A time-varying reliability design optimization method and device fusing multi-strategy active learning and time-varying sequence optimization reliability evaluation framework, equipment, medium and product

Abstract

The application discloses a time-varying reliability design optimization method and device fusing a multi-strategy active learning and a time-varying sequence optimization reliability evaluation framework, equipment, medium and product, and relates to the technical field of time-varying reliability design optimization. The method comprises the following steps: obtaining design variables, random variables, time-varying random process parameters and target reliability, and expanding the time-varying random process to obtain deterministic expansion coefficients; performing super-sphere sampling clustering and screening on the target reliability, and building an inner-loop surrogate model; obtaining a time-varying minimum function measurement point, a most dangerous time node and constructing an offset vector by relying on an expected improvement function; establishing a global surrogate model, and identifying active constraints according to a predicted safety margin; demarcating a local area for the active constraints, and constructing a local surrogate model by using an expected feasibility function; and converting the time-varying reliability constraints into deterministic constraints for solving, and obtaining an optimal scheme. The method can realize reliability design optimization of a structure under the premise of considering time parameters and random processes.

Description

Technical Field

[0001] This application relates to the field of time-varying reliability design optimization technology, and in particular to a time-varying reliability design optimization method, apparatus, equipment, medium and product that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework. Background Technology

[0002] In the engineering design of complex equipment, structures are inevitably affected by various uncertainties such as material properties, geometric manufacturing errors, and external loads. Especially during the service life, the degradation of material properties and dynamic external loads cause the reliability of the structure to exhibit significant time-varying characteristics. Therefore, conducting time-varying reliability design optimization is of significant engineering value for achieving design goals such as lightweighting and low cost while ensuring the reliability of the structure throughout its entire life cycle.

[0003] Traditional deterministic optimization design ignores fluctuations in input parameters, which may lead to structural failure under the influence of uncertainties. To address this, reliability design optimization incorporates reliability requirements as constraints into the optimization process; however, the nested two-layer optimization process is computationally expensive. Time-varying problems also require additional handling of the evolution of stochastic processes over time, further increasing computational complexity. To improve solution efficiency, existing technologies have developed decoupling strategies such as Sequential-Optimization-and-Reliability Assessment (SORA) and introduced surrogate models such as Kriging to replace high-fidelity simulations, thereby reducing the number of calls to the actual functional functions.

[0004] However, existing methods employ a uniform surrogate model evaluation strategy for each constraint during the iteration process, which results in a low reliability and accuracy improvement of the optimization results when considering time parameters and stochastic processes. Summary of the Invention

[0005] This application provides a time-varying reliability design optimization method, apparatus, device, medium, and product that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework, which can achieve reliability design optimization of structure under the premise of considering time parameters and stochastic processes.

[0006] To achieve the above objectives, this application adopts the following technical solution: Firstly, this application provides a time-varying reliability design optimization method that integrates multi-strategy active learning and a time-varying sequence optimization reliability assessment framework, including: Obtain the initial design variables, initial random variables, time-varying stochastic process parameters, and target reliability index; Based on the parameters of the time-varying random process, the time-varying random process is expanded to obtain the deterministic expansion coefficients; Based on initial design variables, initial random variables, and deterministic expansion coefficients, sample generation and clustering are performed on the target reliability hypersphere to construct an inner-loop surrogate model. Active search is then performed using the inner-loop surrogate model and the expected improvement function to obtain the final time-varying minimum functional measure point and the most dangerous time node. An offset vector is constructed based on the time-varying minimum functional measure point. A global surrogate model is constructed using a global sample library composed of initial design variables, initial random variables, deterministic expansion coefficients, and the most dangerous time node. Based on the global surrogate model, the predicted safety margin is calculated for the current design variables, current random parameters, and the most dangerous time node. The predicted safety margin is compared with a preset threshold to obtain active constraints. Local concentrated regions are defined for the active constraints based on the time-varying minimum functional measure point. A local surrogate model is constructed within the local concentrated regions using the expected feasibility function. The time-varying reliability constraints are transformed into deterministic constraints based on the offset vector, and a deterministic optimization problem under deterministic constraints is constructed based on the local surrogate model. The deterministic optimization problem is solved to obtain the updated design variables. When the changes in the updated design variables and the previous round of design variables satisfy the convergence condition, the current design variables are output as the target design scheme.

[0007] In some possible implementations, based on initial design variables, initial random variables, and deterministic expansion coefficients, sample generation and clustering screening are performed on the target reliability hypersphere to construct an inner-loop surrogate model, including: Candidate samples are generated based on the initial design variables, initial random variables, and deterministic expansion coefficients; the candidate samples are projected onto the target reliability hypersphere to obtain hypersphere sample points; K-means clustering is performed on the hypersphere sample points to determine the initial sampling points; and an inner loop surrogate model is constructed based on the initial sampling points and deterministic expansion coefficients.

[0008] In some possible implementations, the time-varying reliability constraints are transformed into deterministic constraints based on the offset vector, and a deterministic optimization problem under deterministic constraints is constructed based on a local surrogate model, including: Based on the offset vector, the time-varying reliability constraints are translated to the deterministic design space to obtain the translated deterministic constraints. The local surrogate model, which is established after the active constraints are identified by the global surrogate model, is used as the active constraint evaluation function. In the deterministic design space, the translated deterministic constraints are used as the constraints, the initial design variables are used as the optimization variables, and the minimization objective function is used as the optimization objective to construct a deterministic optimization problem.

[0009] In some possible implementations, an active search is performed using an inner-loop surrogate model and the expected improvement function to obtain the final time-varying minimum function metric point and the most dangerous time node, including: An inner loop surrogate model is adopted, in which the expected improvement function value of the candidate samples is calculated. The sample point with the largest expected improvement function value is selected as the current time-varying minimum function metric point, and this sample point is fixed to traverse all discrete time nodes to determine the most dangerous time node. The sampling and model update operations are repeated until the maximum value of the expected improvement function is less than the inner convergence threshold, and the final time-varying minimum function metric point and the most dangerous time node are obtained.

[0010] Among some possible implementations, a local proxy model is constructed within a localized region using an expected feasibility function, including: Local candidate samples are generated in local concentrated areas; the expected feasibility function value of each local candidate sample is calculated based on the initial local proxy model; the local candidate sample with the largest expected feasibility function value is selected as the new real evaluation sample; the initial local proxy model is updated based on the new real evaluation sample to complete the construction of the local proxy model.

[0011] In some possible implementations, the time-varying stochastic process is expanded based on its parameters to obtain deterministic expansion coefficients, including: Based on the parameters of the time-varying stochastic process, a covariance matrix is ​​constructed; the covariance matrix is ​​decomposed into eigenvector matrix and eigenvalue diagonal matrix; the time-varying stochastic process is expanded by Karhunen-Loève according to the product of each component of the eigenvector matrix and the square root of the corresponding eigenvalue in the eigenvalue diagonal matrix, and the deterministic expansion coefficients are obtained.

[0012] Secondly, this application provides a time-varying reliability design optimization device that integrates multi-strategy active learning and time-varying sequence optimization reliability evaluation framework, comprising: The acquisition module is used to acquire initial design variables, initial random variables, time-varying stochastic process parameters, and target reliability indicators. The calculation module is used to expand the time-varying stochastic process based on the time-varying stochastic process parameters to obtain deterministic expansion coefficients; based on the initial design variables, initial random variables, and deterministic expansion coefficients, it generates samples and performs clustering screening on the target reliability hypersphere to construct an inner loop surrogate model; it uses the inner loop surrogate model and the expected improvement function to perform active search to obtain the final time-varying minimum functional measure point and the most dangerous time node; it constructs an offset vector based on the time-varying minimum functional measure point; it constructs a global surrogate model based on a global sample library composed of initial design variables, initial random variables, deterministic expansion coefficients, and the most dangerous time node; based on the global surrogate model, it calculates the predicted safety margin for the current design variables, current random parameters, and the most dangerous time node; it compares the predicted safety margin with a preset threshold to obtain active constraints; it delineates local concentrated regions for active constraints based on the time-varying minimum functional measure point; and it constructs a local surrogate model within the local concentrated regions using the expected feasibility function. The optimization module is used to transform time-varying reliability constraints into deterministic constraints based on the offset vector, and construct a deterministic optimization problem under deterministic constraints based on the local surrogate model; solve the deterministic optimization problem to obtain the updated design variables; when the changes in the updated design variables and the previous round of design variables satisfy the convergence condition, the current design variables are output as the target design scheme.

[0013] Thirdly, this application provides a computing device, including a memory and a processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of the first aspects.

[0014] Fourthly, this application provides a computer-readable storage medium for storing a computer program for performing the method as described in any one of the first aspects.

[0015] Fifthly, this application provides a computer program product comprising one or more computer instructions, wherein when the computer instructions are executed by a computer, the computer performs the method as described in any one of the first aspects.

[0016] As can be seen from the above technical solution, this application has at least the following beneficial effects: In this application, the Karhunen-Loève exposition decouples the time-varying stochastic process, transforming the uncertainty of the time dimension into a deterministic coefficient expression. Based on this, the process is executed step-by-step according to the sequence optimization and reliability assessment workflow: First, hyperspherical samples are generated and clustered to construct an inner-loop surrogate model. The expected improvement function is used to search for the time-varying minimum functional metric point and the most dangerous time node. Then, a global surrogate model is built to distinguish between active and inactive constraints. For active constraints, a local concentrated region is defined, and the expected feasibility function is introduced to construct a local high-precision surrogate model within this region. Finally, the time-varying reliability constraints are transformed into deterministic constraints using offset vectors, completing the solution to the optimization problem. This application uses two evaluation functions to screen samples in stages: the inner loop uses EIF to lock in failure risk points, and the outer loop uses EFF to actively encrypt and build local surrogate models only for active constraints in dangerous regions. This effectively reduces the number of calls to high-precision simulations. Simultaneously, the Karhunen-Loève exposition simplifies the calculation of the time-varying stochastic process, reducing the overall computational burden. Ultimately, the prediction accuracy of key failure regions is guaranteed under limited computational cost, improving the reliability of the optimization results.

[0017] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description

[0018] Figure 1 This application scenario diagram illustrates the application environment of a time-varying reliability design optimization method that integrates multi-strategy active learning and a time-varying sequence optimization reliability assessment framework, as provided in this embodiment of the application. Figure 2 A flowchart illustrating a time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework, provided in an embodiment of this application; Figure 3 A structural diagram of a time-varying reliability design optimization device that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework provided in this application embodiment; Figure 4This is a schematic diagram of a computing device provided in an embodiment of this application. Detailed Implementation

[0019] The terms "first," "second," and "third," etc., used in this application specification and accompanying drawings are used to distinguish different objects, not to limit a specific order.

[0020] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0021] This application provides a time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework. To make the technical solution of this application clearer and easier to understand, the application scenarios of the technical solution of this application are described below with reference to the accompanying drawings. Figure 1 As shown in the figure, this figure is an application environment diagram provided by an embodiment of this application.

[0022] In this application environment, the processor acts as the execution entity. Technicians input the initial design variable range, random variable distribution parameters, the autocorrelation function of the time-varying stochastic process, and the target reliability index via a terminal. The terminal then sends these parameters to the processor. Upon receiving the data, the processor performs optimization calculations, transmitting the iteration progress and intermediate results back to the terminal for display. Once the optimization converges, the processor outputs the final target design scheme (including the optimal design variable values ​​and corresponding reliability test results) via the terminal for technicians to use for engineering decisions and subsequent detailed design.

[0023] To make the technical solution of this application clearer and easier to understand, the following describes a time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework, based on the above application scenarios. Figure 2 As shown in the figure, this is a flowchart illustrating a time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment frameworks according to an embodiment of this application. The time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment frameworks includes: S201. Obtain the initial design variables, initial random variables, time-varying stochastic process parameters, and target reliability index.

[0024] Initial design variables are structural dimensional parameters that the processor needs to optimize. Their value ranges and initial values ​​are given in advance by the user; for example, the diameters of rod 1 and rod 2 in a two-bar structure. The processor can read the initial values ​​and variation ranges from the input file or the user interface. Initial random variables are physical parameters affected by uncertainty. Their distribution type and parameters are obtained by the processor before optimization begins; for example, material strength, geometric dimensions, and external loads are all initial random variables. Time-varying stochastic process parameters describe the random fluctuation characteristics that evolve over time, such as the degradation process of material strength during the structure's service life and the random fluctuations of dynamic loads. The processor fully defines this stochastic process by reading parameters such as the autocorrelation function, mean function, and standard deviation function. For example, in the optimization problem of a two-bar structure, the autocorrelation function of the external load stochastic process is... The mean function is μ(t) = 2.2 × The standard deviation function is σ(t) = 2.0 × .

[0025] The target reliability index is the reliability requirement that the design must meet. The value of this index is determined by the engineering specifications or design task book. For example, if the target reliability index is 3.0 (corresponding to a reliability of approximately 99.87%), the processor reads this value from the configuration file and uses it as the benchmark for reliability evaluation during the optimization solution process.

[0026] For example, the processor can read data locally. Technicians can pre-fill the design variable range, random variable distribution, stochastic process correlation coefficient, and target reliability value into a local configuration file. After the processor starts the program, it directly reads all parameters from the file. The processor can also collect data through a real-time interactive process. The processor connects to a terminal, where operators manually input parameters such as the rod diameter range, material strength fluctuation range, load variation parameters over time, and specified reliability indicators. The terminal transmits the input data to the processor for reception. After receiving all the data, the processor can perform basic verification, checking for numerical errors in the upper and lower bounds of the design variables, the distribution type of the random variables, and the number of time discrete nodes. Only after verifying that there are no anomalies will the four types of parameters be cached in memory.

[0027] S202. Based on the parameters of the time-varying random process, expand the time-varying random process to obtain the deterministic expansion coefficients.

[0028] The deterministic expansion coefficients are fixed constants calculated by the processor after the Karhunen–Loève expansion is completed. The Karhunen–Loève expansion is a series expansion that represents a continuous stochastic process as the sum of products of deterministic time functions and independent standard normal random variables.

[0029] One possible approach is to construct a covariance matrix based on the parameters of a time-varying stochastic process; perform eigenvalue decomposition on the covariance matrix to obtain an eigenvector matrix and an eigenvalue diagonal matrix; and perform a Karhunen–Loève expansion on the time-varying stochastic process based on the product of each component of the eigenvector in the eigenvector matrix and the square root of the corresponding eigenvalue in the eigenvalue diagonal matrix to obtain deterministic expansion coefficients.

[0030] The covariance matrix is ​​a square matrix generated by the processor based on the parameters of the time-varying stochastic process. Each element in the matrix represents the correlation of dynamic performance parameters at different service times, and can be used to characterize the correlation of external load fluctuations over time. Each column of the eigenvector matrix is ​​an eigenvector, corresponding to an independent eigendirection, used to characterize different fluctuation patterns of the time-varying stochastic process. For example, in the time-varying load stochastic process of the two-bar example, each column vector represents a type of load fluctuation pattern over time, and all columns combined can completely describe the load fluctuation pattern across the entire time domain. The main diagonal elements of the eigenvalue diagonal matrix are eigenvalues. The eigenvalue values ​​represent the magnitude of the fluctuation energy of the stochastic process in the corresponding eigendirection. The larger the value, the stronger the influence of that set of change patterns on the overall time-varying uncertainty.

[0031] For example, the processor constructs a covariance matrix by iterating through pairwise combinations of the time-varying stochastic process parameters (including the mean function, standard deviation function, and autocorrelation function) across all discrete time points. For any two discrete time points... and The formula for calculating the corresponding element in the covariance matrix is:

[0032] in, It is the element in the i-th row and j-th column of the covariance matrix, representing the time-varying stochastic process at time node. Values ​​and time nodes The combined effect of the correlation and fluctuation range of the values ​​taken; Let be the autocorrelation coefficient of the stochastic process, when hour, =1; It is a random process at time node Standard deviation; It is a random process at time node The standard deviation.

[0033] By iterating through all combinations of discrete time points, the processor generates the complete covariance matrix. This matrix is ​​a real symmetric positive definite matrix, and its dimension equals the total number of discrete time points. The processor calls the eigenvalue decomposition function from the standard numerical linear algebra library to decompose the covariance matrix. Perform eigenvalue decomposition to split it into an eigenvector matrix and an eigenvalue diagonal matrix. The decomposition formula is as follows:

[0034] in, The eigenvector matrix; It is an eigenvalue diagonal matrix, where the elements on the main diagonal are the eigenvalues ​​sorted in descending order. The values ​​in the remaining positions are 0.

[0035] After decomposition, the processor synchronously rearranges the eigenvector matrix and the eigenvalue diagonal matrix according to the eigenvalue values ​​in descending order. The processor then extracts the eigenvector matrix. The processor calculates each component in the matrix and multiplies it by the square root of the corresponding eigenvalue in the eigenvalue diagonal matrix to obtain a fixed set of constant terms, i.e., deterministic expansion coefficients. Specifically, for the k-th eigenvalue and the k-th eigenvector, the processor calculates... ; For the k-th feature vector at the corresponding time node The component value at that location.

[0036] The processor uses this set of deterministic expansion coefficients to perform a Karhunen–Loève expansion on the time-varying stochastic process. After expansion, the time-varying stochastic process can be performed at any discrete time point. The value at this location is represented as: (w) in, For a random process at time t The value of ; For a random process at time t The mean; These are independent random variables that follow a standard normal distribution. The number of features to be truncated and retained is predetermined by the processor based on a threshold for the energy percentage of each feature (typically, the first M features are retained, ensuring their cumulative energy percentage exceeds a preset ratio, such as 99%). The processor will then... All data is aggregated and cached in memory.

[0037] S203. Based on the initial design variables, initial random variables, and deterministic expansion coefficients, sample generation and cluster screening are performed on the target reliability hypersphere to construct an inner loop surrogate model.

[0038] One possible approach is to generate candidate samples based on initial design variables, initial random variables, and deterministic expansion coefficients; project the candidate samples onto the target reliability hypersphere to obtain hypersphere sample points; perform K-means clustering on the hypersphere sample points to determine initial sampling points; and construct an inner loop surrogate model based on the initial sampling points and deterministic expansion coefficients.

[0039] Candidate samples are a set of sample points randomly generated by the processor in standard normal space according to the joint probability density function of multidimensional independent standard normal random variables. For example, in the optimization problem of a two-bar structure, the candidate samples include the diameter of bar 1, the diameter of bar 2, the strength of both bars, the length of both bars, and the standard normal random variable controlling the random process of the external load. Hyperspherical sample points are sample points obtained by the processor stretching or compressing the candidate samples radially from the origin of the standard normal space, projecting them onto a hypersphere with a radius equal to the target reliability index. K-means clustering is a grouping operation performed by the processor on the hyperspherical sample points, dividing samples that are close in distance into the same group. The initial sampling points are the center points of each group output by K-means clustering. The processor uses these points to call the real function to calculate the response, serving as the raw data for training the inner loop surrogate model. The inner loop surrogate model is a Kriging model trained by the processor based on initial sampling points and deterministic expansion coefficients. It is used in SORA (Sequential Optimization and Reliability Assessment) inner loop to quickly predict the constraint response of each sample point, reducing the number of calls to the real black-box model. The Kriging surrogate model is an interpolation model based on a Gaussian process, which can simultaneously provide the mean and standard deviation of the predicted values ​​to achieve reliability analysis.

[0040] For example, during the cold start phase of the processor's loop within the SORA framework, uniform sampling and K-means clustering on the target reliability hypersphere yield a basic training set covering the critical region of the failure boundary with the fewest initial sample points, thus constructing the initial inner loop surrogate model for subsequent active learning search. Based on the initial design variables, initial random variables, and the standard normal random variable controlling the time-varying stochastic process, the processor randomly generates a large number of candidate samples in the standard normal space according to the joint probability density function of the multidimensional independent standard normal random variables. Each candidate sample is composed of the design variables, initial random variables, and the standard normal random variable controlling the time-varying stochastic process. For a standard normal space of dimension n, its joint probability density function... for:

[0041] Where U is an n-dimensional standard normal random vector with components U1, U2, ..., U nEach component independently follows a standard normal distribution N(0,1); u is the value / sample point of the random vector U (a definite vector); k is the traversal index; u k It is the k-th scalar component of vector u.

[0042] After candidate samples are generated, the processor projects each candidate sample radially from the origin of the standard normal space, ensuring it falls on a hypersphere with a radius equal to the target reliability index. Let the coordinate vector of the candidate sample in the standard normal space be... Its module length is The target reliability index is Then the coordinates of the projected hyperspherical sample points for:

[0043] The projected sample points satisfy This means that all hyperspherical sample points lie on the target reliability hypersphere. This projection operation ensures that all candidate samples are constrained to a radius of [missing information]. On the hypersphere, the initial sampling points are focused on the equiprobability density sphere with the largest joint probability density function value.

[0044] The processor performs K-means clustering on all sample points projected onto the target reliability hypersphere. K-means clustering is an unsupervised learning algorithm whose goal is to divide the N sample points on the hypersphere into K clusters (K is a preset number of clusters), such that the distance between sample points within the same cluster is minimized, while the distance between sample points in different clusters is maximized. For the j-th cluster... Its cluster center Determined by minimizing the sum of squares within the cluster:

[0045] In other words, the cluster center of each cluster is the mean vector of all sample points within that cluster. The processor iteratively optimizes the objective function described above, eventually converging to obtain K cluster centers. After clustering, the processor extracts the cluster centers of each cluster as initial sampling points. Because K-means clustering uniformly groups sample points on the hypersphere, the cluster centers of each group exhibit a uniform distribution on the hypersphere, thus ensuring that the initial sample points are evenly distributed on the hypersphere. This avoids the problem of sample clustering leading to overfitting in local areas and insufficient accuracy in other areas by the surrogate model.

[0046] If the number of samples in the global shared physical sample pool is lower than the set minimum threshold (e.g., 15), the processor executes the above sample generation, projection, and clustering filtering process; otherwise, it can directly reuse existing historical samples in the global shared physical sample pool to avoid repeatedly calling the real function.

[0047] After determining the initial sampling points, the processor uses pre-calculated deterministic expansion coefficients to reconstruct the standard normal random variables controlling the time-varying stochastic process in the initial sampling points into time-varying load characteristics with clear physical meaning. Specifically, for the k-th standard normal random variable... The processor compares it with the corresponding deterministic expansion coefficients. Multiply and sum, then add the mean function. This allows you to obtain any time point. Time-varying physical load values ​​at:

[0048] Wherein F(t) i ) represents the reconstructed time-varying physical load at time 10:00. eigenvalues; It is a time-varying random process at time t. The corresponding mean function output value.

[0049] After reconstruction, the processor assembles the design variables from the initial sampling points, other random variables (excluding standard normal random variables that have been replaced by load features), the reconstructed time-varying physical load features, and the time nodes into a dimensionality-reduced training set. This training set removes redundant standard normal variables of the stochastic process from the original high-dimensional space and replaces them with low-dimensional physical load features, thereby effectively reducing the dimensionality of the training set.

[0050] Finally, the processor uses this dimensionality-reduced training set to fit a Kriging surrogate model, which serves as the inner loop surrogate model. The Kriging model is a Gaussian process-based interpolation model that can simultaneously provide the mean response of the predicted points. and the predicted standard deviation .

[0051] In the two-bar structure optimization problem, the processor reads the initial design values ​​of the diameters of bar 1 and bar 2, as well as the distribution parameters of the strength and length of the two bars. Combining this with the deterministic expansion coefficients of the external load stochastic process, candidate samples are randomly generated in the standard normal space. These candidate samples are projected onto the target reliability hypersphere, and 15 initial sampling points are extracted using K-means clustering. The standard normal random variables in each initial sampling point are reconstructed into external load values ​​at each time point using the deterministic expansion coefficient matrix. The design variables, random variables, time-varying physical loads, and time points are assembled into an inner loop training set to train the Kriging surrogate model.

[0052] S204. Active search is performed using the inner loop surrogate model and the expected improvement function to obtain the final time-varying minimum function metric point and the most dangerous time node.

[0053] One possible approach is to use an inner loop surrogate model, in which the expected improvement function value of the candidate samples is calculated in the inner loop; the sample point with the largest expected improvement function value is selected as the current time-varying minimum function metric point, and this sample point is fixed to traverse all discrete time nodes to determine the most dangerous time node; the sampling and model update operations are repeated until the maximum value of the expected improvement function is less than the inner convergence threshold, so as to obtain the final time-varying minimum function metric point and the most dangerous time node.

[0054] The expected improvement function is a function used by the processor to measure the potential for improvement of the model's predicted values ​​at candidate sample points relative to the current known best values. This function comprehensively considers the magnitude of the predicted values ​​and prediction uncertainty, striking a balance between utilizing known optimal solutions and exploring unknown regions. The processor calculates the expected improvement function value for candidate samples according to the following formula:

[0055] in, This represents the minimum true response value for this constraint within the current globally shared physical sample pool. Let be the mean of the predicted response of the inner loop surrogate model at candidate sample u, and s(u) be the corresponding prediction standard deviation. The cumulative distribution function of the standard normal distribution; It is the probability density function of the standard normal distribution. EIF represents the improvement in prediction of the candidate point relative to the current optimal solution, while s(u) reflects the uncertainty of the prediction. When the prediction uncertainty of a certain region is large, the EIF may still be large even if the predicted response value is not small enough, thus guiding the processor to explore that region.

[0056] Candidate samples are sample points generated by the processor in the standard normal space according to the joint probability density function of multidimensional independent standard normal random variables, used for active search. The candidate sample pool consists of two types of samples: one is a globally random exploration sample, used for broad searching throughout the entire design space; the other is a locally concentrated sample based on the previous generation's time-variant minimum performance target point (tMPTP), used for refined searching near the known optimal solution. For example, in the two-bar structure optimization problem, the candidate sample pool consists of 20% globally random exploration samples and 80% local samples based on the previous generation's time-variant minimum performance target point (tMPTP). The processor projects all candidate samples onto a hypersphere with a radius equal to the target reliability index to ensure that the search range is constrained to the target reliability hypersphere. For example, this candidate sample pool consists of two types of samples: (1) Global random exploration samples: randomly generated within the entire standard normal space, used for extensive search in the entire design space to avoid getting trapped in local optima; (2) Local concentrated samples: Based on the time-varying minimum function metric point obtained in the previous iteration (i.e. the previous generation tMPTP point), samples are concentrated in its vicinity to perform a refined search near the known optimal solution.

[0057] The ratio of the two types of samples is determined by the processor according to a preset strategy. After the candidate samples are generated, the processor projects all candidate samples onto a hypersphere with a radius equal to the target reliability index, so that all candidate samples fall on the target reliability hypersphere, thereby constraining the search range to the equiprobability density sphere where failure is most likely to occur.

[0058] The expected improvement function (EIF) value is calculated by the processor after substituting the candidate samples into the EIF. The larger the value, the greater the probability that the candidate sample point will obtain a smaller response value than the currently known optimal value. The processor calculates the EIF value of all candidate samples in the candidate sample pool and selects the candidate sample with the largest value as the optimal spatial perturbation point.

[0059] The most critical time point is determined by using an inner loop surrogate model to predict the response value along the discretized global time axis after fixing the spatial coordinates of the optimal spatial perturbation point. The time point with the smallest predicted response value is then selected. This time point represents the moment when the structure is most likely to fail under the current spatial perturbation point.

[0060] The time-varying minimum function metric (EIF) is the optimal spatial perturbation point ultimately determined by the processor during its active search within the inner loop. The processor iteratively executes the process of "calculating the EIF value → selecting the optimal spatial perturbation point → determining the most dangerous time node → calling the real function for evaluation → updating the globally shared physical sample pool." When the maximum EIF value is less than the inner convergence threshold, the iteration stops, and the current optimal spatial perturbation point is determined as the time-varying minimum function metric.

[0061] The inner convergence threshold is a tolerance parameter pre-set by the processor to determine whether the inner loop's active search has converged. When the maximum EIF value in the candidate sample pool is less than this threshold, it indicates that continuing to add sample points has little contribution to improving the accuracy of the surrogate model, and the processor stops the inner loop iteration.

[0062] For example, in the inner loop of the SORA framework, the most valuable new sample points are adaptively selected through an active learning strategy driven by the expected improvement function (EIF), and the time-varying minimum function metric point (tMPTP) and its corresponding most dangerous time node are accurately searched at the current design point with the fewest real function calls.

[0063] The processor constructs a mixed candidate sample pool using the joint probability density function of multidimensional independent standard normal random variables within the standard normal space.

[0064] In the two-bar structure optimization problem, the candidate sample pool consists of 20% globally random exploration samples and 80% locally concentrated samples based on the previous generation tMPTP points.

[0065] The processor uses an inner-loop surrogate model (Kriging model) to predict the mean response of each candidate sample in the candidate sample pool. And the prediction standard deviation s(u). Here, the response mean represents the predicted value of the function at that point, and the prediction standard deviation reflects the degree of uncertainty in the prediction at that point.

[0066] The processor calculates the EIF value for each candidate sample according to the formula of the Expected Improvement Function (EIF). The EIF function comprehensively considers the magnitude of the predicted value and the prediction uncertainty, achieving a balance between utilizing known optimal solutions (development) and exploring unknown regions (exploration). After calculating the EIF values ​​of all candidate samples in the candidate sample pool, the processor selects the candidate sample with the largest EIF value as the optimal spatial perturbation point for the current step. This point may be a point with a small predicted response value that is expected to surpass the current optimal solution, or a point with high prediction uncertainty and high exploration value, reflecting the EIF function's ability to balance development and exploration. After selecting the optimal spatial perturbation point, the processor fixes the spatial coordinates of the optimal spatial perturbation point (i.e., the coordinates of all design variables and random variables remain unchanged) and only performs a traversal scan along the discretized global time axis. The processor uses an inner loop surrogate model to predict the constraint response value of the spatial perturbation point at each discrete time node, finds the time node that minimizes the predicted response value, and records it as the most dangerous time node. This time point indicates the moment when the structure is most likely to fail under the current spatial disturbance condition.

[0067] After determining the most critical time point, the processor combines the selected optimal spatial perturbation point with the most critical time point to form a complete evaluation point. Then, it calls the real system function to accurately calculate this evaluation point and obtain the true response value. This true response value is unaffected by the prediction error of the surrogate model and is key to improving the accuracy of the surrogate model.

[0068] After the evaluation is completed, the processor will update the new sample point and its corresponding real response value to the global shared physical sample pool, so that the global shared physical sample pool will be continuously enriched.

[0069] The processor repeats the above steps, that is, iteratively executes the complete process of "building a mixed candidate sample pool, calculating the EIF value, selecting the best spatial perturbation point, determining the most critical time node, calling the real function for evaluation, and updating the sample pool". In each iteration, the processor retrains the inner loop surrogate model using the updated globally shared physical sample pool, so that the surrogate model gradually approaches the real failure boundary after each iteration. At the same time, the newly added real evaluation sample points in each iteration are the most valuable sample points adaptively selected by the EIF criterion, thereby achieving the highest surrogate model accuracy improvement with the fewest real function calls.

[0070] When the maximum EIF value calculated by the processor is less than the preset inner-layer convergence threshold, it indicates that there are no candidate points with significant improvement potential in the candidate sample pool, and further increasing the sample points has little contribution to improving the accuracy of the surrogate model, so the inner loop iteration stops. At this time, the processor takes the currently obtained best spatial perturbation point as the time-varying minimum function metric point (tMPTP) under the current design variables, outputs the corresponding most dangerous time node, and constructs the offset vector required for subsequent outer loop deterministic optimization.

[0071] In the two-bar structure optimization problem, the processor uses an inner loop Kriging surrogate model to calculate the EIF value of candidate samples on the hypersphere. The point with the largest EIF is selected as the optimal spatial perturbation point. After fixing this point, the predicted response value is scanned along 501 discrete time nodes, and the moment with the smallest response value is identified as the most critical time node. The actual two-bar structure function is called to evaluate this combination and update the sample pool. This process is repeated until the maximum EIF value is less than the threshold, obtaining the tMPTP point under the current design variables and its corresponding most critical time node.

[0072] S205. Construct an offset vector based on the time-varying minimum function metric point.

[0073] The offset vector is a vector constructed by the processor based on the coordinates of the time-varying minimum function metric point along the design variable dimension. This vector represents the direction from the current design variable to the current minimum function metric point, and is used to quantify the distance that the probabilistic constraints under the current design variables need to be translated in the deterministic design space. The processor uses the offset vector as an input parameter for deterministic optimization, transforming probabilistic constraints into deterministic constraints.

[0074] For example, the coordinate information of the design variable dimension is extracted from the time-varying minimum function metric point (tMPTP) obtained by active search in the inner loop, and it is transformed into the offset vector used for translating probability constraints in the outer loop of the SORA framework, thereby transforming the original time-varying reliability constraints into deterministic constraints in the deterministic design space.

[0075] The processor obtains the time-varying minimum function metric point (tMPTP) output after the inner loop converges in step S204. This tMPTP is located in the standard normal space and is a complete n-dimensional vector, with each dimension's coordinates corresponding to the design variable, random variable, and standard normal random variable controlling the time-varying stochastic process in the standard normal space, respectively.

[0076] The processor extracts only the coordinate components belonging to the design variables from the tMPTP. Assume there are n coordinate components in the time-varying reliability design optimization problem. d If there are n design variables, the processor will extract the corresponding n from tMPTP. d The coordinate values ​​of each design variable dimension form a vector. :

[0077] in, This represents the standard normal coordinate value of tMPTP in the k-th design variable dimension.

[0078] Since tMPTP lies in a standard normal space, its coordinates in each dimension are dimensionless standard normal variable values, while design variables in engineering practice have specific physical dimensions (such as length in meters, diameter in millimeters, etc.). Therefore, the processor needs to convert the extracted standard normal coordinate values ​​into offsets with physical dimensions.

[0079] The processor obtains the standard deviations corresponding to each design variable, which were acquired as input parameters during the initialization phase of step S201. Subsequently, the processor multiplies the standard normal coordinates of each design variable dimension in tMPTP by the corresponding standard deviation of the design variable to obtain the actual offset of that design variable in the deterministic design space.

[0080] in, This is the offset component corresponding to the k-th design variable; Let be the standard deviation of the k-th design variable (k=1,2,...,nd).

[0081] The processor assembles the offset components of all design variable dimensions into a complete vector, namely the offset vector. This operation transforms dimensionless coordinate values ​​in standard normal space into offsets with actual physical dimensions, enabling the offset vectors to be directly used for constraint translation in subsequent deterministic optimization problems.

[0082] After the offset vector is constructed, the processor temporarily stores it in memory as the output parameter of the current SORA outer loop iteration step. The processor will use this offset vector to equivalently translate the time-varying reliability constraints to the deterministic design space, transforming the original probabilistic constraints... Transform into deterministic constraints:

[0083] The design variables are shifted by an offset vector s towards the safety domain, such that when the shifted design variables are used for evaluation in deterministic optimization, the optimal solution corresponds exactly to the design point where the original probabilistic constraints meet the target reliability requirements.

[0084] The magnitude of the offset vector (the absolute value of each component) reflects the distance that needs to be translated in each dimension of the design variable, and reflects the difference in the degree of influence of each design variable on time-varying reliability.

[0085] In the two-bar structure optimization problem, the design variables are the diameters of bar 1 and bar 2, for a total of two design variables. The processor extracts the coordinate values ​​of the first two dimensions from tMPTP. and Multiply by the standard deviation of the corresponding design variable (both are 0.001) to obtain the two-dimensional offset vector. The extraction and calculation process described above is performed independently for each of the two constraints in this example to obtain their respective offsets, which can be used for the equivalent translation of the constraints in subsequent deterministic optimization.

[0086] S206. Construct a global proxy model based on a global sample library consisting of initial design variables, initial random variables, deterministic expansion coefficients, and the most dangerous time nodes.

[0087] The global proxy model is a Kriging model trained by the processor by integrating all historical evaluation samples, used for fast prediction of constraint safety margins in the outer loop.

[0088] For example, all historical simulation evaluation data stored in the globally shared physical sample pool are integrated to construct a global Kriging surrogate model covering the entire design domain and the entire discrete time interval; the global Kriging surrogate model is used to quickly solve the constraint response prediction values ​​corresponding to each design point in the outer loop stage, and output the prediction mean and prediction standard deviation.

[0089] The processor retrieves the globally shared physical sample pool. This pool stores all sample points generated by the active optimization phase of each iteration of the SORA framework, along with the corresponding real constraint response values. The processor iterates through all records stored within the globally shared physical sample pool, filtering for all valid historical evaluation records that match the current target constraint. Each valid historical evaluation record stores five types of data: design variable values, random variable values, standard normal random variables controlling time-varying stochastic processes, discrete-time node indices, and the output response value of the real system function. As the number of SORA main loop iterations increases, the data coverage of the globally shared physical sample pool continuously expands.

[0090] It should be noted that the offset vector is not involved in the construction of the global proxy model training set in this step; the offset vector is a fixed algorithm parameter of the SORA framework. After the processor receives the offset vector, it is stored in the temporary memory cache and used to complete the translation operation of time-varying reliability constraints to the deterministic design space; the global proxy model training dataset only loads the physical simulation evaluation data and corresponding real response labels in the globally shared physical sample pool.

[0091] The processor reads the deterministic expansion coefficients; for each filtered historical evaluation record, the processor transforms the implicit standard normal random variables representing the time-varying stochastic process within the record into time-varying physical load characteristic quantities with physical meaning. For each historical sample record, the processor extracts the standard normal random variables controlling the time-varying stochastic process. , and the corresponding time points The physical load value (i.e., feature value) at that time node is calculated according to the Karhunen–Loève expansion formula. Through the reduction operation, the implicit standard normal random variables without physical interpretation in the original sample are removed and replaced with time-varying load physical features that can be directly used for training, thus simultaneously compressing the feature dimension of the training set and clarifying the physical meaning of the features.

[0092] After restoring the time-varying physical load features, the processor reassembles the valid information from each historical evaluation data point into a complete training sample. Each training sample includes: design variables (structural dimensional parameters to be adjusted during optimization, such as member diameter), random variables (physical parameters affected by uncertainties, such as material strength and geometric dimensions), reconstructed time-varying physical load features (the specific values ​​of the time-varying load at the corresponding time node, restored by deterministic expansion coefficients), time node (the time index value corresponding to the sample, the node position on the discretized time axis), and true response value (the constraint response value calculated by calling the actual system function, used as the training label).

[0093] The processor integrates all training samples corresponding to historical evaluation data to form a global feature training set. This training set covers all design regions and time ranges visited during the SORA iteration process and contains rich failure boundary information. The processor uses the assembled global feature training set to fit a Kriging surrogate model, resulting in the global surrogate model after training. The Kriging model is a Gaussian process-based interpolation model that can simultaneously provide the mean response at the predicted points. and the predicted standard deviation .

[0094] In the two-bar structure optimization problem, the processor extracts all valid historical evaluation data updated for the target constraint from the globally shared physical sample pool, including the diameter of bar 1, the diameter of bar 2, the strength of both bars, the length of both bars, and the restored physical load characteristics (the specific values ​​of the external load over time). These data, along with time node values ​​and actual response values, are assembled into a global training set containing global failure characteristics. This training set is then used to fit a Kriging model to obtain an outer-loop global surrogate model.

[0095] S207. Based on the global proxy model, calculate the current design variables, current random parameters, and the most dangerous time node to obtain the predicted safety margin; compare the predicted safety margin with the preset threshold to obtain the active constraints.

[0096] The predicted safety margin is the predicted value of the time-varying limit function, representing the extra safety margin of the structure from the failure boundary under this operating condition; the preset threshold is a pre-given critical safety margin value, which is converted from the target reliability index and is the criterion for distinguishing whether a constraint is active, and is a fixed constant; active constraints are tight constraints that limit further improvement of optimization objectives (such as lightweighting and cost minimization). When the predicted safety margin is less than or equal to the preset threshold, the corresponding time-varying reliability constraint is determined to be an active constraint.

[0097] For example, in the outer loop of the SORA framework, a global surrogate model is used to quickly evaluate the safety margin of each probabilistic constraint at the current design point, and a threshold comparison mechanism is used to dynamically identify active constraints with failure risk. This allows for the subsequent construction of local high-precision surrogate models only for active constraints, concentrating limited computational resources on critical areas. The processor obtains the current design variable d. (k) (Design point of the kth outer loop iteration), current random parameters (distribution parameters of the random variable, such as mean μ) X ) and the most dangerous time point t min This information is then combined into a complete prediction input point.

[0098] The processor substitutes the predicted input point into the trained global Kriging surrogate model and uses the predictive power of the Kriging model to calculate the constraint response at that point. The Kriging model can simultaneously output two key statistics: Response mean This characterizes the central trend of the predicted value of the function at the design point; Predicted standard deviation The standard deviation represents the degree of uncertainty in the predicted value and reflects the confidence level of the surrogate model at that point. A larger standard deviation indicates sparser historical samples in the region and lower reliability of the prediction.

[0099] Substituting the current design variables, random parameters, and the most critical time point into the global Kriging surrogate model, we obtain the mean response and the predicted standard deviation. Introducing an error tolerance value ξ=0.001, we calculate the predicted safety margin Q:

[0100] The processor compares the calculated predicted safety margin Q with a preset threshold (e.g., ε=2.75) to ensure that the probability of correctly predicting the constraint as an inactive constraint is greater than or equal to 99.7%. Based on the comparison results, constraints are divided into two categories: active constraints and inactive constraints. Inactive constraints: If Q is greater than or equal to ε, meaning the predicted safety margin at the current design point is greater than a preset threshold, it indicates that the predicted response value of the current design variable is at a sufficient safe distance from the failure boundary (g=0), and this constraint does not pose a failure risk at the current design point. For such constraints, the processor determines them to be inactive constraints and directly reuses the global Kriging surrogate model as the evaluation function for this constraint in subsequent deterministic optimization, without the need to construct an additional local surrogate model.

[0101] Active constraints: If Q is less than ε, meaning the predicted safety margin at the current design point is less than or equal to a preset threshold, it indicates that the predicted response value of the current design variable is close to the failure boundary, or may have already entered the failure region. For such constraints, the processor determines them as active constraints, posing a failure risk. A local concentrated region needs to be defined for them, and a local high-precision surrogate model needs to be constructed to ensure the accuracy of the assessment of this dangerous region during the optimization process.

[0102] The processor uses the above determination results as the output parameters of the current outer loop iteration step: marking each constraint as "active" or "inactive". Active constraints will be evaluated using a local high-precision surrogate model, while inactive constraints will be evaluated using a global surrogate model. This significantly reduces the cost of expensive real function calls required for global high-precision modeling while ensuring the accuracy of dangerous areas.

[0103] In the two-bar structure optimization problem, the processor substitutes the current design variables, random parameters, and the most critical time node into the global Kriging surrogate model to calculate the predicted safety margin of each of the two time-varying constraints. By comparing the predicted safety margin with a preset threshold, the processor identifies that both constraints in the current iteration step are active constraints, and a local high-precision surrogate model needs to be constructed for each.

[0104] S208. Based on the time-varying minimum function metric point, delineate a local concentrated region for the active constraints; construct a local proxy model within the local concentrated region using the expected feasibility function.

[0105] The process of constructing a local proxy model can be as follows: generate local candidate samples in a local concentrated region; calculate the expected feasibility function value of each local candidate sample based on the initial local proxy model; select the local candidate sample with the largest expected feasibility function value as the new real evaluation sample; update the initial local proxy model based on the new real evaluation sample to complete the construction of the local proxy model.

[0106] A local surrogate model is a surrogate model constructed only within a localized, concentrated region defined by tMPTP, used to accurately characterize the variation of the limit function within that small region, unlike the global Kriging surrogate model which covers the entire design space. Local candidate samples are a batch of candidate sample points generated according to preset sampling rules within the localized, concentrated region defined by tMPTP. These samples focus on the area surrounding the known optimal solution and do not need to cover the entire design space. New real evaluation samples are selected from all local candidate samples, choosing the sample points with the largest expected feasibility function value and the highest optimization information gain. High-precision real structural simulations / numerical calculations are performed on these samples to obtain the real functional response results. This set of real data is then used to iteratively optimize the initial local surrogate model, improving the model's prediction accuracy in key areas. This is the core incremental data for the iterative update of the local surrogate model.

[0107] For example, the processor obtains the time-varying minimum function metric point (tMPTP) output after the inner loop converges, as well as the prediction center point (i.e., the design point of the current outer loop iteration). For each active constraint, the processor delineates a local concentrated region boundary in standard normal space centered on the prediction center point.

[0108] The method for delineating the boundary of a localized concentrated area is as follows: based on the predicted center point. Centered on this, upper and lower boundary ranges are defined for each design variable dimension by combining the coefficients with the corresponding standard deviations:

[0109]

[0110] in, Let be the coordinates of the time-varying minimum function metric point in the i-th dimension of the X-space, i=1,2,... ; σ is the target reliability index. i n is the standard deviation corresponding to the i-th design variable; d The total number of design variables (the local concentrated region is defined only for the design variable dimension; the mean of other random variable dimensions is frozen when constructing the local proxy model to reduce the local model dimension).

[0111] The selection of this range is based on the following criteria: taking the time-varying minimum functional metric point as the core, accurately surrounding the most dangerous area near the failure boundary, while effectively controlling the size of the local candidate sample pool and avoiding the introduction of redundant sample points far from the failure boundary.

[0112] After defining the boundaries of the local concentrated region, the processor selects historical sample points from the globally shared physical sample pool that fall entirely within the boundaries of this local concentrated region. During the selection process, the processor also requires that other high-dimensional physical features of these historical sample points (such as random variables, time-varying load features, etc.) match the corresponding features in the tMPTP obtained from the inner loop to ensure the physical consistency of the local proxy model.

[0113] If the number of available historical sample points selected is insufficient to meet the preset minimum number of modeling samples, the processor employs a sampling strategy based on low-bias candidate points to supplement the initial samples within a local concentrated region. In this embodiment, the processor uses the Sobol low-bias sequence to perform adaptive truncated supplementary sampling within the boundary of the two-dimensional local concentrated region, and calculates the response values ​​of these supplementary sample points by calling the real system function to complete the basic training sample set.

[0114] The processor utilizes selected historical sample points and newly sampled supplementary sample points to construct an initial local Kriging surrogate model in the dimensionality-reduced local space. This local surrogate model uses only design variables as input dimensions (e.g., 2-dimensional: diameter of rod 1 and diameter of rod 2), while other random variables and time-varying load features are frozen according to their corresponding values ​​in tMPTP, thereby significantly reducing the input dimensionality of the surrogate model and improving modeling efficiency and prediction accuracy.

[0115] Within the boundary of the localized region of concentration, the processor uniformly generates a local candidate sample pool of size Nlocal using a low-bias sampling sequence (such as a Sobol sequence). Compared to random sampling, low-bias sequences offer better spatial filling uniformity, ensuring a uniform distribution of candidate samples within the local region and preventing sample clustering that could lead to the omission of key areas during active learning. In this embodiment, the processor uses a Sobol low-bias sequence to generate the local candidate sample pool.

[0116] The processor uses a local Kriging surrogate model to predict the mean response of each candidate sample in the local candidate pool. The predicted standard deviation s(u) is calculated, and the EFF value for each candidate sample is calculated according to the formula of the expected feasibility function (EFF). The EFF function is a sampling criterion in the field of active learning specifically used to search for failure boundaries (i.e., the limit state surface where g=0). It can guide the processor to focus sampling near the failure boundary, achieving high-precision fitting of local boundaries.

[0117] The formula for calculating the expected feasibility function is:

[0118] in, This represents the mean predicted response of the local Kriging surrogate model at candidate sample v; The standard deviation of the predictions of the local Kriging surrogate model at candidate sample v; Take the tolerance band half-width of the target feasibility area as an example. Φ is used to define the "gray area" near the failure boundary; 0 is the limit state boundary value (i.e., the failure boundary where the function g=0); Φ( φ( is the cumulative distribution function of the standard normal distribution); ) is the probability density function of the standard normal distribution.

[0119] The physical meaning of the EFF function is that the quantized candidate sample points fall into a region centered on the failure boundary with a width of [missing information]. The expected probability within the tolerance band. The larger the EFF value of a candidate point, the closer its response value is to the failure boundary (g=0), meaning it is more likely to be located on the limit state surface. Therefore, selecting the sample point with the largest EFF value for real evaluation can most effectively improve the fitting accuracy of the local surrogate model at the failure boundary.

[0120] The processor selects the candidate sample with the largest EFF value from the local candidate sample pool as the current optimal location for adding a new sample. Then, it calls the real system function to accurately evaluate this location and obtain the true response value. After the evaluation, the processor simultaneously updates the new sample point (including its complete local coordinates and true response value) to both databases. Local feature library: used for retraining the local proxy model in the next round; Globally shared physical sample pool: This ensures that the global agent model can also benefit from the results of local active learning, achieving the sharing and fusion of global and local information.

[0121] The processor retrains the local Kriging surrogate model using the updated local sample set, so that the model gradually approaches the real failure boundary after each iteration.

[0122] The processor repeats the above steps, i.e., iteratively executes the complete process of "generating local candidate samples, calculating EFF values, selecting the point with the maximum EFF, calling the real function for evaluation, and updating the local surrogate model," until the calculated maximum EFF value is less than the preset local convergence tolerance threshold of the outer loop. This indicates that there are no candidate points with significant improvement potential near the local failure boundary, the accuracy of the local surrogate model meets engineering requirements, and the active learning process stops. At this point, the processor outputs a high-precision local high-precision Kriging surrogate model as a dedicated evaluation function for this active constraint in deterministic optimization. This local model has high accuracy only in the local concentrated region of the active constraint, but its fitting accuracy for the failure boundary of the dangerous region is far superior to the global surrogate model, making it a crucial step in ensuring the accuracy of time-varying reliability design optimization.

[0123] In the two-bar structure optimization problem, the processor executes the aforementioned local surrogate model construction process for each of the two active constraints. A two-dimensional local concentrated region is delineated centered on the prediction center point. Historical samples falling into this region are selected from the globally shared physical sample pool, supplemented with Sobol sequences if insufficient. EFF-driven active learning is used to accurately fit the failure boundary within the local region, ultimately outputting two high-precision two-dimensional local Kriging surrogate models.

[0124] S209. Based on the offset vector, the time-varying reliability constraint is transformed into a deterministic constraint, and based on the local surrogate model, a deterministic optimization problem under deterministic constraints is constructed.

[0125] One possible approach is to translate the time-varying reliability constraints to the deterministic design space based on the offset vector, thereby obtaining the translated deterministic constraints; and to construct a deterministic optimization problem within the deterministic design space by using the translated deterministic constraints as constraints, the initial design variables as optimization variables, and the minimization objective function as the optimization objective.

[0126] The translated deterministic constraints are based on the design variable dimension offset vector extracted from the time-varying minimum functional metric point (tMPTP). The deterministic optimization problem uses physical design variables as the only optimization variables, translated deterministic constraints as all constraint boundaries, and minimizing pre-defined objective functions such as structural cost / mass as the optimization objective. It employs a global surrogate model to evaluate inactive constraints and a local surrogate model to evaluate active constraints with high precision, establishing a conventional numerical optimization model that does not contain random variables and does not consider time-varying failure risks.

[0127] For example, the processor obtains the offset vectors corresponding to each constraint. (where subscript) This represents the constraint number, with the superscript m indicating the m-th outer loop iteration. Based on the decoupling principle of the SORA framework, the processor will convert the original constraint number into a constraint number. One time-varying probability constraint:

[0128] This is equivalent to transforming the design variables into translated deterministic constraints in a deterministic design space. The transformation involves shifting the design variables towards the safety region by an offset vector. This ensures that when evaluating deterministic optimization using the shifted design variables, the optimal solution is equivalent to the original probabilistic constraints satisfying the target reliability requirement. The expression for the shifted deterministic constraints is:

[0129] Where d is the design variable vector (to be optimized and solved) in deterministic optimization; For the first The offset vector corresponding to each constraint in the m-th outer loop iteration, each component of which is equal to the coordinate value of the corresponding design variable dimension in the time-varying minimum function metric point (tMPTP) of that constraint multiplied by the standard deviation of the design variable; μ X This is the mean vector of the random variables (in deterministic optimization, the random variables are taken as their mean, and their distribution dispersion is no longer considered). For the first For each constraint, the most dangerous time node is the time node at which deterministic optimization evaluates the constraint only, rather than traversing the entire time axis. The inequality direction is ≥0, which means that the function value at the translated design variable must be greater than or equal to zero, that is, the safety requirement is met.

[0130] The essence of this translation operation is to quantify the "design point offset" caused by the uncertainty of random variables and random processes in reliability assessment into a fixed offset vector, thereby transforming the complex probabilistic constraints into the same deterministic inequality constraint form as in conventional deterministic optimization.

[0131] Based on the results of the active constraint identification (each constraint is marked as "active" or "inactive"), the processor assigns a corresponding surrogate model as its evaluation function g in deterministic optimization for each constraint. j ( ): For inactive constraints: the processor determines that the constraint is far from the failure boundary at the current design point and poses no risk of failure. Therefore, a global surrogate model is used as the evaluation function for this constraint. The global surrogate model covers the entire design domain and can quickly predict the response value of the constraint across the entire domain without requiring additional calls to the actual function.

[0132] For active constraints: The processor determines that this constraint is close to the failure boundary at the current design point, posing a risk of failure and requiring high-precision failure boundary fitting. Therefore, a local high-precision surrogate model is used as the evaluation function for this constraint. While the local surrogate model has high precision only within a local concentrated region, its failure boundary fitting accuracy for this hazardous region is far superior to the global surrogate model, ensuring the accuracy of active constraint evaluation during deterministic optimization.

[0133] By employing the above allocation strategy, the processor can fully utilize the rapid prediction capabilities of the global proxy model while ensuring the accuracy of active constraint evaluation, thus avoiding excessive consumption of computing resources in non-dangerous areas.

[0134] Within the deterministic design space, the processor uses the translated deterministic constraints. As constraints, the initial design variable d is used as the optimization variable, and the objective function f(d) is used as the optimization objective. A complete deterministic optimization problem is constructed, and its mathematical expression is:

[0135] Where f(d) is the objective function (such as economic indicators like the weight, cost, or volume of the structure, which are determined by the specific engineering problem); For the first The evaluation function actually used for each constraint in deterministic optimization, according to the above allocation results, takes the value of either a global surrogate model (inactive constraint) or a local high-precision surrogate model (active constraint). d represents the total number of constraints. L d is the lower bound for the design variable; U This is the lower bound of the design variable, determined by engineering design specifications or manufacturing process constraints.

[0136] In the optimization problem of a two-bar structure, the processor, based on the SORA principle, combines the offset vectors corresponding to the two constraints and the results of active constraints (both constraints are active in this example) to transform the complex probabilistic and stochastic process constraints into deterministic design variables through equivalent translation. The nonlinear inequality constraints. The deterministic optimization problem is specifically formulated as follows: [The following text appears to be incomplete and requires further context: "with the total weight of the two rods..."] The objective function is to minimize it, and the function is then translated. As constraints (both constraints are evaluated using the corresponding high-precision local Kriging surrogate model), and with 0.01≤d1 and d2≤0.25 as the design variable boundaries, a complete deterministic optimization problem is constructed.

[0137] S210. Solve the deterministic optimization problem to obtain the updated design variables; when the changes in the updated design variables and the previous design variables satisfy the convergence condition, output the current design variables as the target design scheme.

[0138] The target design scheme is the final combination of design variables obtained after multiple rounds of SORA outer loop iteration and SQP inner layer optimization iteration convergence.

[0139] For example, the core idea of ​​a deterministic optimization problem is to shift the design variables towards the safe region by translating the offset vector. This allows for the use of shifted design variables in deterministic optimization. When evaluating, the optimal solution corresponds exactly to the design point where the original probabilistic constraints meet the target reliability requirements.

[0140] The processor initializes the solution parameters for the Sequential Quadratic Programming (SQP) algorithm. The SQP algorithm is one of the most efficient numerical methods for solving nonlinear constrained optimization problems. Its basic idea is to transform the original nonlinear optimization problem into a series of quadratic programming (QP) subproblems by making a quadratic approximation of the Lagrangian function in each iteration, and then solve them step by step.

[0141] The specific operations of the processor include: The design point d of the current k-th iteration (m) As the starting point for optimization in the SQP algorithm; by As a constraint condition for nonlinear inequalities (n) c (to constrain the total number); In the design domain space [d L ,d U Within the scope of this function, the SQP algorithm is invoked to find the optimal solution that minimizes the objective function f(d).

[0142] The SQP algorithm approximates the optimal solution to the original problem by iteratively solving QP subproblems of the following form:

[0143] Among them, H m Let Δd be the approximation of the Hessian matrix of the Lagrange function (usually using the BFGS update formula), and let Δd be the change in design variables in the current iteration step. By continuously solving the QP subproblems and updating the design variables, the SQP algorithm can approximate the optimal solution of the original problem with a superlinear convergence speed.

[0144] After the SQP algorithm converges iteratively, the processor denotes the optimal solution as the updated (m+1)th design point d.(m+1) .

[0145] The processor calculates the norm of the change in design variables between two consecutive outer loop iterations and compares it with the preset global convergence tolerance ε. d A comparison was performed. The formula for calculating the norm of change is:

[0146] Where, Δd (m) d is the L2 norm of the change in the design variable during the m-th outer loop iteration; (m+1) The updated design variables obtained from the SQP solution in the current iteration step; d (m) n is the design variable for the previous outer loop iteration; d ε is the total number of design variables. d A global convergence tolerance threshold pre-set for the processor.

[0147] Based on the comparison results, the processor performs the following branch operations: If the convergence condition is met : Determine that the entire time-varying reliability design optimization process has converged, stop the outer loop iteration, and output the current d. (m+1) This is the optimal target design scheme that satisfies the target reliability index.

[0148] If the convergence condition is not met This indicates that the design point has not yet converged, and the processor updates the current design variable to d. (m+1) Then, take it as the new starting point for the next round of outer loop iteration, return to step S203 to continue the inner loop search (i.e., re-search for the time-varying minimum function metric point and the most dangerous time node under the new design point) until the convergence condition is met.

[0149] Once the convergence condition is met and the optimal design scheme is output, the processor can optionally use the Monte Carlo method to verify the optimization results. The processor uses the output optimal design variable d... With fixed parameters, large-scale random sampling is performed based on the probability distributions of each random variable and random process (typically with 10 samples). 5 10 6 (This is repeated several times). The actual time-varying reliability index is estimated by statistically analyzing the proportion of failed sample points to the total sample points. If the reliability index obtained by the Monte Carlo method test is not lower than the target reliability index... If the result is positive, it verifies that the optimal design meets the expected reliability requirements; otherwise, the parameters of the SORA algorithm (such as convergence tolerance, safety margin relaxation parameters, etc.) need to be adjusted and the optimization solution needs to be re-solved.

[0150] In the optimization problem of a two-bar structure, convergence was achieved after four outer loop iterations and 116 calls to the actual function. The design variables for the first iteration were [0.1889, 0.1797], the second [0.2110, 0.1918], the third [0.2157, 0.1931], and the fourth [0.2159, 0.1931]. The L2 norm of the change in design variables gradually decreased between iterations. After the fourth iteration, the change was less than the preset convergence tolerance ε. d When the optimization converges, the optimal design values ​​output are: rod 1 diameter 0.2159, rod 2 diameter 0.1931. Using 10... 6 The results were verified using a second Monte Carlo simulation. The reliability index for the first constraint function was 2.9777, and the reliability index for the second constraint function was 2.9694, both of which met the target reliability index. The requirement of 3.0 (which is very close to the target reliability requirement) proves the effectiveness of the method.

[0151] Based on the above, a time-varying reliability design optimization method integrating multi-strategy active learning and a time-varying sequence optimization reliability assessment framework is proposed. This method uses the Karhunen-Loève unfolding to decouple the time-varying stochastic process, transforming the uncertainty in the time dimension into a deterministic coefficient expression. Following this, the sequence optimization and reliability assessment process is executed step-by-step: First, hyperspherical samples are generated and clustered to construct an inner-loop surrogate model. The expected improvement function is used to search for the time-varying minimum functional metric point and the most dangerous time node. Then, a global surrogate model is built to distinguish between active and inactive constraints. For active constraints, a local concentrated region is defined, and the expected feasibility function is introduced to construct a local high-precision surrogate model within this region. Finally, the time-varying reliability constraints are transformed into deterministic constraints using offset vectors, thus completing the solution to the optimization problem. This application uses two evaluation functions to screen samples in stages: the inner loop uses EIF to lock the failure risk points, and the outer loop uses EFF to actively encrypt the dangerous areas. Only active constraints are built into local proxy models, which effectively reduces the number of calls to high-precision simulation. At the same time, it combines Karhunen-Loève expansion to simplify the calculation of time-varying stochastic processes, which reduces the overall computational burden. Finally, it ensures the prediction accuracy of key failure areas with limited computational cost, and improves the reliability and accuracy of optimization results under the premise of considering time parameters and stochastic processes.

[0152] The above text combined Figures 1 to 2 This application provides a detailed description of the time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework. The apparatus and equipment provided in this application will be described below with reference to the accompanying drawings.

[0153] This application also provides a time-varying reliability design optimization device that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework, such as... Figure 3 As shown in the figure, this is a structural diagram of a time-varying reliability design optimization device that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework provided in an embodiment of this application. The device includes: The acquisition module 301 is used to acquire initial design variables, initial random variables, time-varying random process parameters, and target reliability indicators; The calculation module 302 is used to expand the time-varying stochastic process according to the time-varying stochastic process parameters to obtain deterministic expansion coefficients; based on the initial design variables, initial random variables, and deterministic expansion coefficients, it performs sample generation and clustering screening on the target reliability hypersphere to construct an inner loop surrogate model; it uses the inner loop surrogate model and the expected improvement function to perform active search to obtain the final time-varying minimum functional measure point and the most dangerous time node; it constructs an offset vector based on the time-varying minimum functional measure point; it constructs a global surrogate model based on a global sample library composed of initial design variables, initial random variables, deterministic expansion coefficients, and the most dangerous time node; it calculates the predicted safety margin based on the global surrogate model for the current design variables, current random parameters, and the most dangerous time node; it compares the predicted safety margin with a preset threshold to obtain active constraints; it delineates local concentrated regions for active constraints based on the time-varying minimum functional measure point; and it constructs a local surrogate model within the local concentrated regions using the expected feasibility function. The optimization module 303 is used to transform time-varying reliability constraints into deterministic constraints based on the offset vector, and construct a deterministic optimization problem under deterministic constraints based on the local surrogate model; solve the deterministic optimization problem to obtain the updated design variables; when the changes in the updated design variables and the previous round of design variables satisfy the convergence condition, the current design variables are output as the target design scheme.

[0154] In some possible implementations, the calculation module 302 is specifically used to: generate candidate samples based on the initial design variables, initial random variables, and deterministic expansion coefficients; project the candidate samples onto the target reliability hypersphere to obtain hypersphere sample points; perform K-means clustering on the hypersphere sample points to determine the initial sampling points; and construct an inner loop surrogate model based on the initial sampling points and deterministic expansion coefficients.

[0155] In some possible implementations, the optimization module 303 is specifically used to: translate the time-varying reliability constraints to the deterministic design space according to the offset vector to obtain the translated deterministic constraints; and use the local surrogate model established after the active constraints are identified by the global surrogate model as the active constraint evaluation function to construct a deterministic optimization problem in the deterministic design space with the translated deterministic constraints as constraints, the initial design variables as optimization variables, and the minimization objective function as the optimization objective.

[0156] In some possible implementations, the calculation module 302 is specifically used to: employ an inner loop surrogate model to calculate the expected improvement function value of the candidate samples in the inner loop; select the sample point with the largest expected improvement function value as the current time-varying minimum function metric point, and fix this sample point to traverse all discrete time nodes to determine the most dangerous time node; repeat sampling and model update operations until the maximum value of the expected improvement function is less than the inner convergence threshold, to obtain the final time-varying minimum function metric point and the most dangerous time node.

[0157] In some possible implementations, the calculation module 302 is specifically used to: generate local candidate samples in a local concentrated region; calculate the expected feasibility function value of each local candidate sample based on the initial local proxy model; select the local candidate sample with the largest expected feasibility function value as the new real evaluation sample; and update the initial local proxy model based on the new real evaluation sample to complete the construction of the local proxy model.

[0158] In some possible implementations, the computation module 302 is specifically used to: construct a covariance matrix based on the parameters of the time-varying stochastic process; perform eigenvalue decomposition on the covariance matrix to obtain an eigenvector matrix and an eigenvalue diagonal matrix; and perform a Karhunen–Loève expansion on the time-varying stochastic process based on the product of the components of the eigenvectors in the eigenvector matrix and the square roots of the corresponding eigenvalues ​​in the eigenvalue diagonal matrix to obtain deterministic expansion coefficients.

[0159] The time-varying reliability design optimization apparatus according to the embodiments of this application, which integrates multi-strategy active learning and time-varying sequence optimization reliability assessment frameworks, can correspondingly execute the methods described in the embodiments of this application. Furthermore, the other operations and / or functions of each module / unit of the time-varying reliability design optimization apparatus, which integrates multi-strategy active learning and time-varying sequence optimization reliability assessment frameworks, are respectively for the purpose of implementing… Figure 2 For the sake of brevity, the corresponding processes of each method in the illustrated embodiments will not be described in detail here.

[0160] This application also provides a computing device. For example... Figure 4As shown in the figure, this is a schematic diagram of a computing device provided in an embodiment of this application. The computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other via the bus 401.

[0161] Bus 401 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 4 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0162] Processor 402 can be any one or more of the following processors: central processing unit (CPU), graphics processing unit (GPU), microprocessor (MP), or digital signal processor (DSP).

[0163] Communication interface 403 is used for communication with external devices.

[0164] Memory 404 may include volatile memory, such as random access memory (RAM). Memory 404 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0165] The memory 404 stores executable code, and the processor 402 executes the executable code to execute the aforementioned time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework.

[0166] Specifically, in achieving Figure 3 In the case of the illustrated embodiment, and Figure 3 When the modules or units of the time-varying reliability design optimization device, which integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework, described in the embodiments are implemented in software, the following steps are performed: Figure 3The software or program code required for the functions of each module / unit can be partially or entirely stored in memory 404. Processor 402 executes the program code corresponding to each unit stored in memory 404, and executes the time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework.

[0167] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a computing device can store, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct the computing device to execute the time-varying reliability design optimization method described above, which integrates multi-strategy active learning and time-varying sequence optimization reliability assessment frameworks.

[0168] This application also provides a computer program product comprising one or more computer instructions. When the computer instructions are loaded and executed on a computing device, all or part of the processes or functions described in this application are generated.

[0169] The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center via wired (e.g., coaxial cable, fiber optic) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0170] When the computer program product is executed by a computer, the computer executes any of the methods of the aforementioned time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework. The computer program product can be a software installation package; when any of the methods of the aforementioned time-varying reliability design optimization method that integrates multi-strategy active learning and time-varying sequence optimization reliability assessment framework needs to be used, the computer program product can be downloaded and executed on the computer.

[0171] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0172] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in this application should be covered within the scope of protection of this application.

Claims

1. A time-varying reliability design optimization method integrating multi-strategy active learning and time-varying sequence optimization reliability assessment framework, characterized in that, The method includes: Obtain the initial design variables, initial random variables, time-varying stochastic process parameters, and target reliability index; Based on the parameters of the time-varying random process, the time-varying random process is expanded to obtain the deterministic expansion coefficients; Based on the initial design variables, initial random variables, and deterministic expansion coefficients, sample generation and cluster screening are performed on the target reliability hypersphere to construct an inner loop surrogate model; Active search is performed using an inner loop surrogate model and the expected improvement function to obtain the final time-varying minimum function metric point and the most dangerous time node; Construct an offset vector based on the time-varying minimum function metric point; A global proxy model is constructed based on a global sample library consisting of initial design variables, initial random variables, deterministic expansion coefficients, and the most dangerous time nodes. Based on the global proxy model, the current design variables, current random parameters, and the most dangerous time node are calculated to obtain the predicted safety margin; the predicted safety margin is compared with the preset threshold to obtain the active constraints. Based on the time-varying minimum function metric point, a local concentrated region is defined for the active constraints; a local surrogate model is constructed within the local concentrated region using the expected feasibility function; The time-varying reliability constraints are transformed into deterministic constraints based on the offset vector, and a deterministic optimization problem under deterministic constraints is constructed based on the local surrogate model. Solve the deterministic optimization problem to obtain the updated design variables; when the changes in the updated design variables and the previous design variables satisfy the convergence condition, output the current design variables as the target design scheme.

2. The method according to claim 1, characterized in that, The method involves generating and clustering samples on the target reliability hypersphere based on initial design variables, initial random variables, and deterministic expansion coefficients to construct an inner-loop surrogate model, including: Candidate samples are generated based on the initial design variables, initial random variables, and deterministic expansion coefficients. The candidate samples are projected onto the target reliability hypersphere to obtain hypersphere sample points; K-means clustering is performed on the hyperspherical sample points to determine the initial sampling points; An inner loop proxy model is constructed based on the initial sampling points and deterministic expansion coefficients.

3. The method according to claim 1, characterized in that, The process of transforming time-varying reliability constraints into deterministic constraints based on offset vectors, and constructing a deterministic optimization problem under deterministic constraints based on a local surrogate model, includes: Based on the offset vector, the time-varying reliability constraints are translated to the deterministic design space to obtain the translated deterministic constraints; Using the local surrogate model established after identifying active constraints through the global surrogate model as the active constraint evaluation function, a deterministic optimization problem is constructed within the deterministic design space with the translated deterministic constraints as constraints, the initial design variables as optimization variables, and the minimization objective function as the optimization objective.

4. The method according to claim 1, characterized in that, The active search using the inner loop surrogate model and the expected improvement function to obtain the final time-varying minimum function metric point and the most dangerous time node includes: An inner loop surrogate model is used to calculate the expected improvement function value of candidate samples in the inner loop; Select the sample point with the largest expected improvement function value as the current time-varying minimum function metric point, and fix this sample point to traverse all discrete time nodes to determine the most dangerous time node. Repeated sampling and model update operations are performed until the maximum value of the desired improvement function is less than the inner convergence threshold, thus obtaining the final time-varying minimum function metric point and the most dangerous time node.

5. The method according to claim 1, characterized in that, The method of constructing a local proxy model within a local concentrated region using the expected feasibility function includes: Generate local candidate samples in locally concentrated regions; The expected feasibility function value for each local candidate sample is calculated based on the initial local proxy model; Select the local candidate sample with the largest expected feasibility function value as the new real evaluation sample; Based on the newly added real evaluation samples, the initial local proxy model is updated to complete the construction of the local proxy model.

6. The method according to claim 1, characterized in that, The step of expanding the time-varying random process based on its parameters to obtain deterministic expansion coefficients includes: Construct the covariance matrix based on the parameters of the time-varying stochastic process; The covariance matrix is ​​decomposed into eigenvector matrix and eigenvalue diagonal matrix. The deterministic expansion coefficients are obtained by performing a Karhunen-Loève expansion on a time-varying stochastic process using the product of each component of the eigenvector in the eigenvector matrix and the square root of the corresponding eigenvalue in the eigenvalue diagonal matrix.

7. A time-varying reliability design optimization device integrating multi-strategy active learning and time-varying sequence optimization reliability assessment framework, characterized in that, The device includes: The acquisition module is used to acquire initial design variables, initial random variables, time-varying stochastic process parameters, and target reliability indicators. The calculation module is used to expand the time-varying stochastic process based on the time-varying stochastic process parameters to obtain deterministic expansion coefficients; based on the initial design variables, initial random variables, and deterministic expansion coefficients, it generates samples and performs clustering screening on the target reliability hypersphere to construct an inner loop surrogate model; it uses the inner loop surrogate model and the expected improvement function to perform active search to obtain the final time-varying minimum functional measure point and the most dangerous time node; it constructs an offset vector based on the time-varying minimum functional measure point; it constructs a global surrogate model based on a global sample library composed of initial design variables, initial random variables, deterministic expansion coefficients, and the most dangerous time node; based on the global surrogate model, it calculates the predicted safety margin for the current design variables, current random parameters, and the most dangerous time node; it compares the predicted safety margin with a preset threshold to obtain active constraints; it delineates local concentrated regions for active constraints based on the time-varying minimum functional measure point; and it constructs a local surrogate model within the local concentrated regions using the expected feasibility function. The optimization module is used to transform time-varying reliability constraints into deterministic constraints based on the offset vector, and construct a deterministic optimization problem under deterministic constraints based on the local surrogate model; solve the deterministic optimization problem to obtain the updated design variables; when the changes in the updated design variables and the previous round of design variables satisfy the convergence condition, the current design variables are output as the target design scheme.

8. A computing device, characterized in that, Including memory and processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program for performing the method as described in any one of claims 1 to 6.

10. A computer program product, characterized in that, The computer program product includes one or more computer instructions that, when executed by a computer, perform the method as described in any one of claims 1 to 6.

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