A reliability analysis method based on an adaptive surrogate model and importance sampling

Abstract

The present application relates to a kind of reliability analysis method based on adaptive agent model and importance sampling, belong to the technical field of interventional medical stent, solve the low efficiency of medical stent reliability analysis in prior art, for the reliability analysis of mechanical thrombectomy stent, including the following steps: quantifying the random parameter probability distribution of mechanical thrombectomy stent, initialization algorithm parameter;Random sample is generated, and training sample set and candidate sample set are obtained;Kriging agent model of the finite element model of mechanical thrombectomy stent is constructed and trained, and updated hypersphere is established;The convergence of updated hypersphere radius is judged;The accuracy of the Kriging agent model after training is verified by leave-one-out cross-validation;Failure probability is calculated;Failure probability variation coefficient is calculated and convergence is judged, when judging convergence end program, failure probability is used for the safety evaluation and optimization design of mechanical thrombectomy stent, otherwise, candidate sample set size is expanded and random sample is regenerated.

Description

Technical Field

[0001] This invention relates to the field of interventional medical device technology, and specifically to a reliability analysis method based on an adaptive surrogate model and importance sampling. Background Technology

[0002] Mechanical thrombectomy stents are the main medical devices used in interventional treatment of stroke. By inserting a mechanical thrombectomy stent into the embolized segment of a cerebral blood vessel, the stent, through its deployment process, embeds the thrombus and withdraws it back into the catheter, thus capturing and removing the thrombus.

[0003] For mechanical thrombectomy stents, radial support force and bending compliance are important indicators determining their mechanical performance. However, due to significant uncertainties in the manufacturing process of the stent, these uncertainties affect the mechanical performance of the stent, thereby impacting the success rate of thrombectomy and leading to reliability issues.

[0004] The main analytical methods for mechanical products include finite element simulation and experimental testing. When the data sample is large enough, the reliability of the mechanical bolt retrieval support can be obtained through Monte Carlo simulation.

[0005] However, the analysis of mechanical thrombectomy stents requires high-fidelity models or expensive prototypes and equipment. Therefore, both finite element analysis and experimental testing incur prohibitive costs. Furthermore, the more complex the mechanical thrombectomy stent model, the higher the computational cost and the longer the computation time. This high cost of reliability analysis hinders the development of reliability research on mechanical thrombectomy stents. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a reliability analysis method based on an adaptive surrogate model and importance sampling for performing reliability analysis on mechanical thrombectomy stents. The numerous technical effects of the preferred solutions among the various technical methods provided by this invention are detailed below.

[0007] To achieve the above objectives, this invention provides a reliability analysis method based on an adaptive surrogate model and importance sampling for the reliability analysis of mechanical thrombectomy stents, comprising the following steps:

[0008] Step S100: Quantify the probability distribution of the design parameters of the mechanical thrombectomy stent. These design parameters include the stent's diameter, wire width, wire thickness, length, fillet radius, 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, transform them into standard normal random variables using Rosenblatt, transforming them to a standard normal space. Initialize the algorithm parameters, including the initial hypersphere radius β. 0 Initial training sample set size Size of the first sorted set Hypersphere convergence index ∈ β and the size of the candidate sample set N cand Based on the initial hypersphere radius β 0 Construct a hypersphere and a finite element simulation model of the compression and bending of the mechanical thrombectomy support;

[0009] Step S200: Based on the probability distribution of the quantified design parameters, establish the hypersphere truncation sampling probability function based on the hypersphere radius, and generate random samples. Use a portion of these random samples as the training sample set and the remainder as the candidate sample set.

[0010] Step S300: Construct and train the Kriging surrogate model of the finite element model of the mechanical thrombectomy stent based on the training sample set. Substitute the candidate sample set into the trained Kriging surrogate model to obtain the response set of the candidate samples. Sort and filter the response set of the candidate samples twice to obtain the 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 the updated hypersphere.

[0011] Step S400: Perform a convergence judgment on the updated hypersphere radius. If the hypersphere radius is determined to be convergent, proceed to step S500; otherwise, return to step S300.

[0012] Step S500: The accuracy of the trained Kriging surrogate model is cross-validated using leave-one-out cross-validation. An index function constructed from the trained Kriging surrogate model is used to filter the candidate sample set obtained from the currently updated hypersphere out-of-sphere sampling. Samples whose index function is zero are selected to form a new candidate sample set. If the accuracy of the trained Kriging surrogate model meets the specified requirements, the augmentation failure probability p is calculated. f∈ If the sample selection process proceeds to step S600, then the adaptive learning function is used to select samples from the new candidate sample set and add them to the training set, and the process returns to step S300.

[0013] Step S600: Using the new candidate sample set obtained from step S500, the Kriging surrogate model is further refined using the adaptive learning function until the learning function termination condition is met, and the correction factor α is calculated. 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. If the coefficient of variation of the failure probability converges, the program ends, and the failure probability is used for the safety assessment and optimization design of the mechanical thrombectomy stent; otherwise, expand the candidate sample set size N. cand Then 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. These design parameters include stent diameter, wire width, wire thickness, length dimension, corner radius, and wire angle. These design parameters form a random vector X. For the non-standard normal random variables in the probability distribution of these design parameters, use Rosenblatt transformation to transform them into a standard normal space. Also, initialize the algorithm parameters, including the initial hypersphere radius β. 0 Initial training sample set size Size of the first sorted set Hypersphere convergence index ∈ β and the size of the candidate sample set N cand Based on the initial hypersphere radius β 0 Construct a hypersphere;

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

[0018] The limit state functions for the two failure modes of the mechanical thrombectomy support—bending stiffness and radial support force—are as follows:

[0019]

[0020] Among them, G w (X) represents the bending stiffness of the mechanical bolt retrieval support calculated based on finite element simulation, and G... r (X) represents the radial support force of the mechanical bolt retrieval support calculated based on finite element simulation, t w To set the bending stiffness failure threshold according to actual engineering needs, t r To set the radial support force failure threshold in accordance with actual engineering needs, X is a random vector composed of the design parameters of the mechanical thrombectomy support.

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

[0022] Step S210: The probability density of sampling outside the hypersphere is the truncated sampling probability density. The truncated sampling probability density function outside the hypersphere is established as follows:

[0023]

[0024] Where x is the sampled sample, β is the hypersphere radius, r is the Mahalanobis distance and in the standard normal space r = ||x||, and φ(x,r) is the standard normal probability density function. Let be the chi-square distribution probability function, and n be the vector dimension of the sample x;

[0025] Step S220: Establish the hypersphere-outside truncation sampling probability function. Integrate the hypersphere-outside truncation sampling probability density function to obtain the corresponding hypersphere-outside truncation sampling probability function:

[0026]

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

[0028] Step S230: Obtained from inverse conversion sampling:

[0029]

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

[0031] The truncated sampled data outside the hypersphere is obtained as follows:

[0032]

[0033] Where v is an n-dimensional normally distributed random vector sample;

[0034] Step S240: The generated truncated sample x is used as a random sample, a portion of which is used as the initial training sample set, and the remainder is used as the candidate sample set. This initial training sample set satisfies the set initial training sample set size. The candidate sample set satisfies the condition that the candidate sample set size N is... cand .

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

[0036] Step S310: Input the initial training sample set obtained in step S240 into the finite element simulation model of the compression and bending of the mechanical thrombectomy bracket, calculate the simulation output, and form a training set S based on the simulation output and the current training samples. t The Kriging proxy model of the finite element model of the mechanical thrombectomy support is constructed and trained. The candidate sample set obtained in step S240 is substituted into the trained Kriging proxy model to obtain the Kriging proxy model response as the candidate sample response set.

[0037] Step S320: Sort and filter the absolute values ​​of the Kriging surrogate model responses in the candidate sample response set from smallest to largest, and select the top-ranked responses. The number of candidate samples are used to form the candidate sample set selected in the first sorting and screening.

[0038] Step S330: For the candidate sample set selected in the first sorting and screening, a second sorting and screening is performed based on the vector magnitude of the candidate samples. The candidate sample with the smallest vector magnitude in the second sorting is selected as the approximate value of the most likely failure point in the reliability analysis.

[0039] Step S340: Use the vector magnitude of the approximate value of the most likely failure point selected through two sorting processes as the updated hypersphere radius β for the current round. i An updated hypersphere is constructed around the origin of the standard normal spatial coordinate system. The interior of this updated hypersphere is the safe region, while the failure region is contained outside the updated hypersphere, where β i Let represent the updated hypersphere radius determined in the i-th iteration.

[0040] Optionally, step S400 specifically includes:

[0041] Update the hypersphere radius β for the current round i Perform a convergence check, that is

[0042] β i -β i-1 ≤∈ β , i≥1

[0043] Where, ∈ β Indicates the hypersphere radius convergence index;

[0044] If we determine the updated hypersphere radius β in the current round i If the above equation is satisfied, it means that the currently updated hypersphere radius is a convergent hypersphere radius, then step S500 is executed; otherwise, the candidate sample and its Kriging surrogate model response are fed into the U learning function, i.e.

[0045]

[0046] in, and Let x' be the expected response and standard deviation of the Kriging surrogate model for candidate sample x′, respectively, and let x' be the candidate sample that minimizes the value of the U learning function. * =min(U) is added as a training sample to the training set S t Then, return to step S300 to perform the next round of updates to the hypersphere radius and the Kriging proxy model.

[0047] Optionally, step S500 specifically includes:

[0048] Step S510: Use leave-one-out cross-validation to measure the accuracy of the current Kriging surrogate model based on the current training samples. Leave-one-out cross-validation is expressed as follows:

[0049]

[0050] in, This represents the leave-one-out cross-validation value of the correction factor, where j represents the training sample number, and N... t This represents the number of samples in the training set. Let represent the j-th sample in the training set, and t represent the sample label in the training set. S represents the index function based on the limit state function. t Represents the training set. Indicates based on S t Delete The index function of the Kriging surrogate model trained on the training set after training;

[0051] Step S520: Sample the currently updated hypersphere outside to obtain a set of candidate samples, which will be based on S t Delete The index function of the Kriging surrogate model trained on the training set after training. Samples with a value of 0 are filtered to form a new set of candidate samples;

[0052] Step S530, for the obtained Make a judgment when If the sample falls within the range [0.1, 10], it indicates that the trained Kriging surrogate model has reached 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 agent model;

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

[0054]

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

[0056]

[0057] in, For the optimal importance sampling density, I F (x′) is the reliability integral index function, and π(x′) is the reliability integral index function.F The Kriging surrogate model index function of (x′), α corr p is a correction factor, representing a correction to the previous failure probability. f∈ To augment the failure probability, the failure probability is estimated based on the Kriging surrogate model.

[0058] Get p f∈ for

[0059]

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

[0061] Optionally, step S600 specifically includes:

[0062] Step S610: Further filter the new candidate sample set obtained in step S520 based on the index function π(x′) of the trained Kriging surrogate model, and form a candidate sample set from the samples in the new candidate sample set that satisfy π(x′)≤0; combined with the U learning function, select the candidate sample that maximizes the value of the U learning function from the 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 In the middle, and based on this, add the updated training set S. t Update the Kriging proxy model;

[0063] Step S620: The obtained updated Kriging proxy model is used to determine the convergence of the Kriging proxy model through the U learning function. When the Kriging surrogate model converges, the update of the Kriging surrogate model is terminated and the correction factor is calculated.

[0064]

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

[0066] Step S630: Based on the failure probability decomposition formula 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, the reliability analysis method based on adaptive proxy model and importance sampling provided by the embodiments of the present invention has at least the following advantages.

[0068] 1) Used for reliability analysis of mechanical thrombectomy stents, it fully considers the randomness of mechanical thrombectomy stent design parameters, and significantly improves the efficiency of reliability analysis by combining importance sampling and surrogate models.

[0069] 2) The probability density function and probability function of the hypersphere truncated sampling were constructed. The standard normal space was divided into a safe region inside the hypersphere and a region outside the hypersphere containing the failure region by using the hypersphere truncated sampling method. The region inside the hypersphere does not need to be considered when performing sampling, Kriging surrogate model construction and reliability analysis, which effectively improves the efficiency of the method.

[0070] 3) This includes constructing an importance sampling algorithm framework based on a surrogate model, in which the failure probability is decomposed into augmented failure probability and correction factor, and these two steps are calculated in multiple steps to finally calculate the failure probability efficiently. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the embodiments will be briefly introduced below. The features and advantages of the present invention can be more clearly understood by referring to the accompanying drawings. The accompanying drawings are schematic and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 A flowchart illustrating the algorithm of a reliability analysis method based on an adaptive proxy model and importance sampling according to an embodiment of the present invention.

[0073] Figure 2 A schematic diagram of a mechanical tack bolt holder bending stiffness test in an example of applying the reliability analysis method based on an adaptive surrogate model and importance sampling provided according to an embodiment of the present invention.

[0074] Figure 3 A schematic diagram of a simulation of radial support force test of a mechanical thrombectomy bracket, used in an example of applying a reliability analysis method based on an adaptive surrogate model and importance sampling according to an embodiment of the present invention.

[0075] Figure 4 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 according to an embodiment of the present invention.

[0076] Figure 5 for Figure 4 An enlarged view of the support ring unit of the mechanical thrombectomy support.

[0077] Figure 6 for Figure 5 A partial magnified view of the support ring unit.

[0078] Figure 7 for Figure 4 A side view of the support ring unit of the mechanical thrombectomy bracket. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of the present invention clearer, various exemplary embodiments described below will be referenced to the accompanying drawings, which form part of the exemplary embodiments, illustrating various exemplary embodiments that may be used to implement the present invention. Unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. It should be understood that they are merely examples of processes, methods, and apparatuses consistent with some aspects of the present invention disclosed as detailed in the appended claims, and other embodiments may be used, or structural and functional modifications may be made to the embodiments listed herein without departing from the scope and spirit of the present invention.

[0080] To illustrate the technical solution described in this invention, specific embodiments are described below, showing only the parts related to the embodiments of this invention.

[0081] Symbol explanation:

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

[0083] β is the radius of the hypersphere;

[0084] β 0 Indicates the initial hypersphere radius;

[0085] i represents the number of iterations of the Kriging proxy model and i≥1;

[0086] β i This represents the hypersphere radius calculated in the i-th iteration update of the Kriging proxy model;

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

[0088] Indicates the size of the set during the first sort;

[0089] ∈ β This represents the hypersphere convergence index;

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

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

[0092] G w (X) represents the bending stiffness of the mechanical bolt retrieval support calculated based on finite element simulation.

[0093] G r (X) represents the radial support force of the mechanical bolt retrieval support calculated based on finite element simulation.

[0094] t w The bending stiffness failure threshold is set to meet the actual engineering needs.

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

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

[0097] x represents the sampled sample;

[0098] n is the vector dimension of the 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 outside-truncation sampling probability function of the hypersphere;

[0102] Let the chi-square distribution probability function be used.

[0103] p is a uniformly sampled sample in the interval [0,1].

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

[0105] v is an n-dimensional normally distributed random vector sample;

[0106] S t Represents the training set;

[0107] U represents the value of the U learning function;

[0108] x′ represents a candidate sample;

[0109] This represents the expected response of the Kriging surrogate model to candidate sample x′;

[0110] The standard deviation of the response of the Kriging surrogate model to candidate sample x′ is represented.

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

[0112] j represents the sample number of the training set;

[0113] N t Indicates the number of samples in the training set;

[0114] This represents the j-th sample in the training set;

[0115] t represents the sample label of the training set;

[0116] Represents an index function based on a limit state function;

[0117] Indicates based on S t delete The index function of the Kriging surrogate model trained on the training set after training;

[0118] p f Indicates the probability of failure;

[0119] To achieve the optimal importance sampling density;

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

[0121] π(x′) is I F Kriging surrogate model index function for (x′);

[0122] p f∈ To increase the probability of failure;

[0123] α corr As a correction factor;

[0124] x′ k This represents the k-th candidate sample;

[0125] k represents the candidate sample number, and k = 1, ..., N cand .

[0126] like Figure 1 As 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 reliability analysis of mechanical thrombectomy stents, 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, transform them into standard normal random variables using Rosenblatt, transforming them to the standard normal space. Initialize the algorithm parameters, including the initial hypersphere radius β. 0 Initial training sample set size Size of the first sorted set Hypersphere convergence index ∈ β and the size of the candidate sample set N cand Based on the initial hypersphere radius β 0 Construct a hypersphere and a finite element simulation model of the compression and bending of the mechanical thrombectomy support. See [link to documentation]. Figures 4 to 7 The design parameters of the mechanical thrombectomy bracket may include its diameter, wire width, wire thickness, length, fillet radius, and wire angle. For example... Figure 2 and Figure 3 The diagram illustrates a finite element simulation of the compression and bending of a mechanical thrombectomy stent constructed in an example applying this implementation method. Step S100 specifically includes the following steps.

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

[0129] Step S120: Construct a black-box finite element model of the mechanical bolt retrieval support as the limit state function, based on finite element simulations of compression and bending. As an optional implementation, the limit state functions for both bending stiffness and radial support force of the mechanical bolt retrieval support can be constructed as follows:

[0130]

[0131] Among them, G w (X) represents the bending stiffness of the mechanical bolt retrieval support calculated based on finite element simulation, and G... r (X) represents the radial support force of the mechanical bolt retrieval support calculated based on finite element simulation, tw To set the bending stiffness failure threshold according to actual engineering needs, t r To meet the actual engineering requirements, the radial support force failure threshold is set, and X is a random vector composed of the design parameters of the mechanical thrombectomy support. In this embodiment, the random vector X may include various parameters that affect the performance of the mechanical thrombectomy support, including structural design parameters, material parameters, and environmental parameters. Specifically, design parameters may include the length, diameter, number of mesh openings, mesh wire width, mesh wire thickness, mesh wire angle, and corner radius of the mechanical thrombectomy support. Material parameters may include elastic modulus and Poisson's ratio. Environmental parameters may include ambient temperature.

[0132] Step S200: Based on the probability distribution of the quantified design parameters, establish a hypersphere truncation sampling probability function based on the hypersphere radius, and generate random samples. A portion of these random samples is used as the training sample set, and the remainder as the candidate sample set. Step S200 specifically includes the following steps.

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

[0134]

[0135] Where x is the sampled sample, β is the hypersphere radius, r is the Mahalanobis distance, and in the standard normal space, r = ||x||, φ(x,r) is the standard normal probability density function. Let be the chi-squared probability function, and n be the vector dimension of the sample x. In the initial rounds, the hypersphere radius here uses the initial hypersphere radius β. 0 In subsequent rounds, for example, in the i-th round, the updated hypersphere radius β obtained in step S300 of the previous round is used. i-1 The hypersphere radius in steps S220 and S230 is similar.

[0136] Step S220: Construct the hypersphere-outside truncated sampling probability function. Integrate the hypersphere-outside truncated sampling probability density function to obtain the corresponding hypersphere-outside truncated sampling probability function:

[0137]

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

[0139] Step S230: Based on the inverse conversion sampling,

[0140]

[0141]

[0142] Where p is a uniformly sampled sample in the interval [0,1], φ -1 The inverse of the standard normal distribution probability function is given; the truncated sample is represented as...

[0143]

[0144] Where v is an n-dimensional normally distributed random vector sample.

[0145] Step S240: Use the generated truncated sample x as a random sample, a portion of which is used as the initial training sample set, and the remainder as the candidate sample set. This initial training sample set satisfies the set initial training sample set size. The candidate sample set satisfies the condition that the candidate sample set size N is... cand .

[0146] Step S300: Construct and train a Kriging surrogate model of the finite element model of the mechanical thrombectomy stent based on the training sample set, and substitute the candidate sample set into the trained Kriging surrogate model to obtain the response set of the candidate samples. Perform two sorting and filtering operations on the response set of the candidate samples 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 the updated hypersphere. Step S300 specifically includes the following steps.

[0147] Step S310: Input the initial training sample set obtained in step S240 into the finite element simulation model of the compression and bending of the mechanical thrombectomy bracket, calculate the simulation output, and form a training set S based on the simulation output. t The Kriging surrogate model of the finite element model of the mechanical thrombectomy support is constructed and trained. The candidate sample set obtained in step S240 is substituted into the trained Kriging surrogate model to obtain the Kriging surrogate model response as the candidate sample response set.

[0148] Step S320: Sort and filter the absolute values ​​of the Kriging surrogate model responses in the candidate sample response set from smallest to largest, and select the top-ranked responses. The number of candidate samples forms the candidate sample set selected in the first sorting and screening.

[0149] Step S330: For the candidate sample set selected in the first sorting and screening, perform a second sorting and screening based on the vector magnitude of the candidate samples, and select the candidate sample with the smallest vector magnitude in the second sorting as the approximate value of the most likely failure point in the reliability analysis.

[0150] Step S340: Use the vector magnitude of the approximate value of the most likely failure point selected through two sorting processes as the updated hypersphere radius β for the current round. i An updated hypersphere is constructed around the origin of the standard normal spatial coordinate system. The interior of this updated hypersphere is the safe region, while the failure region is contained outside the updated hypersphere, where β i Let represent the updated hypersphere radius determined in the i-th iteration.

[0151] Step S400: Perform a convergence judgment on the updated hypersphere radius. If the hypersphere radius is determined to be convergent, proceed to step S500; otherwise, return to step S300.

[0152] This step S400 specifically includes: updating the hypersphere radius β for the current round. i Perform a convergence check, that is

[0153] β i -β i-1 ≤∈ β ,

[0154] Where, β i Let ∈ represent the hypersphere radius determined by the surrogate model in the i-th iteration update. β Indicates the hypersphere radius convergence index;

[0155] If we determine the updated hypersphere radius β in the current round i If the above equation is satisfied, it means that the currently updated hypersphere radius is a convergent hypersphere radius, then step S500 is executed; otherwise, the candidate sample and its Kriging surrogate model response are fed into the U learning function, i.e.

[0156]

[0157] in, and Let x' be the expected response and standard deviation of the Kriging surrogate model for candidate sample x′, respectively, and let x' be the candidate sample that minimizes the value of the U learning function. * =min(U) is added as a training sample to the training sample set S. t Then, return to step S300 to perform the next round of updates to the hypersphere radius and the Kriging proxy model.

[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 by the two sorting processes gradually approach the most likely failure points. At this point, the hypersphere gradually converges to the maximum hypersphere.

[0159] Step S500: Cross-validate the accuracy of the trained Kriging surrogate model using leave-one-out cross-validation. If the accuracy of the trained Kriging surrogate model meets the specified requirements, use the index function constructed by the trained Kriging surrogate model to filter the candidate sample set obtained from the currently updated hypersphere out-of-sampling. Samples whose index function is 0 are selected to form a new candidate sample set, and the augmentation failure probability p is calculated. f∈ If the process continues, proceed to step S600; otherwise, use an adaptive learning function to select samples from the new candidate sample set and add them to the training set S. t Then return to step S300.

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

[0161] Step S500 specifically includes the following steps.

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

[0163]

[0164] in, This represents the leave-one-out cross-validation value of the correction factor, where j represents the training sample number, and N... t This represents the number of samples in the training sample set. Let represent the j-th sample in the training set, and t represent the sample label in the training set. S represents the index function based on the limit state function. t Represents the training set. Indicates based on S t Delete The index function of the Kriging surrogate model trained on the training set.

[0165] Step S520: Sample the currently updated hypersphere outside to obtain a set of candidate samples, which will be based on S t Delete The index function of the Kriging surrogate model trained on the training set after training. Samples with a value of 0 are filtered to form a new set of candidate samples.

[0166] Step S530, for the obtained Make a judgment when If the sample falls within the range [0.1, 10], it indicates that the trained Kriging surrogate model has reached 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 Then return to step S300 to update the Kriging agent model.

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

[0168]

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

[0170]

[0171]

[0172] in, For the optimal importance sampling density, I F (x′) is the reliability integral index function, and π(x′) is the reliability integral index function. F The Kriging surrogate model index function of (x′), α corr p is a correction factor, representing a correction to the previous failure probability. f∈ To augment the failure probability, the failure probability is estimated based on the Kriging surrogate model.

[0173] Get p f∈ for

[0174]

[0175] Where, x′ k Let k represent the k-th candidate sample, where k represents the candidate sample number and k = 1, ..., N. cand .

[0176] In this step, the hypersphere radius used here is the current hypersphere radius, depending on the iteration round. For example, in the i-th round, the updated hypersphere radius β obtained in step S300 of that round is used. i .

[0177] Step S600: Using the new candidate sample set obtained from step S500, the Kriging surrogate model is further refined using the adaptive learning function until the learning function terminates. The correction factor α is then calculated. corrThe failure probability is further calculated. The termination criterion for this second-stage surrogate model is an adaptive learning function, characterized by including all adaptive learning functions, such as the U learning function, H learning function, expected improvement learning function, EFF learning function, etc. Step S600 specifically includes the following steps.

[0178] Step S610: Further filter the new candidate sample set obtained in step S520 based on the index function π(x′) of the trained Kriging surrogate model, and form a candidate sample set from the samples in the new candidate sample set that satisfy π(x′)≤0; Combine with the U learning function, select the candidate sample that maximizes the value of the U learning function from the 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.

[0179] Step S620: The obtained updated Kriging proxy model is used to determine the convergence of the Kriging proxy model through the U learning function. When the Kriging surrogate model converges, the update of the Kriging surrogate model is terminated and the correction factor is calculated.

[0180]

[0181] Otherwise, when Then return to step S610 and continue updating the Kriging surrogate model until the convergence criterion is met. In this step, the hypersphere radius used here is the current hypersphere radius, depending on the iteration round. For example, in the i-th round, the updated hypersphere radius β obtained in step S300 of that round is used. i .

[0182] Step S630: Based on the failure probability decomposition formula 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∈ To increase the failure probability, α corr This is a correction factor.

[0185] Step S700: Calculate the coefficient of variation of the failure probability based on the failure probability and perform a convergence judgment. If the coefficient of variation of the failure probability converges, the program ends, and the failure probability is used for the safety assessment and optimization design of the mechanical thrombectomy stent; otherwise, expand the candidate sample set size N.cand Then return to step S200.

[0186] The reliability analysis method based on an adaptive surrogate model and importance sampling provided in this embodiment performs reliability analysis on mechanical thrombectomy stents. It requires only a small number of initial training and candidate samples, and by combining an adaptive surrogate model and a two-stage screening strategy, it gradually adds samples to the training sample set, thereby improving the efficiency of the reliability analysis algorithm and thus enhancing the efficiency and effectiveness of mechanical thrombectomy stent reliability analysis. Therefore, the mechanical thrombectomy stent reliability analysis method provided in this embodiment can significantly reduce computation time and resource consumption.

[0187] As an optional approach, this implementation uses an adaptive Kriging surrogate model. In the first stage, an adaptive learning function is used in conjunction with the candidate sample set to update the Kriging surrogate model. The stopping criterion for updating the surrogate model in this stage is leave-one-out cross-validation. After falling into the [0.1, 10] interval, the first stage terminates and the augmentation failure probability p is calculated. f∈ Otherwise, the surrogate model is further refined. In the second stage, the Kriging surrogate model is updated using an adaptive learning function combined with the index function of the Kriging surrogate model to filter the candidate sample point set. In this stage, the Kriging surrogate model update stopping criterion uses the U learning function. At that time, the second stage terminates and the correction factor α is calculated. corr .in, This represents the mean response of the Kriging proxy model. This represents the response variance of the Kriging proxy model.

[0188] All of the above-mentioned optional technical solutions can be combined in any way to form the optional embodiments of this application, and will not be described in detail here.

[0189] It should be understood that the sequence number of each step in the above embodiments does not imply 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 on the implementation process of the embodiments of the present invention.

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

Claims

1. A reliability analysis method based on an adaptive surrogate model and importance sampling, characterized in that, Reliability analysis for mechanical thrombectomy stent, comprising the following steps: Step S100, quantifying the probability distribution of the design parameters of the mechanical thrombectomy stent, the design parameters including the diameter, wire width, wire thickness, length size, fillet and wire clamping angle of the mechanical thrombectomy stent, which form a random vector X, for non-standard normal random variables in the probability distribution of the design parameters, converting to standard normal random variables by Rosenblatt transformation to standard normal space; initializing algorithm parameters, the algorithm parameters including an initial hypersphere radius β 0 , an initial training sample set size , a first sorting set size , a hypersphere convergence index ∈ β , and a candidate sample set size N cand , constructing a hypersphere based on the initial hypersphere radius β 0 , and constructing a finite element simulation model of compression and bending of the mechanical thrombectomy stent; Step S200, based on the hyper-sphere radius, establish a hyper-sphere outer truncated sampling probability function according to the probability distribution of the quantized design parameters, and generate random samples, a part of which is taken as a training sample set, and the rest is taken as a candidate sample set; Step S300, based on the training sample set, construct and train a 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 a response set of the candidate sample, sort and screen the response set of the candidate sample twice to obtain an approximate value of the most likely failure point, update the hyper-sphere radius based on the approximate value of the most likely failure point, and establish an updated hyper-sphere; Step S400, make a convergence judgment on the updated hyper-sphere radius, if it is judged that the hyper-sphere radius converges, execute step S500, otherwise return to step S300; Step S500, the accuracy of the trained Kriging surrogate model is verified by using the leave-one-out cross-validation method, the index function constructed by using the trained Kriging surrogate model is used to screen the candidate sample set obtained by sampling outside the current updated hyper-sphere, 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 surrogate model reaches the specified requirement, the augmented failure probability p is calculated f∈ , and step S600 is performed; otherwise, samples are selected from the new candidate sample set by using the adaptive learning function and added to the training set, and step S300 is returned. Step S600, using the filtered new candidate sample set obtained from step S500, combining the adaptive learning function to continue to refine the Kriging surrogate model until the learning function termination condition is reached, and calculating the correction factor a corr and further calculating the failure probability; Step S700, calculate the failure probability variation coefficient based on the failure probability and make a convergence judgment, when judging that the failure probability variation coefficient converges, end the program, and use the failure probability for safety evaluation and optimization design of the mechanical bail stent; otherwise, expand the candidate sample set size N cand And return to step S200.

2. The reliability analysis method based on an adaptive proxy model and importance sampling according to claim 1, characterized in that, The step S100 specifically comprises the following steps: Step S110, quantifying the probability distribution corresponding to the design parameters of the mechanical thrombectomy stent, the design parameters including stent diameter, wire width, wire thickness, length size, fillet, and wire clamping angle, these design parameters forming a random vector X, non-standard normal random variables in the probability distribution of the design parameters are converted to a standard normal space by using Rosenblatt transformation, and algorithm parameters are initialized, the algorithm parameters including an initial hypersphere radius β 0 , an initial training sample set size , a first sorting set size , a hypersphere convergence index ∈ β , and a candidate sample set size N cand , constructing a hypersphere based on the initial hypersphere radius β 0 ; Step S120, a finite element simulation model of compression and bending of the mechanical thrombectomy stent is constructed, and a bending stiffness G of the mechanical thrombectomy stent is obtained based on the finite element simulation model w (X) and the radial support force G r (X), wherein the bending stiffness is a ratio of the bending load F and the bending deformation θ, The limit state functions of the bending stiffness and the radial support force of the mechanical thrombectomy stent are constructed as follows: where G w (X) is the bending stiffness of the mechanical stentriever calculated according to finite element simulation, G r (X) is the radial support force of the mechanical stentriever calculated according to 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 a random vector composed of design parameters of the mechanical stentriever.

3. The reliability analysis method based on adaptive surrogate model and importance sampling according to claim 2, characterized in that, The step S200 specifically comprises the following steps: Step S210, the probability density of sampling outside the hyper-sphere is a truncated sampling probability density, and the truncated sampling probability density function outside the hyper-sphere is established as follows: where x is a sample, β is a hypersphere radius, r is a Mahalanobis distance and has r = ||x|| in the standard normal space, φ(x, r) is a standard normal probability density function, is a chi-square distribution probability function, n is a vector dimension of the sample x. Step S220, establish the truncated sampling probability function outside the hyper-sphere, and integrate the truncated sampling probability density function outside the hyper-sphere to obtain the corresponding truncated sampling probability function outside the hyper-sphere as follows: Wherein, φ(x, r) is a standard normal probability function; Step S230, according to the inverse conversion sampling, the following is obtained: where 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 hyper-sphere are obtained as follows: Wherein, v is an n-dimensional normal distribution random vector sample; Step S240, taking the generated truncated sampling sample x as a random sample, part of which is taken as an initial training sample set, and the rest is taken as a candidate sample set, the initial training sample set satisfying a set initial training sample set size The candidate sample set satisfies a candidate sample set size N cand .

4. The reliability analysis method based on adaptive surrogate model and importance sampling according to claim 3, characterized in that, The step S300 specifically comprises the following steps: Step S310, the initial training sample set obtained in step S240 is brought into the finite element simulation model of the compression and bending of the mechanical stent, the simulation output is calculated, and the training set is constituted according to the simulation output and the current training sample t , a Kriging surrogate model of the finite element model of the mechanical stent is constructed and trained, the candidate sample set obtained in step S240 is substituted into the trained Kriging surrogate model, and a Kriging surrogate model response constitutes a candidate sample response set; Step S320, the absolute value of the Kriging proxy model response in the candidate sample response set is sorted in ascending order for the first time, and the candidate sample set filtered out in the first sorting is composed of the top K of the sorted set the number of candidate samples, to form a candidate sample set filtered out in the first sorting Step S330, for the candidate sample set screened out by the first sorting and screening, according to the vector module length of the candidate sample, the second sorting and screening is carried out, and the candidate sample with the smallest vector module length in the second sorting is screened as the approximate value of the most likely failure point in the reliability analysis; Step S340, the vector module length of the approximate value of the most possible failure point screened out in two times of sorting is the updated hypersphere radius β of the current round i And an updated hypersphere is constructed around the standard normal space coordinate origin, the inside of the updated hypersphere is a safety domain, and a failure domain is contained outside the updated hypersphere, wherein β i represents the updated hypersphere radius determined in the i-th iteration.

5. The reliability analysis method based on adaptive surrogate model and importance sampling according to claim 4, characterized in that, The step S400 specifically comprises: a hypersphere radius β for the current iteration i a convergence determination is made, i.e. β i -β i-1 ≤∈ β ，i≥1 where ∈ β represents the hypersphere radius convergence index; If it is judged that the updated hyper-sphere radius β of the current round satisfies the following formula i If the updated hyper-sphere radius of the current round satisfies the following formula, it indicates that the current updated hyper-sphere radius is the convergent hyper-sphere radius, and then step S500 is executed, otherwise the candidate sample and the Kriging surrogate model response of the candidate sample are brought into the U-learning function, that is, wherein, and are the response expectation and the response standard deviation of the Kriging surrogate model for the candidate sample x', respectively, and the candidate sample x * that minimizes the function value U is added to the training set S as a training sample t and the procedure returns to step S300 for the next iteration of the hypersphere radius and the Kriging surrogate model update.

6. The reliability analysis method based on adaptive surrogate model and importance sampling according to claim 5, characterized in that, The step S500 specifically comprises: Step S510, the precision of the current Kriging surrogate model is measured according to the current training sample by using the leave-one-out cross-validation method, and the leave-one-out cross-validation method is represented as follows: 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 label, 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 S t after deleting from S Step S520, sampling outside the current updated hypersphere to obtain a sampled candidate sample set, which will be based on the S t deleted from the training set after training the index function of the Kriging surrogate model The sample judged as 0 is screened to form a new candidate sample set; Step S530, judging whether the obtained belongs to the interval [0.1, 10], indicating that the trained Kriging surrogate model reaches the specified precision, and executing step S540, otherwise, selecting a sample from the new candidate sample set obtained from step S520 using the U learning function and adding it to the training set S t and returning to step S300 to update the Kriging surrogate model;​ Step S540, the optimal importance sampling probability density function is represented as The failure probability integral under the importance sampling outside the hyper-sphere is as follows: wherein, is the optimal importance sampling density, I F (x') is the reliability integral indicator function, π(x') is the I F (x') is the Kriging surrogate model indicator function, α corr is the correction factor, representing a 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, obtained p f∈ to where x ′ k denotes the k-th candidate sample, k denotes the number of the candidate sample and k = 1,..., N cand .

7. The reliability analysis method based on adaptive surrogate model and importance sampling according to claim 6, characterized in that, The step S600 specifically comprises: Step S610, further screening the new candidate sample set obtained in step S520 according to the index function π(x') of the trained Kriging surrogate model, and forming a candidate sample set from samples in the new candidate sample set satisfying π(x')≤0; combining the U learning function, selecting a candidate sample with the maximum U learning function value from the formed candidate sample set as a sample with the greatest contribution to improving the precision of the Kriging surrogate model, and adding a response obtained by substituting the sample into the limit state function provided in step S120 into the training set S t , and updating the training set S t based on the addition, and updating the Kriging surrogate model; Step S620, the obtained updated Kriging surrogate model is subjected to Kriging surrogate model convergence judgment by the U learning function, when the Kriging surrogate model is judged to converge, at this time the updating of the Kriging surrogate model is terminated and the correction factor is calculated Otherwise, when step S610 is returned, and the updating of the Kriging surrogate model is continued until the convergence criterion is met. Step S630, based on the decomposition formula of the failure probability 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∈ α corr .

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