A mode filter, topology optimization method and ultrasonic guided wave damage imaging artifact suppression method

Abstract

The application relates to a mode filter, a topology optimization method and an ultrasonic guided wave damage imaging artifact suppression method, relates to the field of ultrasonic detection and imaging, and the topology optimization method comprises the following steps: acquiring initial design parameters, generating an initial population, each chromosome individual in the initial population is coded by a binary logic matrix representing material distribution and meeting design constraints; a population is optimized by using a genetic algorithm, an adaptability function in the genetic algorithm is constructed based on a mode purity index and an energy transmission index, the mode purity index is the ratio of in-plane displacement integral in a transmission area in finite element simulation with the mode filter to total displacement integral, and the energy transmission index is the ratio of relative energy at a transmission end in the finite element simulation with the mode filter to relative energy of an S0 mode; and final optimized material distribution of the mode filter is output. Compared with the prior art, the application has the advantages of effectively suppressing background artifacts, giving consideration to mode regulation performance and substrate structure integrity and the like.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic testing and imaging, and in particular to a mode filter, a topology optimization method, and a method for suppressing artifacts in ultrasonic guided wave damage imaging. Background Technology

[0002] Plate structures are widely used in aerospace, energy equipment, and petrochemical industries. During long-term service, they are prone to structural damage such as cracks, corrosion, fatigue, and creep, posing a potential threat to structural safety. Therefore, achieving high-precision non-destructive testing of plate structures is of significant engineering importance. Ultrasonic guided wave technology is widely used due to its advantages of long propagation distance and high detection efficiency, with Lamb waves being the most commonly used guided wave form for plate structure testing. However, the inherent multimodal and dispersion characteristics of Lamb waves often lead to mode aliasing in the actual acquired signals, thereby reducing damage localization accuracy and imaging quality. To address this problem, various modal selective excitation methods based on the excitation end have been proposed, such as optimizing piezoelectric element size parameters, using phased array excitation, designing transducers with special structures, and non-contact excitation methods. Although these methods can improve modal purity to some extent, they generally rely on complex transducer structures, precise parameter matching, or high system costs, limiting their engineering applications. Besides improvements at the excitation end, another type of research focuses on modal separation and feature extraction at the post-processing level, such as wavelet transform, short-time Fourier transform, empirical mode decomposition, and deep learning. These methods typically rely on high signal-to-noise ratio data, complex algorithm parameter tuning, and strong prior assumptions, making it difficult to fundamentally eliminate the physical complexity introduced by multimodal propagation. Compared to specific excitation methods and signal processing algorithms, reducing modal complexity at the physical level is more conducive to improving modal purity, thereby improving subsequent detection performance.

[0003] In recent years, acoustic metamaterials have been increasingly introduced into the field of guided wave manipulation due to their unique advantages in wave propagation control. Metamaterials have enormous application potential in guided wave manipulation, but early designs often relied on empirical configurations, limiting structural forms, and related optimizations were mostly parameter scans or geometric fine-tuning, easily getting trapped in local optima. Topology optimization, without relying on empirical configurations, performs a global search of the material distribution within the design domain, providing an effective approach for complex wave manipulation. However, existing metamaterial designs based on topology optimization still have certain limitations, such as a single optimization objective, complex and difficult-to-manufacture structures, and the possibility of damage to the tested structure. For example, patent application CN120951676A discloses a design method for a second-harmonic filtering metasurface based on topology optimization. The method includes: establishing a two-dimensional simulation model comprising a second-harmonic filtering metasurface substrate and a scatterer; encoding a binary matrix representing the material distribution into chromosomes based on a preset target bandgap, using the bandgap frequency covering the second-harmonic target range as the fitness function, and performing chromosome optimization iterations to obtain the chromosome with the largest fitness function value; during the optimization iteration, constructing the material distribution corresponding to the chromosome on the two-dimensional simulation model, obtaining its band structure, and calculating the fitness function value; outputting the final optimized material distribution of the second-harmonic filtering metasurface based on the binary matrix of the chromosome with the largest fitness function value, and verifying the performance of the results through simulation to obtain a second-harmonic filtering metasurface where the fundamental frequency wave can pass through but the second-harmonic wave is blocked. This method only considers the intersection of the bandgap frequency range in the band structure and the target frequency band, without involving constraints on the magnitude of transmission loss, and has a single optimization objective.

[0004] Therefore, in order to achieve effective control of guided wave modes and artifact suppression in damage imaging, it is necessary to develop a topology optimization method that balances mode control performance with matrix structural integrity. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a mode filter, topology optimization method, and ultrasonic guided wave damage imaging artifact suppression method that can effectively suppress background artifacts while taking into account mode modulation performance and matrix structure integrity.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A mode filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging includes the following steps:

[0008] Obtain initial design parameters and generate an initial population. Each chromosome individual in the initial population is encoded by a binary logic matrix that represents the material distribution and satisfies the design constraints.

[0009] A genetic algorithm is used to optimize the population. The fitness function in the genetic algorithm is constructed based on the mode purity index and the energy transmission index. The mode purity index is the ratio of the in-plane displacement integral of the transmission region to the total displacement integral in the finite element simulation with added mode filter. The energy transmission index is the ratio of the relative energy of the transmission end to the relative energy of the S0 mode in the finite element simulation with added mode filter.

[0010] The final optimized material distribution is obtained by using the binary logic matrix output mode filter corresponding to the optimal individual obtained by the genetic algorithm.

[0011] Furthermore, the design constraints include bottom continuity constraints and effective fill cell number constraints.

[0012] Furthermore, the design constraints are expressed as follows:

[0013]

[0014]

[0015] in, θ i,j express m × n The first in the matrix i OK j The column cell value is 1 if material is present, and 0 if material is removed. N The number of effective fill cells.

[0016] Furthermore, the relative energy of the transmission end is the integral of the square of the in-plane displacement and out-of-plane displacement of the transmission end cross-section.

[0017] Furthermore, the fitness function is expressed as:

[0018]

[0019] in, var 1 represents the model purity index. f 1( var 1) is a fitness function based on the model purity index. var 2 represents the energy transmission index. ω 2( var 2) is a weighting function based on the energy transmission index.

[0020] Furthermore, the aforementioned f 1( var 1) is a piecewise nonlinear function, expressed as:

[0021]

[0022] in, θ 1. θ 2 represents the key threshold for the model purity control stage; α 1. ß 1. α 2. ß 2. ß 3. To control the baseline level and growth rate of the piecewise function; p 1. p 2. p 3 is the sensitivity adjustment parameter for fitness to changes in model purity.

[0023] Furthermore, the aforementioned ω 2( var 2) is a piecewise decay function, expressed as:

[0024]

[0025]

[0026] in, b 1. b 2. b 3 represents deviation from the threshold. γ 1. γ 2. γ 3 represents the weight decay coefficient within different intervals. q 1. q 2. q 3 represents a non-linear exponent. δ It is a dimensionless deviation.

[0027] Furthermore, structural stability is addressed each time a new population is generated.

[0028] The present invention also provides a mode filter, which is designed and obtained by the mode filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging as described above.

[0029] The present invention also provides a method for suppressing artifacts in ultrasonic guided wave damage imaging, wherein the mode filter described above is attached to the object under test to obtain an imaging result with artifact suppression.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. This invention constructs a composite fitness function using modal purity and energy transmission as core indicators, realizing the automatic evolution and generation of mode selective meta-filters (MSMs), and providing a systematic method for the design of complex wave modulation structures. The designed MSM attenuates the A0 mode by approximately 96.5% within the 200kHz frequency band, while maintaining high transmittance for the S0 mode, demonstrating excellent mode selectivity performance.

[0032] 2. The designed MSM was applied to the probabilistic imaging method for damage. Imaging simulation verified that after introducing MSM, the energy focusing of the damaged area was significantly enhanced, background artifacts were significantly reduced, and the imaging signal-to-noise ratio and spatial resolution were effectively improved. Attached Figure Description

[0033] Figure 1 This is a schematic diagram illustrating the mode filtering working principle of the topology-optimized mode filter in an embodiment of the present invention;

[0034] Figure 2 This describes the population evolution process during topology optimization design of the mode filter in this embodiment of the invention.

[0035] Figure 3 This is a schematic diagram of the fitness change during the topology optimization iteration process in an embodiment of the present invention, wherein (a) is the fitness change curve, and (b) is the final topology optimization configuration of the mode filter;

[0036] Figure 4 The energy band diagram of the topology-optimized mode filter designed in this embodiment of the invention;

[0037] Figure 5 The above are in-plane displacement field diagrams at 200 kHz in the frequency domain simulation model of this invention, wherein (a) is the A0 mode excitation in the plate, (b) is the A0 mode excitation after attaching the mode filter, (c) is the S0 mode excitation in the plate, (d) is the S0 mode excitation after attaching the mode filter, (e) is the A0+S0 mixed mode excitation in the plate, and (f) is the A0+S0 mixed mode excitation after attaching the mode filter.

[0038] Figure 6 The waveguide time-domain signal propagating at a distance of 300 mm under A0+S0 mixed mode excitation at a frequency of 200 kHz in this embodiment of the invention is shown in (a) without MSM and (b) with MSM.

[0039] Figure 7 This is a schematic diagram illustrating the working principle of ultrasonic guided wave damage imaging with a topology-optimized mode filter in an embodiment of the present invention.

[0040] Figure 8 This is a flowchart of ultrasonic guided wave damage imaging artifact suppression based on topology-optimized mode filters in an embodiment of the present invention.

[0041] Figure 9 The diagram shows the imaging structure in an embodiment of the present invention, wherein (a) is the normalized amplitude imaging of damage in the plate, (b) is the logarithmic dB scale imaging of damage in the plate, (c) is the normalized amplitude imaging of damage after the plate is fitted with a mode filter, and (d) is the logarithmic dB scale imaging of damage after the plate is fitted with a mode filter. Detailed Implementation

[0042] 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.

[0043] Example 1

[0044] To achieve the design goal of suppressing A0 mode while maintaining high transmission efficiency of S0 mode, this embodiment provides a mode filter suitable for suppressing artifacts in ultrasonic guided wave damage imaging. It can effectively suppress A0 mode propagation and maintain high transmission efficiency of S0 mode. Its working principle is illustrated in the following diagram. Figure 1 As shown. The topology optimization method for the mode filter includes the following steps: obtaining initial design parameters and generating an initial population, wherein each chromosome individual in the initial population is encoded by a binary logic matrix representing the material distribution and satisfying design constraints; optimizing the population using a genetic algorithm, wherein the fitness function in the genetic algorithm is constructed based on the mode purity index and the energy transmission index, wherein the mode purity index is the ratio of the in-plane displacement integral of the transmission region to the total displacement integral in the finite element simulation with the mode filter added, and the energy transmission index is the ratio of the relative energy at the transmission end to the relative energy of the S0 mode in the finite element simulation with the mode filter added; and outputting the final optimized material distribution of the mode filter based on the binary logic matrix corresponding to the optimal individual obtained by the genetic algorithm.

[0045] The above method introduces a genetic algorithm as an optimization tool and constructs a topology optimization inverse design framework. The overall process is as follows: initialize parameters, generate an initial population, and perform structural stability processing; perform frequency domain simulation on each individual using the finite element simulation software COMSOL to calculate its modal response; evaluate performance based on the fitness function and perform selection, crossover, and mutation operations to generate a new generation of population; when the convergence condition is met, output the optimal configuration. The mode filter designed using the above method can effectively suppress the A0 mode and maintain the high transmission efficiency of the S0 mode at the physical level, filtering out interference modes at the source to obtain a pure S0 mode, ultimately achieving effective suppression of background artifacts and a significant improvement in imaging resolution.

[0046] The key steps will be explained below.

[0047] The population evolution process during topology optimization design of the mode filter MSM is as follows: Figure 2 As shown, the material distribution state in the MSM design domain adopts... m × n The design is described using a binary logic matrix, and the relevant design variables are as follows:

[0048] (1)

[0049] (2)

[0050] in, For logical matrices, θ i,j express m × n The first in the matrix i OK j The column cell can take values ​​of 1 to indicate the presence of material and 0 to indicate the removal of material.

[0051] To improve the mechanical coupling performance of the MSM, a bottom continuous constraint is applied to the design domain, while simultaneously introducing an effective number of filling elements. N And impose certain restrictions on it:

[0052] (3)

[0053] (4)

[0054] To address the Lamb wave mode modulation problem, this invention employs a product-based approach to construct the fitness function. F It is used to quantitatively evaluate the quality of candidate structures during the optimization process of genetic algorithms, while suppressing pseudo-optimal solutions caused by excessive amplification of a single index.

[0055] (5)

[0056] in, var 1 and var 2 is the evaluation index. Considering that the MSM needs to effectively suppress the A0 mode and achieve pure S0 mode transmission within the target frequency band, based on finite element frequency domain analysis, the ratio of the in-plane displacement integral to the total displacement integral in the transmission region is defined as the mode purity index. var 1. To achieve a quantitative characterization of the output pattern composition.

[0057] (6)

[0058] in, u This represents the in-plane displacement value. v This is the out-of-plane displacement value. V This is the transmission region.

[0059] The S0 mode is dominated by in-plane displacement, while the A0 mode is dominated by out-of-plane displacement. The S0 and A0 modes are excited separately in the finite element simulation. var The values ​​are 0.999 and 0.097 respectively, consistent with wave structure characteristics. Therefore, when varWhen the value is close to 1, the wavefield at the transmission end can be considered to be almost entirely dominated by the S0 mode, and the A0 mode is effectively filtered out. (Mode purity index) var Within the high-value range close to 1, small improvements often correspond to more significant mode suppression effects. To guide the optimization process towards a high-performance solution, this embodiment will... f 1( var 1) Construct it as a piecewise nonlinear function:

[0060] (7)

[0061] In the formula, θ 1. θ 2 represents the key threshold for the model purity control stage; α 1. ß 1. α 2. ß 2. ß 3. To control the baseline level and growth rate of the piecewise function; p 1. p 2. p 3 is the sensitivity adjustment parameter for fitness to changes in model purity.

[0062] When 0 ≤ var1 < θ At time 1, the S0 mode has a low proportion, and a weak linear reward is used to maintain population diversity; when θ 1≤var1< θ At time 2, the proportion of the S0 mode increases, and higher-order functions are introduced to enhance selection pressure; when θ When 2 ≤ var1 ≤ 1, the S0 mode has a higher proportion, and a stronger nonlinear reward is used to achieve a more refined performance improvement. This segmented strategy helps avoid the genetic algorithm getting stuck in local optima in the early stages. Although some optimization results have high... var While the value is 1, its overall transmission energy may be low or even close to zero, making it difficult to meet practical detection requirements. Therefore, an energy transmission index is further introduced. var 2. Define the cross-section of the transmission end. S The integral of the squares of the in-plane displacement and the out-of-plane displacement is the relative energy. E :

[0063] (8)

[0064] Exciting A0, S0, and A0+S0 modes of the same amplitude, relative energy E It satisfies a linear superposition relationship, that is:

[0065] (9)

[0066] in, E S0+A0This is the sum of the relative energies of the S0 and A0 modes. E A0 The relative energy of mode A0. E S0 The relative energy of mode S0.

[0067] After adding the MSM, exciting the A0+S0 mode with the same amplitude, the relative energy at the transmission end is obtained as follows: Let the energy transmission index var2 and the dimensionless deviation be... δ for:

[0068] (10)

[0069] (11)

[0070] when var When 2>1, it indicates that the A0 pattern has not been completely filtered out. var When 2 < 1, it indicates insufficient transmission in the S0 mode. Therefore, var The ideal value for 2 is 1. Considering the inevitable mode coupling during Lamb wave propagation, a piecewise attenuation function is constructed around the neighborhood of var2=1. ω 2( var 2):

[0071] (12)

[0072] in, b 1. b 2. b 3 represents deviation from the threshold. γ 1. γ 2. γ 3 represents the weight decay coefficient within different intervals. q 1. q 2. q 3 represents a non-linear exponent.

[0073] When δ > b3, the weighting function is set to zero to eliminate low-performance solutions; when b 2<δ≤ b When 3, a monotonically decaying weight is used to accelerate the elimination of inferior solutions; when b 1<δ≤ b At time 2, the weights are smoothly adjusted using a nonlinear function to guide the search towards the high-performance region; when 0 ≤ δ ≤ b When the value is 1, only a weak nonlinear penalty is applied to maintain stable search near the high-performance solution. This piecewise strategy helps to balance search efficiency and overall performance.

[0074] This topology optimization framework is implemented using COMSOL Multiphysics 6.2 and MATLAB. It ran for 140 generations on a computer equipped with an Intel Core i7-10700 processor, with an average execution time of approximately 4.18 hours.

[0075] Figure 3 (a) presents six sets of fitness iteration curves, showing that the method can quickly identify effective structures and achieve stable convergence. Figure 3 (b) shows the final optimized configuration obtained after the convergence of the corresponding iterative process. Its structural features reflect the adaptive adjustment of material distribution by topology optimization within the design domain. The topology optimization of this invention is based on frequency domain steady-state research, but the actual excitation signal has a certain bandwidth, and the optimal solution at a single frequency point in the frequency domain may not be optimal under time domain excitation conditions. Therefore, by comprehensively evaluating the time domain response characteristics in the neighborhood of the target frequency, the optimization result of case 2 is selected as the final configuration.

[0076] To analyze the modulation characteristics of MSM on different Lamb wave modes, a "MSM-adhesive layer-aluminum plate" primitive was constructed. The characteristic frequencies were solved, and color mapping was performed using var1 values. The band structure results are as follows: Figure 4 As shown. It can be seen that around 200 kHz... var The value of 1 approaches 1, indicating that MSM almost only allows the S0 mode to pass. Subsequent numerical verification will be conducted from both the frequency domain and the time domain.

[0077] In the frequency domain analysis, the A0 mode, S0 mode, and A0+S0 hybrid mode were excited in the flat panel and MSM-attached structures, respectively. The results are as follows: Figure 5 As shown. Comparison Figure 5 From (a) and (b), it can be seen that under A0 mode excitation, MSM can significantly suppress its propagation, accompanied by partial mode switching; according to Figure 5 From (c) and (d), it can be seen that under S0 mode excitation, MSM is allowed to pass effectively; further analysis Figure 5 As can be seen from (e) and (f), under mixed-mode excitation, the A0 mode is effectively filtered out, while the S0 mode maintains high transmission.

[0078] In time-domain analysis, a 200 kHz A0+S0 mixed mode is excited in both the flat plate and the MSM-attached structure. The guided wave time-domain signal at a propagation distance of 300 mm is as follows: Figure 6 As shown, it can be seen that after attaching the MSM, the A0 mode is significantly attenuated under mixed excitation, while the S0 mode shows no significant change, further verifying the modal filtering capability of the MSM over a wide frequency range.

[0079] Based on the above topology optimization method, a mode filter that effectively suppresses background artifacts can be obtained.

[0080] Example 2

[0081] This embodiment provides a method for suppressing artifacts in ultrasonic guided wave damage imaging based on the mode filter obtained in Embodiment 1. The mode filter described above is pasted onto the object under test to obtain an imaging result with artifact suppression.

[0082] The principle of imaging is as follows Figure 7 As shown, there is a circular through-hole damage in the aluminum plate. A one-dimensional linear piezoelectric array is arranged on both sides of the aluminum plate, with 8 piezoelectric plates on each side. Each transducer is used as an individual excitation source in sequence, and the transducer on the opposite side is used as a receiving end, thus forming multiple transmission propagation paths. Data acquisition uses full matrix capture (FMC) mode.

[0083] To verify the performance improvement effect of MSM on damage imaging, the signal difference coefficient (SDC) and elliptic-Gaussian probability weighting strategy were improved based on the classic probabilistic damage imaging algorithm. The workflow diagram is as follows. Figure 8 As shown, the imaging results before and after the introduction of MSM are compared and analyzed. One-dimensional linear piezoelectric arrays (PZTs) are arranged on both sides of an aluminum plate, each side containing M=8 piezoelectric elements with a center-to-center spacing of 14mm. A 12mm diameter circular hole is set in the center of the aluminum plate. Data acquisition uses full matrix acquisition (FMC) mode: each PZT transducer is used sequentially as an individual excitation source, and the opposite PZT transducer serves as the receiving end, thus forming multiple transmission propagation paths. i Transducer excitation and j When the transducer receives signals, the time-domain signals obtained under healthy and damaged states are denoted as follows: H ij ( t )and D ij ( t ), within the effective time window interval [ t a , t b The signal is intercepted within the [internal range], and SDC is defined as:

[0084] (13)

[0085] in, for i Transducer excitation and j The average time-domain signal obtained by the transducer in a healthy state during reception. for i Transducer excitation and j The average time-domain signal obtained by the transducer under damaged conditions. A larger SDC value indicates a more significant change in the path signal caused by damage, meaning the path is more sensitive to damage. For any imaging point... r (x , y If it reaches the excitation point r i ( x i ，y i ) and receiving point r j ( x j ，y j Euclidean distance L ij (r) and actual propagation distance When the ratio is less than the elliptical window shape factor α, a composite weighting function is introduced. w ij (r):

[0086] (14)

[0087] In the formula, μ Centered on the Gaussian core; σ The width of the Gaussian kernel. The weight for spatial points that do not satisfy the elliptic constraint. w ij (r) is 0. For the th i Secondary excitation, its damage probability distribution I i (r) is:

[0088] (15)

[0089] in, Indicates the stimulation i Select the top [values] after sorting them in descending order based on their SDC values. N The set of indices of the optimal receiving sensors, and the final damage probability imaging matrix I. total (r):

[0090] (16)

[0091] To facilitate visualization analysis, I total (r) is normalized to obtain I (r), and convert it to dB scale. I dB (r):

[0092] (17)

[0093] In the formula, ε It is a very small positive value. Simulations are performed based on an improved imaging method, and according to... I (r) andI dB (r) Perform damage imaging. Figure 9 (a) and (b) show the simulated imaging results of damage in the slab without MSM attachment. Obvious artifacts exist in the imaging area, and the damage focus is poor. After MSM attachment, the damage imaging results are as follows: Figure 9 As shown in (c) and (d), due to the effective filtering of the A0 mode, the damage location is accurately located and the background artifacts are significantly reduced.

[0094] To address the problem of low damage localization accuracy caused by the generation of numerous background artifacts due to mode aliasing interference in conventional ultrasonic testing of mixed A0 and S0 excitation modes, this embodiment employs a mode filter designed as in Embodiment 1. This filter can effectively suppress the A0 mode at the physical level while maintaining the high transmission efficiency of the S0 mode. By filtering out interference at the source to obtain a pure S0 mode, the physical complexity brought about by multimodal processing is overcome, damage focusing is significantly enhanced, and ultimately, effective suppression of background artifacts and a significant improvement in imaging resolution are achieved.

[0095] This invention reverse-engineers a waveguide mode (MSM) through topology optimization, achieving effective selective filtering of waveguide modes. Combined with an improved imaging method, it enhances damage detection accuracy, effectively suppresses artifacts, and has good potential for engineering applications.

[0096] 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 mode filter topology optimization method suitable for suppressing artifacts in ultrasonic guided wave damage imaging, characterized in that, Includes the following steps: Obtain initial design parameters and generate an initial population. Each chromosome individual in the initial population is encoded by a binary logic matrix that represents the material distribution and satisfies the design constraints. A genetic algorithm is used to optimize the population. The fitness function in the genetic algorithm is constructed based on the mode purity index and the energy transmission index. The mode purity index is the ratio of the in-plane displacement integral of the transmission region to the total displacement integral in the finite element simulation with added mode filter. The energy transmission index is the ratio of the relative energy of the transmission end to the relative energy of the S0 mode in the finite element simulation with added mode filter. The final optimized material distribution of the output mode filter based on the binary logic matrix corresponding to the optimal individual obtained by the genetic algorithm; The fitness function is expressed as follows: in, var 1 represents the model purity index. f 1( var 1) is a fitness function based on the model purity index. var 2 represents the energy transmission index. ω 2( var 2) is a weighting function based on the energy transmission index; The f 1( var 1) is a piecewise nonlinear function, expressed as: in, θ 1. θ 2 represents the key threshold for the model purity control stage; α 1. ß 1. α 2. ß 2. ß 3. To control the baseline level and growth rate of the piecewise function; p 1. p 2. p 3 is a parameter that modulates the sensitivity of fitness to changes in model purity; The ω 2( var 2) is a piecewise decay function, expressed as: in, b 1. b 2. b 3 represents deviation from the threshold. γ 1. γ 2. γ 3 represents the weight decay coefficient within different intervals. q 1. q 2. q 3 represents a non-linear exponent. δ It is a dimensionless deviation.

2. The mode filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging according to claim 1, characterized in that, The design constraints include bottom continuity constraints and effective fill cell number constraints.

3. The mode filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging according to claim 1 or 2, characterized in that, The design constraints are expressed as follows: in, θ i,j express m × n The first in the matrix i OK j The column cell value is 1 if material is present, and 0 if material is removed. N The number of effective fill cells.

4. The mode filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging according to claim 1, characterized in that, The relative energy of the transmission end is the integral of the square of the in-plane displacement and out-of-plane displacement of the transmission end cross-section.

5. The mode filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging according to claim 1, characterized in that, Structural stability is handled each time a new population is generated.

6. A mode filter, characterized in that, The pattern filter topology optimization method for suppressing artifacts in ultrasonic guided wave damage imaging, as described in any one of claims 1-5, was used to design the filter.

7. A method for suppressing artifacts in ultrasonic guided wave damage imaging, characterized in that, The mode filter as described in claim 6 is attached to the object under test to obtain an imaging result with artifact suppression.

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