A radial acoustic filter topology optimization design method considering machining conditions and a micro-crack nonlinear ultrasonic enhanced detection system

Abstract

The application belongs to the field of acoustics and relates to a radial acoustic filter topology optimization design method considering machining conditions and a micro-crack nonlinear ultrasonic enhanced detection system. The method comprises the following steps: iteratively optimizing the material distribution topology of a square design domain by using a genetic algorithm, the genetic algorithm adopts an improved genetic algorithm considering machining conditions, and the iteratively optimizing is performed according to specified rules: the initial population is generated by using a shape expansion method; in the crossover process, the column is cut and exchanged based on a pixel binary matrix, and in the mutation process, the mutation direction is determined according to the density of the same elements in the neighborhood; after the genetic operation is completed, all new individuals are modified based on the machining conditions; the modified new individuals and the original individuals in the population are combined, the repeated structures are removed, and the elite individuals are reserved to enter the next round of iteration cycle. Compared with the prior art, the application can realize low distortion transmission of the fundamental wave and high attenuation of the nonlinear harmonic components of the system under the premise that the component meets the machining size requirements.

Description

Technical Field

[0001] This invention belongs to the field of acoustics, specifically relating to a radial acoustic filter that takes into account processing conditions and a topology optimization design method, and constructing a microcrack nonlinear ultrasonic enhancement detection system based on the designed radial acoustic filter. Background Technology

[0002] Achieving damage identification and early warning while maintaining the structural integrity of equipment is crucial for ensuring long-term safe and stable operation. Traditional linear ultrasonic guided wave technology is suitable for locating macroscopic defects but is insensitive to early microscopic damage. Nonlinear ultrasonic guided wave technology, on the other hand, assesses early material degradation by measuring second harmonics or beam mixing, demonstrating excellent and efficient detection capabilities for early microscopic defects such as fatigue cracks and thermal aging, thus attracting widespread attention. However, this technology faces significant challenges in practical applications: coupling agents, adhesives, and electronic devices such as signal generators and power amplifiers in the detection system can introduce system nonlinear signals unrelated to damage characteristics, leading to signal distortion in the received signal. Furthermore, the nonlinear components of damage caused by changes in the material's microstructure are usually extremely weak, and may even be overwhelmed by system nonlinearity. Therefore, the ability to accurately and reliably extract damage-related nonlinear components is a core prerequisite for the practical application of nonlinear ultrasonic guided wave structural health monitoring technology.

[0003] To address the aforementioned issues, researchers have introduced metamaterials into the field of nonlinear ultrasonic guided wave detection. Metamaterials are specially designed artificial structures possessing wavefield manipulation capabilities unattainable by natural materials, such as bandgap, sound absorption, and negative refraction. Phononic crystals, as a typical type of acoustic metamaterial, are essentially periodic functional materials, with their most significant characteristic being their bandgap properties, which can suppress wave propagation within a specific frequency range. Based on this property, researchers have proposed using phononic crystals as mechanical filters in nonlinear guided wave detection. By rationally designing their bandgap range, the nonlinear components of the excitation signal can be effectively filtered out, purifying the detection signal and thus increasing the proportion of damage-related nonlinear components in the received signal. This strategy provides a new technical approach for overcoming system nonlinear interference and improving the reliability and practicality of nonlinear guided wave detection.

[0004] Currently, significant progress has been made in the research of filtering properties of conventional elastic metamaterials both domestically and internationally. However, research on radial filtering metamaterials with omnidirectional bandgap is limited. According to literature reports, some researchers have introduced topology optimization algorithms into the design of conventional metamaterial filters, expanding the possibilities for shape variations and enabling the reverse design of acoustic filters with specified bandgap. However, due to limitations in the design freedom and manufacturing methods of radial acoustic filters, existing radial acoustic filter structures still rely on empirical or parametric shape optimization, resulting in limitations in the bandgap frequency range and thus limited engineering application significance. Based on the inventor's research and investigation, Chinese patent application CN121351460A discloses a radial second harmonic acoustic filter metamaterial and its topology optimization design method. A two-dimensional axisymmetric simulation model is established, corresponding to the cross-section of the radial second harmonic acoustic filter metamaterial along the radial direction. This model includes periodically arranged unit structures, each comprising a main body and a square design domain. Floquet periodic boundary conditions are applied to the parallel boundaries of the unit structures along the radial direction, while the remaining boundaries are set as free boundaries. A genetic algorithm is used to iteratively optimize the material distribution topology of the square design domain, obtaining the optimal material distribution topology for the square design domain, and thus obtaining the final optimized shape of the radial second harmonic acoustic filter metamaterial. However, existing radial acoustic filter design methods based on topology optimization generally suffer from problems such as "disconnect between ideal configuration and processing technology" and "limited functionality, unsuitable for nonlinear ultrasonic physics environments." Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art by providing a radial acoustic filter topology optimization design method with minimum processing feature constraints and considering processing conditions, and a microcrack nonlinear ultrasonic enhancement detection system. Through process constraint algorithms and a collaborative optimization framework based on nonlinear detection frequency, low distortion transmission of the fundamental wave and high attenuation of the system's nonlinear harmonic components are achieved while ensuring that the components meet the processing size requirements. On this basis, a microcrack ultrasonic enhancement detection system is constructed, filling the gap in the prior art in this field.

[0006] The objective of this invention can be achieved through the following technical solutions: A radial acoustic filter topology optimization design method considering processing conditions, the method comprising: A two-dimensional axisymmetric simulation model is established, which corresponds to the cross-section of the radial acoustic filter along the radial direction. This model includes periodically arranged unit structures, each comprising a substrate and a square design domain. Floquet periodic boundary conditions are applied to the parallel boundaries of the unit structures along the radial direction, while other boundaries are set as free boundaries. A genetic algorithm is used to iteratively optimize the material distribution topology of the square design domain to obtain the optimal material distribution topology, thereby obtaining the optimal radial acoustic filter. The square design domain is discretized into a pixel binary matrix, and chromosome individuals in the genetic algorithm are generated based on this pixel binary matrix. The genetic algorithm employs an improved genetic algorithm that considers processing conditions, and performs iterative optimization according to specified rules, which include: The initial population was generated using the morphological expansion method; During the crossover process, the pixels are split and exchanged column by column based on the binary matrix. During the mutation process, the direction of mutation is determined by the density of the same elements in the neighborhood. After completing the genetic operations, all new individuals are modified based on the processing conditions; The corrected new individuals are merged with the original individuals in the population, duplicate structures are removed, and elite individuals are retained to enter the next iteration cycle.

[0007] Furthermore, in the pixel binary matrix, "1" represents the filling material at the corresponding pixel point, and "0" represents an air region or a pixel point without filling material.

[0008] Furthermore, the morphological dilation method specifically includes: Initial individuals are generated by randomly moving an all-1 matrix within an all-0 matrix, where the size of the all-1 matrix is ​​smaller than the size of the all-0 matrix.

[0009] Furthermore, when using the improved genetic algorithm that takes into account processing conditions for iterative optimization, the intersection of the actual bandgap and the target bandgap is used as the fitness function.

[0010] Furthermore, the actual bandgap is obtained based on the band distribution diagram of the current model.

[0011] Furthermore, the method also includes: The performance of a radial acoustic filter based on a square design domain with optimal material distribution topology is verified.

[0012] Furthermore, the modification includes: Delete new individuals whose minimum wall thickness is less than the set threshold.

[0013] Furthermore, the modification includes: Delete new individuals with unprocessable structures.

[0014] The present invention also provides a radial acoustic filter, which is designed using the radial acoustic filter topology optimization design method that takes into account the processing conditions as described above.

[0015] The present invention also provides a nonlinear ultrasonic enhancement detection system for microcracks, including the radial acoustic filter described above.

[0016] Compared with the prior art, the present invention has the following beneficial effects: (1) Existing technologies only focus on the design of theoretical filter configurations, which are limited by the processing methods and precision limitations of metal 3D printing and do not have practical engineering application significance. In contrast, this invention uses an improved genetic algorithm that takes into account processing conditions to design the topology of the radial acoustic filter. It uses the morphological expansion method to generate initial individuals to meet the minimum processing feature constraints. Through the process constraint algorithm and the collaborative optimization framework based on nonlinear detection frequency, it achieves low distortion transmission of the fundamental wave and high attenuation of the nonlinear harmonic components of the system while ensuring that the components meet the processing size requirements. It is manufacturable and can be applied to real-world detection scenarios.

[0017] (2) The radial acoustic filter in this invention is obtained by topology design method, which breaks through the design limitations of traditional size optimization and provides an important reference for realizing high degree of freedom and reverse design for complex application scenarios.

[0018] (3) The radial acoustic filter in this invention can be installed in a ring around the piezoelectric sheet. It has specific frequency band filtering characteristics in the 360º direction, which can ensure that the fundamental frequency passes through while suppressing the propagation of the second harmonic. It can effectively filter out the unavoidable system nonlinearity in nonlinear ultrasonic Lamb wave detection. Applying this structure to a nonlinear ultrasonic detection system can effectively improve the sensitivity of the detection system and has great application value in the field of structural health monitoring.

[0019] (4) The radial acoustic filter with topology designed in this invention realizes the leap from functional simulation to engineering application and has engineering practicality. Attached Figure Description

[0020] Figure 1 This is a three-dimensional structural schematic diagram of the radial acoustic filter in this invention; Figure 2 This is a schematic diagram of an example model of topology optimization in this invention; Figure 3 This is a flowchart of the genetic algorithm in this invention; Figure 4 This is the iterative change curve of the optimal and average fitness values ​​during the topology design process in this invention, and it also provides schematic diagrams of the intermediate and optimal structures corresponding to some feature point locations. Figure 5 This is the band structure calculated from the optimal radial acoustic filter structure in this invention; Figure 6 These are the steady-state S0 mode Lamb wave field diagrams of the optimal radial acoustic filter obtained in this embodiment of the invention under different excitation frequencies, wherein (a) is the wave field diagram at the fundamental frequency of 300 kHz excitation frequency, and (b) is the wave field diagram at the second harmonic excitation frequency of 600 kHz. Figure 7 These are time-domain signal diagrams collected from the propagation of the S0 mode Lamb wave in the light plate and the aluminum plate with the radial acoustic filter installed in the embodiment of the present invention. Among them, (a) is a time-domain signal diagram with a frequency of 300 kHz, and (b) is a time-domain signal diagram with a frequency of 600 kHz. Figure 8 This is a schematic diagram of a nonlinear ultrasonic enhancement detection system using a radial acoustic filter in an embodiment of the present invention; Figure 9 The spectrum of the time-domain signal of the S0 mode Lamb wave with a frequency of 300 kHz under different conditions, which includes the nonlinearity of the system, is obtained by Fourier transform. Among them, (a) is the spectrum measured in the undamaged plate and the cracked plate, and (b) is the spectrum measured in the plate and the damaged plate when the radial acoustic filter is installed. Figure 10 This is a comparison chart of the damage coefficient β after normalization based on the nonlinear parameters of the lossless state when the system includes nonlinearity. Detailed Implementation

[0021] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0022] Example 1 This embodiment provides a radial acoustic filter topology optimization design method considering processing conditions. It employs finite element simulation software COMSOL Multiphysics and COMSOL Multiphysics with MATLAB in conjunction with MATLAB to perform topology design on the radial acoustic filter shape. The method includes: (1) A two-dimensional axisymmetric simulation model is established through the solid mechanics module. The two-dimensional axisymmetric simulation model corresponds to the cross section of the radial acoustic filter along the radial direction, including periodically set unit structures. The unit structures include a substrate and a square design domain (scatterer).

[0023] The three-dimensional structure of the radial acoustic filter to be designed in this embodiment is as follows: Figure 1 As shown, it includes a motherboard 1 and a super filter 2 mounted on the motherboard 1. Figure 2 This is a schematic diagram of the two-dimensional axisymmetric simulation model constructed in this embodiment, including substrate 3 and square design domain 4.

[0024] In this embodiment, the cross-section of the scatterer's design domain is square. This design domain is discretized into a pixel binary matrix with a size of 15×15 pixels. "1" represents solid material filling the corresponding pixel, and "0" represents air, meaning no material filling the corresponding pixel. Key geometric parameters mainly include the side length of the design domain. l Thickness of the bottom substrate d and the lattice constant of the scattering unit a The specific dimensional parameters used in this embodiment are shown in Table 1.

[0025] Table 1 Geometric Dimensions In this embodiment, the motherboard is made of aluminum, and the radial acoustic filter unit is made of the same material as the motherboard. The material parameters are shown in Table 2. ρ For density, E For elastic modulus, ν It is Poisson's ratio.

[0026] Table 2 Material Parameters (2) Setting up the physical field and calculating the band structure: Using the solid mechanics module of COMSOL software, the filter unit structure was set up. r Floquet periodicity conditions are applied to the left and right boundaries of the direction, while other boundaries are set as free boundaries. In the characteristic frequency study, a parametric scan is set, with a wavenumber scan range of 0-π / a The step size is 0.1π / a To obtain different wave numbers k By connecting the corresponding intrinsic frequency points in sequence, the band distribution diagram can be obtained.

[0027] In this embodiment, both the substrate and the design domain are divided using free triangular meshes. To achieve a good balance between computation time and accuracy, the maximum size of the substrate mesh cell is set to 0.8 mm, and the maximum size of the design domain mesh cell is set to 0.1 mm. The band structure of the current model can be obtained through calculation.

[0028] (3) The material distribution topology of the square design domain is iteratively optimized using a genetic algorithm to obtain the optimal material distribution topology of the square design domain, thereby obtaining the optimal radial acoustic filter. In this embodiment, the topology design based on the genetic algorithm is implemented using COMSOL with MATLAB.

[0029] Specifically, the genetic algorithm adopts an improved genetic algorithm that takes into account the processing conditions. Based on the processing characteristics of the radial acoustic filter, the rules for population generation, crossover, mutation and other steps in the algorithm are modified to form specified rules for iterative optimization, and a correction step is added to ensure that the generated structure meets the processing requirements.

[0030] Since radial acoustic filters cannot be generated using the cross-sectional stretching 3D printing technology widely used in traditional metamaterial filters, the design must avoid creating difficult-to-achieve structures such as holes, thin pillars, and narrow slots. Furthermore, due to structural strength requirements, the minimum wall thickness in the design should not be less than 0.8 mm. Based on these processing requirements, the following rules for the genetic algorithm were defined: The initial population was generated using the morphological expansion method; During the crossover process, the pixels are split and exchanged column by column based on the binary matrix. During the mutation process, the direction of mutation is determined by the density of the same elements in the neighborhood. After completing the genetic operations, all new individuals are modified based on the processing conditions; The corrected new individuals are merged with the original individuals in the population, duplicate structures are removed, and elite individuals are retained to enter the next iteration cycle.

[0031] like Figure 3 As shown, the iterative optimization process based on the improved genetic algorithm considering processing conditions includes the following steps: S1. Chromosomal gene representation based on pixel binary matrix encoding.

[0032] S2. Generate an initial population. This initial population is no longer composed of random discrete elements, but rather uses a morphological expansion method. It generates holistic initial individuals by randomly moving a small all-one matrix within a large all-zero matrix. The large all-zero matrix is ​​determined based on a preset design domain, while the small all-one matrix is ​​the minimum structural size set according to the radial structure processing dimensions.

[0033] Specifically, in this embodiment, the large all-zero matrix is ​​a 15×15 all-zero matrix, and the small all-one matrix is ​​a 4×4 all-one matrix. Since each element in the matrix corresponds to a 0.2×0.2mm structural square, the design domain size corresponding to the large all-zero matrix is ​​3×3mm, while the minimum structural size is 0.8×0.8mm, which meets the minimum structural size requirements for metal 3D printing.

[0034] The morphological expansion method is used to preserve the structural diversity of the topology optimization process to the greatest extent possible while meeting the processing conditions.

[0035] S3. By calling COMSOL to calculate the corresponding band curves of each chromosome model in the current population, the intersection of the actual band gap and the target band gap is used as the fitness function to extract key parameters and calculate the fitness value.

[0036] In this embodiment, the target passband of the fundamental frequency is preset to 250-320 kHz, corresponding to a target bandgap range of 500-640 kHz for the second harmonic. The target function is expressed in the following mathematical form based on the target: In the formula: This represents all bandgap ranges calculated by the current model; Indicates the target restricted area; Indicates the target passband range; This represents the weight value of each part.

[0037] S4. Perform crossover operation based on probability: based on column-wise splitting and swapping of pixel binary matrices.

[0038] Traditional genetic algorithms flatten a 15×15 matrix into a 1×225 row vector and perform crossover operations. This involves randomly generating a number x within the range of 1 to 224 as the crossover point, combining the 1-x portion of individual A with the x+1-225 portion of individual B, and then combining the 1-x portion of individual B with the x+1-225 portion of individual A, thus forming two new individuals for the next generation. Because this method is prone to creating tiny holes in the structure, this step is replaced with column-wise swapping in this method. Each column is treated as a whole, and the 15×15 matrix is ​​treated as a 1×15 row vector. A number y within the range of 1 to 14 is randomly generated as the crossover point, and the remaining swapping steps are the same as the previous method.

[0039] S5. Probability-based mutation operation: The mutation direction is determined by the density of identical elements in the neighborhood.

[0040] Specifically, in the randomly selected matrix of mutated individuals, a 1 element is randomly selected, and the number of 1 elements in the neighborhood of that element is obtained. If the number of 1 elements in the 8 neighborhood elements is greater than 4, then all the remaining 0 elements in the neighborhood are converted to 1; otherwise, they are all converted to 0 elements.

[0041] S6. To prevent new unprocessable structures from arising due to crossover mutations, all individuals that have undergone the above operations are modified according to the processing conditions.

[0042] Specifically, starting from the first row and first column, each element is scanned sequentially from top to bottom and from left to right. If the current element is 1 and the number of 1s in its four neighboring regions (up, down, left, and right) does not exceed one, it is considered an isolated point and is erased to 0. If the current element is 0 and the number of 0s in its four neighboring regions does not exceed one, it is considered a micro-hole and is filled with 1.

[0043] S7. Merge the corrected new individuals with the original individuals in the population, remove some duplicate structures to prevent the algorithm from converging too quickly, retain the elite individuals to enter the next iteration loop, and repeat steps S3-S7.

[0044] S8. Continuously calculate the fitness of each group in each iteration. After a preset number of iterations, an individual with the maximum fitness can be obtained.

[0045] (4) Output the final optimization results.

[0046] Figure 4 The iterative change curve of the objective function is given. Based on the individual with the highest fitness after reaching the preset conditions, the corresponding radial acoustic filter model is constructed as the final optimization result.

[0047] (5) Result verification.

[0048] The band structure diagram obtained by performing band structure calculations on the optimized radial acoustic filter model in COMSOL is shown below. Figure 5 As shown in the diagram, the band structure reveals complete bandgaps between 511.6-543.6 kHz and 592.7-642.7 kHz, consistent with the target bandgaps of 500-640 kHz. Furthermore, the bandgaps pass through the target passband of 250-320 kHz without interruption. These results demonstrate that the genetic algorithm-based topology design method described above can achieve our goal of controlling the bandgaps.

[0049] 5.1 Verification of the frequency domain filtering performance of the radial acoustic filter To evaluate the filtering performance of the radial acoustic filter designed above, verification was performed from a frequency domain perspective. The steady-state wave field was calculated using the solid mechanics module of the finite element software COMSOL. The obtained design structure was imported into the model, which contains 8 repeating elements attached to a 2 mm thick aluminum plate. A specified displacement along the r-direction was applied at the excitation end to simulate the S0 mode Lamb wave input. Perfectly matched layer conditions were added to the left and right boundaries of the model to minimize reflected waves. A steady-state solver was selected to calculate the wave field distribution under 300 kHz excitation (passband fundamental wave) and 600 kHz excitation (stopband second harmonic), respectively. Figure 6As shown in the figure, the data corresponding to the colors are the amplitudes of the in-plane displacements within the plate (normalized based on the maximum amplitude). Since the S0 mode guided wave is primarily composed of in-plane displacements, the propagation process of the S0 mode guided wave is characterized by extracting the amplitudes of the in-plane displacements within the plate during the simulation. Figure 6 It can be clearly observed that the 300 kHz wave can penetrate the acoustic filter and continue to propagate along the board, while the 600 kHz wave component is effectively suppressed.

[0050] 5.2 Verification of the time-domain filtering performance of the radial acoustic filter The transient solver was selected to calculate the above model. Ten-cycle sinusoidal pulse signals with center frequencies of 300 kHz (fundamental) and 600 kHz (second harmonic) were excited respectively, modulated with a Hanning window. The in-plane displacement amplitude was extracted at a distance of 400 mm from the excitation position. Figure 7 As shown, fundamental frequency sound waves can propagate through the filter, while second harmonic sound waves cannot pass through the acoustic filter. From Figure 7 As can be seen from (a), the in-plane displacement signal at 300 kHz can pass through the acoustic filter with relatively small attenuation, while from... Figure 7 As can be seen from (b), the in-plane displacement signal at 600 kHz can hardly pass through the acoustic filter, proving that the radial acoustic filter structure has good filtering function.

[0051] Example 2 In this embodiment, the radial acoustic filter obtained based on the method of Embodiment 1 is bonded to an aluminum plate to achieve omnidirectional second harmonic filtering, ensuring the smooth passage of the fundamental frequency while suppressing second harmonic propagation. Furthermore, this acoustic filter is used in nonlinear ultrasonic detection of microcracks to construct a nonlinear detection system with high signal-to-noise ratio and high sensitivity. Figure 8 As shown. In previous nonlinear ultrasonic testing systems, the nonlinear signal originating from the testing system may overwhelm the nonlinear signal of the damage, making the damage difficult to detect; however, the introduction of a radial acoustic filter filters out the nonlinear signal of the system, ensuring that the nonlinear components in the signal received at the back end are basically derived from the damage, thereby effectively improving the sensitivity of nonlinear ultrasonic testing.

[0052] In Example 1, a crack in the model plate, simulated by a contact boundary pair, is introduced. The crack length is set to 1 mm. A 300 kHz, 10-cycle Hanning window modulated sinusoidal pulse signal is excited to simulate the fundamental frequency signal. A 600 kHz signal with an amplitude one-tenth of the fundamental frequency signal is superimposed on this signal as a co-excitation of the system's nonlinear interference. A Fourier transform of the received time-domain signal yields the following... Figure 9 The spectrum shown is Figure 9 (a) shows the case with nonlinear disturbances in the system. It can be seen that the lossy and lossless models do not show obvious differences at the second harmonic position, and it is difficult to distinguish the damage component. Figure 9 (b) shows the case with a radial acoustic filter installed. It can be seen that even with nonlinear interference, the lossy model still exhibits a significant damage component at the second harmonic position. The peak value A1 at the fundamental frequency and the peak value A2 at the second harmonic position are extracted from the figure. The damage coefficient β = A2 / A1 is calculated and normalized to the lossless case, yielding... Figure 10 As shown in the bar chart, the system nonlinearity clearly overwhelms the damage nonlinearity, making it difficult to effectively distinguish between damaged and undamaged conditions during the detection process. However, after installing the radial acoustic filter, the second harmonic amplitudes under damaged and undamaged conditions show a significant difference, making it easier to determine whether damage exists and significantly improving the sensitivity of nonlinear ultrasonic guided wave detection.

[0053] This invention first uses an improved genetic algorithm to design the topology of functional units based on the processing characteristics of radial acoustic filters, as described in Example 1, to obtain a structure with filtering characteristics within a preset frequency band and meeting the processing conditions. Then, the filtering performance of this design is verified in both the frequency and time domains, demonstrating that the designed acoustic filter can suppress second harmonic propagation while ensuring the fundamental frequency passes smoothly, and that it can be flexibly customized according to the required frequency range. Finally, Example 2 verifies that the nonlinear ultrasonic enhancement detection system built based on this design can effectively improve detection sensitivity, successfully solving the problem of low damage detection rate caused by system nonlinearity, and has broad application prospects in the field of structural health monitoring.

[0054] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A radial acoustic filter topology optimization design method considering processing conditions, the method comprising: A two-dimensional axisymmetric simulation model is established, which corresponds to the cross-section of the radial acoustic filter along the radial direction. This model includes periodically arranged unit structures, each comprising a substrate and a square design domain. Floquet periodic boundary conditions are applied to the parallel boundaries of the unit structures along the radial direction, while other boundaries are set as free boundaries. A genetic algorithm is used to iteratively optimize the material distribution topology of the square design domain to obtain the optimal material distribution topology, thereby obtaining the optimal radial acoustic filter. The square design domain is discretized into a pixel binary matrix, and chromosome individuals in the genetic algorithm are generated based on this pixel binary matrix. The characteristic is that the genetic algorithm employs an improved genetic algorithm that considers processing conditions, and performs the iterative optimization according to specified rules, the specified rules including: The initial population was generated using the morphological expansion method; During the crossover process, the pixels are split and exchanged column by column based on the binary matrix. During the mutation process, the direction of mutation is determined by the density of the same elements in the neighborhood. After completing the genetic operations, all new individuals are modified based on the processing conditions; The corrected new individuals are merged with the original individuals in the population, duplicate structures are removed, and elite individuals are retained to enter the next iteration cycle. In the pixel binary matrix, "1" represents that the corresponding pixel is filled with material, and "0" represents an air region or no filling material in the corresponding pixel. The morphological dilation method specifically refers to: The initial individual is generated by randomly moving an all-one matrix within an all-zero matrix. The size of the all-one matrix is ​​smaller than that of the all-zero matrix. The all-zero matrix is ​​determined based on a preset design domain range, and the all-one matrix is ​​the minimum structural size set according to the radial structure processing size limit.

2. The radial acoustic filter topology optimization design method considering processing conditions according to claim 1, characterized in that, When using the improved genetic algorithm that takes into account processing conditions for iterative optimization, the intersection of the actual bandgap and the target bandgap is used as the fitness function.

3. The radial acoustic filter topology optimization design method considering processing conditions according to claim 2, characterized in that, The actual bandgap is obtained based on the band distribution diagram of the current model.

4. The radial acoustic filter topology optimization design method considering processing conditions according to claim 1, characterized in that, The method also includes: The performance of a radial acoustic filter based on a square design domain with optimal material distribution topology is verified.

5. The radial acoustic filter topology optimization design method considering processing conditions according to claim 1, characterized in that, The correction includes: Delete new individuals whose minimum wall thickness is less than the set threshold.

6. The radial acoustic filter topology optimization design method considering processing conditions according to claim 1, characterized in that, The correction includes: Delete new individuals with unprocessable structures.

7. A radial acoustic filter, characterized in that, The radial acoustic filter topology optimization design method considering processing conditions as described in any one of claims 1-6 was used to design the filter.

8. A nonlinear ultrasonic enhancement detection system for microcracks, characterized in that, Includes the radial acoustic filter as described in claim 7.

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