A method for optimizing experimental parameters of mixed-mode nonlinear ultrasonic testing based on monte carlo markov chain

Abstract

The application discloses a mixed-frequency nonlinear ultrasonic detection experimental parameter optimization method based on Monte Carlo Markov chain, which is suitable for automatic scanning water-immersed mixed-frequency nonlinear ultrasonic detection experiment and belongs to the field of nondestructive testing. Firstly, the variable and parameter variation range of the excitation parameter to be optimized are determined; the initial value of the detection parameter is screened by using simulated annealing; MATLAB and LabVIEW intercommunication transmission control is established, MATLAB transmits the variable combination to be optimized to LabVIEW, and LabVIEW transmits the received signal to MATLAB; based on the fuzzy optimization theory, a mixed-frequency response detection effect evaluation index fusion is carried out, and a mixed-frequency effect strength evaluation function is established; a Monte Carlo Markov chain optimization method is selected to construct and correct the optimization parameter; iteration is carried out, and according to whether the candidate detection combination is accepted or not, the sampling distribution of the detection parameter is modified or kept, so that the parameter combination distribution corresponding to the optimal detection parameter is approached. The method overcomes the influence of experimental conditions on experimental results, and realizes the optimization of multiple excitation parameters of the mixed-frequency ultrasonic detection experiment.

Description

Technical Field

[0001] This invention relates to an optimization method for mixed-frequency nonlinear ultrasonic testing experiments, particularly a method for optimizing testing experimental parameters based on MATLAB Monte Carlo Roman chain. This method is applicable to automated scanning water immersion mixed-frequency nonlinear ultrasonic testing experiments and belongs to the field of nondestructive testing technology. Background Technology

[0002] Nonlinear ultrasonic testing technology has attracted much attention due to its high sensitivity to early damage in structures. Material degradation or minute changes such as microcracks can cause nonlinear effects in the propagation of ultrasonic waves in a medium, such as mixing and harmonics. When two ultrasonic waves of different frequencies propagating in a structure interact with micro-damage, new frequency components such as the sum and difference frequencies of the original signal are generated; this phenomenon is called the mixing nonlinear effect. The newly generated frequencies and wave vectors are closely related to the frequencies and wave vectors of the two incident waves. To ensure that the two ultrasonic waves converge simultaneously on the area to be tested, precise control of the mixing detection parameters (such as the frequency ratio, direction, and wave type of the incident sound waves) is required. Domestic and international scholars have conducted extensive research on the experimental conditions for mixing nonlinear ultrasonic testing. Korneev VA et al. [Possible second-order nonlinear interactions of plane waves in an elastic solid[J]. The Journal of the Acoustical Society of America, 2014, 135(2): 591-598.] detailed the conditions (including parameters such as frequency, interaction angle, and scattering angle) for generating a third-order mixing wave under the condition of 10 incident wave combinations satisfying resonance. Alston et al. [Nonlinear non-collinear ultrasonic detection and characterisation of kissing bonds[J]. NDT&E International, 2018, 99: 105-116.] studied the influence of the interaction angle α and frequency ratio r of two incident shear waves on the nonlinear mixing effect in the nonlinear mixing detection of the interface of horizontal adhesive layers, and used the mixing α-r characteristic diagram composed of the sum frequency longitudinal wave amplitude under different interaction angles α and frequency ratios r as the evaluation index of the adhesive layer. However, in the testing experiment, due to the influence of sensor frequency response characteristics and instruments, the sound field distribution in the actual structure is very different from the theoretical prediction value. Under the theoretical testing conditions, the best mixing detection effect cannot be achieved, and the detection parameters used in the experiment need to be further optimized.

[0003] For the problem of optimizing excitation parameters in multi-parameter mixed-frequency ultrasonic testing experiments, the Monte Carlo chain stochastic algorithm is an effective method for multi-module coordination. It estimates the global state of the experimental results using subjective probabilities. Its sampling number is not limited by the system size. Compared to traditional analytical methods that select the system state through enumeration, the Monte Carlo chain method demonstrates greater advantages when the number of experiments is limited.

[0004] Therefore, based on fuzzy evaluation theory and using mixing intensity as the evaluation function, a Monte Carlo Roman chain-based method for optimizing mixing detection parameters is proposed. Based on the mixing detection results under finite parameter combinations, the main mixing detection parameters affecting the experimental results are optimized. Summary of the Invention

[0005] The purpose of this invention is to provide a method for overall optimization of excitation parameters in mixed-frequency nonlinear ultrasonic testing experiments, particularly a multi-parameter optimization method based on MATLAB Monte Carlo Roman chains and a mixed-frequency nonlinear ultrasonic testing system. This method applies intelligent optimization algorithms to optimize parameters in mixed-frequency ultrasonic testing experiments. Based on the nonlinear mixed-frequency ultrasonic testing experiment, the excitation parameters of the nonlinear ultrasonic testing system are controlled by MATLAB using LabVIEW, and the MATLAB Monte Carlo Roman chains are used to optimize the excitation parameters of the mixed-frequency testing experiment.

[0006] This invention proposes a method for optimizing excitation parameters in mixing nonlinear ultrasonic testing experiments based on Monte Carlo Roman chain in MATLAB. The basic principle of this method is as follows:

[0007] The Monte Carlo chain method, a widely used stochastic algorithm, estimates the global state of the detection result using subjective probability when the number of experiments is limited. It obtains the mixing response under a finite combination of parameters through mixing nonlinear experiments and uses Bayes' theorem to correct the corresponding current state. In the Monte Carlo chain method, the number of samplings is not limited by the system size, and parameter optimization can be completed in a finite number of experiments. Its main computational flow is as follows: Figure 1 As shown.

[0008] The Monte Carlo Roman chain algorithm mainly consists of four steps: initializing detection parameters, constructing and candidate combination parameters, evaluating parameter combinations, and updating candidate parameters. First, data optimization parameters (predetermined number of iterations, sampling distribution parameters, acceptance probability distribution parameters, etc.) are initialized, and an optimized parameter set is established based on the possible value range of the parameters. To accelerate the iteration process, the initial values ​​should be as close as possible to the global minimum. Before entering the iteration process, simulated annealing is used to filter the initial values ​​of the detection parameters. After Na iterations, the simulated annealing process is exited, and the variance of the mixing intensity change rate distribution is changed from S1 = 20σ. 2 Gradually decrease to SNa =σ 2 Its convergence process can be expressed as:

[0009]

[0010] In the formula, n is the current cycle number; S is the variance of the mixing intensity change rate distribution; at the same time, the variance of the change of different detection parameters also follows formula (1), from S1=5σ 2 Gradually decrease to S Na =σ 2 .

[0011] The fuzzy influence of evaluation indicators on the results was quantified by using membership functions, and the mixing intensity of the received signal corresponding to the parameter combination X was evaluated based on the mixing intensity evaluation function DC(X) of the target signal.

[0012] Based on the relationship between the normalized amplitudes of the fundamental frequency and the mixing stress wave factor and the strength of the mixing effect, a slightly smaller ridge distribution function and a slightly larger Gaussian distribution function are selected as the membership functions for the fundamental frequency amplitude U1 and the mixing amplitude U2, respectively. The ridge distribution membership function χ for the fundamental frequency amplitude... U1 (X U1,j This can be expressed as:

[0013]

[0014] In the formula χ U1 (X U1,j )——X U1,j The membership function that maps to the membership space M(0:1) reflects the degree of satisfaction of each evaluation index with the experimental results of this set of experiments;

[0015] X U1,j Let be the fundamental frequency amplitude of the received signal for the j-th parameter combination.

[0016] When the membership value approaches 1, the satisfaction with the current detection result is high; conversely, the satisfaction is low. When X... U1,j When ≤0.01, the membership function value of coefficient D1 is 1, indicating that the results in this region are completely satisfactory; when 0.01 <X U1,j When X ≤ 1.1, the membership function follows a ridge-shaped distribution, gradually decreasing, and the satisfaction with the detection results also decreases accordingly; when X U1,j When the membership value is greater than 1.1, the membership value drops to 0, indicating that the results in this region are completely unsatisfactory.

[0017] Gaussian distribution membership function χ of the normalized amplitude U2 of the mixing components U2 (X U2,j ) can be represented as

[0018]

[0019] In the formula χ U2 (X U2,j ) is X U2,j Membership function for mapping to membership space M(0:1); X U2,j Let X be the mixing amplitude of the received signal for the j-th parameter combination. U2,j If X < 0.9, the membership function of coefficient P follows a Gaussian distribution, and as it gradually increases, satisfaction gradually increases. U2,j ≥0.9, at which point the membership value is 1, which means that the mixing amplitude result of the current detection signal is completely satisfactory.

[0020] After determining the membership function, the weight coefficients are assigned based on the average membership value of the membership function obtained from the experiments, thus obtaining the final fuzzy evaluation model. Equation (4) gives the resulting fuzzy evaluation function for the mixing effect:

[0021]

[0022] Assuming that the mixing intensity evaluation coefficients under the different parameter combinations mentioned above are random and independent, the likelihood distribution of the mixing effect intensity in the received signal corresponding to combination X can be expressed as:

[0023]

[0024] The acceptance probability of candidate detection parameter combinations is estimated by subtracting the mixing evaluation result from the previous iteration's accepted parameter combinations. In summary, the detection parameter optimization process is transformed into finding suitable detection combination parameters that maximize the mixing intensity evaluation function, i.e.

[0025] X=argmax(χ(X)),X=[X1,X2…X n (6)

[0026] Equation (6) is solved through a Monte Carlo chain iterative process:

[0027] 1) From {P1, P2, P3……P} N The initial combination of parameters randomly generated in} is the combination X. 0 ={p 0 1,p 0 2,p 0 3……p 0 N} and X 1 ={p 1 1,p 1 2,p 1 3……p 1 N}

[0028] 2) The mixing effect intensity corresponding to the combination of detection parameters is obtained through experiments. The initial combination X can be obtained from equation (5). 0 With X 1 The likelihood distribution of mixing intensity under parameter combinations is obtained by subtracting the corresponding rate of change.

[0029] 3) Generate candidate states X* for detection parameter combinations from the previous parameter combination Xn-1. The selection principle for candidate parameter combinations can be expressed as:

[0030]

[0031] 4) Repeat step 2) to obtain the detection parameter combination X. n-1 With X * The rate of change of the corresponding mixing effect intensity is estimated by the likelihood function using equation (5).

[0032] 5) The applicability of the candidate parameter combination can be judged by the ratio of the likelihood function of the mixing effect intensity under the previous parameter combination and the candidate parameter combination:

[0033]

[0034] In the formula, α is a random number between 0 and 1. When formula (8) is true, the current candidate parameter combination is accepted as the new parameter combination; otherwise, the previous parameter combination is accepted.

[0035] 6) Repeat steps 3)-5) to obtain the sample set {X} for estimating the optimal parameter combination. 1 ,X 2 ,X 3 ...X N From the parameter distribution in the sample set at the end of the iteration, the posterior estimates of each detection parameter in the optimal combination that satisfies the acceptance probability can be obtained, and the mean of the distribution is used as the estimated value of each detection parameter in the optimal combination.

[0036] The technical solution adopted in this invention is a method for optimizing experimental parameters of mixing nonlinear ultrasonic testing based on the Monte Carlo Roman chain algorithm. The method includes the following steps:

[0037] Step 1: Determine the excitation parameters, optimization variables, and parameter variation range.

[0038] During the experiment, the excitation parameters that significantly affect the experimental results are optimized as variables. The parameter range of the excitation parameters is calculated based on the relationship between the experimental probe displacement, rotation angle, and the generation angle of the mixed sound wave. To avoid the influence of the harmonic component on the detection results when the frequency ratio is 1, the frequency ratio will not be equal to 1 within the parameter variation range.

[0039] Step 2: Set the initial values ​​of the experimental excitation parameters.

[0040] Write a LabVIEW program to control the excitation parameters of a nonlinear ultrasonic testing system. These parameters include the amplitude, frequency, and period of the excitation signal, the positions and angles of the two excitation probes, and the position and angle of the receiving probe. The excitation frequency 'a' is fixed, while the excitation frequency 'b' is varied according to different excitation frequency ratios. Simulated annealing is used to filter the initial values ​​of the testing parameters, making them as close as possible to the global minimum. The initialization parameters are set, and the mixing nonlinear testing experiment is started. The nonlinear ultrasonic testing system receives the received signal, and the processed signal is acquired by an oscilloscope and transmitted to LabVIEW.

[0041] Step 3: Establish interoperability and control between MATLAB and LabVIEW.

[0042] The LabVIEW program extracts the fundamental frequency amplitude and the mixing stress wave factor obtained by the sliding correlation method. These two frequency domain parameters are used as evaluation indicators, which represent the nonlinear response generated by mixing during the detection process. The evaluation indicators are then transferred to MATLAB for further optimization.

[0043] Step 4: Establish a function to evaluate the intensity of the mixing effect.

[0044] Based on fuzzy optimization theory, a MATLAB program fuses multiple evaluation indicators for mixing response detection. According to the degree of change of the optimization variable with different evaluation indicators, different weights are assigned to evaluation indicators with different degrees of influence, transforming them into a comprehensive evaluation indicator as the mixing effect intensity. The transformation process uses membership functions to quantify the weights of two characteristic indicators: the fundamental frequency amplitude of the received signal and the normalized result of the mixing component amplitude. A linear weighting method is then used to allocate the weights of each evaluation indicator, obtaining a fuzzy comprehensive evaluation indicator that integrates multiple evaluation indicators. The detection effect is then evaluated by a fuzzy evaluation function.

[0045] Step 5: Select the Monte Carlo Roman chain optimization method to construct and modify the optimization parameters.

[0046] The Monte Carlo chain algorithm provides the posterior distribution of detection parameters based on the evaluation results. It samples the optimized parameter set according to the optimized sampling distribution and uses the sampling results as candidate detection parameter combinations. MATLAB transmits the selected candidate detection parameter values ​​to LabVIEW. The LabVIEW program adjusts to the corresponding values ​​of the candidate excitation parameters, performs a mixing nonlinear detection experiment, and collects the detection signal as the mixing detection result under the corresponding parameter combination.

[0047] Step 6: Enter the iterative process to obtain the optimal combination of detection parameters.

[0048] Repeat steps three through five, modifying or maintaining the sampling distribution of the detection parameters based on whether or not candidate detection combinations are accepted, so that it approximates the parameter combination distribution corresponding to the optimal detection parameters. Each accepted parameter combination in the iteration constitutes a posterior distribution estimate of the optimal detection parameters. The optimal detection parameters are then selected based on the estimation results.

[0049] This invention has the following advantages: 1) The Monte Carlo chain algorithm is used for the optimal selection of experimental parameters in mixed-frequency ultrasonic testing. The evaluation index is quantified through the membership function, achieving overall optimization of multi-parameter combinations. 2) Compared with conventional traversal methods, the Monte Carlo chain method greatly reduces the amount of experimentation and achieves posterior distribution estimation in a limited sample. Attached Figure Description

[0050] Figure 1 A schematic diagram of the parameter optimization process.

[0051] Figure 2 Flowchart of a method for optimizing experimental parameters in mixed-frequency ultrasonic detection based on Monte Carlo Roman chain.

[0052] Figure 3 Schematic diagram of sensor and specimen arrangement.

[0053] Figure 4 Membership function for a small-scale ridge distribution.

[0054] Figure 5 Membership function of a skewed Gaussian distribution.

[0055] Figure 6 Parameter iteration curve.

[0056] Figure 7 Posterior distribution of parameters. Detailed Implementation

[0057] The invention will be further illustrated below with specific experiments:

[0058] This experiment optimizes the experimental parameters for water immersion mixed-frequency nonlinear ultrasonic testing of bonded structures. The sensor and specimen arrangement are as follows: Figure 3 As shown. An adhesive specimen was constructed by bonding aluminum with epoxy resin. Minor damage to the interface layer of the adhesive structure was detected by mixed-frequency ultrasound. The distance from the probe clamp to the probe excitation-receiving surface was x0. The X-axis distance of excitation probe 1 from the sound wave encounter point was x1, the X-axis distance of excitation probe 2 from the sound wave encounter point was x2, and the X-axis distance of the receiving probe from the sound wave encounter point was x3. The distance from the receiving probe clamp to the lower surface of the specimen was x4, and the distance from the clamps of both excitation probes to the upper surface of the specimen was x5. Simultaneously, the deflection angles of the excitation and receiving probes were α. 水1 α 水2 With θ 水The lengths of the upper and lower parts of the specimen in the Y-axis direction are D1 and D2, respectively.

[0059] Step 1: Determine the optimization variables and the range of parameter variation for the excitation parameters;

[0060] During the experiment, the probe incident angle, excitation frequency ratio, and receiving probe angle had a significant impact on the experimental results. These three factors were selected as optimization variables for the excitation parameters. Based on Snell's theorem, the relationship between the displacement and rotation angles of the three probes and the generation angle of the mixing sound wave was calculated as follows:

[0061]

[0062] In the formula, v 铝1 v 铝2 v 环氧1 v 环氧2 —Excitation sound wave f A f B Wave velocity in aluminum blocks and epoxy resin; v 铝3 v 环氧3 —Mixed sound wave f 混 Wave velocity in aluminum blocks and epoxy resin.

[0063] The range of parameters for the incident angle, receiving angle, and frequency ratio can be calculated using the formula. To avoid the influence of the harmonic component on the detection results when the frequency ratio is 1, the frequency ratio will not be equal to 1 within the parameter variation range.

[0064] P 入射 = [50°, 60°…140°]; P 扫查 = [30°, 35°…150°]; P 频率比 = [0.6, 0.7…0.9, 1.1…1.4].

[0065] Step 2: Set the initial values ​​of the experimental excitation parameters.

[0066] A LabVIEW program was written to control the excitation parameters of the nonlinear ultrasonic testing system. These parameters included the excitation signal amplitude, frequency, and period; the positions and angles of the two excitation probes; and the position and angle of the receiving probe. The excitation frequency 'a' was fixed at 5MHz, while the excitation frequency 'b' varied according to different excitation frequency ratios. To flexibly change the incident and scattering angles of the sound waves, the specimen was placed in a water tank, with its upper surface 200mm from the excitation axis and its lower surface 70mm from the receiving axis. Simulated annealing was used to filter the initial values ​​of the testing parameters, making them as close as possible to the global minimum. The initialization parameters were set, and the mixing nonlinear testing experiment was started. The nonlinear ultrasonic testing system received the signal, and the processed signal was acquired by an oscilloscope and transmitted to LabVIEW.

[0067] Step 3: Establish interoperability and control between MATLAB and LabVIEW.

[0068] The LabVIEW program extracts the fundamental frequency amplitude and the mixing stress wave factor obtained by the sliding correlation method. These two frequency domain parameters are used as evaluation indicators, which represent the nonlinear response generated by mixing during the detection process. The evaluation indicators are then transferred to MATLAB for further optimization.

[0069] Step 4: Establish a function to evaluate the intensity of the mixing effect.

[0070] Based on fuzzy optimization theory, multiple evaluation indicators for mixing response detection are fused. According to the degree of change of the optimization variable with different evaluation indicators, different weights are assigned to evaluation indicators with different degrees of influence, transforming them into a comprehensive evaluation indicator as the mixing effect intensity. The transformation process uses a membership function to quantify the weights of two feature indicators: the received signal fundamental frequency amplitude and the normalized result of the mixing component amplitude. A linear weighting method is then used to allocate the weights of each evaluation indicator, obtaining a fuzzy comprehensive evaluation indicator that integrates multiple evaluation indicators. The detection effect is then evaluated by a fuzzy evaluation function.

[0071] Step 5: Select the Monte Carlo Romano chain optimization method to construct and modify the optimization parameters;

[0072] The Monte Carlo chain algorithm provides the posterior distribution of detection parameters based on the evaluation results. It samples the optimized parameter set according to the optimized sampling distribution and uses the sampling results as candidate detection parameter combinations. MATLAB transmits the selected candidate detection parameter values ​​to LabVIEW. The LabVIEW program adjusts to the corresponding values ​​of the candidate excitation parameters, performs a mixing nonlinear detection experiment, and collects the detection signal as the mixing detection result under the corresponding parameter combination.

[0073] Step 6: Enter the iterative process to obtain the optimal combination of detection parameters.

[0074] Repeat steps three through five, modifying or maintaining the sampling distribution of the detection parameters based on whether or not candidate detection combinations are accepted, so that it approximates the parameter combination distribution corresponding to the optimal detection parameters. Each accepted parameter combination in the iteration constitutes a posterior distribution estimate of the optimal detection parameters. The optimal detection parameters are then selected based on the estimation results.

[0075] After 100 simulated annealing cycles and 400 Monte Carlo Markov chain iterations, the posterior distribution of the parameter combination optimization results is obtained. Figure 4 , Figure 5 These are the membership functions for a sparsely populated ridge distribution and a sparsely populated Gaussian distribution, respectively. Figure 6 The parameter iteration curves are given. Figure 7The posterior sample set and fitted distribution are shown. From the iterative change curves, it can be observed that in the early stages of the simulated annealing process in the first 100 iterations, the parameters underwent significant changes within their respective ranges. As the number of simulated annealing iterations increased, the degree of change in the three parameters decreased, gradually concentrating on a local optimum. After entering the Monte Carlo Rohrkov chain process, the three parameters gradually found their global optimum values. After 300 iterations, the degree of parameter change gradually stabilized. Simultaneously, due to the judgment condition, i.e., the setting of equation (8), after finding the current optimum, the optimization process will continue to accept new candidate parameters, thus the parameters will still change within a relatively small range. As the iterations continue, the distribution of the accepted samples gradually approaches the posterior distribution of the final optimization results of the three parameters. Figure 7 The distribution of the received sample set is given, and the posterior distribution is fitted using a Gaussian distribution as the distribution type.

[0076] After 500 iterations, the mean values ​​of the sample distributions corresponding to the excitation frequency ratio, incident angle, and scanning angle were 0.8, 80°, and 105°, respectively. To ensure that the incident angle of the sound wave in the epoxy resin is the same, the excitation probe T is then... a Excitation frequency f a =5MHz, generating a transverse wave incident angle of 42°; excitation probe T b Excitation frequency is f b =4MHz, the resulting longitudinal wave incident angle is 37°; the receiving probe R2 has a receiving angle of 105°.

[0077] The above is a typical application of the present invention, but the applications of the present invention are not limited thereto.

Claims

1. A method for optimizing experimental parameters of mixing nonlinear ultrasonic testing based on Monte Carlo Roman chain, characterized in that: This method is implemented through the following steps: Step 1: Determine the optimization variables and the range of parameter variation for the excitation parameters; Select the excitation parameter optimization variables and choose an appropriate range of excitation parameters based on the arrangement of the experimental probe and the specimen. Step 2: Set the initial values ​​of the experimental excitation parameters; Write a LabVIEW program to control the excitation parameters of a nonlinear ultrasonic testing system. The excitation parameters include the amplitude, frequency, and period of the excitation signal, the position and angle of the two excitation probes, and the position and angle of the receiving probe. Fix the excitation frequency 'a', and change the excitation frequency 'b' according to different excitation frequency ratios. Use simulated annealing to filter the initial values ​​of the testing parameters so that the initial values ​​are as close as possible to the global minimum. Set initialization detection parameters to start the mixing nonlinear detection experiment; the nonlinear ultrasonic detection system receives the received signal, and the signal processed by the nonlinear ultrasonic detection system is acquired by an oscilloscope and transmitted to LabVIEW; Step 3: Establish interoperability and control between MATLAB and LabVIEW; The LabVIEW program extracts the fundamental frequency amplitude and the mixing stress wave factor obtained by the sliding correlation method. These two frequency domain parameters are used as evaluation indicators, which represent the nonlinear response generated by mixing during the detection process. The evaluation metrics are then transmitted to MATLAB for further optimization. Step 4: Establish a function to evaluate the intensity of the mixing effect; Based on fuzzy optimization theory, the MATLAB program integrates multiple evaluation indicators for mixing response detection performance. Based on the degree of change of the optimization variable with different evaluation indicators, different weights are assigned to evaluation indicators with different degrees of influence, and a comprehensive evaluation indicator is transformed into the mixing effect intensity. The conversion process uses a membership function to quantify the weights of two characteristic indicators: the fundamental frequency amplitude of the received signal and the normalized result of the amplitude of the mixing component. The linear weighting method is used to allocate the weights of each evaluation index, and a fuzzy comprehensive evaluation index that integrates multiple evaluation indicators is obtained. The detection effect is then evaluated by the fuzzy evaluation function. Step 5: Select the Monte Carlo Romano chain optimization method to construct and modify the optimization parameters; The Monte Carlo Roman chain algorithm provides the posterior distribution of detection parameters based on the evaluation results. It samples the optimized parameter set according to the optimized sampling distribution and uses the sampling results as candidate detection parameter combinations. MATLAB transmits the selected candidate detection parameter values ​​to LabVIEW. The LabVIEW program adjusts the excitation optimization parameters to the corresponding values ​​of the candidate detection parameters, conducts a mixing nonlinear detection experiment, and collects detection signals as the mixing detection results under the corresponding parameter combinations. Step Six: Proceed to the iteration process to obtain the optimal combination of detection parameters; Repeat steps three through five, modifying or maintaining the sampling distribution of detection parameters based on whether candidate detection combinations are accepted, so that it approximates the parameter combination distribution corresponding to the optimal detection parameters; the parameter combinations accepted in each iteration constitute the posterior distribution estimate of the optimal detection parameters, and the optimal selection of detection parameters is achieved through the estimation results; The process of establishing the evaluation function for the mixing effect intensity in step four is as follows: The fuzzy influence of evaluation indicators on the results was quantified by using membership functions, and the mixing intensity of the received signal corresponding to the parameter combination X was evaluated based on the mixing intensity evaluation function DC(X) of the target signal. Based on the relationship between the normalized amplitudes of the fundamental frequency and the mixing stress wave factor and the strength of the mixing effect, a slightly smaller ridge distribution function and a slightly larger Gaussian distribution function are selected as the membership functions of the fundamental frequency amplitude U1 and the mixing amplitude U2, respectively; the ridge distribution membership function of the fundamental frequency amplitude χ U1 (X U1,j This can be expressed as: (2)； In the formula, j is the number of parameter combinations; X U1,j χ is the fundamental frequency amplitude of the received signal of the j-th parameter combination; U1 (X U1,j ) is X U1,j The membership function that maps to the membership space M(0:1) reflects the degree of satisfaction of each evaluation index with the experimental results of this set of experiments; When the membership value approaches 1, the satisfaction with the current detection result is high; conversely, the satisfaction is low. When X... U1,j When ≤0.01, the membership function value of coefficient D1 is 1, indicating that the results in this region are completely satisfactory; when 0.01 < X U1,j When X ≤ 1.1, the membership function follows a ridge-shaped distribution, gradually decreasing, and the satisfaction with the detection results also decreases accordingly; when X U1,j When the value is > 1.1, the membership degree drops to 0, indicating that the results in this region are completely unsatisfactory; Gaussian distribution membership function χ of the normalized amplitude U2 of the mixing components U2 (X U2,j ) is represented as: (3)； In the formula, χ U2 (X U2,j ) is X U2,j Membership function for mapping to membership space M(0:1); X U2,j Let X be the mixing amplitude of the received signal of the j-th parameter combination; when the index value X U2,j If X < 0.9, the membership function of coefficient P follows a Gaussian distribution; as it gradually increases, satisfaction gradually increases. U2,j ≥ 0.9, at which point the membership value is 1, which means that the mixing amplitude result of the current detection signal is completely satisfactory; After determining the membership function, the weight coefficients are assigned based on the average membership value of the membership function obtained from the experimental results, thus obtaining the final fuzzy evaluation model; Equation (4) gives the fuzzy evaluation function for the mixing effect obtained therefrom: (4)； In the formula, DC(x) is the fuzzy evaluation function for mixing effects; i is the evaluation index; w i Assign weight coefficients to the i-th indicator; The mixing intensity evaluation coefficients under different parameter combinations are random and independent. Therefore, the likelihood distribution of the mixing effect intensity in the received signal corresponding to combination X can be expressed as: (5)； In the formula, The set variance value; The acceptance probability of candidate detection parameter combinations is estimated by subtracting the mixing evaluation result from the previous iteration's accepted parameter combinations. In summary, the detection parameter optimization process is transformed into finding suitable detection combination parameters that maximize the mixing intensity evaluation function. (6)。 2. The method for optimizing experimental parameters of mixed-frequency nonlinear ultrasonic testing based on Monte Carlo Roman chain according to claim 1, characterized in that: The process of selecting the initial values ​​of the detection parameters using simulated annealing in step two is as follows: Before entering the iterative process, simulated annealing is used to filter the initial values ​​of the detection parameters, making the initial values ​​as close as possible to the global minimum. After performing Na iterations, the simulated annealing process is exited, and the variance of the mixing intensity change rate distribution is changed from S1=20σ. 2 Gradually decrease to S Na =σ 2 Its convergence process can be expressed as: (1)； In the formula, n is the current loop count; Na is the total loop count; S1 is the variance of the initial mixing intensity change rate distribution; S Na Let be the variance of the rate of change distribution of the mixing intensity of order Na; and S be the variance of the rate of change distribution of the mixing intensity. Meanwhile, the variance of the different detection parameters also follows equation (1), from S1=5σ 2 Gradually decrease to S Na =σ 2 .

3. The method for optimizing experimental parameters of mixed-frequency nonlinear ultrasonic testing based on Monte Carlo Roman chain according to claim 1, characterized in that: The Monte Carlo Romano chain iteration process in step five is as follows: 1) From {P1, P2, P3……P} N The initial combination X obtained by using simulated annealing in} 0 ={p 0 1,p 0 2,p 0 3…… p 0 N } and X 1 ={p 1 1,p 1 2,p 1 3…… p 1 N }; 2) The mixing effect intensity corresponding to the combination of detection parameters is obtained through experiments. The initial combination X can be obtained from equation (5). 0 With X 1 The likelihood distribution of mixing intensity under parameter combinations is obtained by subtracting the corresponding rate of change. 3) Based on the previous parameter combination X n-1 Candidate state X for generating combination of detection parameters * The selection principle for candidate parameter combinations is expressed as follows: (7)； 4) Repeat step 2) to obtain the detection parameter combination X. n-1 With X * The rate of change of the corresponding mixing effect intensity is estimated by the likelihood function using equation (5); 5) The applicability of the candidate parameter combination can be judged by the ratio of the likelihood function of the mixing effect intensity under the previous parameter combination and the candidate parameter combination: (8)； In the formula, α is a random number between 0 and 1; X * For candidate combinations of detection parameters; X n-1 For X * The previous parameter combination; When equation (8) is true, the current candidate parameter combination is accepted as the new parameter combination; otherwise, the previous parameter combination is accepted. 6) Repeat steps 3)-5) to obtain the sample set {X} for estimating the optimal parameter combination. 1 ,X 2 ,X 3 ...X N }; From the parameter distribution in the sample set at the end of the iteration, the posterior estimates of each detection parameter in the optimal combination that satisfies the acceptance probability can be obtained, and the mean of the distribution is used as the estimated value of each detection parameter in the optimal combination.

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