Reliability analysis method based on adaptive agent model and importance sampling

Abstract

The invention relates to a reliability analysis method based on a self-adaptive agent model and importance sampling, belongs to the technical field of interventional medical stents, solves the problem of low reliability analysis efficiency of medical stents in the prior art, and is used for reliability analysis of mechanical thrombectomy stents. Comprising the following steps: quantifying random parameter probability distribution of a mechanical thrombectomy stent, and initializing algorithm parameters; generating a random sample, and obtaining a training sample set and a candidate sample set; constructing and training a Kriging agent model of the finite element model of the mechanical thrombectomy stent, and establishing an updated hypersphere; carrying out convergence judgment on the updated hypersphere radius; performing cross validation on the precision of the trained Kriging agent model by using a leave-one-out method; calculating a failure probability; and calculating a failure probability variable coefficient and carrying out convergence judgment, and when a convergence ending program is judged, applying the failure probability to safety evaluation and optimization design of the mechanical thrombectomy stent, otherwise, expanding the size of the candidate sample set and returning to regenerate a random sample.

Description

Technical Field

[0001] The present invention relates to the technical field of interventional medical devices, and particularly to a reliability analysis method based on an adaptive surrogate model and importance sampling. Background Art

[0002] The mechanical thrombectomy stent is the main medical device for interventional treatment of stroke. By inserting the mechanical thrombectomy stent into the embolized segment of the cerebral blood vessel, the thrombus is captured and removed by fitting the thrombus during the stent deployment process and retracting it into the catheter.

[0003] For the mechanical thrombectomy stent, its radial support force and bending flexibility are important indicators determining its mechanical properties. However, due to the large uncertainties in the machining errors during the stent processing, these uncertainties affect the mechanical properties of the stent, thereby affecting the thrombectomy success rate and causing reliability problems.

[0004] The main analysis methods for mechanical products include finite element simulation and experimental test analysis. When the data samples are large enough, the reliability of the mechanical thrombectomy stent can be obtained through the Monte Carlo simulation method.

[0005] However, since the analysis of the mechanical thrombectomy stent requires the use of high-fidelity models or expensive samples and equipment. Therefore, whether using finite element analysis or experimental test analysis, it is necessary to pay an unaffordable cost. And the more complex the mechanical thrombectomy stent model is, the higher the calculation cost and the longer the calculation time. The high cost of reliability analysis hinders the development of the reliability research of the mechanical thrombectomy stent. Summary of the Invention

[0006] Aiming at the above problems, the present invention provides a reliability analysis method based on an adaptive surrogate model and importance sampling for reliability analysis of the mechanical thrombectomy stent. The many technical effects that can be produced by the preferred technical solutions among the many technical methods provided by the present invention are described in detail below.

[0007] To achieve the above object, a reliability analysis method based on an adaptive surrogate model and importance sampling for reliability analysis of the mechanical thrombectomy stent includes the following steps:

[0008] Step S100, quantifying the probability distribution of the design parameters of the mechanical thrombectomy stent, where the design parameters include the diameter, wire width, wire thickness, length dimension, fillet and wire angle of the mechanical thrombectomy stent. These design parameters form a random vector X. For non-standard normal random variables in the probability distribution of the design parameters, they are converted into standard normal random variables through Rosenblatt transformation and transformed into the standard normal space; initializing the algorithm parameters, where the algorithm parameters include the initial hypersphere radius β 0 , the initial size of the training sample set The size of the first sorted set The hyper-sphere convergence index ∈ β and the size N of the candidate sample set cand , based on the initial hyper-sphere radius β 0 Construct a hyper-sphere, and construct a finite element simulation model for the compression and bending of a mechanical thrombectomy stent;

[0009] Step S200: According to the probability distribution of the quantified design parameters, establish an out-of-hyper-sphere truncation sampling probability function based on the hyper-sphere radius, and generate random samples. Take a part of the random samples as the training sample set, and the rest as the candidate sample set;

[0010] Step S300: Based on the training sample set, construct and train the Kriging surrogate model of the finite element model of the mechanical thrombectomy stent. Substitute the candidate sample set into the trained Kriging surrogate model to obtain the response set of the candidate samples. Perform two sorts and screenings on the response set of the candidate samples to obtain an approximation of the most likely failure point. Update the hyper-sphere radius based on the approximation of the most likely failure point, and establish an updated hyper-sphere;

[0011] Step S400: Judge the convergence of the updated hyper-sphere radius. If it is judged as the convergent hyper-sphere radius, execute step S500; otherwise, return to step S300;

[0012] Step S500: Use the leave-one-out cross-validation to verify the accuracy of the trained Kriging surrogate model. Use the index function constructed by the trained Kriging surrogate model to screen the sampled candidate sample set outside the current updated hyper-sphere. Screen the samples judged as 0 by the index function to form a new candidate sample set. If the accuracy of the trained Kriging surrogate model reaches the specified requirement, calculate the augmented failure probability p f∈ , and execute step S600; otherwise, use the adaptive learning function to select samples from the new candidate sample set and add them to the training set, and return to step S300;

[0013] Step S600: Use the new candidate sample set obtained by screening in step S500, combined with the adaptive learning function, to further refine the Kriging surrogate model until the termination condition of the learning function is reached, calculate the correction factor α corr , and further calculate the failure probability;

[0014] Step S700: Calculate the coefficient of variation of the failure probability based on the failure probability and perform a convergence judgment. When it is judged that the coefficient of variation of the failure probability converges, end the program, and use the failure probability for the safety assessment and optimization design of the mechanical thrombectomy stent; otherwise, expand the size N of the candidate sample set cand and return to step S200.

[0015] Optionally, step S100 specifically includes the following steps:

[0016] Step S110: Quantify the probability distribution corresponding to the design parameters of the mechanical thrombectomy stent. The design parameters include stent diameter, wire width, wire thickness, length dimension, fillet, and wire angle. These design parameters form a random vector X. For non-standard normal random variables in the probability distribution of the design parameters, perform Rosenblatt transformation to the standard normal space, and initialize the algorithm parameters. The algorithm parameters include the initial hypersphere radius β 0 , the initial size of the training sample set The size of the first sorting set The hypersphere convergence index ∈ β and the size N of the candidate sample set cand , and construct a hypersphere based on the initial hypersphere radius β 0 ;

[0017] Step S120: Construct a finite element simulation model for the compression and bending of the mechanical thrombectomy stent, and obtain the bending stiffness G w (X) and the radial support force G r (X) of the mechanical thrombectomy stent based on this finite element simulation model. Among them, the bending stiffness is the ratio of the bending load F to the bending deformation θ,

[0018] Construct the limit state functions for the two failure modes of the bending stiffness and radial support force of the mechanical thrombectomy stent as:

[0019]

[0020] where G w (X) is the bending stiffness of the mechanical thrombectomy stent calculated according to the finite element simulation, G r (X) is the radial support force of the mechanical thrombectomy stent calculated according to the finite element simulation, t w is the bending stiffness failure threshold set in combination with the actual engineering needs, t r is the radial support force failure threshold set in combination with the actual engineering needs, and X is the random vector composed of the design parameters of the mechanical thrombectomy stent.

[0021] Optionally, step S200 specifically includes the following steps:

[0022] Step S210: The probability density for sampling outside the hypersphere is the truncated sampling probability density, and establish the truncated sampling probability density function outside the hypersphere as:

[0023]

[0024] Wherein, x is a sampling sample, β is the radius of the hypersphere, r is the Mahalanobis distance and in the standard normal space, r = ‖x‖, φ(x, r) is the standard normal probability density function, is the chi-square distribution probability function, and n is the vector dimension of the sampling sample x;

[0025] Step S220: Establish a truncated sampling probability function outside the hypersphere, and integrate the truncated sampling probability density function outside the hypersphere to obtain the corresponding truncated sampling probability function outside the hypersphere as:

[0026]

[0027] Wherein, φ(x, r) is the standard normal probability function;

[0028] Step S230: Obtain according to inverse transform sampling:

[0029]

[0030] Wherein, p is a uniformly sampled sample in the interval [0, 1], and φ -1 is the inverse of the standard normal distribution probability function;

[0031] The truncated sampling sample outside the hypersphere is obtained as:

[0032]

[0033] Wherein, v is an n-dimensional normal distribution random vector sample;

[0034] Step S240: Use the generated truncated sampling sample x as a random sample, and use a part of it as the initial training sample set and the rest as the candidate sample set. The initial training sample set satisfies the set size of the initial training sample set The candidate sample set satisfies the candidate sample set size N cand .

[0035] Optionally, the step S300 specifically includes the following steps:

[0036] Step S310: Substitute the initial training sample set obtained in step S240 into the finite element simulation model of the compression and bending of the mechanical thrombectomy stent, calculate the simulation output, and form a training set S according to the simulation output and the current training samples t , construct and train the Kriging surrogate model of the finite element model of the mechanical thrombectomy stent, substitute the candidate sample set obtained in step S240 into the trained Kriging surrogate model, and obtain the Kriging surrogate model response to form a candidate sample response set;

[0037] Step S320: Perform the first sorting and screening on the absolute values of the Kriging surrogate model responses in the candidate sample response set in ascending order, and select the top number of candidate samples to form the candidate sample set screened by the first sorting;

[0038] Step S330: For the candidate sample set screened by the first sorting, perform the second sorting and screening based on the vector norm of the candidate samples, and screen the candidate sample with the smallest vector norm in the second sorting as the approximation of the most likely failure point in the reliability analysis;

[0039] Step S340: Use the vector norm of the approximation of the most likely failure point screened by the two sorts as the updated hypersphere radius β i in the current round, and construct an updated hypersphere around the origin of the standard normal space coordinates. The interior of the updated hypersphere is the safe region, and the failure region is contained outside the updated hypersphere, where β i represents the updated hypersphere radius determined in the i-th iteration.

[0040] Optionally, the step S400 specifically includes:

[0041] Perform a convergence judgment on the updated hypersphere radius β i in the current round, that is

[0042] β i -β i-1 ≤∈ β ,i≥1

[0043] where, ∈ β represents the hypersphere radius convergence index;

[0044] If it is judged that the updated hypersphere radius β i in the current round satisfies the above formula, indicating that the current updated hypersphere radius is the convergent hypersphere radius, then execute step S500; otherwise, substitute the candidate samples and the Kriging surrogate model responses of the candidate samples into the U learning function, that is

[0045]

[0046] where, and are the response expectation and response standard deviation of the Kriging surrogate model of the candidate sample x′ respectively. The candidate sample x * =min(U) that minimizes the U learning function value is added to the training set S t and return to execute step S300 to perform the update of the hypersphere radius and the Kriging surrogate model in the next round.

[0047] Optionally, step S500 specifically includes:

[0048] Step S510: Measure the accuracy of the current Kriging surrogate model according to the current training samples by using the leave-one-out cross-validation method, and the leave-one-out cross-validation method is expressed as:

[0049]

[0050] Wherein, represents the leave-one-out cross-validation value of the correction factor, j represents the training sample number, N t represents the number of training set samples, represents the jth sample in the training set, t represents the training set sample flag, represents the index function based on the limit state function, S t represents the training set, represents the index function of the Kriging surrogate model trained based on the training set obtained by deleting t from S ;

[0051] Step S520: Sample outside the current updated hypersphere to obtain a set of candidate samples for sampling, and screen the samples for which the index function t of the Kriging surrogate model trained based on the training set obtained by deleting from S is judged to be 0 to form a new set of candidate samples;

[0052] Step S530: Judge the obtained . When belongs to the interval [0.1, 10], it means that the trained Kriging surrogate model reaches the specified accuracy, and execute step S540. Otherwise, use the U learning function to select samples from the new set of candidate samples obtained in step S520 and add them to the training set S t , and return to step S300 to update the Kriging surrogate model;

[0053] Step S540: Express the optimal importance sampling probability density function as

[0054]

[0055] The integral of the failure probability under the importance sampling outside the hypersphere is:

[0056]

[0057] Wherein, is the optimal importance sampling density, I F (x′) is the reliability integral index function, and π(x′) is IF Kriging surrogate model metric function of (x′), α corr is the correction factor, representing the correction to the previous failure probability, p f∈ is the augmented failure probability, which is the failure probability estimated based on the Kriging surrogate model

[0058] Obtain p f∈ is

[0059]

[0060] where x ′ k represents the k-th candidate sample, and k represents the number of the candidate sample and k = 1, …, N cand .

[0061] Optionally, the step S600 specifically includes:

[0062] Step S610: Further screen the new candidate sample set obtained in step S520 according to the metric function π(x′) of the trained Kriging surrogate model, and form a candidate sample set with the samples in the new candidate sample set that satisfy π(x′) ≤ 0; Combine with the U learning function, select the candidate sample with the largest U learning function value from the formed candidate sample set as the sample that contributes the most to improving the accuracy of the Kriging surrogate model, and add the response obtained by substituting it into the limit state function provided in step S120 to the training set S t and update the Kriging surrogate model based on the updated training set S t after the addition;

[0063] Step S620: For the obtained updated Kriging surrogate model, perform Kriging surrogate model convergence judgment through the U learning function. When , judge that the Kriging surrogate model converges. At this time, terminate the update of the Kriging surrogate model and calculate the correction factor

[0064]

[0065] Otherwise, when , return to step S610 and continue to update the Kriging surrogate model until the convergence criterion is met;

[0066] Step S630: Based on the decomposition formula of the failure probability provided in step S540, calculate the failure probability according to the augmented failure probability and the failure probability correction factor: p f = p f∈ α corr .

[0067] Compared with the prior art, a reliability analysis method based on an adaptive surrogate model and importance sampling provided by an embodiment of the present invention has at least the following advantages.

[0068] 1) It is used for the reliability analysis of a mechanical thrombectomy stent, fully considering the randomness of the design parameters of the mechanical thrombectomy stent, and significantly improving the reliability analysis efficiency by combining importance sampling and a surrogate model.

[0069] 2) The probability density function and probability function of truncated sampling outside the hypersphere are constructed. The method of truncated sampling outside the hypersphere divides the standard normal space into a safe region inside the hypersphere and a region outside the hypersphere containing the failure domain. When performing sampling, constructing a Kriging surrogate model, and reliability analysis, the region inside the hypersphere does not need to be considered, which effectively improves the method efficiency.

[0070] 3) It includes constructing an importance sampling algorithm framework based on a surrogate model. In this framework, the failure probability is decomposed into an augmented failure probability and a correction factor, and these two steps are calculated in multiple steps and finally the failure probability is calculated efficiently. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. By referring to the drawings, the features and advantages of the present invention can be more clearly understood. The drawings are schematic and should not be construed as imposing any limitation on the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0072] Figure 1 FIG. is an algorithm flowchart of a reliability analysis method based on an adaptive surrogate model and importance sampling provided by an embodiment of the present invention.

[0073] Figure 2 FIG. is a schematic diagram of a simulation of the bending stiffness test of a mechanical thrombectomy stent in an example of applying the reliability analysis method based on an adaptive surrogate model and importance sampling provided by an embodiment of the present invention.

[0074] Figure 3 FIG. is a schematic diagram of a simulation of the radial support force test of a mechanical thrombectomy stent in an example of applying the reliability analysis method based on an adaptive surrogate model and importance sampling provided by an embodiment of the present invention.

[0075] Figure 4 FIG. is a schematic diagram of a mechanical thrombectomy stent in an example of applying the reliability analysis method based on an adaptive surrogate model and importance sampling provided by an embodiment of the present invention.

[0076] Figure 5 ForFigure 4 An enlarged view of the stent ring unit of the mechanical thrombectomy stent in

[0077] Figure 6 is Figure 5 A partial enlarged view of the stent ring unit of

[0078] Figure 7 is Figure 4 A side view of the stent ring unit of the mechanical thrombectomy stent in Detailed implementation manners

[0079] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, various exemplary embodiments to be described below will refer to the corresponding drawings, which form a part of the exemplary embodiments and describe various exemplary embodiments that may be adopted to implement the present invention. Unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all implementation manners consistent with the present disclosure. It should be understood that they are only examples of processes, methods, devices, etc. that are consistent with some aspects of the present invention disclosed in detail in the appended claims. Other embodiments may also be used, or structural and functional modifications may be made to the embodiments listed herein without departing from the scope and essence of the present invention.

[0080] In order to illustrate the technical solutions described in the present invention, the following will be described through specific examples, and only the parts related to the embodiments of the present invention are shown.

[0081] Symbol description:

[0082] X represents a random vector composed of the design parameters of the mechanical thrombectomy stent;

[0083] β is the radius of the hypersphere;

[0084] β 0 represents the initial radius of the hypersphere;

[0085] i represents the number of iterative updates of the Kriging surrogate model and i≥1;

[0086] β i represents the radius of the hypersphere calculated by the i-th iterative update of the Kriging surrogate model;

[0087] represents the size of the initial training sample set;

[0088] represents the size of the first sorting set;

[0089] ∈ β represents the hypersphere convergence index;

[0090] N cand represents the size of the candidate sample set;

[0091] G(X) represents the limit state function of the mechanical thrombectomy stent;

[0092] G w (X) is the bending stiffness of the mechanical thrombectomy stent calculated according to finite element simulation;

[0093] G r (X) is the radial support force of the mechanical thrombectomy stent calculated according to finite element simulation;

[0094] t w is the bending stiffness failure threshold set according to the actual engineering needs;

[0095] t r is the radial support force failure threshold set according to the actual engineering needs;

[0096] f(x; β, r) represents the probability density function of truncated sampling outside the hypersphere;

[0097] x is the sampling sample;

[0098] n is the vector dimension of the sampling sample x;

[0099] r is the Mahalanobis distance;

[0100] φ(x, r) is the standard normal probability density function;

[0101] F(x; β, r) is the probability function of truncated sampling outside the hypersphere;

[0102] is the probability function of the chi-square distribution;

[0103] p is the uniform sampling sample in the interval [0, 1];

[0104] φ -1 is the inverse of the standard normal distribution probability function;

[0105] v is the sample of the n-dimensional normal distribution random vector;

[0106] S t represents the training set;

[0107] U represents the U learning function value;

[0108] x′ represents the candidate sample;

[0109] represents the response expectation of the Kriging surrogate model of the candidate sample x′;

[0110] Denote the response standard deviation of the Kriging surrogate model for the candidate sample \(x'\);

[0111] Denote the leave-one-out cross-validation value of the correction factor;

[0112] \(j\) denotes the sample number of the training set;

[0113] \(N\) t Denote the number of samples in the training set;

[0114] Denote the \(j\)-th sample in the training set;

[0115] \(t\) denotes the sample flag of the training set;

[0116] Denote the index function based on the limit state function;

[0117] Denote the one based on \(S\) t Delete The index function of the Kriging surrogate model after training with the training set after deletion;

[0118] \(p\) f Denote the failure probability;

[0119] Is the optimal importance sampling density;

[0120] \(I\) F \((x')\) is the reliability integral index function;

[0121] \(\pi(x')\) is the Kriging surrogate model index function of \(I\) F \((x')\);

[0122] \(p\) f∈ Is the augmented failure probability;

[0123] \(\alpha\) corr Is the correction factor;

[0124] \(x'\) k Denote the \(k\)-th candidate sample;

[0125] \(k\) denotes the number of the candidate sample and \(k = 1,\ldots,N\) cand 。

[0126] As Figure 1 shown, according to an embodiment of the present invention, a reliability analysis method based on an adaptive surrogate model and importance sampling is provided for the reliability analysis of a mechanical thrombectomy stent, including the following steps.

[0127] Step S100: Quantify the probability distribution of the design parameters of the mechanical thrombectomy stent. These design parameters form a random vector X. For non-standard normal random variables in the probability distribution of the design parameters, convert them to standard normal random variables through Rosenblatt transformation and transform them into the standard normal space; initialize the algorithm parameters, which include the initial hypersphere radius β 0 , the size of the initial training sample set The size of the first sorting set The hypersphere convergence index ∈ β and the size N of the candidate sample set cand , based on the initial hypersphere radius β 0 Construct a hypersphere and construct a finite element simulation model for the compression and bending of the mechanical thrombectomy stent. See Figures 4 to 7 , the design parameters of the mechanical thrombectomy stent may include the diameter, wire width, wire thickness, length dimension, fillet, wire angle, etc. of the mechanical thrombectomy stent. As shown in Figure 2 and Figure 3 , a schematic diagram of the finite element simulation of the compression and bending of the constructed mechanical thrombectomy stent is shown in an example applying this embodiment. This step S100 specifically includes the following steps.

[0128] Step S110: Quantify the probability distribution corresponding to the design parameters of the mechanical thrombectomy stent. The design parameters include the stent diameter, wire width, wire thickness, length dimension, fillet and wire angle. These design parameters form a random vector X. For non-standard normal random variables in the probability distribution of the design parameters, use Rosenblatt transformation to transform them into the standard normal space, and initialize the algorithm parameters, which include the initial hypersphere radius β 0 , the size of the initial training sample set The size of the first sorting set The hypersphere convergence index ∈ β and the size N of the candidate sample set cand , based on the initial hypersphere radius β 0 Construct a hypersphere.

[0129] Step S120: Construct a black box finite element model of the finite element simulation of the compression and bending of the mechanical thrombectomy stent as the limit state function. As an alternative embodiment, the limit state functions of the two failure modes of the bending stiffness and radial support force of the mechanical thrombectomy stent can be constructed as:

[0130]

[0131] where G w (X) is the bending stiffness of the mechanical thrombectomy stent calculated according to the finite element simulation, and G r (X) is the radial support force of the mechanical thrombectomy stent calculated according to the finite element simulation, tw t is the bending stiffness failure threshold set according to the actual engineering needs r X is the radial support force failure threshold set according to the actual engineering needs, and X is a random vector composed of the design parameters of the mechanical thrombectomy stent. In this embodiment, the random vector X may include various parameters that affect the performance of the mechanical thrombectomy stent, including structural design parameters, material parameters, and environmental parameters, etc. Specifically, the design parameters may include the length, diameter, number of mesh holes, width of mesh wires, thickness of mesh wires, included angle of mesh wires, and fillet size of the mechanical thrombectomy stent. The material parameters may include elastic modulus, Poisson's ratio, etc. The environmental parameters may include environmental temperature, etc.

[0132] Step S200: According to the probability distribution of the quantified design parameters, establish an out-of-sphere truncation sampling probability function based on the radius of the hypersphere, and generate random samples. Part of the random samples are used as the training sample set, and the rest are used as the candidate sample set. This step S200 specifically includes the following steps.

[0133] Step S210: Construct an out-of-sphere truncation sampling probability density function. The probability density of sampling outside the hypersphere is the truncation sampling probability density, which is:

[0134]

[0135] where x is the sampling sample, β is the radius of the hypersphere, r is the Mahalanobis distance, r = ‖x‖ in the standard normal space, φ(x,r) is the standard normal probability density function, is the chi-square distribution probability function, and n is the vector dimension of the sampling sample x. In the initial round, the radius of the hypersphere here uses the initial hypersphere radius β 0 , and in subsequent rounds, for example, in the i-th round, the updated hypersphere radius β i-1 obtained from step S300 of the previous round is used. The hypersphere radii in the following steps S220 and S230 are the same.

[0136] Step S220: Construct an out-of-sphere truncation sampling probability function, and integrate the truncation sampling probability density function outside the hypersphere to obtain the corresponding out-of-sphere truncation sampling probability function as:

[0137]

[0138] where φ(x,r) is the standard normal probability function.

[0139] Step S230: According to the inverse transform sampling, there is

[0140]

[0141]

[0142] Among them, p is a uniformly sampled sample in the interval [0, 1], and φ -1 is the inverse of the probability function of the standard normal distribution; the truncated sampling sample is obtained and expressed as

[0143]

[0144] where v is a sample of an n-dimensional normal distribution random vector.

[0145] Step S240: Use the generated truncated sampling sample x as a random sample, and use a part of it as the initial training sample set, and the rest as the candidate sample set. The initial training sample set satisfies the set size of the initial training sample set The candidate sample set satisfies the candidate sample set size N cand .

[0146] Step S300: Based on the training sample set, construct and train the Kriging surrogate model of the finite element model of the mechanical thrombectomy stent (Kriging surrogate model), and substitute the candidate sample set into the trained Kriging surrogate model to obtain the response set of the candidate samples. Perform two sorts and screenings on the response set of the candidate samples to obtain an approximation of the most likely failure point. Update the hyper-sphere radius based on the approximation of the most likely failure point, and establish an updated hyper-sphere. This step S300 specifically includes the following steps.

[0147] Step S310: Substitute the initial training sample set obtained in step S240 into the finite element simulation model of the compression and bending of the mechanical thrombectomy stent, calculate the simulation output, and form the training set S according to the simulation output t , construct and train the Kriging surrogate model of the finite element model of the mechanical thrombectomy stent, and substitute the candidate sample set obtained in step S240 into the trained Kriging surrogate model to obtain the candidate sample response set composed of the Kriging surrogate model responses.

[0148] Step S320: Perform the first sorting and screening on the absolute values of the Kriging surrogate model responses in the candidate sample response set in ascending order, and take the first number of candidate samples to form the candidate sample set selected by the first sorting and screening.

[0149] Step S330: For the candidate sample set selected by the first sorting and screening, perform the second sorting and screening according to the vector norm of the candidate samples, and select the candidate sample with the smallest vector norm in the second sorting as the approximation of the most likely failure point in the reliability analysis.

[0150] Step S340: Use the vector norm of the approximate values of the most likely failure points selected through two rounds of sorting as the updated hypersphere radius β for the current round. i , and construct an updated hypersphere around the origin of the standard normal space coordinates. The interior of this updated hypersphere is the safe domain, while the failure domain is contained outside the updated hypersphere, where β i represents the updated hypersphere radius determined in the i-th iteration.

[0151] Step S400: Conduct a convergence judgment on the updated hypersphere radius. If it is judged to be a convergent hypersphere radius, execute Step S500; otherwise, return to Step S300.

[0152] This Step S400 specifically includes: Conduct a convergence judgment on the updated hypersphere radius β for the current round, that is, i namely

[0153] β i - β i-1 ≤ ∈ β ,

[0154] where β i represents the hypersphere radius determined by the i-th iteration update of the surrogate model, and ∈ β represents the hypersphere radius convergence index;

[0155] If it is judged that the updated hypersphere radius β for the current round i satisfies the above formula, indicating that the current updated hypersphere radius is a convergent hypersphere radius, then execute Step S500; otherwise, substitute the candidate sample and the Kriging surrogate model response of the candidate sample into the U learning function, that is,

[0156]

[0157] where, and are respectively the response mean and response standard deviation of the Kriging surrogate model of the candidate sample x′. Take the candidate sample x * = min(U) as the training sample and add it to the training sample set S t , and return to execute Step S300 to update the hypersphere radius and the Kriging surrogate model in the next round.

[0158] After multiple iterations, as the accuracy of the surrogate model improves, the candidate samples corresponding to the approximate values of the most likely failure points selected through two rounds of sorting gradually approach the most likely failure point. At this time, the hypersphere gradually converges to the maximum hypersphere.

[0159] Step S500: Use the leave-one-out cross-validation method to verify the accuracy of the trained Kriging surrogate model. If the accuracy of the trained Kriging surrogate model meets the specified requirements, use the performance function constructed by the trained Kriging surrogate model to screen the candidate sample set sampled outside the current updated hypersphere, and screen the samples with the performance function judged as 0 to form a new candidate sample set, and calculate the augmented failure probability p f∈ , and execute Step S600; otherwise, use the adaptive learning function to select samples from the new candidate sample set and add them to the training set S t , and return to Step S300.

[0160] The estimation of the failure probability is divided into two stages. The first stage is used to estimate the augmented failure probability. The termination condition of the first stage adopts the cross-validation method, which can include all cross-validation methods that can verify the accuracy of the surrogate model, such as the leave-one-out method, random subsampling verification, and K-fold cross-validation. In this embodiment, the leave-one-out cross-validation method is used to measure the accuracy of the surrogate model according to the training samples.

[0161] This step S500 specifically includes the following steps.

[0162] Step S510: Use the leave-one-out cross-validation method to measure the accuracy of the current Kriging surrogate model according to the current training samples. The leave-one-out cross-validation method is expressed as:

[0163]

[0164] where represents the leave-one-out cross-validation value of the correction factor, j represents the training sample number, N t represents the number of samples in the training sample set, represents the jth sample in the training set, t represents the training set sample flag, represents the performance function based on the limit state function, S t represents the training set, represents the performance function of the Kriging surrogate model trained based on the training set after deleting t from S .

[0165] Step S520: Sample outside the current updated hypersphere to obtain a candidate sample set, and screen the samples with the performance function t of the Kriging surrogate model trained based on the training set after deleting from S judged as 0 to form a new candidate sample set.

[0166] Step S530: For the obtained Make a judgment. When it belongs to the interval [0.1, 10], it means that the trained Kriging surrogate model reaches the specified accuracy, and step S540 is executed. Otherwise, use the U learning function to select samples from the new candidate sample set obtained in step S520 and add them to the training set S t , and return to step S300 to update the Kriging surrogate model.

[0167] Step S540: Express the optimal importance sampling probability density function as

[0168]

[0169] The integral of the failure probability under importance sampling outside the hypersphere is:

[0170]

[0171]

[0172] Among them, is the optimal importance sampling density, I F (x′) is the reliability integral index function, and π(x′) is the Kriging surrogate model index function of I F (x′), α corr is the correction factor, indicating the correction of the previous failure probability, p f∈ is the augmented failure probability, which is the failure probability estimated based on the Kriging surrogate model,

[0173] Obtain p f∈ as

[0174]

[0175] Among them, x′ k represents the k-th candidate sample, and k represents the number of the candidate sample and k = 1, …, N cand .

[0176] In this step, according to the iteration round, the hypersphere radius here uses the current hypersphere radius. For example, in the i-th round, use the updated hypersphere radius β obtained in step S300 of this round i .

[0177] Step S600: Adopt the filtered new candidate sample set obtained in step S500, and continue to refine the Kriging surrogate model in combination with the adaptive learning function until the termination condition of the learning function is reached. By calculating the correction factor α corrAnd further calculate the failure probability. The termination criterion for the refinement of the second-stage surrogate model is an adaptive learning function, which is characterized by including all adaptive learning functions, such as U learning function, H learning function, expected improvement learning function, EFF learning function, etc. The step S600 specifically includes the following steps.

[0178] Step S610: Further screen the new candidate sample set obtained in step S520 according to the index function π(x′) of the trained Kriging surrogate model, and form a candidate sample set with the samples in the new candidate sample set that satisfy π(x′) ≤ 0; Combining with the U learning function, select the candidate sample with the largest U learning function value from the formed candidate sample set as the sample that contributes the most to improving the accuracy of the Kriging surrogate model, and add the response obtained by substituting it into the limit state function provided in step S120 to the training set, and update the Kriging surrogate model based on the updated training set after this addition.

[0179] Step S620: For the obtained updated Kriging surrogate model, perform convergence judgment on the Kriging surrogate model through the U learning function. When When it is satisfied, it is judged that the Kriging surrogate model converges. At this time, terminate the update of the Kriging surrogate model and calculate the correction factor

[0180]

[0181] Otherwise, when When it is not satisfied, return to step S610 and continue to update the Kriging surrogate model until the convergence criterion is met. In this step, according to the iteration round, the hyper-sphere radius here uses the current hyper-sphere radius. For example, in the i-th round, use the updated hyper-sphere radius β obtained in step S300 of this round i .

[0182] Step S630: Based on the decomposition formula of the failure probability provided in step S540, calculate the failure probability according to the augmented failure probability and the failure probability correction factor:

[0183] p f = p f∈ α corr

[0184] where p f∈ is the augmented failure probability, and α corr is the correction factor.

[0185] Step S700: Calculate the coefficient of variation of the failure probability based on the failure probability and perform convergence judgment. When it is judged that the coefficient of variation of the failure probability converges, end the program and use this failure probability for the safety assessment and optimal design of the mechanical thrombectomy stent; otherwise, expand the size N of the candidate sample setcand Return to step S200.

[0186] The reliability analysis method based on the adaptive surrogate model and importance sampling provided by this embodiment performs reliability analysis on the mechanical thrombectomy stent. Based on only a relatively small number of initial training samples and candidate samples, it combines the adaptive surrogate model and two screening strategies to gradually add samples to the training sample set, thereby improving the efficiency of the reliability analysis algorithm and enhancing the efficiency and effect of the reliability analysis of the mechanical thrombectomy stent. Therefore, the mechanical thrombectomy stent reliability analysis method provided by this embodiment can greatly reduce the calculation time and resource consumption.

[0187] As an optional method, the adaptive Kriging surrogate model is selected in this embodiment. In the first stage, an adaptive learning function is used to update the Kriging surrogate model in combination with the candidate sample set. The criterion for stopping the update of the surrogate model in this stage adopts the leave-one-out cross-validation method. When falls within the interval [0.1, 10], the first stage terminates and the augmented failure probability p f∈ is calculated. Otherwise, the surrogate model continues to be refined. In the second stage, an adaptive learning function is used to update the Kriging surrogate model in combination with the set of candidate sample points screened by the index function of the Kriging surrogate model. In this stage, the criterion for stopping the update of the Kriging surrogate model adopts the U learning function. When is satisfied, the second stage terminates and the correction factor α corr is calculated. Among them, represents the response mean of the Kriging surrogate model, and represents the response variance of the Kriging surrogate model.

[0188] All the above optional technical solutions can be combined arbitrarily to form optional embodiments of the present application, which will not be elaborated one by one here.

[0189] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0190] The above is only a specific and preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A reliability analysis method based on an adaptive proxy model and importance sampling, characterized in that: The reliability analysis of the mechanical thrombectomy stent includes the following steps: Step S100, quantify the probability distribution of design parameters of the mechanical thrombectomy stent, the design parameters include the diameter, wire width, wire thickness, length, fillet and wire angle of the mechanical thrombectomy stent, these design parameters constitute a random vector X, for the probability distribution of the design parameters, non-standard normal random variables are converted to standard normal random variables by Rosenblatt, and then transformed to the standard normal space; initialize the algorithm parameters, the algorithm parameters include the initial hypersphere radius β 0 , the initial training sample set size The size of the first sorted set Hypersphere convergence index ∈ β and the candidate sample set size N cand , based on the initial hypersphere radius β 0 Constructing a hypersphere, as well as a finite element simulation model of compression and bending of a mechanical thrombectomy stent; Step S200: According to the probability distribution of the quantized design parameters, a hypersphere outer truncated sampling probability function is established based on the hypersphere radius, and random samples are generated, a part of the random samples is used as a training sample set, and the rest is used as a candidate sample set; Step S300: construct and train a Kriging proxy model of a finite element model of a mechanical thrombectomy stent based on a training sample set, substitute a candidate sample set into the trained Kriging proxy model to obtain a response set of candidate samples, sort and screen the response set of candidate samples twice to obtain an approximate value of the most likely failure point, update the hypersphere radius based on the approximate value of the most likely failure point, and establish an updated hypersphere; Step S400, performing convergence judgment on the updated hypersphere radius, if it is judged to be a converged hypersphere radius, executing step S500, otherwise returning to step S300; Step S500: Use the leave-one-out cross-validation method to verify the accuracy of the trained Kriging proxy model. Use the index function constructed by the trained Kriging proxy model to screen the candidate sample set obtained by the currently updated hypersphere sampling. The samples judged as 0 by the index function are screened to form a new candidate sample set. If the accuracy of the trained Kriging proxy model meets the specified requirements, the augmented failure probability p is calculated. f∈ , and execute step S600; otherwise, use the adaptive learning function to select samples from the new candidate sample set and add them to the training set, and return to step S300; Step S600: Use the new candidate sample set obtained from step S500 and combine it with the adaptive learning function to continue to refine the Kriging proxy model until the termination condition of the learning function is reached, and calculate the correction factor α corr , and further calculate the failure probability; Step S700: Calculate the failure probability variation coefficient based on the failure probability and make a convergence judgment. When it is judged that the failure probability variation coefficient converges, the program ends and the failure probability is used for the safety assessment and optimal design of the mechanical thrombectomy stent. Otherwise, expand the candidate sample set size N. cand And return to step S200.

2. The reliability analysis method based on adaptive proxy model and importance sampling according to claim 1 is characterized in that: The step S100 specifically includes the following steps: Step S110, quantify the probability distribution corresponding to the design parameters of the mechanical thrombectomy stent, the design parameters include stent diameter, wire width, wire thickness, length, fillet and wire angle, these design parameters constitute a random vector X, the non-standard normal random variables in the probability distribution of the design parameters are transformed into the standard normal space using Rosenblatt, and the algorithm parameters are initialized, the algorithm parameters include the initial hypersphere radius β 0 , the initial training sample set size The size of the first sorted set Hypersphere convergence index ∈ β and the candidate sample set size N cand , based on the initial hypersphere radius β 0 Constructing a hypersphere; Step S120: construct a finite element simulation model of compression and bending of the mechanical thrombectomy stent, and obtain the bending stiffness G of the mechanical thrombectomy stent based on the finite element simulation model. w (X) and radial support force G r (X), where the bending stiffness is the ratio of the bending load F to the bending deformation θ, The limit state functions of the two failure modes of the mechanical thrombectomy stent, bending stiffness and radial support force, are constructed as follows: Among them, G w (X) is the bending stiffness of the mechanical thrombectomy stent calculated by finite element simulation, G r (X) is the radial support force of the mechanical thrombectomy stent calculated by finite element simulation, t w The bending stiffness failure threshold is set according to the actual engineering needs, t r The radial support force failure threshold is set in combination with actual engineering needs, and X is a random vector composed of the design parameters of the mechanical thrombectomy stent.

3. The reliability analysis method based on adaptive proxy model and importance sampling according to claim 2 is characterized in that: The step S200 specifically includes the following steps: Step S210: The probability density of sampling outside the hypersphere is the truncated sampling probability density, and the truncated sampling probability density function outside the hypersphere is established as: Among them, x is the sample, β is the radius of the hypersphere, r is the Mahalanobis distance and in the standard normal space, r = ‖x‖, φ(x,r) is the standard normal probability density function, is the chi-square distribution probability function, n is the vector dimension of the sampling sample x; Step S220: establish a truncated sampling probability function outside the hypersphere, and integrate the truncated sampling probability density function outside the hypersphere to obtain the corresponding truncated sampling probability function outside the hypersphere: Where φ(x,r) is the standard normal probability function; Step S230, obtain according to the inverse conversion sampling: Among them, p is a uniformly sampled sample in the interval [0,1], φ -1 is the inverse of the standard normal distribution probability function; The truncated sampling samples outside the hypersphere are obtained as follows: Where v is a random vector sample of n-dimensional normal distribution; Step S240: The generated truncated sample x is used as a random sample, a part of which is used as an initial training sample set, and the rest is used as a candidate sample set. The initial training sample set meets the set initial training sample set size. The candidate sample set meets the candidate sample set size N cand .

4. The reliability analysis method based on adaptive proxy model and importance sampling according to claim 3 is characterized in that: The step S300 specifically includes the following steps: Step S310: bring the initial training sample set obtained in step S240 into the finite element simulation model of compression and bending of the mechanical thrombectomy stent, calculate the simulation output, and form a training set S based on the simulation output and the current training samples. t , constructing and training a Kriging proxy model of the finite element model of the mechanical thrombectomy stent, substituting the candidate sample set obtained in step S240 into the trained Kriging proxy model, and obtaining the Kriging proxy model responses to form the candidate sample response set; Step S320: sort and filter the absolute values ​​of the Kriging proxy model responses in the candidate sample response set from small to large for the first time, and take the first The number of candidate samples constitutes the candidate sample set selected by the first sorting; Step S330: sort and screen the candidate sample set selected by the first sorting for the second time according to the vector modulus of the candidate samples, and select the candidate sample with the smallest vector modulus in the second sorting as the approximate value of the most likely failure point in the reliability analysis; Step S340: The vector modulus of the approximate value of the most likely failure point screened out by the two sortings is the updated hypersphere radius β of the current round. i , and construct an updated hypersphere around the origin of the standard normal space coordinates. The inside of the updated hypersphere is the safety domain, and the failure domain is contained outside the updated hypersphere, where β i represents the updated hypersphere radius determined at the i-th iteration.

5. The reliability analysis method based on adaptive proxy model and importance sampling according to claim 4 is characterized in that: The step S400 specifically includes: The radius of the hypersphere updated for the current round is β i Convergence judgment is performed, that is, β i -β i-1 ≤∈ β ，i≥1 Among them, ∈ β represents the hypersphere radius convergence index; If we determine the updated hypersphere radius β of the current round i If the above formula is satisfied, it means that the current updated hypersphere radius is the convergent hypersphere radius, then step S500 is executed. Otherwise, the candidate sample and the Kriging proxy model response of the candidate sample are brought into the U learning function, that is, in, and The expected response and standard deviation of the Kriging surrogate model of the candidate sample x′ are respectively, and the candidate sample x that minimizes the value of the U learning function is * = min(U) is added as a training sample to the training set S t And return to step S300 to update the hypersphere radius and Kriging proxy model for the next round.

6. The reliability analysis method based on adaptive proxy model and importance sampling according to claim 5 is characterized in that: The step S500 specifically includes: Step S510: Use the leave-one-out cross-validation method to measure the accuracy of the current Kriging proxy model according to the current training sample. The leave-one-out cross-validation method is expressed as: in, represents the leave-one-out cross-validation value of the correction factor, j represents the training sample number, N t represents the number of samples in the training set, represents the jth sample in the training set, t represents the sample flag of the training set, represents the index function based on the limit state function, S t represents the training set, Indicates that based on S t Delete The indicator function of the Kriging surrogate model after training the training set; Step S520: Sampling the currently updated hypersphere to obtain a candidate sample set. t Delete The indicator function of the Kriging surrogate model after training the training set The samples judged as 0 are screened to form a new candidate sample set; Step S530: Make a judgment, when When it is in the interval [0.1, 10], it means that the trained Kriging proxy model reaches the specified accuracy, and step S540 is executed. Otherwise, the U learning function is used to select samples from the new candidate sample set obtained in step S520 and add them to the training set S t , and return to step S300 to update the Kriging proxy model; Step S540: Express the optimal importance sampling probability density function as The failure probability integral under importance sampling outside the hypersphere is: in, is the optimal important sampling density, I F (x′) is the reliability integral index function, π(x′) is I F (x′) Kriging surrogate model indicator function, α corr is the correction factor, which represents the correction of the previous failure probability, p f∈ To augment the failure probability, the failure probability is estimated based on the Kriging surrogate model. Get p f∈ for Among them, x ′ k represents the kth candidate sample, k represents the number of the candidate sample and k=1,…,N cand .

7. The reliability analysis method based on adaptive proxy model and importance sampling according to claim 6 is characterized in that: The step S600 specifically includes: Step S610: further screen the new candidate sample set obtained in step S520 according to the indicator function π(x′) of the trained Kriging proxy model, and form a candidate sample set with samples satisfying π(x′)≤0 in the new candidate sample set; combine the U learning function, select the candidate sample with the largest U learning function value from the formed candidate sample set as the sample that contributes most to improving the accuracy of the Kriging proxy model, and add the response obtained by substituting it into the limit state function provided in step S120 to the training set S t and based on this, add the updated training set S t Update Kriging proxy model; Step S620: The obtained updated Kriging proxy model is used to perform Kriging proxy model convergence judgment through the U learning function. When , the Kriging proxy model is judged to be converged, at which time the update of the Kriging proxy model is terminated and the correction factor is calculated Otherwise, when Return to step S610 and continue to update the Kriging proxy model until the convergence criterion is met; Step S630: Based on the failure probability decomposition formula provided in step S540, the failure probability is calculated according to the augmented failure probability and the failure probability correction factor. p f =p f∈ a corr 。

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