMF components obtained are divided into effective ultrasonic signal components and noise components using the correlation coefficient method. In this example, the correlation coefficient threshold is set to 0.5. For noise components with correlation coefficients less than the threshold, improved wavelet threshold processing is performed; for effective ultrasonic signal components with correlation coefficients greater than the threshold, no processing is performed. Figure 6As shown, on this basis, the noise component after noise reduction and the effective ultrasonic signal component are superimposed and reconstructed to obtain the air-coupled ultrasonic signal after noise reduction, which effectively enhances the signal-to-noise ratio, which can provide a basis for further realizing high-precision detection of defects in honeycomb sandwich structures. It should be noted that the above embodiments are not used to limit the protection scope of the present invention, and equivalent changes or substitutions made on the basis of the above technical solutions fall within the scope of protection of the claims of the present invention.

Claims

1. A method for processing air-coupled ultrasonic signals based on COA-VMD combined with improved wavelet threshold, characterized in that: The method comprises the following steps: Step 1: First, the meta-heuristic algorithm Coati (COA) is used, and the minimum envelope entropy is introduced as the fitness function of the algorithm as the evaluation criterion for the optimal solution. For the air-coupled ultrasonic signal in the honeycomb sandwich structure, the COA algorithm is used to adaptively optimize the variational mode decomposition (VMD) to obtain the best combination of decomposition parameters. Step 2: Using the optimized VMD decomposition parameters, the noisy part in the air-coupled ultrasonic signal is decomposed into multiple intrinsic mode function (IMF) components. Step 3: Based on step 2, the correlation coefficient method is used to distinguish the effective ultrasonic signal component f1 and the noise component f2 in the detected IMF component. Step 4: Use the improved wavelet threshold function algorithm to process the noise component f2 to obtain the IMF component f22 after noise reduction, and then superimpose and reconstruct f22 and f1 to obtain the air-coupled ultrasonic signal after noise reduction.

2. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 1 is characterized in that: The specific implementation process of step 1 is as follows: (1-1) Problem definition and parameter initialization. First, define the parameters of the COA algorithm to optimize VMD decomposition as the penalty factor and the number of decomposition modes. Then, initialize the parameters of the COA algorithm, including the number of raccoons (each raccoon represents a set of candidate solutions), the maximum number of iterations, and the range of parameter variation. Suppose there are M raccoons, and the location information of the raccoons is represented by X i (i=1, 2, ..., M), the position of the raccoon is randomly generated, and the maximum number of iterations is T, which is defined as follows: X i =lb+r·(ub-lb) (1) Where ub is the upper limit matrix of VMD parameters, lb is the lower limit matrix of VMD parameters, and r is a randomly generated number between 0 and 1. (1-2) Definition of fitness function. In air-coupled ultrasonic signal processing, when the original signal is decomposed into K IMFs through the VMD algorithm, the fewer noise components contained in the IMF, the stronger the correlation with the original signal, and the smaller the average envelope entropy. The minimum average envelope entropy is selected as the fitness function of COA. Then, before the first round of iteration of the COA algorithm, the initial fitness value f(X i ), as an indicator for evaluating the VMD decomposition parameters, in the population, the member that can make the objective function achieve the best value is called the best member. Since the candidate solution is continuously updated during the algorithm iteration process, the best member of the population will also be updated in each iteration. (1-3) Simulating raccoon predation behavior for air-coupled ultrasonic signal processing, (1-4) In the process of parameter optimization of ultrasonic signal processing, if the parameter combination causes the result to fall into a local optimum, further processing is performed. (1-5) Finally, greedy selection is performed on the population to obtain the global optimal solution, and the optimal solution is stored and output, which is the penalty factor of VMD and the variational mode decomposition number.

3. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 2 is characterized in that: Steps (1-3) simulate the raccoon's predation behavior and apply it to air-coupled ultrasonic signal processing, as follows: (1) Grouping and target setting: When the algorithm is initialized, all raccoons (representing different VMD parameter combinations) are divided into two groups. One group remains stationary and does not change the current parameter settings, simulating raccoons "resting in a tree". The other group actively explores new parameter combinations, simulating raccoons "looking for prey on the ground". (2) Fitness evaluation and update: The fitness of each raccoon is evaluated based on its impact on the ultrasonic signal processing results, such as the quality of signal reconstruction or the effect of noise suppression. The optimal solution (prey) is considered to be the best parameter combination currently found. The raccoons on the ground will update their parameter settings based on this optimal solution, that is, move towards a better parameter combination. The mathematical expression for the raccoons in the trees is: in and Represent the location information of the i-th raccoon in the t+1th iteration and the tth iteration respectively; is the position of the lizard on the tree in the tth iteration, that is, the best parameter combination found so far, I is a random integer in [1,2], t is the current iteration number, When the lizard falls from the tree, the best position is randomly updated, and the raccoon's position is also updated accordingly. The fitness of the individual at this time is calculated. The strategy in the predation stage causes the raccoon to move to different positions in the search space, which reflects the exploration ability of the COA algorithm to conduct global search in the problem-solving space. For the raccoon waiting for prey on the ground and the position of the fallen lizard, the mathematical expression is: <h2 style=";text-align:left;direction:ltr">Iguana<h2 style=";text-align:left;direction:ltr"> t <h2 style=";text-align:left;direction:ltr"> (lb+r·(ub-lb) (4) in, Represents the fitness value corresponding to the position of the i-th raccoon in the t-th iteration; Iguana t represents the position of the lizard that fell from the tree in the tth iteration.

4. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 2 is characterized in that: In the process of parameter optimization of ultrasonic signal processing in step (1-4), the parameter combination may cause the result to fall into a local optimum. The specific processing is as follows: (1) Escape strategy: When some raccoon parameter combinations show stagnation or degradation, these solutions will simulate the behavior of escaping from predators, that is, randomly changing their parameter settings to escape possible local optimal traps. This helps to explore new parameter spaces and find better global solutions. When a predator attacks a raccoon, the raccoon flees from its location, and the math for this is as follows: Among them, lb local andub local They represent the local lower and upper bounds of the VMD decomposition parameters, t is the current iteration number, (2) Maintaining exploration capability: Through this escape mechanism, the algorithm can continue to explore uncovered parameter areas, enhance global search capabilities, and avoid premature convergence.

5. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 2 is characterized in that: Steps (1-5) perform greedy selection on the population to obtain the global optimal solution, store and output the optimal solution. The greedy selection is shown in formula (6):

6. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 2 is characterized in that: The specific implementation process of step 2 is as follows: based on step 1, the VMD algorithm is used to select the penalty factor α and variational mode decomposition number K obtained in step 1, and the air-coupled ultrasonic signal in the honeycomb sandwich structure is decomposed by VMD to obtain multiple IMF components.

7. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 1 is characterized in that: The specific implementation process of step 3 is as follows: after VMD decomposition of the original air-coupled ultrasonic signal, the correlation coefficient method is introduced to select the IMF components obtained by decomposition, and the correlation coefficient threshold is set to 0.

5. For IMF components with correlation coefficients less than the threshold, improved wavelet threshold processing is performed, and for IMF components with correlation coefficients greater than the threshold, no processing is performed.

8. The air-coupled ultrasonic signal processing method based on COA-VMD combined with improved wavelet threshold according to claim 1 is characterized in that: The specific implementation process of step 4 is as follows: using the improved wavelet threshold function, the formula is as follows: Where a and β are adjustment parameters of the threshold function. When 0<a<1, β is a constant with a positive sign. The value range of parameter a is 0<a<1, indicating that the threshold function is adjusted between the soft threshold and the hard threshold. j,k is the wavelet coefficient, is the thresholded wavelet coefficient; sgn is the sign function; λ is the threshold.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the air-coupled ultrasonic signal processing method based on COA-VMD combined improved wavelet threshold as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by the processor, the air-coupled ultrasonic signal processing method based on COA-VMD combined improved wavelet threshold as described in any one of claims 1 to 8 is implemented.

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