CN114462307B - Structural reliability analysis method and device, electronic equipment and storage medium - Google Patents
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Abstract
The invention discloses a structural reliability analysis method, a device, electronic equipment and a storage medium, wherein the method comprises the following steps: determining characteristic parameters of a product structure, a function and a random variable in the field to be analyzed, calculating a gradient value of an objective function, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain an end point; when the function value meets a first preset condition, taking the end point as a starting point of a reliability analysis method; taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining a search direction and an iteration step length; performing iterative processing according to the starting point, the searching direction and the iterative step length, and outputting a maximum possible failure point and a reliable index which meet a second preset condition; solving the maximum possible failure point under the original space, and calculating the structural failure probability on the basis of the reliable index. The invention improves the efficiency, the effectiveness and the universality, and can be widely applied to the technical field of reliability analysis.
Description
Technical Field
The invention relates to the technical field of reliability analysis, in particular to a structural reliability analysis method, a structural reliability analysis device, electronic equipment and a storage medium.
Background
The reliability analysis of structures or products in the fields of civil engineering, mechano-electronics, aerospace and the like reasonably considers uncertainty parameters existing in the engineering, is widely accepted by wide engineering technicians, and is an important means for the development of engineering structure or product design theory. The random structure or product reliability is mainly analyzed to influence objective factors derived from load, material properties and the manufacturing process of the structure or product, and has great significance for safety assessment of engineering practice, safety operation of the structure or product and improvement of important influencing factors and safety reserve.
The functional functions of normal working capacity or critical safety of large complex structures or product characterization structures in the fields of civil engineering, mechano-electronics, aerospace and the like tend to be highly nonlinear, and under the condition, reliability analysis on the structures or products is difficult or low in efficiency no matter the conventional general first-order second-order moment method or the Monte Carlo method is carried out, or the phenomenon of periodic oscillation or chaos non-convergence is generated, or calculation is extremely time-consuming, and especially when the structures and products with strong nonlinear/ultra-strong nonlinear performance functions are faced, the accuracy and efficiency requirements of engineering practice reliability analysis are difficult to be met by the conventional first-order second-order moment method.
The first second moment method is used as the earliest developed reliability analysis method, lays a foundation for other reliability analysis methods, has simple calculation process and can meet higher precision requirements, and is widely applied to the reliability analysis process of structures or products in the fields of civil engineering, mechatronics, aerospace and the like. Compared with the Monte Carlo simulation method, the method avoids a large amount of structural response analysis, can ensure good reliability analysis precision, greatly improves the reliability analysis efficiency, and is more and more widely valued and applied in engineering practice.
The traditional first-order reliability analysis method, such as a first-order reliability analysis method based on chaos control and a first-order reliability analysis method of control step length, improves the robustness of a classical HL-RF method to a certain extent, but like the HL-RF method, periodic oscillation phenomenon or chaos is generated in different degrees when the problem of higher nonlinearity degree is faced, and the stability of results is poor and the calculation precision is not ideal when the method is used for analyzing the reliability of large-scale complex structures or products in the fields of civil engineering, mechatronics, aerospace and the like.
Compared with the traditional steepest descent method, the conjugate gradient method has higher convergence speed and does not need to calculate a sea plug matrix, the calculation efficiency of a first-order second-order moment method can be improved to a great extent theoretically on the premise of selecting a proper objective function, however, the traditional single-phase conjugate gradient method presents hypodynamia in a complex structure, and on the basis, a plurality of methods such as three-phase conjugate gradient method and the like are presented to improve the performance of the single-phase conjugate gradient method, and the good performance of BB step length with good robustness and high calculation efficiency in the iterative process is combined, so that the application range of the traditional first-order second-order moment method on the aspect of high nonlinearity can be expanded to a great extent, and the method has good engineering application prospects in the fields of analysis of structures or product reliability in the fields of civil engineering, mechatronics, aerospace and the like.
Therefore, the three-item conjugate Barzilai-Borwein first-order reliability analysis method with simple calculation and good robustness is selected for high-efficiency and high-precision reliability analysis of the structure, and has important significance in the structural reliability analysis field by adopting a first second-order moment method.
Disclosure of Invention
In view of this, the embodiment of the invention provides a method, a device, an electronic device and a storage medium for analyzing the structural reliability with strong universality.
One aspect of the present invention provides a structural reliability analysis method, including:
Determining product structure, function and random variable characteristic parameters in the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed;
Calculating a gradient value of an objective function according to the product structure, the function and the random variable characteristic parameter, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain an end point;
when the function value meets a first preset condition, the end point is used as a starting point of a first-order reliability analysis method of three conjugate Barzilai-Borwein;
Taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method;
Performing iterative processing according to the starting point, the searching direction and the iterative step length, and outputting a maximum possible failure point and a reliable index which meet a second preset condition;
And solving the maximum possible failure point in the original space, and calculating the structural failure probability on the basis of the reliable index.
Optionally, the method further comprises:
According to a non-monotonic line search technique and a deformed machine learning formula, the method satisfies a descent condition and adjusts the iteration step size to a target range.
Alternatively, the expression of the descent direction is:
The calculation formula of the attenuation of the iteration step length is as follows:
Wherein, Representing a search direction; a gradient representing a limit state equation; a Euclidean norm representing the gradient; representing the step size; ρ represents a parameter for adjusting the step size; k represents an iteration counter; i represents the first stage of the algorithm.
Optionally, the expression of the objective function is:
Wherein f (z) represents an objective function; z represents an iteration point in a standard normal space; g (z) represents a limit state equation; c represents a number greater than or equal to Constant of (2); a gradient representing a limit state equation; representing the Euclidean norm of the gradient.
Optionally, the calculation formula of the falling direction of the objective function is:
Wherein d k represents the falling direction of the kth step objective function; z k+1 represents the design check point of step k+1; z k represents the design verification point of step k.
Optionally, in the step of adjusting the iterative step size to the target range according to a non-monotonic line search technique and a modified machine learning formula such that the method satisfies a fall condition,
When the objective function value is smaller than the moving average value, a non-monotonic line search technique based on Armijo criterion is adopted to determine the descending direction and the corresponding step size.
Optionally, in the step of adjusting the iterative step size to the target range according to a non-monotonic line search technique and a modified machine learning formula such that the method satisfies a fall condition,
When the objective function value overflows from the moving average value in the non-monotonic line searching technology, a deformed machine learning formula is selected to calculate a new iteration point in the non-linear searching stage.
Another aspect of the embodiment of the present invention further provides a structural reliability analysis device, including:
the first module is used for determining the product structure, the function and the random variable characteristic parameters of the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed;
the second module is used for calculating the gradient value of the objective function according to the product structure, the function and the random variable characteristic parameter, selecting the negative gradient direction as the descending direction, determining the iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain the end point;
A third module, configured to use the end point as a start point of a first-order reliability analysis method of three conjugates Barzilai-Borwein when the function value meets a first preset condition;
A fourth module, configured to determine a search direction and an iteration step size of the first-order reliability analysis method of the three conjugates Barzilai-Borwein by using a non-negative cost function that does not involve gradient calculation as an objective function;
a fifth module, configured to perform iterative processing according to the starting point, the search direction, and the iteration step, and output a maximum possible failure point and a reliability indicator that satisfy a second preset condition;
and a sixth module, configured to solve a maximum possible failure point in the original space, and calculate a structural failure probability based on the reliable index.
Another aspect of the embodiment of the invention also provides an electronic device, which includes a processor and a memory;
The memory is used for storing programs;
the processor executes the program to implement the method as described above.
Another aspect of the embodiments of the present invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement a method as described above.
Embodiments of the present invention also disclose a computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The computer instructions may be read from a computer-readable storage medium by a processor of a computer device, and executed by the processor, to cause the computer device to perform the foregoing method.
The embodiment of the invention determines the characteristic parameters of the product structure, the function and the random variable in the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed; calculating a gradient value of an objective function according to the product structure, the function and the random variable characteristic parameter, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain an end point; when the function value meets a first preset condition, the end point is used as a starting point of a first-order reliability analysis method of three conjugate Barzilai-Borwein; taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method; performing iterative processing according to the starting point, the searching direction and the iterative step length, and outputting a maximum possible failure point and a reliable index which meet a second preset condition; and solving the maximum possible failure point in the original space, and calculating the structural failure probability on the basis of the reliable index. The invention improves the efficiency and expands the effectiveness and the universality in the reliability analysis problem.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of the overall steps provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a primary and secondary dynamic system architecture in an embodiment of the invention.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
Aiming at the problems existing in the prior art, the invention provides a three-term conjugate Barzilai-Borwein first-order reliability analysis method which has strong universality and can be suitable for the structural reliability analysis of various nonlinear function functions, a non-negative cost function which does not involve gradient calculation is respectively introduced as an objective function, a three-term conjugate gradient method and Barzilai-Borwein step length are used for enhancing the robustness and the efficiency of a first-order second-order moment method, and a non-monotonic line search technology based on Armijo criterion and a deformed machine learning formula are combined to ensure the global convergence of the algorithm, so that the method is an extension of the existing first-order structural reliability analysis method.
Specifically, an aspect of the present invention provides a structural reliability analysis method, including:
Determining product structure, function and random variable characteristic parameters in the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed;
Calculating a gradient value of an objective function according to the product structure, the function and the random variable characteristic parameter, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain an end point;
when the function value meets a first preset condition, the end point is used as a starting point of a first-order reliability analysis method of three conjugate Barzilai-Borwein;
Taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method;
Performing iterative processing according to the starting point, the searching direction and the iterative step length, and outputting a maximum possible failure point and a reliable index which meet a second preset condition;
And solving the maximum possible failure point in the original space, and calculating the structural failure probability on the basis of the reliable index.
Optionally, the method further comprises:
According to a non-monotonic line search technique and a deformed machine learning formula, the method satisfies a descent condition and adjusts the iteration step size to a target range.
Alternatively, the expression of the descent direction is:
The calculation formula of the attenuation of the iteration step length is as follows:
Wherein, Representing a search direction; a gradient representing a limit state equation; a Euclidean norm representing the gradient; representing the step size; ρ represents a parameter for adjusting the step size; k represents an iteration counter; i represents the first stage of the algorithm.
Optionally, the expression of the objective function is:
Wherein f (z) represents an objective function; z represents an iteration point in a standard normal space; g (z) represents a limit state equation; c represents a number greater than or equal to Constant of (2); a gradient representing a limit state equation; representing the Euclidean norm of the gradient.
Optionally, the calculation formula of the falling direction of the objective function is:
Wherein d k represents the falling direction of the kth step objective function; z k+1 represents the design check point of step k+1; z k represents the design verification point of step k.
Optionally, in the step of adjusting the iterative step size to the target range according to a non-monotonic line search technique and a modified machine learning formula such that the method satisfies a fall condition,
When the objective function value is smaller than the moving average value, a non-monotonic line search technique based on Armijo criterion is adopted to determine the descending direction and the corresponding step size.
Optionally, in the step of adjusting the iterative step size to the target range according to a non-monotonic line search technique and a modified machine learning formula such that the method satisfies a fall condition,
When the objective function value overflows from the moving average value in the non-monotonic line searching technology, a deformed machine learning formula is selected to calculate a new iteration point in the non-linear searching stage.
Another aspect of the embodiment of the present invention further provides a structural reliability analysis device, including:
the first module is used for determining the product structure, the function and the random variable characteristic parameters of the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed;
the second module is used for calculating the gradient value of the objective function according to the product structure, the function and the random variable characteristic parameter, selecting the negative gradient direction as the descending direction, determining the iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain the end point;
A third module, configured to use the end point as a start point of a first-order reliability analysis method of three conjugates Barzilai-Borwein when the function value meets a first preset condition;
A fourth module, configured to determine a search direction and an iteration step size of the first-order reliability analysis method of the three conjugates Barzilai-Borwein by using a non-negative cost function that does not involve gradient calculation as an objective function;
a fifth module, configured to perform iterative processing according to the starting point, the search direction, and the iteration step, and output a maximum possible failure point and a reliability indicator that satisfy a second preset condition;
and a sixth module, configured to solve a maximum possible failure point in the original space, and calculate a structural failure probability based on the reliable index.
Another aspect of the embodiment of the invention also provides an electronic device, which includes a processor and a memory;
The memory is used for storing programs;
the processor executes the program to implement the method as described above.
Another aspect of the embodiments of the present invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement a method as described above.
Embodiments of the present invention also disclose a computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The computer instructions may be read from a computer-readable storage medium by a processor of a computer device, and executed by the processor, to cause the computer device to perform the foregoing method.
The specific implementation principle of the invention is described in detail below with reference to the drawings of the specification:
as shown in fig. 1, the method for analyzing the first-order reliability of the three conjugated Barzilai-Borwein provided by the embodiment of the invention comprises the following steps:
S1, specifying a product structure of the field to be analyzed, a functional function reflecting the normal working capacity or the safety working critical state of the structure or the product in the field to be analyzed, and a random variable characteristic parameter, and converting a required non-normal random variable into a standard normal space by using a Rosenblatt conversion method;
S2, calculating a gradient value of the objective function, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration;
S3, checking whether the function value g (z) is smaller than 0, if yes, continuing the next step, otherwise, returning to S2, and continuing iteration;
S4, taking the end point obtained by the steepest descent method as the start point of a first-order reliability analysis method of three-term conjugate Barzilai-Borwein;
S5, taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method;
S6, adopting a non-monotonic line search technology and a deformed machine learning formula to ensure the global convergence of the method, enabling the algorithm to meet the descending condition and adjusting the step size to a reasonable range;
S7, checking whether coordinates of the t step and the t-1 step meet the value of [ z k-zk-1 ] tau or not, if so, outputting a most probable failure point and a reliable index, and if not, returning to S5 to iterate a new coordinate point continuously, wherein tau is a positive parameter with a preset value of 10 -5;
S8, solving the maximum possible failure point under the original space, and calculating the structural failure probability on the basis of the obtained reliable index.
Optionally, in the three-term conjugate Barzilai-Borwein first-order reliability analysis method, since the average point is often taken as the iteration start point, and the average point is generally located in the safety domain and is far away from the limit state surface, the steepest descent method with the attenuation step in step S2 is adopted to reach the vicinity of the limit state surface as soon as possible, where the descent direction and the attenuation step are calculated according to the following expressions
Wherein,Representing a search direction; a gradient representing a limit state equation; a Euclidean norm representing the gradient; Representing the step size; ρ represents a parameter for adjusting the step size; k represents an iteration counter; i represents the first stage of the algorithm. In the iterative process, the closer to the limit state surface, the smaller the step length is, and under the constraint of the convergence criterion in the step S3, the algorithm can approach to the limit state surface as much as possible without causing excessive errors, and a good starting point is provided for the subsequent steps.
Optionally, in the step S5, the objective function selected in the third-term conjugate Barzilai-Borwein is
Wherein f (z) represents an objective function; z represents an iteration point in a standard normal space; g (z) represents a limit state equation; c represents a number greater than or equal toConstant of (2); wherein the method comprises the steps ofA gradient representing a limit state equation; Representing the Euclidean norm of the gradient. And the falling direction of the objective function is calculated according to the following expression:
Wherein d k represents the falling direction of the kth step objective function; z k+1 represents the design check point of step k+1; z k represents the design verification point of step k.
Meanwhile, BB step length is introduced into a three-term conjugate gradient method and combined with the objective function to obtain the following iterative formula:
wherein the search direction is
The step size is calculated according to the following expression
Optionally, in the step S6, when the objective function value is smaller than the moving average, a non-monotonic line search technique based on Armijo criterion is used to ensure a sufficient decreasing direction and a proper step size.
Optionally, in the step S6, when the objective function value overflows the moving average value in the non-monotonic line search technique, a deformed machine learning formula is selected to calculate a new iteration point in the non-linear search stage, so as to further ensure the global convergence of the algorithm, where the formula is as follows:
wherein phi is a constant between (0, 1).
The implementation process of the method of the present invention is described in detail below in terms of two embodiments in specific application scenarios:
example 1:
the present invention is further illustrated in this embodiment 1 by an application example combining exponential and logarithmic operations, and a method for analyzing the first-order reliability of three conjugates Barzilai-Borwein, comprising the steps of:
S1, designating a structure to be analyzed, wherein the structural function of the structure is g (x) =0.5 ln { exp [2 (1+x 1-x2)]+exp[2(5-5x1-x2) ] } and all variables are mutually independent and subject to normal distribution, and the mean value and standard deviation of x 1 and x 2 are respectively 0 and 1. Then converting the non-normal random variables into a standard normal space by using Rosenblatt conversion method;
S2, calculating a gradient value of the objective function, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration;
S3, checking whether the function value g (z) is smaller than 0, if yes, continuing the next step, otherwise, returning to S2, and continuing iteration;
S4, taking the end point obtained by the steepest descent method as the start point of a first-order reliability analysis method of three-term conjugate Barzilai-Borwein;
S5, taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method;
S6, adopting a non-monotonic line search technology and a deformed machine learning formula to ensure the global convergence of the method, enabling the algorithm to meet the descending condition and adjusting the step size to a reasonable range;
S7, checking whether coordinates of the t step and the t-1 step meet the value of [ z k-zk-1 ] tau or not, if so, outputting a most probable failure point and a reliable index, and if not, returning to S5 to iterate a new coordinate point continuously, wherein tau is a positive parameter with a preset value of 10- 5;
S8, solving the maximum possible failure point under the original space, and calculating the structural failure probability on the basis of the obtained reliable index.
The reliability analysis method disclosed in example 1 is compared with the reliability indexes calculated by other methods and the corresponding iteration times thereof are shown in table 1 (HL-RF is a classical first-order reliability analysis method, yang is a first-order reliability analysis method based on chaos control, FAL is a first-order reliability method based on limiting the Armijo search direction, TCFS is a three-term conjugate gradient method directly conjugated to the gradient of the finite state function, ABB-TCG represents the three-term conjugate Barzilai-Borwein first-order reliability analysis method disclosed by the invention), and as can be seen from table 1, the high nonlinearity problem which cannot be solved by HL-RF, yang, FAL and TCFS methods is solved by adopting the three-term conjugate Barzilai-Borwein first-order reliability analysis method, the iteration times are less, and therefore, the robustness and the efficiency are better.
TABLE 1 comparative table of reliability index and iteration number calculated by various methods of EXAMPLE 1
Example 2
The present embodiment further illustrates the present invention in terms of an application example of a primary and secondary dynamic system architecture. The first-order reliability analysis method of the three-term conjugate Barzilai-Borwein comprises the following steps:
s1, appointing a structure to be analyzed, namely a primary and secondary dynamic system structure (shown in figure 2), wherein the structural function is that Wherein the method comprises the steps ofWherein γ＝Ms/Mp,ωP＝（Kp/Mp）1/2,ωS＝(Ks/Ms)1/2,ωa＝(ωP+ωS)/2,ζa＝(ζP+ζS)/2,6＝(ωP-ωS)/ωa, wherein M, K and ζ represent mass, spring rate and damping coefficient, respectively, subscripts p and S are the codes of the primary and secondary oscillators, respectively, F S represents the maximum bearing capacity of the secondary spring, and S 0 is the noise intensity. They all obey a lognormal distribution and the corresponding mean and standard deviation are M p, respectively: 1 and 0.1; m s: 0.01 and 0.001; k p: 1 and 0.2; k s: 0.01 and 0.002; ζ P: 0.05 and 0.02; ζ S: 0.02 and 0.01; f S: 15 and 1.5; s 0: 100 and 10; then converting the non-normal random variables into a standard normal space by using Rosenblatt conversion method;
S2, calculating a gradient value of the objective function, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration;
S3, checking whether the function value g (z) is smaller than 0, if yes, continuing the next step, otherwise, returning to S2, and continuing iteration;
S4, taking the end point obtained by the steepest descent method as the start point of a first-order reliability analysis method of three-term conjugate Barzilai-Borwein;
S5, taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method;
S6, adopting a non-monotonic line search technology and a deformed machine learning formula to ensure the global convergence of the method, enabling the algorithm to meet the descending condition and adjusting the step size to a reasonable range;
S7, checking whether coordinates of the t step and the t-1 step meet the value of [ z k-zk-1 ] tau or not, if so, outputting a most probable failure point and a reliable index, and if not, returning to S5 to iterate a new coordinate point continuously, wherein tau is a positive parameter with a preset value of 10 -5;
S8, solving the maximum possible failure point under the original space, and calculating the structural failure probability on the basis of the obtained reliable index.
The reliability analysis method disclosed in example 2 is compared with the reliability indexes calculated by other methods and the corresponding iteration times thereof in table 2 (HL-RF is a classical first-order reliability analysis method, yang is a first-order reliability analysis method based on chaos control, FAL is a first-order reliability method based on limiting the Armijo search direction, TCFS is a three-term conjugate gradient method directly conjugated to the gradient of the finite state function, ABB-TCG represents the three-term conjugate Barzilai-Borwein first-order reliability analysis method disclosed by the invention), and as can be seen from table 2, the highly nonlinear structure problem which cannot be solved by the HL-RF method is solved by adopting the three-term conjugate Barzilai-Borwein first-order reliability analysis method of the invention, compared with Yang, FAL and TCFS methods, the iteration times of the three-order reliability analysis method are greatly lower than those methods, and the accuracy and the speed are high, so that the robustness and the efficiency are better.
TABLE 2 comparative table of reliability index and iteration number calculated by various methods of EXAMPLE 2
In summary, compared with the prior art, the invention has the following advantages and effects:
(1) The invention firstly uses a traditional steepest descent method with exponential decay step length to reach the vicinity of the limit state surface as soon as possible, is ready for the next accurate search, and has a better starting point compared with other methods.
(2) The invention takes a non-negative cost function which does not involve gradient calculation as an objective function, fully exerts the excellent performance of a three-term conjugate gradient method to ensure higher precision requirement, combines Barzilai-Borwein gradient method to update iteration step length to improve algorithm efficiency, and is suitable for complex engineering problems with strong nonlinear/super-strong nonlinear function.
(3) The three-item conjugate Barzilai-Borwein first-order reliability analysis method with good robustness and high calculation efficiency is used for reliability analysis, the effectiveness and universality of the first-order second-moment method in the problem of structural reliability analysis are expanded, and the method has important significance in the field of reliability analysis.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
Furthermore, while the invention is described in the context of functional modules, it should be appreciated that, unless otherwise indicated, one or more of the described functions and/or features may be integrated in a single physical device and/or software module or one or more functions and/or features may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary to an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be apparent to those skilled in the art from consideration of their attributes, functions and internal relationships. Accordingly, one of ordinary skill in the art can implement the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative and are not intended to be limiting upon the scope of the invention, which is to be defined in the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present application has been described in detail, the present application is not limited to the embodiments described above, and those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present application, and these equivalent modifications or substitutions are included in the scope of the present application as defined in the appended claims.
Claims (10)
1. A structural reliability analysis method, comprising:
Determining product structure, function and random variable characteristic parameters in the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed;
Calculating a gradient value of an objective function according to the product structure, the function and the random variable characteristic parameter, selecting a negative gradient direction as a descending direction, determining an iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain an end point;
when the function value meets a first preset condition, the end point is used as a starting point of a first-order reliability analysis method of three conjugate Barzilai-Borwein;
Taking a non-negative cost function which does not involve gradient calculation as an objective function, and determining the search direction and the iteration step length of the three-term conjugate Barzilai-Borwein first-order reliability analysis method;
Performing iterative processing according to the starting point, the searching direction and the iterative step length, and outputting a maximum possible failure point and a reliable index which meet a second preset condition;
And solving the maximum possible failure point in the original space, and calculating the structural failure probability on the basis of the reliable index.
2. A method of structural reliability analysis according to claim 1, wherein the method further comprises:
According to a non-monotonic line search technique and a deformed machine learning formula, the method satisfies a descent condition and adjusts the iteration step size to a target range.
3. A structure reliability analysis method according to claim 1, wherein,
The expression of the descending direction is:
The calculation formula of the attenuation of the iteration step length is as follows:
Wherein, Representing a search direction; a gradient representing a limit state equation; a Euclidean norm representing the gradient; representing the step size; ρ represents a parameter for adjusting the step size; k represents an iteration counter; i represents the first stage of the algorithm.
4. A structure reliability analysis method according to claim 1, wherein,
The expression of the objective function is:
Wherein f (z) represents an objective function; z represents an iteration point in a standard normal space; g (z) represents a limit state equation; c represents a number greater than or equal to Constant of (2); a gradient representing a limit state equation; representing the Euclidean norm of the gradient.
5. The structural reliability analysis method according to claim 4, wherein the calculation formula of the falling direction of the objective function is:
Wherein d k represents the falling direction of the kth step objective function; z k+1 represents the design check point of step k+1; z k represents the design verification point of step k.
6. A structure reliability analysis method according to claim 2, wherein in the step of adjusting the iterative step size to the target range according to the non-monotonic line search technique and the deformed machine learning formula such that the method satisfies the falling condition,
When the objective function value is smaller than the moving average value, a non-monotonic line search technique based on Armijo criterion is adopted to determine the descending direction and the corresponding step size.
7. The method of claim 6, wherein in the step of adjusting the iterative step size to the target range according to a non-monotonic line search technique and a modified machine learning formula such that the method satisfies a decreasing condition,
When the objective function value overflows from the moving average value in the non-monotonic line searching technology, a deformed machine learning formula is selected to calculate a new iteration point in the non-linear searching stage.
8. A structural reliability analysis device, characterized by comprising:
the first module is used for determining the product structure, the function and the random variable characteristic parameters of the field to be analyzed; the function is used for determining the normal working capacity or the safe working critical state of a reflecting structure or a product in the field to be analyzed;
the second module is used for calculating the gradient value of the objective function according to the product structure, the function and the random variable characteristic parameter, selecting the negative gradient direction as the descending direction, determining the iteration step length which decays exponentially along with the iteration times, and starting iteration to obtain the end point;
A third module, configured to use the end point as a start point of a first-order reliability analysis method of three conjugates Barzilai-Borwein when the function value meets a first preset condition;
A fourth module, configured to determine a search direction and an iteration step size of the first-order reliability analysis method of the three conjugates Barzilai-Borwein by using a non-negative cost function that does not involve gradient calculation as an objective function;
a fifth module, configured to perform iterative processing according to the starting point, the search direction, and the iteration step, and output a maximum possible failure point and a reliability indicator that satisfy a second preset condition;
and a sixth module, configured to solve a maximum possible failure point in the original space, and calculate a structural failure probability based on the reliable index.
9. An electronic device comprising a processor and a memory;
The memory is used for storing programs;
the processor executing the program implements the method of any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that the storage medium stores a program that is executed by a processor to implement the method of any one of claims 1 to 7.
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