Reliability design optimization-oriented hybrid dynamic mean value conjugate algorithm and application
By combining the AMV and DCG methods in the HDMC algorithm, and using a dual criterion to determine convexity, the problem of high computational cost and poor convergence in existing methods when dealing with convex and concave functional functions is solved, and efficient and accurate MPTP derivation is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-14
- Publication Date
- 2026-04-03
AI Technical Summary
Existing reliability design optimization methods suffer from high computational costs and poor convergence when dealing with convex and concave functional functions. In particular, the Hybrid Dynamic Mean Conjugate (HCC) algorithm exhibits poor convergence when dealing with highly nonlinear functions.
A hybrid dynamic mean conjugate (HDMC) algorithm is developed, which combines the AMV and DCG methods. It uses a dual criterion to accurately determine the concavity and convexity of the function and accelerates the derivation of the MPTP point through dynamic conjugate gradient vectors.
It achieves high efficiency, accuracy, and robustness in handling convex and concave functional functions, improves the efficiency and accuracy of MPTP derivation, and reduces computational costs.
Smart Images
Figure CN121786987A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of reliability design optimization, and in particular to a hybrid dynamic mean conjugate algorithm for reliability design optimization and its application. Background Technology
[0002] As crucial equipment for modern navies, underwater products' combat and survivability heavily rely on the electrical performance of their energy systems. The energy batteries for underwater products must not only provide energy for propulsion systems, life support systems, and various electronic devices, but also maintain high stability and reliability. Against this backdrop, designing underwater product energy systems based on reliability-based design optimization methods has significant practical engineering implications.
[0003] Reliability analysis is crucial for improving the efficiency and robustness of reliability design optimization. Stochastic simulation, approximate modeling, and approximate analytical methods are widely used in reliability analysis. Commonly used approximate analytical methods include first-order and second-order reliability methods. Second-order reliability methods offer high accuracy and adaptability, but are computationally expensive. In contrast, first-order reliability methods are more popular in engineering and academia due to their simplicity and efficiency. The most classic first-order reliability method is the Advanced Mean Value (AMV) method. However, the AMV method is only applicable to convex function functions; when dealing with concave function functions, it introduces instability problems such as periodic oscillations, divergence, and chaos. The Conjugate Mean Value (CMV) method can efficiently solve for the Minimum Performance Target Point (MPTP) of concave function functions. However, the CMV method is less efficient for convex function functions. Combining the AMV and CMV methods, the Hybrid Mean Value (HMV) method was proposed to stably derive the MPTP points for both convex and concave function functions. However, the HMV method exhibits a certain probability of divergence when dealing with highly nonlinear concave functional functions. Furthermore, methods such as Chaos Control (CC), Modified Chaos Control (MCC), and Hybrid Chaos Control (HCC), which apply chaotic control theory, have been used to derive MPTP points for random variables / parameters. The CC method controls the oscillation and divergence problems of the AMV method to obtain a stable convergent solution, but its computational cost is high. The MCC method reduces time consumption by forcing the MPTP iteration points to lie on the target reliability sphere. However, the efficiency of applying the MCC method to solve convex functional functions is low. To address this, the HCC method, combining the MCC and AMV methods, was developed. However, the HCC method exhibits poor convergence when dealing with highly nonlinear functions.
[0004] Conjugate Gradient Analysis (CGA) searches for MPTP points on the target reliability sphere based on conjugate directions, exhibiting superior stability and convergence compared to the HMV method. However, traditional CGA is inefficient for handling convex functional functions. To address this, the Self-adaptive Conjugate Gradient (SCG) method was proposed, applying an adaptive conjugate scalar factor to reduce the MPTP search time for highly nonlinear problems. The dynamic conjugate scalar factor value of the SCG method is smaller than that of the traditional CGA method. For convex functional functions, this setting can improve the convergence rate of inverse reliability analysis but reduces the MPTP solution efficiency for concave functional functions. The Bi-directional Adaptive Conjugate Gradient (BACG) algorithm uses a concavity / convexity decision criterion to determine the concavity / convexity of the functional function, thereby adaptively accelerating the derivation of MPTP points. However, this concavity / convexity decision criterion has flaws, which can easily lead to the failure of the BACG method in accelerating the solution. Summary of the Invention
[0005] To address the aforementioned problems, this invention aims to develop a Hybrid Dynamic Mean Conjugate (HDMC) algorithm and its applications, which possess superior problem-solving capabilities for concave / convex problems. This HDMC algorithm effectively integrates the AMV method and the Dynamic Conjugate Gradient (DCG) method, and applies a dual criterion to accurately determine the concave / convex properties of the function, thereby fully leveraging the advantages of each: the AMV method is stronger at handling convex problems, while the DCG method is stronger at deriving concave problems.
[0006] This invention is implemented by providing a hybrid dynamic mean conjugate algorithm for reliability design optimization, which balances the efficiency, accuracy and robustness of MPTP derivation.
[0007] A hybrid dynamic mean-conjugate algorithm for reliability design optimization, the method comprising: (1) Initial iteration, i.e. The random variables / random parameters take the mean, and the target reliability index, inverse reliability analysis convergence tolerance, random variable / random parameter variance and maximum allowable iteration steps are set. The dynamic conjugate gradient vector is taken as the zero vector. (2) The normal random space - Transform the space into a standard normal space -space; (3) Calculate the normalized steepest descent direction of the function at the MPTP iteration point; (4) Derive the static conjugate scalar factor based on gradient information; (5) When If the condition is met, calculate the dynamic factor value and jump to step (8); otherwise, calculate the conjugate gradient vector using the traditional CGA method. (6) Evaluate the angle between the conventional conjugate gradient vector and the steepest descent direction; (7) Apply the dual criterion to accurately evaluate the concavity and convexity of the function and calculate the dynamic factor value; (8) Calculate the dynamic conjugate gradient vector for the next iteration step; (9) Derive new MPTP iteration points based on dynamic conjugate gradient vectors; (10) Determine whether the HDMC algorithm has converged. If the convergence condition is met, stop the iteration and derive the final MPTP point; otherwise, execute... Then proceed to step (3).
[0008] Furthermore, step (1) specifically refers to: at the beginning of the iteration, i.e. The random variable / random parameter takes the mean, that is , And set target reliability indicators. Inverse reliability analysis convergence tolerance Variance of random variables / random parameters / and the maximum allowed number of iterations Dynamic conjugate gradient vector Take the zero vector .
[0009] Furthermore, steps (2)-(4) are as follows: (2) Application , normal space - Transform the space into a standard normal space -space:
[0010] In the formula, Indicates the MPTP iteration point; and Let them represent the random variable and the random parameter, respectively; and These represent the mean of the random variable and the random parameter, respectively. and Let Variance and variance be represented by , respectively, for the random variable and the random parameter. Indicates the number of iterations; (3) Calculate the function at the MPTP iteration point The normalized steepest descent direction at the point :
[0011] In the formula, Indicates the direction of the steepest descent under normalization; The gradient vector representing the function of performance; Indicates the MPTP iteration point; Indicates the number of iterations; (4) Deriving the static conjugate scalar factor based on gradient information :
[0012] In the formula, Represents the static conjugate scalar factor; and They represent the first Iteration step and the The gradient vector of the function of the iteration step; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations.
[0013] Furthermore, step (5) specifically involves: judge Value, when Then, dynamic factor The value is 0; when At that time, calculate :
[0014] In the formula, This indicates that parameter 2 is being evaluated. Indicates the target reliability index; Indicates the direction of the steepest descent under normalization; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations; like Then dynamic factor The value is 0; if Then dynamic factor The value is 1, and then the process jumps to step (8). when When using the CGA method to calculate the traditional conjugate gradient vector... :
[0015] In the formula, Represents the traditional conjugate gradient vector; Represents the gradient vector of the function; Represents the static conjugate scalar factor; Represents the dynamic conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
[0016] Furthermore, step (6) specifically involves: evaluating the conventional conjugate gradient vector. Angle value between the direction of steepest descent and the direction of most rapid descent :
[0017] In the formula, This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Represents the gradient vector of the function; Represents the traditional conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
[0018] Furthermore, step (7) specifically involves: evaluating the concavity and convexity of the function based on the dual criterion and calculating the dynamic factor. The specific steps are as follows: (7-1) Calculate using judgment criterion 1
[0019] In the formula, Indicates that parameter 1 is used for judgment; , and They represent the first Iteration step, the first Iteration step and the The normalized steepest descent direction of the iteration step; Indicates the number of iterations; (7-2) If Then calculate judgment criterion 2, that is Proceed to step (7-3); otherwise, proceed to step (7-4):
[0020] In the formula, This indicates that parameter 2 is being evaluated. Indicates the target reliability index; Indicates the direction of the steepest descent under normalization; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations; (7-3) If The dynamic factor takes the value of Otherwise, calculate the dynamic factor using the following formula; then proceed to step (8).
[0021] In the formula, Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; It is a constant; This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Indicates the MPTP iteration point; Represents the number of iterations; dynamic conjugate gradient vector It is expressed as:
[0022] In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations; (7-4) Calculate the dynamic conjugate gradient vector The angle between the direction of the steepest descent and the direction of the steepest descent :
[0023] In the formula, Represents the dynamic conjugate gradient vector The angle between the direction of the steepest descent and the direction of the most rapid descent; Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations; In the formula, the dynamic conjugate gradient vector for:
[0024] In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations; (7-5) If The dynamic factor is then derived based on the following formula. Otherwise, dynamic factors The value is set to 1, and the process jumps to step (8):
[0025] In the formula, Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; It is a constant; This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Indicates the MPTP iteration point; Represents the number of iterations; dynamic conjugate gradient vector The calculation method is shown in step (7-3).
[0026] Furthermore, step (8) specifically involves: (8) Derive the dynamic conjugate gradient vector for the next iteration step. :
[0027] In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations.
[0028] Furthermore, step (9) specifically involves: Calculate the normalized sensitivity vector for the next iteration. :
[0029] In the formula, This represents the normalized sensitivity vector; Represents the dynamic conjugate gradient vector; Calculate the new MPTP iteration point based on the normalized sensitivity vector. :
[0030] In the formula, Indicates the MPTP iteration point; Indicates the target reliability index; This represents the normalized sensitivity vector.
[0031] A computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the above-described method.
[0032] A computer device includes a memory, a processor, and a program stored in the memory and executable thereon, the program being executed by the processor to implement the steps of the method described above.
[0033] The advantages and technical effects of this invention are as follows: This invention provides a hybrid dynamic mean-conjugate (HDMC) algorithm for reliability design optimization, which has a more comprehensive MPTP derivation capability and combines high efficiency, robustness, and accuracy. The HDMC algorithm provided by this invention effectively combines the AMV and DCG methods, and utilizes a dual criterion to accurately determine the concavity / convexity of the function to fully leverage their respective advantages: the AMV algorithm is used to quickly solve for the optimal MPTP point of a convex function; for concave problems, the DCG algorithm is used, which, based on dynamic conjugate gradient vectors, can accelerate the derivation of the MPTP point of a concave function. Attached Figure Description
[0034] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.
[0035] Figure 1 This is a flowchart illustrating the technical process of the present invention.
[0036] Figure 2 This is a technical roadmap for the present invention. Detailed Implementation
[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0038] A hybrid dynamic mean conjugate (HDMC) algorithm for reliability design optimization, the method comprising: (1) Initial iteration (i.e.) The random variable / random parameter takes the mean, that is... , And set target reliability indicators. Inverse reliability analysis convergence tolerance Variance of random variables / random parameters / and the maximum allowed number of iterations Dynamic conjugate gradient vector Take the zero vector .
[0039] (2) Application , the normal space ( -space) is transformed into standard normal space ( -space).
[0040] (1) In the formula, Indicates the MPTP iteration point; and Let them represent the random variable and the random parameter, respectively; and These represent the mean of the random variable and the random parameter, respectively. and Let Variance and variance be represented by , respectively, for the random variable and the random parameter. Indicates the number of iterations.
[0041] (3) Calculate the function at the MPTP iteration point The normalized steepest descent direction at the point .
[0042] (2) In the formula, Indicates the direction of the steepest descent under normalization; The gradient vector representing the function of performance; Indicates the MPTP iteration point; Indicates the number of iterations.
[0043] (4) Deriving the static conjugate scalar factor based on gradient information .
[0044] (3) In the formula, Represents the static conjugate scalar factor; and They represent the first Iteration step and the The gradient vector of the function of the iteration step; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations.
[0045] (5) Judgment Value, when Then, dynamic factor The value is 0; when At that time, calculate : (4) In the formula, This indicates that parameter 2 is being evaluated. Indicates the target reliability index; Indicates the direction of the steepest descent under normalization; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations.
[0046] like Then dynamic factor The value is 0; if Then dynamic factor The value is 1. Then proceed to step (8).
[0047] when When using the CGA method to calculate the traditional conjugate gradient vector... : (5) In the formula, Represents the traditional conjugate gradient vector; Represents the gradient vector of the function; Represents the static conjugate scalar factor; Represents the dynamic conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
[0048] (6) Evaluate the traditional conjugate gradient vector Angle value between the direction of steepest descent and the direction of most rapid descent : (6) In the formula, This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Represents the gradient vector of the function; Represents the traditional conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
[0049] (7) Evaluate the concavity and convexity of the function based on the dual criterion and calculate the dynamic factor. The specific steps are as follows: (7-1) Calculate using judgment criterion 1 (7) In the formula, Indicates that parameter 1 is used for judgment; , and They represent the first Iteration step, the first Iteration step and the The normalized steepest descent direction of the iteration step; Indicates the number of iterations.
[0050] (7-2) If Then calculate the judgment criterion 2 (i.e. If the condition is met, proceed to step (7-3); otherwise, proceed to step (7-4).
[0051] (8) In the formula, This indicates that parameter 2 is being evaluated. Indicates the target reliability index; Indicates the direction of the steepest descent under normalization; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations.
[0052] (7-3) If The dynamic factor takes the value of Otherwise, derive equation (9) to calculate the dynamic factor; then proceed to step (8).
[0053] (9) In the formula, Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; It is a constant; This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Indicates the MPTP iteration point; Indicates the iteration step number. Dynamic conjugate gradient vector. It is expressed as: (10) In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations.
[0054] (7-4) Calculate the dynamic conjugate gradient vector The angle between the direction of the steepest descent and the direction of the steepest descent : (11) In the formula, Represents the dynamic conjugate gradient vector The angle between the direction of the steepest descent and the direction of the most rapid descent; Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
[0055] Dynamic conjugate gradient vector for: (12) (7-5) If Then, the dynamic factor is derived based on equation (13). Otherwise, dynamic factors The value is set to 1. Then proceed to step (8).
[0056] (13) In the formula, Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; It is a constant; This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Indicates the MPTP iteration point; Indicates the iteration step number. Dynamic conjugate gradient vector. The calculation method is detailed in equation (10).
[0057] (8) Derive the dynamic conjugate gradient vector for the next iteration step. : (14) In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations.
[0058] (9) Calculate the normalized sensitivity vector for the next iteration step. : (15) In the formula, This represents the normalized sensitivity vector; This represents the dynamic conjugate gradient vector.
[0059] (10) Calculate the new MPTP iteration point based on the normalized sensitivity vector : (16) In the formula, Indicates the MPTP iteration point; Indicates the target reliability index; This represents the normalized sensitivity vector.
[0060] (11) Determine whether the HDMC algorithm has converged. If the convergence condition is met, stop the iteration and derive the final MPTP point. Otherwise, execute. Proceed to step (3).
[0061] The following comparisons with existing mature reliability design optimization methods, using Examples 1-3, further illustrate the superiority of the hybrid dynamic mean-conjugate algorithm for reliability design optimization provided by this invention. The comparison methods include AMV, BACG, CC, CGA, CMV, HCC, HMV, MCC, and SCG methods.
[0062] Example 1 The following description, in conjunction with Example 1, further illustrates the hybrid dynamic mean-conjugate algorithm for reliability design optimization provided by the present invention: Consider the convex function presented by equation (17): (17) In the formula, Indicates a random parameter; This represents a function.
[0063] Its random information is (18) Table 1 shows the MPTP information and iteration steps under different reliability design optimization algorithms. For Example 1, the Hybrid Dynamic Mean Conjugate (HDMC) algorithm provided by this invention has optimal iteration efficiency while maintaining accuracy. The HDMC algorithm only requires 8 iterations to derive the optimal MPTP point. For convex function functions, the AMV method has excellent solution capability, with an iteration step count of 8. Both the HCC and HMV methods call the AMV method to derive the MPTP point, therefore their iteration efficiency is equivalent to that of the AMV method. At that time, the CC method requires 141 MPTP searches to finally converge; At that time, the CC method required 26 inverse reliability analyses. The MCC method improves the efficiency of inverse reliability analysis by forcing the MPTP point to lie on the target reliability sphere. However, its convergence speed is still significantly lower than that of the HDMC algorithm, by 987.5% and 125.0%, respectively. The traditional CGA method is less efficient and less accurate in handling this convex function, requiring 1362 inverse reliability analyses, significantly higher than the HDMC algorithm. The BACG method improves the ability of the traditional CGA method to handle convex functions through an adaptive acceleration factor, but it still requires 17 inverse reliability analyses to converge, with an iteration efficiency 112.5% lower than the HDMC algorithm. The CMV and SCG methods require 14 and 45 iterations to derive the MPTP point, respectively, with convergence efficiencies decreasing by 75.0% and 462.5% compared to the HDMC algorithm.
[0064] Table 1 Comparison of reliability design optimization efficiency and accuracy in Example 1
[0065] Example 2 The following description, in conjunction with Example 2, further illustrates the hybrid dynamic mean-conjugate algorithm for reliability design optimization provided by the present invention: This embodiment studies a highly nonlinear function, whose expression is: (19) In the formula, Indicates a random parameter; This represents a function.
[0066] Its random information is (20) The MPTP search results for Example 2 are shown in Table 2. For this highly nonlinear function, the HDMC algorithm provided by this invention only requires 7 iterations to converge to the optimal MPTP point, combining high efficiency and solution accuracy. In contrast, the CC method based on chaotic control theory exhibits periodic oscillations and fails to converge. The CGA method and MCC method (…) The iteration steps of the BACG method, CMV method, HCC method, HMV method, and MCC method are 65, 56, and 38 respectively, and their iteration efficiency is significantly lower than that of the HDMC algorithm provided in this invention. Furthermore, the iteration steps of the BACG method, CMV method, HCC method, HMV method, and MCC method are also significantly lower. The convergence iterations of the algorithm are fewer, but its efficiency is still significantly worse than that of the HDMC algorithm.
[0067] Table 2 Comparison of reliability design optimization efficiency and accuracy in Example 2
[0068] Example 3 The following, with reference to Example 3, further illustrates the hybrid dynamic mean-conjugate algorithm for reliability design optimization provided by the present invention: (twenty one) In the formula, Indicates a random parameter; This represents a function.
[0069] Its random information is (twenty two) Table 3 summarizes the inverse reliability analysis results of ten MPTP search techniques. In this embodiment, only the CGA and HDMC methods converged, with MPTP iteration steps of 260 and 49, respectively. Compared to the traditional CGA method, the HDMC algorithm provided in this invention improves the iterative efficiency of deriving the optimal MPTP point by 430.6%. The other eight reliability design optimization algorithms all exhibited periodic oscillations or chaotic problems and failed to converge.
[0070] Table 3 Comparison of reliability design optimization efficiency and accuracy in Example 3
[0071] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented, in whole or in part, as a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape) or an optical medium.
[0072] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.
Claims
1. A hybrid dynamic mean-conjugate algorithm for reliability design optimization, characterized in that, The method includes: (1) Initial iteration, i.e. The random variables / random parameters take the mean, and the target reliability index, inverse reliability analysis convergence tolerance, random variable / random parameter variance and maximum allowable iteration steps are set. The dynamic conjugate gradient vector is taken as the zero vector. (2) The normal random space - Transform the space into a standard normal space -space; (3) Calculate the normalized steepest descent direction of the function at the MPTP iteration point; (4) Derive the static conjugate scalar factor based on gradient information; (5) When If the condition is met, calculate the dynamic factor value and jump to step (8); otherwise, calculate the conjugate gradient vector using the traditional CGA method. (6) Evaluate the angle between the conventional conjugate gradient vector and the steepest descent direction; (7) Apply the dual criterion to accurately evaluate the concavity and convexity of the function and calculate the dynamic factor value; (8) Calculate the dynamic conjugate gradient vector for the next iteration step; (9) Derive new MPTP iteration points based on dynamic conjugate gradient vectors; (10) Determine whether the HDMC algorithm has converged. If the convergence condition is met, stop the iteration and derive the final MPTP point; otherwise, execute... Then proceed to step (3).
2. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 1, characterized in that, Step (1) specifically refers to: at the beginning of the iteration, i.e. The random variable / random parameter takes the mean, that is , ; And set target reliability indicators Inverse reliability analysis convergence tolerance Variance of random variables / random parameters / and the maximum allowed number of iterations Dynamic conjugate gradient vector Take the zero vector .
3. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 2, characterized in that, Steps (2)-(4) are as follows: (2) Application , normal space - Transform the space into a standard normal space -space: In the formula, Indicates the MPTP iteration point; and These represent the random variable and the random parameter, respectively. and These represent the mean of the random variable and the random parameter, respectively. and Let represent the variances of the random variable and the random parameter, respectively. Indicates the number of iterations; (3) Calculate the function at the MPTP iteration point The normalized steepest descent direction at the point : In the formula, Indicates the direction of the steepest descent under normalization; The gradient vector representing the function of performance; Indicates the MPTP iteration point; Indicates the number of iterations; (4) Deriving the static conjugate scalar factor based on gradient information : In the formula, Represents the static conjugate scalar factor; and They represent the first Iteration step and the The gradient vector of the function of the iteration step; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations.
4. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 3, characterized in that, Step (5) is as follows: judge Value, when Then, dynamic factor The value is 0; when At that time, calculate : In the formula, This indicates that parameter 2 is being evaluated. Indicates the target reliability index; Indicates the direction of the steepest descent under normalization; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations; like Then dynamic factor The value is 0; if Then dynamic factor The value is 1, and then the process jumps to step (8). when When using the CGA method to calculate the traditional conjugate gradient vector... : In the formula, Represents the traditional conjugate gradient vector; Represents the gradient vector of the function; Represents the static conjugate scalar factor; Represents the dynamic conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
5. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 4, characterized in that, Step (6) specifically involves: evaluating the conventional conjugate gradient vector. Angle value between the direction of steepest descent and the direction of most rapid descent : In the formula, This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Represents the gradient vector of the function; Represents the traditional conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations.
6. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 5, characterized in that, Step (7) specifically involves: evaluating the concavity and convexity of the function based on the dual criterion and calculating the dynamic factor. The specific steps are as follows: (7-1) Calculate using judgment criterion 1 In the formula, Indicates that parameter 1 is used for judgment; , and They represent the first Iteration step, the first Iteration step and the The normalized steepest descent direction of the iteration step; Indicates the number of iterations; (7-2) If Then calculate judgment criterion 2, that is Proceed to step (7-3); otherwise, proceed to step (7-4): In the formula, This indicates that parameter 2 is being evaluated. Indicates the target reliability index; Indicates the direction of the steepest descent under normalization; and They represent the first Iteration step and the MPTP iteration point of the iteration step; Indicates the number of iterations; (7-3) If The dynamic factor takes the value of Otherwise, calculate the dynamic factor using the following formula; then proceed to step (8). In the formula, Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; It is a constant; This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Indicates the MPTP iteration point; Represents the number of iterations; dynamic conjugate gradient vector It is expressed as: In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations; (7-4) Calculate the dynamic conjugate gradient vector The angle between the direction of the steepest descent and the direction of the steepest descent : In the formula, Represents the dynamic conjugate gradient vector The angle between the direction of the steepest descent and the direction of the most rapid descent; Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; Indicates the MPTP iteration point; Indicates the number of iterations; In the formula, the dynamic conjugate gradient vector for: In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations; (7-5) If The dynamic factor is then derived based on the following formula. ; Otherwise, dynamic factors The value is set to 1, and the process jumps to step (8): In the formula, Represents the gradient vector of the function; Represents the dynamic conjugate gradient vector; It is a constant; This represents the angle between the traditional conjugate gradient vector and the steepest descent direction. Indicates the MPTP iteration point; Represents the number of iterations; dynamic conjugate gradient vector The calculation method is shown in step (7-3).
7. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 6, characterized in that, Step (8) is as follows: (8) Derive the dynamic conjugate gradient vector for the next iteration step. : In the formula, and They represent the first Iteration step and the The dynamic conjugate gradient vector of the iteration step; Represents the gradient vector of the function; Indicates a dynamic factor; Represents the static conjugate scalar factor; Represents the product of a dynamic factor and a static conjugate scalar factor; Indicates the MPTP iteration point; Indicates the number of iterations.
8. The hybrid dynamic mean-conjugate algorithm for reliability design optimization according to claim 7, characterized in that, Step (9) is as follows: Calculate the normalized sensitivity vector for the next iteration. : In the formula, This represents the normalized sensitivity vector; Represents the dynamic conjugate gradient vector; Calculate the new MPTP iteration point based on the normalized sensitivity vector. : In the formula, Indicates the MPTP iteration point; Indicates the target reliability index; This represents the normalized sensitivity vector.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device on which the computer-readable storage medium is located to perform the method as described in any one of claims 1-8.
10. A computer device, characterized in that, The computer device includes a memory, a processor, and a program stored in and executable on the memory, the program being executed by the processor to implement the steps of the method as described in any one of claims 1-8.