Air coupled ultrasonic signal processing method for honeycomb sandwich structure based on coa-vmd combined improved wavelet threshold

Abstract

The application relates to an air-coupled ultrasonic signal processing method based on a COA-VMD combined improved wavelet threshold value, and specifically comprises the following steps: step 1: first, a meta-heuristic algorithm Coati is adopted, and minimum envelope entropy is introduced as a fitness function of the algorithm, which is used as an evaluation criterion of an optimal solution; step 2: by using optimized VMD decomposition parameters, a noisy part in the air-coupled ultrasonic signal is decomposed into multiple intrinsic mode function components; step 3: on the basis of step 2, a correlation coefficient method is adopted to distinguish effective ultrasonic signal components f1 and noise components f2 in the detected IMF components; and step 4: an improved wavelet threshold function algorithm is adopted to process the noise components f2, so that the air-coupled ultrasonic signal after noise reduction is obtained. The application combines the COA-VMD and the improved wavelet threshold noise reduction method, effectively improves a signal-to-noise ratio, and provides a technical basis for high-precision detection of defects in a honeycomb sandwich structure.

Description

Technical Field

[0001] This invention relates to a signal processing method, specifically to an air-coupled ultrasonic signal processing method based on COA-VMD joint improved wavelet threshold, belonging to the field of ultrasonic detection technology. Background Technology

[0002] Honeycomb sandwich structures, due to their lightweight, high strength, and excellent rigidity, are widely used in aerospace, automotive manufacturing, and construction industries. The integrity of these structures is crucial, directly affecting their performance and safety. However, the complex porous nature of honeycomb sandwich structures presents challenges to conventional contact ultrasonic testing methods, such as poor coupling, low testing efficiency, and potential damage to the tested material. Therefore, selecting a non-contact testing technology is particularly important. Non-contact air-coupled ultrasonic testing utilizes air as the transmission medium, overcoming the complexity and material damage risks associated with liquid coupling agents in conventional methods. This technology does not require physical contact with the object under test, enabling rapid and flexible testing, thus improving testing efficiency. However, air-coupled ultrasonic testing has a low signal-to-noise ratio, which will affect the detection accuracy of defects in honeycomb sandwich structures. Therefore, a new solution is urgently needed to address the aforementioned technical problems. Summary of the Invention

[0003] This invention addresses the technical problems existing in the prior art by providing an air-coupled ultrasonic signal processing method based on a combined improved wavelet thresholding method using COA-VMD. This invention effectively enhances the signal-to-noise ratio by employing a noise reduction method that combines VMD parameters optimized based on the COA algorithm with an improved wavelet threshold, providing a foundation for further high-precision detection of defects in honeycomb sandwich structures.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows: a method for processing air-coupled ultrasonic signals based on COA-VMD jointly improved wavelet threshold, the method comprising the following steps:

[0005] The method includes the following steps:

[0006] Step 1: First, the metaheuristic algorithm Coati (COA) is adopted, 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 optimal combination of decomposition parameters is obtained by adaptively optimizing Variational Mode Decomposition (VMD) using the COA algorithm. 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 between the effective ultrasonic signal component f1 and the noise component f2 in the detected IMF components.

[0008] Step 4: The noise component f2 is processed using an improved wavelet threshold function algorithm to obtain the denoised IMF component f22. Then, f22 is superimposed and reconstructed with f1 to obtain the denoised air-coupled ultrasonic signal.

[0009] In this invention, Variational Mode Decomposition (VMD) is a non-recursive method that decomposes supersignals into band-limited intrinsic mode functions (BIMFs). Unlike empirical mode decomposition, VMD does not produce residuals and reduces mode aliasing, thereby effectively improving the ability to distinguish signals from noise. However, the selection of parameters α and K in VMD decomposition is usually based on empirical judgment, and excessively large or small α and K values ​​can lead to the decomposition results failing to accurately represent the true characteristics and information of the signal. To solve this problem, this invention proposes to use the metaheuristic algorithm COA, with the minimum envelope entropy as the fitness function, to find the optimal solution for VMD parameters. Then, the improved VMD is used to decompose the actual air-coupled ultrasonic detection signal into multiple IMF components. The correlation coefficient method is used to distinguish between the effective ultrasonic signal component and the noise signal component. In the post-processing, the improved wavelet threshold function algorithm is used to process the noise signal component. The noise-reduced noise component is superimposed and reconstructed with the effective ultrasonic signal component to obtain the noise-reduced air-coupled ultrasonic signal. This can provide a basis for further realizing high-precision detection of defects in honeycomb sandwich structures.

[0010] Variational mode decomposition algorithm

[0011] Variational Modulation (VMD) is an adaptive, non-recursive decomposition method that achieves signal decomposition through variational optimization without requiring pre-defined basis functions or wavelet functions. VMD decomposes a complex signal into several immutable modal components (IMFs) with different center frequencies and finite bandwidths. 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 k-th IMF; Ak (t) is the instantaneous amplitude of the k-th 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 mode functions u. k (t) is used to minimize the total bandwidth of all decomposed IMFs, and their sum equals the input source signal. The specific steps are as follows:

[0015] (1) Constructing a variational problem:

[0016]

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

[0018] (2) Introducing a penalty factor α and a multiplicative operator λ, equation (10) is transformed into an equivalent unconstrained variational problem using the Lagrangian method. The value of α ensures the accuracy of signal decomposition, and the value of λ ensures the strictness of the constraints. The augmented Lagrangian function is:

[0019]

[0020] [] represents the inner product operation.

[0021] Coati optimized VMD algorithm

[0022] Coati Optimization (COA) is a novel population-based intelligent optimization algorithm proposed by Mohammad Dehghani et al. in January 2023 for optimizing VMD parameter settings. This algorithm mimics the natural behavior of raccoons hunting lizards and avoiding predators to find the optimal solution. Unlike classic intelligent optimization algorithms such as genetic algorithms and particle swarm optimization, COA constructs a mathematical model by simulating the natural behavior of raccoons. Its search mechanism consists of two phases: predation and avoidance. It has the ability to perform global search and local optimization, and it does not require setting complex parameters. The specific steps of COA in optimizing VMD parameters are as follows:

[0023] Step (1-1): Problem Definition and Parameter Initialization. First, define the parameters of the COA algorithm for optimizing 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 variations. Assume there are M raccoons, and their location information is represented as X. i (i = 1, 2, ..., M), the raccoon's position is randomly generated, the maximum number of iterations is T, and it is defined by equation (1).

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

[0025] The 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, i.e., the fitness or superiority of the solution. The fitness function typically maps the solution to a real number or vector; this value can be used to compare the performance of different solutions and guide selection, crossover, and mutation operations during the search process. In air-coupled ultrasound signal processing, this function can be 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 signal quality or minimize error. As a fitness function, the average envelope entropy effectively reflects the sparsity of the signal. When the original signal is decomposed into K IMFs by the VMD algorithm, the fewer noise components contained in each 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 for COA.

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

[0027] Steps (1-3): Simulating raccoon predation behavior and applying it to air-coupled ultrasonic signal processing

[0028] 1. Grouping and Goal Setting: During algorithm initialization, all raccoons (representing different combinations of VMD parameters) are divided into two groups. One group remains stationary, without changing the current parameter settings, simulating raccoons "resting in trees." The other group actively explores new parameter combinations, simulating raccoons "hunting for prey on the ground."

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

[0030] When the lizard falls from the tree, its optimal position is randomly updated, and the raccoon's position is also updated accordingly. The fitness of the individual at this point is then calculated. The predation strategy causes the raccoon to move to different positions in the search space, demonstrating the COA algorithm's ability to explore the problem space globally.

[0031] The mathematical expressions for the positions of the raccoon waiting for prey on the ground and the lizard that has fallen are represented by equations (3) and (4).

[0032] Steps (1-4): In the process of optimizing parameters in ultrasonic signal processing, parameter combinations may cause the results to fall into local optima. This invention can make the following improvements.

[0033] 1. Escape Strategy: When certain raccoon parameter combinations exhibit improvement plateau or degradation, these solutions will simulate predator evasion behavior, i.e., randomly changing their parameter settings to escape potential local optima. This helps explore new parameter spaces and may uncover better global solutions.

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

[0035] 2. Maintaining exploration capability: Through this escape mechanism, the algorithm can continuously explore uncovered parameter regions, enhance global search capability, and avoid premature convergence.

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

[0037] Improved wavelet thresholding for noise reduction

[0038] The calculation of wavelet coefficients needs to be determined by a threshold. If the threshold is chosen too large, some useful signals will be incorrectly filtered out as noise. Conversely, 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] Conventional hard thresholding functions can preserve more of the true signal's peak characteristics, but due to poor continuity, oscillations occur during reconstruction. The continuous difference between the estimated and true values ​​leads to some errors in the reconstructed signal, even though soft thresholding functions offer greater continuity and the reconstructed signal is smoother. The expressions for hard and soft thresholding are shown below:

[0042] Hard threshold function:

[0043]

[0044] Soft threshold function:

[0045]

[0046] Where ω j,k For wavelet coefficients, w j, k represents the thresholded wavelet coefficients, and sgn is the sign function.

[0047] This invention employs an improved threshold function. Equation (14) is the mathematical formula for the function:

[0048]

[0049] Here, 'a' and 'β' are adjustment parameters of the threshold function. When 0 < a < 1, β is a positive constant. By adjusting the parameters 'a' and 'β', the threshold function can be adjusted between soft and hard thresholds, thereby achieving better noise reduction and reducing errors. This invention utilizes an improved wavelet threshold function algorithm to denoise the noise component. Based on this, the denoised IMF component is superimposed and reconstructed with the effective ultrasonic signal component to obtain the denoised air-coupled ultrasonic signal.

[0050] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aforementioned method for processing air-coupled ultrasonic signals in a cellular sandwich structure based on improved variational mode decomposition and improved wavelet thresholding.

[0051] A computer-readable storage medium storing computer instructions thereon, which, when executed by a processor, implement the aforementioned method for processing air-coupled ultrasonic signals in a honeycomb sandwich structure based on improved variational mode decomposition and improved wavelet thresholding.

[0052] Compared with existing technologies, this invention has the following advantages: 1) Improved Variational Mode Decomposition (VMD) technology: An improved VMD technology is proposed, which improves the signal-to-noise ratio (SNR) of air-coupled ultrasonic signals by optimizing 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 penalty factor and the number of decomposed modes need to be manually set in the traditional VMD algorithm. This improved algorithm can more effectively separate and extract complex signal components in honeycomb sandwich structures, including signal changes caused by noise and defects. This improvement increases the signal-to-noise ratio, which can provide a foundation for further 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 the COA-VMD jointly improved wavelet threshold can effectively detect internal defects in honeycomb sandwich structures without physical contact. This non-contact detection method not only reduces potential damage to the sample, but also enhances the flexibility and safety of the detection process. The application of air coupling technology makes this algorithm particularly suitable for evaluating materials and structures that are sensitive to contact or difficult to access, further expanding the application scope of ultrasonic detection technology. Attached Figure Description

[0053] Figure 1 The graph shows the wavelet threshold function.

[0054] Figure 2 This is a schematic diagram of the overall process of the present invention.

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

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

[0057] Figure 5 This is a schematic diagram of the IMF components in VMD decomposition.

[0058] Figure 6 This is a comparison chart of the original signal and the denoised signal. Detailed Implementation

[0059] Example 1: See Figures 1-6 A method for processing air-coupled ultrasonic signals in a honeycomb sandwich structure based on improved variational mode decomposition combined with improved wavelet thresholding, characterized in that the method includes the following steps:

[0060] Step 1: First, the metaheuristic algorithm Coati (COA) is adopted, and the minimum envelope entropy is introduced as the fitness function of the algorithm as the evaluation criterion for the optimal solution. For air-coupled ultrasonic signals in a honeycomb sandwich structure, the COA algorithm is used to adaptively optimize Variational Mode Decomposition (VMD) to obtain the optimal combination of decomposition parameters. Variational Mode Decomposition (VMD) is an adaptive and completely non-recursive signal processing method suitable for complex non-stationary signals, aiming to decompose the signal into several intrinsic mode functions (IMFs) with different center frequencies and finite bandwidths. The COA optimization algorithm is a population-based intelligent optimization algorithm used to optimize the parameter settings of VMD. This algorithm mimics the natural behavior of raccoons hunting 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, and it has the ability of global search and local optimization without the need to set complex parameters. To address the challenge of noise masking in air-coupled ultrasonic signals, this invention employs a signal processing method based on COA-VMD. The advantage of the COA algorithm lies in its ability to effectively solve the problem of manually setting the penalty factor and the number of decomposed modes in traditional VMD algorithms. By introducing the COA algorithm, the performance of VMD is significantly improved, providing a foundation for subsequent improved wavelet thresholding of noise components, making noise suppression and feature extraction of ultrasonic echo signals more accurate and convenient.

[0061] Step 2: Using the optimized VMD decomposition parameters, the noisy component of the air-coupled ultrasound 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 components.

[0063] Step 4: The noise component f2 is processed using an improved wavelet threshold function algorithm to obtain the denoised IMF component f22. Then, f22 is superimposed and reconstructed with f1 to obtain the denoised air-coupled ultrasonic signal. This invention combines COA-VMD and an improved wavelet threshold denoising method, effectively improving the signal-to-noise ratio and providing 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, the parameters for optimizing VMD decomposition using the COA algorithm are defined as the penalty factor and the number of decomposition modes. Then, the parameters of the COA algorithm are initialized, including the number of raccoons (each raccoon represents a set of candidate solutions), the maximum number of iterations, and the range of parameter variations. Assume there are M raccoons, and their location information is represented as X. i (i = 1, 2, ..., M), the raccoon's position is randomly generated, the maximum number of iterations is T, and it is defined by equation (1):

[0066] (1-2) Definition of Fitness Function: The 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, i.e., the fitness or superiority of the solution. The fitness function typically 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 ultrasound signal processing, this fitness function is constructed based on factors such as the signal reconstruction quality after VMD decomposition, the degree of background noise reduction, and signal fidelity. The goal of the fitness function is to maximize signal quality or minimize error. Average envelope entropy, as a fitness function, effectively reflects the sparsity of the signal. When the original signal is decomposed into K IMFs by the VMD algorithm, the fewer noise components contained in each 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 iteration of the COA algorithm, the initial fitness value f(xi) of each individual is calculated as an indicator to evaluate the VMD decomposition parameters. In metaheuristic algorithms (such as COA), the standard for measuring the quality of candidate solutions is the value of the objective fitness function. Therefore, the group members that lead to the optimal evaluation of the objective function are called the best members in the population. Since candidate solutions are continuously updated during algorithm iteration, the best members of the population are also updated in each iteration.

[0067] (1-3) Simulated raccoon predation behavior is applied to air-coupled ultrasonic signal processing, as detailed below.

[0068] (1) Grouping and Target Setting: During algorithm initialization, all raccoons (representing different VMD parameter combinations) are divided into two groups. One group remains stationary, without changing the current parameter settings, simulating raccoons "resting in trees." The other group actively explores new parameter combinations, simulating raccoons "searching for prey on the ground."

[0069] (2) Fitness assessment and update: The fitness of each raccoon is assessed based on its impact on the results of ultrasonic signal processing, 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 at present. Raccoons on the ground will update their parameter settings based on this optimal solution, that is, move to a better parameter combination. The mathematical model for raccoons in trees is represented by equation (2).

[0070] When the lizard falls from the tree, its optimal position is randomly updated, and the raccoon's position is also updated accordingly. The fitness of each individual is then calculated. The predation strategy during the hunting phase causes the raccoon to move to different positions in the search space, demonstrating the COA algorithm's ability to explore the problem space through global search.

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

[0072] (1-4) In the process of optimizing parameters in ultrasound signal processing, if the parameter combination causes the result to get stuck in a local optimum, further processing is required. The specific processing is as follows:

[0073] (1) Escape strategy: When certain raccoon parameter combinations exhibit improvement stagnation or degradation, these solutions will simulate predator evasion behavior, i.e., randomly changing their parameter settings to escape potential local optima. This helps explore new parameter spaces and may discover better global solutions.

[0074] When a predator attacks a raccoon, the raccoon will flee its location, as represented by the mathematical model in equation (5).

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

[0076] (1-5) Finally, a 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 and variational mode decomposition number of VMD; the greedy selection is represented by equation (6).

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

[0078] Step 3 is implemented 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. The correlation coefficient threshold is set to 0.5. For IMF components with correlation coefficients less than the threshold, improved wavelet thresholding is performed. For IMF components with correlation coefficients greater than the threshold, no processing is performed. This method effectively divides the IMF components after VMD decomposition into effective ultrasonic signal components and noise components using the correlation coefficient method, laying the foundation for subsequent improved wavelet thresholding.

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

[0080] When a and β take different values, compared with hard thresholding and soft thresholding functions, for example... Figure 1 As shown, by Figure 1 As can be seen, the improved threshold function has the flexibility of parameter adjustment, and can be adjusted between soft and hard threshold functions according to the signal, thereby achieving better noise reduction effect and reducing error. This invention uses an improved wavelet threshold function algorithm to denoise the noise component, and then superimposes and reconstructs the denoised IMF component with the effective ultrasonic signal component to obtain the denoised air-coupled ultrasonic signal.

[0081] This invention performs noise reduction processing on the air-coupled ultrasonic signals of the actually acquired honeycomb sandwich structure. Figure 3 The actual acquired air-coupled ultrasonic signal is used. The following Coati algorithm is executed to optimize the VMD decomposition signal. The raccoon population size 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 The fitness function curve is displayed. The fitness function reaches its minimum value of 6.45 at iteration number 4.

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

[0083] like Figure 6 As shown, the obtained IMF components are divided into effective ultrasound 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 thresholding is performed; for effective ultrasound signal components with correlation coefficients greater than the threshold, no processing is performed. Figure 6As shown, based on this, the noise component after noise reduction and the effective ultrasonic signal component are superimposed and reconstructed to obtain the noise-reduced air-coupled ultrasonic signal, which effectively enhances the signal-to-noise ratio. This provides a foundation for further high-precision detection of defects in honeycomb sandwich structures. It should be noted that the above embodiments are not intended to limit the scope of protection of this invention. Equivalent transformations or substitutions made based on the above technical solutions fall within the scope of protection of the claims of this invention.

Claims

1. A method for processing air coupled ultrasonic signals based on a joint improvement of wavelet thresholding based on COA-VMD, characterized in that, The method comprises the following steps: Step 1: Firstly, the meta-heuristic algorithm COA is adopted, and the minimum envelope entropy is introduced as the fitness function of the algorithm, as the evaluation criterion of the optimal solution, for the air-coupled ultrasonic signal in the honeycomb sandwich structure, the adaptive optimization VMD of the air-coupled ultrasonic signal is obtained by using the COA algorithm, Step 2: the noise-containing part in the air-coupled ultrasonic signal is decomposed into a plurality of IMF components by using the optimized VMD decomposition parameter, Step 3: on the basis of step 2, the correlation coefficient method is adopted to distinguish the effective ultrasonic signal component f1 and the noise component f2 in the detected IMF component, Step 4: the improved wavelet threshold function algorithm is adopted to process the noise component f2, and the IMF component f22 after noise reduction of the noise component is obtained, then f22 and f1 are superimposed and reconstructed to obtain the air-coupled ultrasonic signal after noise reduction; Wherein, the specific implementation process of step 4 is as follows: the improved wavelet threshold function is used, and the formula is as follows, （7） wherein and are the adjustment parameters of the threshold function, when , is a positive constant, and the parameter has a value range of , indicating that the threshold function is adjusted between the soft threshold and the hard threshold; is the wavelet coefficient, is the thresholded wavelet coefficient; is the sign function; is the threshold.

2. The COA-VMD combined improved wavelet threshold based air coupled ultrasonic signal processing method according to claim 1, 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 for optimizing VMD decomposition as penalty factor and decomposition mode number, then initialize the parameters of the COA algorithm, including the number of raccoons, the maximum number of iterations, the range of parameter changes, and each raccoon represents a candidate solution, assuming that there are M raccoons, the position information of the raccoon is represented as i = 1, 2,..., M, the position of the raccoon is randomly generated, the maximum number of iterations is T, which is defined as follows: wherein is an upper bound matrix of VMD parameters, is a lower bound matrix of VMD parameters, 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 IMF by VMD algorithm, the less noise component contained in the IMF, the stronger the correlation with the original signal, the smaller the average envelope entropy, the minimum average envelope entropy is selected as the fitness function of COA, then, before the first iteration of COA algorithm, the initial fitness value of the individual is calculated , as an evaluation index of VMD decomposition parameters, the member that can make the objective function reach the best value in the population is called the best member, since the candidate solution is updated in the iteration process of the algorithm, the best member of the population will also be updated in each iteration, (1-3) the simulation of the raccous predation behavior is applied to the air-coupled ultrasonic signal processing, (1-4) in the parameter optimization process of the ultrasonic signal processing, if the parameter combination leads to the result falling into local optimum, further processing is carried out, (1-5) finally, greedy selection is performed on the population to obtain the global optimal solution, and the optimal solution is stored and output, that is, the penalty factor of VMD and the number of variational mode decomposition.

3. The COA-VMD combined improved wavelet threshold based air coupled ultrasonic signal processing method according to claim 2, characterized in that, Step (1-3) the simulation of the raccous predation behavior is applied to the air-coupled ultrasonic signal processing, and the specific process is as follows, (1) grouping and target setting: when the algorithm is initialized, all raccoons are divided into two groups, one group remains static and does not change the current parameter setting, simulating the raccoon resting on the tree, and the other group actively explores new parameter combinations, simulating the raccoon searching for prey on the ground, (2) fitness evaluation and update: the fitness of each raccoon is evaluated according to the influence of the ultrasonic signal processing result, and the optimal solution is considered as the best parameter combination found at present, and the raccoon on the ground will update its parameter setting according to this optimal solution, that is, move to a better parameter combination, and the mathematical expression of the raccoon on the tree is: wherein with respectively represent the position information of the i-th raccoon in the t+1th iteration and the tth iteration; is the lizard position on the tree in the tth iteration, i.e., the best parameter combination currently found, I is a random integer in [1,2], and t is the current iteration number, When the lizard falls from the tree, the best position is randomly updated, the raccoon position is also updated, and the fitness of the individual at this time is calculated, the strategy of the predation stage causes the raccoon to move to different positions in the search space, which reflects the exploration ability of the COA algorithm in the global search of the problem space, For the raccoon waiting for prey on the ground and the position of the lizard falling from the tree, the mathematical expression is: wherein, represents the fitness value corresponding to the position of the i-th opossum in the t-th iteration; represents the position of the lizard that fell from the tree in the t-th iteration.

4. The COA-VMD combined improved wavelet threshold based air coupled ultrasonic signal processing method according to claim 2, characterized in that, Step (1-4) in the parameter optimization process of the ultrasonic signal processing, the parameter combination may lead to the result falling into local optimum, and the specific processing is as follows: (1) escape strategy: when the parameter combination of some raccoons shows improvement stagnation or degradation, these solutions will simulate the behavior of escaping from the predator, that is, randomly change their parameter settings, so as to escape from the possible local optimal trap, which helps to explore new parameter space and find better global solution, When the predator attacks the raccoon, the raccoon will escape from its position, and the mathematical formula is as follows: wherein, and denote the local lower and upper bounds of the VMD decomposition parameters, respectively, t is the current iteration number, (2) Maintain the ability to explore: through this escape mechanism, the algorithm can continuously explore the un-covered parameter region, enhance the global search ability, and avoid premature convergence.

5. The COA-VMD combined improved wavelet threshold-based air-coupled ultrasonic signal processing method according to claim 2, characterized in that, Step (1-5) greedily selects the population to obtain a global optimal solution, and stores and outputs the optimal solution, and the greedy selection is as shown in formula (6): 。 6. The COA-VMD combined improved wavelet threshold based air coupled ultrasonic signal processing method according to claim 2, characterized in that, The step 2 is specifically implemented as follows: on the basis of the step 1, a VMD algorithm is used, and the penalty factor obtained in the step 1 is selected and the number K of variational mode decomposition, the air-coupled ultrasonic signals in the honeycomb sandwich structure are decomposed by VMD to obtain a plurality of IMF components.

7. The COA-VMD combined improved wavelet threshold based air coupled ultrasonic signal processing method according to claim 1, characterized in that, The specific implementation process of step 3 is as follows: after the original air-coupled ultrasonic signal is decomposed by VMD, the correlation coefficient method is introduced to select the IMF components obtained by decomposition, the correlation coefficient threshold is set to 0.5, for the IMF component with a correlation coefficient less than the threshold, the improved wavelet threshold processing is performed, and for the IMF component with a correlation coefficient greater than the threshold, no processing is performed.

8. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that: The processor executes the program to implement the COA-VMD combined improved wavelet threshold-based air-coupled ultrasonic signal processing method according to any one of claims 1 to 7.

9. A computer readable storage medium having stored thereon computer instructions, characterized in that: The computer instructions are executed by the processor to implement the COA-VMD combined improved wavelet threshold-based air-coupled ultrasonic signal processing method according to any one of claims 1 to 7.

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