Structural reliability optimization design method and device based on uncertainty measure

Abstract

The embodiment of the invention discloses a structural reliability optimization design method and device based on uncertainty measure, and the method comprises the steps: determining a performance parameter of a structure, and constructing a limit state function of the structure under cognitive uncertainty according to an uncertain variable affecting the performance parameter, the uncertain variables obey continuous or regular uncertain distribution; according to the limit state function in combination with uncertain distribution or uncertain inverse distribution, constructing a reliability measurement model of the structure based on the uncertain test; determining a structural optimization design objective function, and establishing a design optimization model with the structural performance reliability constraint and the objective function in combination with the reliability measurement model; and constructing an equivalent analytic solution model of the design optimization model, and obtaining an optimal design variable in combination with boundary conditions of the design variables. By means of the method, product reliability analysis can be achieved and the optimal design scheme can be obtained under the condition that cognition is uncertain.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of structural reliability analysis, and in particular to a structural reliability optimization design method and device based on uncertainty measurement. Background Art

[0002] Reliability is a key quality characteristic of a product throughout its life cycle, which can be defined as the ability of a product to complete specified functions under specified conditions and within a specified time. Reliability-Based Design Optimization (RBDO) aims to find the best design solution for a product while ensuring that the reliability of the required performance criteria is not lower than the acceptable threshold. For example, in the reliability analysis and design process of mechanical structures, there are various inevitable uncertainties in material properties, geometric dimensions, and external loads. Sample data of these uncertainties are lacking, and there are differences in the measurement space. Traditional reliability theory based on probability measure requires the use of a large amount of statistical data to determine the probability distribution function of the input variables through the law of large numbers, and then obtain the performance reliability in the probability space and optimize the design. However, when all input variables are fuzzy or unclear in the reliability analysis process, and it is impossible to obtain sufficient historical statistical data and test sample data, these input variables can only be characterized by domain expert information with epistemic uncertainty. Since the exact probability density function of the input variables cannot be obtained, directly using probabilistic reliability theory to characterize reliability under epistemic uncertainty will result in the phenomenon that the analysis results are not in line with reality.

[0003] In order to solve this problem, it is necessary to find new quantitative theoretical tools and establish reasonable non-probabilistic reliability analysis models and optimization design methods. In the case of lack of sample data information and difficulty in obtaining accurate probability distribution characteristics, the measurement of cognitive uncertainty can be achieved based on non-probability theory. The most widely used non-probability theories include fuzzy set theory, possibility theory, interval theory, convex set theory, and evidence theory. On the one hand, when there is not enough sample statistical data to verify the accuracy of the membership function, the analysis results based on fuzzy set theory are questionable. On the other hand, due to the interval expansion problem of interval operations, the reliability indicators estimated by reliability analysis methods based on possibility theory, interval theory, convex set theory or evidence theory are generally too conservative.

[0004] In order to make up for the shortcomings of the above non-probabilistic epistemic uncertainty quantification theory, Liu Baoding first proposed the uncertainty theory in 2007 and supplemented and improved it in 2010. Because the uncertainty measure defined in the uncertainty space not only satisfies the subadditivity of epistemic uncertainty, but also has self-duality. Uncertainty theory has been widely used in many fields in recent years, including maintenance strategy, optimal decision, uncertain finance, uncertain risk analysis, availability analysis and residual life prediction. At present, there are few applications of uncertainty theory to structural performance reliability modeling and optimization design analysis. Summary of the invention

[0005] In view of the above problems, an embodiment of the present invention provides a structural reliability optimization design method and device based on uncertainty measurement, which overcomes the above problems or at least partially solves the above problems.

[0006] According to one aspect of an embodiment of the present invention, a structural reliability optimization design method based on uncertainty measurement is provided, the method comprising: determining performance parameters of the structure, and constructing a limit state function of the structure under cognitive uncertainty according to uncertain variables affecting the performance parameters, wherein the uncertain variables obey a continuous or regular uncertain distribution; constructing a reliability measurement model of the structure based on uncertainty measurement according to the limit state function combined with the uncertain distribution or the uncertain inverse distribution; determining a structural optimization design objective function, and establishing a design optimization model with the structural performance reliability constraints and the objective function in combination with the reliability measurement model; constructing an equivalent analytical solution model of the design optimization model, and obtaining the optimal design variables in combination with the boundary conditions of the design variables.

[0007] Optionally, the step of constructing a reliability measurement model of the structure based on uncertainty measurement according to the limit state function in combination with uncertainty distribution includes: calculating the reliability of the structure based on uncertainty measurement according to the limit state function through the uncertainty distribution of uncertain variables. The reliability measurement model of the structure based on uncertainty measurement is obtained:

[0008]

[0009] Among them, τ is the uncertainty vector τ=(τ1,τ2,…,τ n ) T,τ1,τ2,…,τ n is an uncertain variable, which obeys the continuous uncertain distribution γ1,γ2,…,γ n , the limit state function g(τ1,τ2,…,τ n ) about τ1,τ2,…,τ m is strictly monotonically increasing, and about τ m+1 ,τ m+2 ,…,τ n Strictly monotonically decreasing, is the confidence of the failure event, and sup represents the upper bound.

[0010] Optionally, constructing the reliability measurement model of the structure based on uncertainty measure according to the limit state function in combination with uncertain inverse distribution includes: solving the reliability measurement model of the structure based on uncertainty measure according to the limit state function using uncertain inverse distribution:

[0011]

[0012] Among them, τ1, τ2, …, τ n is an uncertain variable, which obeys the regular uncertain distribution γ1,γ2,…,γ n , the failure reliability of the structure α is the solution of the equation, the reliability based on the uncertainty measure is 1-α, and the limit state function g(τ1,τ2,…,τ n ) about the uncertain variables τ1,τ2,…,τ m Strictly monotonically increasing, and with respect to the uncertain variable τ m+1 ,τ m+2 ,…,τ n Strictly monotonically decreasing.

[0013] Optionally, determining the structural optimization design objective function includes: if the structure needs to satisfy multiple mutually constrained optimization objective functions, assigning corresponding weight factors to each objective function according to its importance; and performing weighted summation on the multiple objective functions to obtain the total objective function of the structure.

[0014] Optionally, the determination of the structural optimization design objective function and the establishment of a design optimization model with the structural performance reliability constraint and the objective function in combination with the reliability measurement model also include: for any of the limit state functions, obtaining the performance reliability value of the structure according to the reliability measurement model based on uncertainty measurement; and building a reliability design optimization model of the structure that meets the corresponding expected reliability value according to the overall objective function and performance reliability value of the structure.

[0015] Optionally, the input variables of the structure include design variables and uncertain non-design variables, and the design variables include: deterministic design variables and uncertain design variables, and the uncertain design variables and the uncertain non-design variables are uncertain variables. The determination of the structural optimization design objective function, combining the reliability measurement model to establish a design optimization model with the structural performance reliability constraint and the objective function, also includes: constructing a reliability-based structural design optimization model according to the objective function and the reliability constraint conditions determined based on the reliability measurement model combined with the boundary conditions of the design variables in the structure:

[0016] Solving for {d,x}

[0017]

[0018] Satisfy: reliability constraints,

[0019] Boundary conditions, d Lower ≤d≤d Upper ,x Lower ≤x≤x Upper ,j=1,2,…,N g

[0020] Among them, d, x, τ are vectors composed of deterministic design variables, uncertain design variables and uncertain non-design variables, respectively, and f i (d,x,τ),ω i are the i-th objective function and the corresponding weight factor, N f is the total number of objective functions, g j (d,x,τ), are the reliability, limit state function and expected reliability value of the jth reliability constraint condition, respectively. g is the number of reliability constraints, d Lower and d Upper are the upper and lower bound vectors of the deterministic design variables, x Lower and x Upper are respectively the upper and lower bound vectors of the uncertain design variables; the reliability-based design optimization model is solved to obtain the optimal design variables that meet the reliability constraints of the structure.

[0021] Optionally, constructing an equivalent analytical solution model of the design optimization model and obtaining optimal design variables in combination with boundary conditions of design variables further includes: performing equivalent planning analysis on the reliability-based design optimization model to convert the reliability-based design optimization model into a clear equivalent planning model as described below:

[0022] Solving for {d,x}

[0023]

[0024] Satisfy: reliability constraints,

[0025]

[0026] Boundary conditions, d Lower ≤d≤d Upper ,x Lower ≤x≤x Upper ,j=1,2,…,N g ;

[0027] The clear equivalent programming model is solved to obtain the optimal design variables that meet the reliability constraint conditions of the structure.

[0028] Based on the same inventive concept, a structural reliability optimization design device based on uncertainty measurement is provided, including: a limit state function acquisition unit, used to determine the performance parameters of the structure, and construct the limit state function of the structure under cognitive uncertainty according to the uncertain variables affecting the performance parameters, and the uncertain variables obey continuous or regular uncertain distribution; a reliability analysis acquisition unit, used to construct a reliability measurement model of the structure based on uncertainty measurement according to the limit state function combined with uncertain distribution or uncertain inverse distribution; a design optimization model acquisition unit, used to determine the structural optimization design objective function, and establish a design optimization model with the structural performance reliability constraint and objective function in combination with the reliability measurement model; a design optimization solution unit, used to construct an equivalent analytical solution model of the design optimization model, and obtain the optimal design variables in combination with the boundary conditions of the design variables.

[0029] Based on the same inventive concept, an embodiment of the present invention further proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the aforementioned method when executing the program.

[0030] Based on the same inventive concept, an embodiment of the present invention further proposes a computer storage medium, in which at least one executable instruction is stored, and the executable instruction enables a processor to execute the aforementioned method.

[0031] The embodiment of the present invention determines the performance parameters of the structure, and constructs the limit state function of the structure under cognitive uncertainty according to the uncertain variables affecting the performance parameters, wherein the uncertain variables obey a continuous or regular uncertain distribution; constructs a reliability measurement model of the structure based on uncertainty measurement according to the limit state function combined with the uncertain distribution or the uncertain inverse distribution; determines the structural optimization design objective function, and establishes a design optimization model with the structural performance reliability constraint and the objective function in combination with the reliability measurement model; constructs an equivalent analytical solution model of the design optimization model, and obtains the optimal design variables in combination with the boundary conditions of the design variables, so as to realize product reliability analysis under cognitive uncertainty and obtain the optimal design solution.

[0032] The above description is only an overview of the technical solution of the embodiment of the present invention. In order to more clearly understand the technical means of the embodiment of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the embodiment of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0034] Figure 1 A schematic diagram of a flow chart of a structural reliability optimization design method based on uncertainty measurement provided by an embodiment of the present invention is shown;

[0035] Figure 2 A schematic diagram of a structural reliability optimization design method based on uncertainty measurement according to an embodiment of the present invention is shown;

[0036] Figure 3 An example diagram showing a reliability optimization design of a hatch door latch mechanism according to an embodiment of the present invention is shown;

[0037] Figure 4 A schematic diagram showing the reliability optimization design result of the hatch door latch mechanism according to an embodiment of the present invention is shown;

[0038] Figure 5 An example diagram showing a reliability optimization design of a vehicle torque arm structure according to an embodiment of the present invention;

[0039] Figure 6 A schematic diagram showing the reliability optimization design result of the automobile torque arm structure according to an embodiment of the present invention is shown;

[0040] Figure 7A schematic diagram of the structure of a structural reliability optimization design device based on uncertainty measurement provided by an embodiment of the present invention is shown;

[0041] Figure 8 A schematic diagram of an electronic device in an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0042] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to enable the scope of the present invention to be fully communicated to those skilled in the art.

[0043] Figure 1 FIG. 2 is a flow chart of a structural reliability optimization design method based on uncertainty measurement provided by an embodiment of the present invention. Figure 1 As shown in FIG. 1 , the structural reliability optimization design method based on uncertainty measurement is applied to the server, including:

[0044] Step S11: determining performance parameters of the structure, and constructing a limit state function of the structure under epistemic uncertainty according to uncertain variables affecting the performance parameters, wherein the uncertain variables obey a continuous or regular uncertainty distribution.

[0045] For uncertain variables that affect structural performance parameters, the performance limit state of the structure under a certain failure mode is generally described by the limit state function of the uncertain variables. The limit state function involves n-dimensional uncertain variables x1, x2, …, x n , including material properties, geometric dimensions, and external load conditions. The epistemic uncertainty problem can be defined as the effect of epistemic uncertainty on all uncertain variables, which can be expressed as an uncertainty vector τ = (τ1, τ2, …, τ n ) T In uncertain space All input variables are uniformly represented. Uncertain variables obey continuous or regular uncertainty distribution, such as normal uncertainty distribution, zigzag uncertainty distribution and linear uncertainty distribution, etc., which are not specifically limited here. The embodiments of the present invention do not specifically limit the structure, which can be a mechanism that can complete a certain function or a single component structure. For example, the structure can be a hatch lock mechanism or a torque arm structure.

[0046] In uncertainty theory, in order to reasonably describe the epistemic uncertainty information and address the problem that non-probability measures such as possibility measures do not satisfy the self-duality, a class of uncertainty measures with subadditive properties that satisfy the self-dual property is adopted. ).

[0047] Definition of uncertainty measure: If Γ is a non-empty set, it is a σ-algebra in Γ, where each element Λ is an event. Then if the set function If the following four axioms are satisfied, it is defined as an uncertainty measure:

[0048] Axiom 1 (Normality) For all sets Γ,

[0049] Axiom 2 (Duality) For any event Λ,

[0050] Axiom 3 (Subadditivity) For any countable sequence of events Λ1, Λ2, …, it satisfies:

[0051]

[0052] Axiom 4 (Product Axiom) If is a series of uncertain spaces, Λ k For any If we select an event from , k = 1, 2, ..., then the product of uncertainty measures is still an uncertainty measure and satisfies the following equation:

[0053]

[0054] Definition of uncertainty space: If Γ is a non-empty set, is a σ-algebra in Γ, is an uncertain measure, then the triple consisting of the above elements An uncertain space.

[0055] Definition of uncertain variables: The uncertain variable ξ is a variable from the uncertain space A measurable function of {ξ∈B} to the set of real numbers is an event on any real Borel set B.

[0056] Assume ξ1,ξ2,…,ξ n is a set of uncertain variables, f is a real-valued measurable function, then ξ=f(ξ1,ξ2,…,ξ n ) is also an uncertain variable, that is, for any τ∈Γ, ξ(τ) can be expressed as follows:

[0057] ξ(τ)=f(ξ1(τ),ξ2(τ),…,ξ n(τ)

[0058] Satisfies Theorem 1 (independence): uncertain variables ξ1,ξ2,…,ξ n Mutual independence occurs if and only if the following equations are satisfied:

[0059]

[0060] Among them, B1, B2, …, B n is any Bore set on the set of real numbers.

[0061] Definition of uncertainty distribution: If ξ is an uncertain variable, then the uncertainty distribution Φ(x) of ξ with respect to any real number x can be defined as follows:

[0062]

[0063] In general, if the uncertainty distribution Φ(x) is a continuous function that is strictly monotonically increasing with respect to x and satisfies 0<Φ(x)<1, lim x→-∞ Φ(x)=0,lim x→∞ Φ(x)=1, then the uncertainty distribution is defined as the canonical uncertainty distribution function.

[0064] Example (normal uncertainty distribution): If the uncertain variable ξ has the following normal uncertainty distribution, it is defined as a normal uncertain variable:

[0065]

[0066] It is expressed as Where m and σ are the uncertainty expectation and uncertainty variance, respectively. In particular, if m = 0 and σ = 1 in the normal uncertainty distribution, it is called the standard normal uncertainty distribution, which is expressed as

[0067] Satisfies Theorem 2: Let ξ1,ξ2,…,ξ n is a set of independent uncertain variables, each with a continuous uncertainty distribution function Φ1, Φ2, …, Φ n If f(ξ1,ξ2,…,ξ n ) is the value of ξ1,ξ2,…,ξ m Monotonically increasing, about ξ m+1 ,ξ m+2 ,…,ξ n If the function ξ(ξ1,ξ2,…,ξ n ) can be expressed as:

[0068]

[0069] In addition, assuming Φ1, Φ2, …, Φ n is a regular uncertain distribution function, then the uncertain distribution f(ξ1,ξ2,…,ξ n ) can be expressed as follows:

[0070]

[0071] Definition of uncertain programming: If ξ is an uncertain vector, x is a decision vector, and f(x,ξ) is an uncertain objective function. i (x,ξ)≤0,i=1,2,…,l does not necessarily hold. Decision makers naturally hope that the uncertain constraints are within the confidence level α1,α2,…,α l The following relationship is satisfied:

[0072]

[0073] Since it is impossible to directly minimize the uncertain variable f(x,ξ), the decision maker can minimize the expectation of f(x,ξ) In order to obtain the minimum optimal solution with uncertain expected target value under a set of chance constraints, the uncertain programming model can be defined as follows:

[0074]

[0075] The characteristic of this chance-constrained uncertain programming model is that the objective function and constraints are composed of uncertain variables rather than random variables.

[0076] In the embodiment of the present invention, the performance reliability analysis is performed based on the “stress-strength interference” model, where the generalized stress S (τ1, τ2, …, τ n ,ω) includes load, temperature and corrosion, etc., and the corresponding generalized strength R(τ1,τ2,…,τ n ,ω) includes fatigue strength, heat resistance and corrosion resistance, etc., then the uncertainty limit state function (ULSF) can be defined as follows:

[0077] Z(τ)=g(τ1,τ2,…,τ n )=R(τ1,τ2,…,τ n )-S(τ1,τ2,…,τ n )

[0078] The reliability of structural performance can be measured by uncertainty The confidence of the quantitative reliable event {Z(τ)>0}, namely the Uncertain Measure Based Reliability (UMBR), is defined as follows:

[0079]

[0080] in, Different from probabilistic reliability, when the sample data of the input variables is insufficient, it is impossible to obtain an accurate probability distribution function and perform structural reliability estimation. The embodiment of the present invention proposes a reliability measurement model based on uncertainty measurement in an uncertain space to make up for the defects of the probabilistic reliability measurement model.

[0081] Step S12: constructing a reliability measurement model of the structure based on uncertainty measure according to the limit state function combined with uncertainty distribution or uncertain inverse distribution.

[0082] Assume that the limit state function Z(τ)=g(τ1,τ2,…,τ n ) obeys an uncertain distribution Φ z(τ) (z), where τ1,τ2,…,τ n are mutually independent uncertain variables, then the reliability of the failure event {Z(τ)≤0} can be calculated as:

[0083]

[0084] However, in actual engineering structural problems, it is often difficult for designers to obtain the uncertainty distribution Φ of the uncertain limit state function. z(τ) (z), the above formula is difficult to solve and apply. In order to solve this problem and improve the practicality of the unified reliability measurement model in the uncertain space established by the present invention, a method for solving the UMBR reliability under different conditions will be proposed below.

[0085] In step S12, optionally, first, for any of the limit state functions, a reliability measurement model of the structure is constructed according to the limit state function combined with uncertain variable characteristics, and then the reliability of the structure based on the uncertainty measure is calculated.

[0086] In the embodiment of the present invention, if the limit state function Z(τ)=g(τ1,τ2,…,τ n ) are independent uncertain variables τ1,τ2,…,τ n Obey the continuous uncertain distribution γ1,γ2,…,γ n When the limit state function is about τ1,τ2,…,τ m is strictly monotonically increasing, and about τ m+1 ,τ m+2 ,…,τn Strictly monotonically decreasing, the reliability measurement model of the structure is constructed according to the limit state function combined with the characteristics of uncertain variables, and the reliability of the structure based on uncertainty measurement is calculated

[0087]

[0088] Among them, τ is the uncertainty vector τ=(τ1,τ2,…,τ n ) T ,τ1,τ2,…,τ n are mutually independent uncertain variables, obeying the uncertain distribution γ1,γ2,…,γ n , the limit state function g(τ1,τ2,…,τ n ) about τ1,τ2,…,τ m is strictly monotonically increasing, and about τ m+1 ,τ m+2 ,…,τ n Strictly monotonically decreasing, is the confidence of the failure event, and sup is the upper bound.

[0089] Considering the difficulty in calculating the above formula due to the complexity of the limit state function, the embodiment of the present invention also proposes the following solution to UMBR based on the uncertain inverse distribution method (IDBM). If the performance limit state function Z(τ)=g(τ1,τ2,…,τ n ) are independent uncertain variables τ1,τ2,…,τ n Obeying regular uncertain distribution functions (Regular Uncertainty Distributions) γ1,γ2,…,γ n When the limit state function is about τ1,τ2,…,τ m is strictly monotonically increasing, and about τ m+1 ,τ m+2 ,…,τ n Strictly monotonically decreasing, the structural failure reliability is And the UMBR reliability can be calculated as According to the limit state function, the uncertainty inverse distribution is used to construct the reliability measurement model of the structure based on uncertainty measurement:

[0090]

[0091] Here, α is the solution of the equation.

[0092] Step S13: determining the structural optimization design objective function, and establishing a design optimization model with the structural performance reliability constraint and the objective function in combination with the reliability measurement model.

[0093] In the embodiment of the present invention, the engineering structure design problem may include N f There are mutually constrained objective functions f that need to be considered simultaneously i (d,x;τ),i=1,2,…,N f , while uncertain multi-objective optimization belongs to uncertain programming, and its constraints and objective functions contain uncertain variables. In step S13, if the structure needs to satisfy multiple mutually constrained optimization objective functions, corresponding weight factors are assigned according to the importance of each objective function; weighted summation is performed on the multiple objective functions to obtain the total objective function of the structure.

[0094] On the basis of the reliability measurement model based on uncertainty measurement established above, UMBR reliability is introduced as a constraint condition of reliability-based design optimization (RBDO) model, and a design optimization model based on UMBR reliability (Uncertainty Reliability-Based Design Optimization, URBDO) under cognitive uncertainty is constructed.

[0095] In order to solve the structural design optimization problem with cognitive uncertainty under the condition of insufficient sample data, an embodiment of the present invention proposes a structural design optimization URBDO model based on UMBR reliability and uncertain programming model. Under the condition of cognitive uncertainty, the URBDO model uses uncertain variables to uniformly describe the input variables, introduces the UMBR reliability requirements into the constraints of the classic RBDO model, and achieves the goal of ensuring the structural safety requirements while seeking the optimal design under the objectives of minimum cost or lightest weight by changing the design variables.

[0096] The input variables of the structural optimization design problem include design variables and uncertain non-design variables, and the design variables include: deterministic design variables and uncertain design variables, and the uncertain design variables and the uncertain non-design variables are uncertain variables. g The limit state function g j (d,x;τ),j=1,2,…,N g The reliability optimization design problem is: x=(x1,x2…,x m ) T and τ=(τ1,τ2,…,τ n ) Tare vectors of deterministic design variables, uncertain design variables, and uncertain non-design variables. Design engineers tend to ensure that the UMBR reliability is higher than the target reliability. Combined with the definition of UMBR reliability given above, the corresponding reliability constraint can be expressed as:

[0097]

[0098] Structural design includes N f There are mutually constrained objective functions f that need to be considered simultaneously i (d,x;τ),i=1,2,…,N f By weighted summing each objective function, the following general URBDO model based on UMBR reliability can be established. Therefore, in step S13, firstly, a reliability-based design optimization model is constructed according to the objective function and the reliability constraint conditions determined based on the reliability measurement model combined with the boundary conditions of the design variables:

[0099] Solving for {d,x}

[0100]

[0101] Satisfy: reliability constraints,

[0102] Boundary conditions, d Lower ≤d≤d Upper ,x Lower ≤x≤x Upper ,j=1,2,…,N g

[0103] Among them, d, x, τ are deterministic design variables, uncertain design variables and uncertain non-design variables, respectively, and f i (d,x,τ),ω i are the i-th objective function and the corresponding weight factor, and satisfy N f is the number of objective functions, g j (d,x,τ), are the reliability, limit state function and expected reliability value of the jth reliability constraint condition, respectively. g is the number of reliability constraints, d Lower and d Upper are the upper and lower bound vectors of the deterministic design variables, x Lower and x Upperare the upper and lower bound vectors of uncertain design variables respectively. Then the reliability-based design optimization model is solved to obtain the optimal design variables that meet the reliability constraints of the structure. Since the objective function is also an uncertain variable, the objective function f is directly minimized. i (d,x;τ) is more difficult. Therefore, minimizing f i The uncertain expectation E[f i (d,x;τ)] is more reasonable.

[0104] Step S14: constructing an equivalent analytical solution model of the design optimization model, and obtaining optimal design variables in combination with boundary conditions of the design variables.

[0105] In an embodiment of the present invention, in order to solve the reliability-based design optimization (URBDO) model constructed above, an equivalent programming analytical calculation method is proposed in the embodiment of the present invention. The URBDO model established above can be converted into a crisp equivalent programming (CEP) model under certain conditions. The crisp equivalent programming model facilitates engineering designers to quickly obtain the optimal design solution in the initial design stage of the structure.

[0106] Assume that the performance limit state function corresponding to the jth constraint condition in structural optimization is g j (d,τ),j=1,2,…,N g ,in, and τ=(τ1,τ2,…,τ n ) T are vectors of deterministic design variables and uncertain variables, respectively. The uncertain variables are independent of each other and all obey the regular uncertain distribution γ1,γ2,…,γ n If the limit state function g j (d,τ1,τ2,…,τ n )about is strictly monotonically increasing, and about Strictly monotonically decreasing. The objective function i i (d; τ1, τ2, …, τ n ), i=1,2,…,N f about is strictly monotonically increasing, and about Strictly monotonically decreasing. Optionally, the design optimization model based on UMBR reliability is subjected to equivalent planning analytical transformation, and the design optimization model based on UMBR reliability is converted into the following clear equivalent planning CEP model:

[0107] Solving for {d,x}

[0108]

[0109] Satisfy: reliability constraints,

[0110]

[0111] Boundary conditions, d Lpwer ≤d≤d Upper ,x Lower ≤x≤x Upper ,j=1,2,…,N g ;

[0112] Then the clear equivalent planning model is solved to obtain the optimal design variables that meet the reliability constraints of the structure. After converting the general URBDO model into an equivalent CEP model, structural engineers can use classical numerical methods or heuristic algorithms to optimize the design.

[0113] The complete structural reliability optimization design method based on uncertainty measurement of the embodiment of the present invention is as follows: Figure 2 As shown, including:

[0114] Step 100: Determine the input variables of the structure.

[0115] The input variables of the structure are determined according to the design requirements of the structure, wherein the input variables include design variables and uncertain non-design variables, and the design variables may include deterministic design variables and uncertain design variables, and the uncertain design variables and uncertain non-design variables are uncertain variables. Deterministic design variables refer to input variables that do not obey any distribution.

[0116] Step 101: Construct the limit state function of the structure.

[0117] According to the relationship between the structural performance parameters and the input variables, the performance reliability analysis is carried out based on the "stress-strength interference" model, and the corresponding limit state function is constructed:

[0118] Z(τ)=g(τ1,τ2,…,τ n )=R(τ1,τ2,…,τ n )-S(τ1,τ2,…,τ n )

[0119] Z(τ), g(τ1,τ2,…,τ n ) is the limit state function, S(τ1,τ2,…,τ n ) is the generalized stress of the structure, R(τ1,τ2,…,τ n ) is the corresponding generalized intensity, τ1,τ2,…,τ n is an uncertain variable.

[0120] Step 102: τ1, τ2, …, τn They are represented by continuous uncertain distributions respectively.

[0121] That is, the uncertain variables τ1, τ2, …, τ n can obey continuous uncertain distribution respectively.

[0122] Step 103: τ1, τ2, …, τ n They are represented by regular uncertain distributions respectively.

[0123] That is, the uncertain variables τ1, τ2, ..., τ n can obey regular uncertain distribution respectively.

[0124] Step 104: Uncertainty measure based reliability UMBR.

[0125] Through uncertainty measurement Quantify the confidence of reliable events {Z(τ)>0}, that is, the reliability based on uncertainty measurement (UMBR): in, Different from probabilistic reliability, a reliability measurement model based on uncertainty measure is constructed based on the continuous uncertainty distribution of uncertain variables, or a reliability measurement model based on uncertainty measure is constructed based on the uncertainty inverse distribution.

[0126] Step 105: URBDO model with UMBR constraints.

[0127] According to the reliability constraints, the final objective function and the boundary conditions of the structural design variables, a UMBR reliability-based design optimization (URBDO) model under cognitive uncertainty is constructed to obtain the optimal design variables that meet the structural reliability constraints. f The multiple mutually constrained objective functions that need to be considered simultaneously are weighted summed to obtain the final objective function of the structure.

[0128] Step 106: Clarify the equivalent planning CEP model.

[0129] The UMBR reliability-based design optimization (URBDO) model is converted into an equivalent planning model to obtain the corresponding clear equivalent planning (CEP) model. Based on the CEP model, engineering designers can quickly obtain the optimal design solution in the initial design stage of the structure.

[0130] Step 107: Determine whether it is an optimal solution. If yes, go to step 108, otherwise return to step 104.

[0131] It is determined whether the design variables obtained based on the clear equivalent programming model in step 106 are the optimal solution.

[0132] Step 108: Obtain optimal design variables.

[0133] If the design variables obtained based on the clear equivalent programming model in step 106 are the optimal solutions, the optimal solutions are output to complete the reliability optimization design of the current structure.

[0134] The embodiment of the present invention takes the structural reliability optimization design problem as the main research object, based on the performance limit state, for reliability quantitative analysis, around the key point of reliability modeling and solving under uncertainty information conditions, with the uncertainty theory with sub-additive characteristics as the mathematical theoretical basis, a performance reliability analysis model that characterizes cognitive uncertainty through uncertain variables is proposed, and then the reliability design optimization problem is discussed based on the sub-additive measurement reliability theory, and finally the reliability optimization design is achieved under the cognitive uncertainty conditions based on small samples. The present invention provides methodological theoretical support for reliability design and optimization analysis of actual engineering products throughout their life cycle. The following is an explanation of the hatch lock mechanism and the torque arm structure respectively.

[0135] The reliability analysis of the hatch lock mechanism can be simplified to the reliability analysis problem of a crank slider mechanism, such as Figure 3 As shown in the figure, according to the kinematic analysis of the crank slider mechanism, the horizontal distance between the fulcrum and the lock end point can be expressed as:

[0136]

[0137] Among them, the input variable α1 is the angle between the crank and the horizontal direction, and the input variables r, L1, L2, and e are size parameters, and α1, r, L1, L2, and e are uncertain variables.

[0138] When the length of the performance parameter L is not less than L3 (mm), the lock can work normally, otherwise the lock cannot work normally. Due to the lack of sample data, it is assumed that all input variables ξ=(α1,r,L1,L2,e) T All obey mutually independent normal uncertainty distributions, then the following uncertain limit state function of the locking mechanism can be established:

[0139] g(α1,r,L1,L2,e)=L(α1,r,L1,L2,e)-L3

[0140] The distribution parameters of the input variables in the embodiment of the present invention are shown in Table 1. The reliability analysis method based on uncertainty measurement established by the present invention is applied to evaluate the reliability of the locking mechanism. In order to verify the effectiveness and superiority of the method of the embodiment of the present invention, the traditional first-order reliability method (FORM) method based on probability theory is also applied to this implementation case. At this time, all input variables are considered to obey the normal probability distribution, as shown in Table 1. When L3∈[286,291], the reliability estimation results of the locking mechanism obtained by the probabilistic reliability method and the method of the present invention are compared. Figure 4 shown.

[0141] Table 1 Distribution type and parameters of input variables in Example 1

[0142]

[0143]

[0144] according to Figure 4 It can be seen that as L3 increases, both UMBR reliability and probability measure based reliability (PMBR) will decrease, and the change trends of UMBR and PMBR are consistent overall, because as L3 increases, the reliability of the locking mechanism will decrease. Therefore, the UMBR reliability proposed in the present invention can effectively describe the change trend of mechanism reliability under epistemic uncertainty.

[0145] It is worth noting that the reliability estimated by the uncertainty measurement method of the present invention is smaller than the result calculated based on the probability measurement. For the reliability problem under cognitive uncertainty, assuming that the uncertain variables are random variables, the use of probability measurement theory analysis will ignore the impact of cognitive uncertainty, resulting in overly optimistic calculation results. On the one hand, when the relevant information of the input variables is insufficient and the specific probability distribution function cannot be obtained, it is suitable to use the structural reliability measurement model based on uncertainty measurement for analysis. On the other hand, when the relevant statistical information of the input variables is sufficient to obtain the actual frequency, it is more reasonable to use probability measurement theory. When the statistical data of the input variables is lacking, the information of cognitive uncertainty can be obtained by combining incomplete sample data and the subjective experience of experts, and the reliability measurement model based on uncertainty measurement proposed by the present invention is used for analysis, which can ensure the safety of the structure / mechanism to a greater extent.

[0146] If the structure is a car torque arm structure, such as Figure 5 As shown in the figure, the geometrical parameters a, d1, d2 and l of the automobile torque arm structure are design variables. Other input variables include Young's modulus E, yield strength S yand external stress Q are uncertain variables. Under the conditions of strength and buckling constraints, the structural volume is required to be minimized, and its initial deterministic design optimization model can be expressed as follows:

[0147] Solve d = [a, d1, d2, l] T

[0148]

[0149] satisfy

[0150]

[0151] 5≤a≤15

[0152] 45≤d1≤55

[0153] 55≤d2≤75

[0154] 110≤l≤210

[0155] Where d is the vector of deterministic design variables, the objective function V(d) represents the volume of the torque arm, and the limit state function g1(d; Q, S y ) means Figure 5 The yield failure of section AA is shown, where The limit state function g2(d; E, Q) corresponding to the second constraint condition represents the buckling failure of the two connecting rods.

[0156] Table 2 Distribution type and parameters of torque arm input variables

[0157]

[0158] Assume that due to insufficient sample data, Q, S y and E can be respectively represented by the normal uncertainty distribution γ Q (x), and γ E (x) description. Table 2 lists the distribution types and parameters of the input variables. Since the first limit state function g1(d; Q, S y ) is continuous and about S y The second limit state function g2(d; E, Q) is also continuous and strictly increasing with respect to E, and strictly decreasing with respect to Q. Therefore, the URBDO model of the torque arm structure can be equivalently replaced by a clear equivalent planning model, and the following is established at different expected reliability levels: The torque arm CEP model with epistemic uncertainty is as follows:

[0159] Solve d = [a, d1, d2, l] T

[0160]

[0161] satisfy

[0162]

[0163] 5≤a≤15

[0164] 45≤d1≤55

[0165] 55≤d2≤75

[0166] 110≤l≤210

[0167] After the uncertain planning problem is transformed into a CEP model, the model can be solved using MATLAB software. In order to demonstrate the rationality of the proposed method, when Q, S y and E are considered to obey normal probability distribution, that is, Q~N(5500,900 2 ), S y ~N(170,30 2 ) and E~N(2.1×10 11 ,(2.0×10 10 ) 2 ), the classic RBDO model based on probability measure and its reliability index approach (RIA) are used for reference comparison. In addition, when all input variables are regarded as constants equal to their expected values, the deterministic optimization design method is also used for reference. When the expected reliability is within [0.50, 0.99], the optimization results of the objective function are compared. Figure 6 As shown, Table 3 lists the detailed comparison results when the expected reliability is 0.90 and 0.99 respectively.

[0168] Table 3 Comparison of optimization results when the expected reliability is 0.9 and 0.99 respectively

[0169]

[0170] Depend on Figure 6 The optimization design results shown in the figure show that as the reliability requirements increase, more materials are needed to manufacture the torque arm. According to the comparison results, the optimal volume change trends estimated by the RBDO and URBDO models are basically similar. Figure 6As shown in Table 3, when the reliability level is in the range of [0.50, 0.98], the target value calculated by the URBDO model is lower than the target value estimated by the RBDO model. However, when the reliability level is in the range of [0.98, 0.99], the target value estimated by the URBDO model is significantly higher than the target value calculated by the RBDO model. This is because in the RBDO model, uncertain variables with epistemic uncertainty are also regarded as random variables, and the significant impact of epistemic uncertainty is ignored by the RBDO model. When epistemic uncertainty information appears, the URBDO model based on uncertainty measurement can more accurately handle the structural optimization design problem under epistemic uncertainty. As the reliability requirements increase, the performance difference between the two optimization models increases, that is, the structural design is more sensitive to the impact of epistemic uncertainty. Therefore, the URBDO model can measure and reflect the significant impact of epistemic uncertainty on the optimization design of engineering structures. In addition, the design variables a and d2 have a significant impact on the optimization results of the torque arm, and structural engineers should focus on these two design variables during the design process.

[0171] When sample data of input variables in reliability analysis and design optimization problems are lacking, that is, when cognitive uncertainty exists, the reliability measurement model based on uncertainty measurement and its URBDO model can obtain the optimal design solution in the initial design stage of the product and provide theoretical guidance for engineering designers.

[0172] In summary, the structural reliability optimization design method based on uncertain measurement in the embodiment of the present invention determines the performance parameters of the structure, and constructs the limit state function of the structure under cognitive uncertainty according to the uncertain variables affecting the performance parameters, and the uncertain variables obey continuous or regular uncertain distribution; constructs a reliability measurement model of the structure based on uncertain measurement according to the limit state function combined with the uncertain distribution or the uncertain inverse distribution; determines the structural optimization design objective function, and establishes a design optimization model with the structural performance reliability constraint and the objective function in combination with the reliability measurement model; constructs an equivalent analytical solution model of the design optimization model, and obtains the optimal design variables in combination with the boundary conditions of the design variables, so as to realize product reliability analysis under cognitive uncertainty and obtain the optimal design solution.

[0173] The above specific embodiments of the present invention are described. In some cases, the actions or steps recorded in the embodiments of the present invention can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the process depicted in the accompanying drawings does not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0174] Based on the same concept, the embodiment of the present invention also provides a structural reliability optimization design device based on uncertainty measurement. Applied to a server. Figure 7 As shown, the structural reliability optimization design device based on uncertainty measurement includes: a limit state function acquisition unit, a reliability analysis acquisition unit, a design optimization model acquisition unit and a design optimization solution unit.

[0175] A limit state function acquisition unit, used for determining performance parameters of the structure, and constructing a limit state function of the structure under epistemic uncertainty according to uncertain variables affecting the performance parameters, wherein the uncertain variables obey a continuous or regular uncertainty distribution;

[0176] A reliability analysis acquisition unit, used to construct a reliability measurement model of the structure based on uncertainty measurement according to the limit state function combined with uncertainty distribution or uncertain inverse distribution;

[0177] A design optimization model acquisition unit is used to determine the structural optimization design objective function, and to establish a design optimization model having the structural performance reliability constraint and the objective function in combination with the reliability measurement model;

[0178] The design optimization solution unit is used to construct an equivalent analytical solution model of the design optimization model and obtain the optimal design variables in combination with the boundary conditions of the design variables.

[0179] For the convenience of description, the above device is described as various modules according to their functions. Of course, when implementing the embodiment of the present invention, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0180] The device of the above embodiment is applied to the corresponding method in the above embodiment, and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0181] Based on the same inventive concept, an embodiment of the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method described in any one of the above embodiments is implemented.

[0182] An embodiment of the present invention provides a non-volatile computer storage medium, wherein the computer storage medium stores at least one executable instruction, and the computer executable instruction can execute the method described in any of the above embodiments.

[0183] Figure 8A more specific schematic diagram of the hardware structure of an electronic device provided in this embodiment is shown, and the device may include: a processor 801, a memory 802, an input / output interface 803, a communication interface 804, and a bus 805. The processor 801, the memory 802, the input / output interface 803, and the communication interface 804 are connected to each other in communication within the device through the bus 805.

[0184] The processor 801 can be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solution provided by the method embodiment of the present invention.

[0185] The memory 802 may be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 802 may store an operating system and other application programs. When the technical solution provided by the method embodiment of the present invention is implemented by software or hardware, the relevant program code is stored in the memory 802 and is called and executed by the processor 801.

[0186] The input / output interface 803 is used to connect the input / output module to realize information input and output. The input / output module can be configured in the device as a component (not shown in the figure), or it can be externally connected to the device to provide corresponding functions. The input device may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output device may include a display, a speaker, a vibrator, an indicator light, etc.

[0187] The communication interface 804 is used to connect a communication module (not shown) to realize communication interaction between the device and other devices. The communication module can realize communication through wired mode (such as USB, network cable, etc.) or wireless mode (such as mobile network, WIFI, Bluetooth, etc.).

[0188] The bus 805 includes a path to transmit information between various components of the device (eg, the processor 801 , the memory 802 , the input / output interface 803 , and the communication interface 804 ).

[0189] It should be noted that, although the above device only shows the processor 801, the memory 802, the input / output interface 803, the communication interface 804 and the bus 805, in the specific implementation process, the device may also include other components necessary for normal operation. In addition, it can be understood by those skilled in the art that the above device may also only include the components necessary for implementing the embodiment of the present invention, and does not necessarily include all the components shown in the figure.

[0190] Those skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present disclosure is limited to these examples. Under the concept of the present disclosure, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present invention as described above, which are not provided in detail for the sake of simplicity.

[0191] This application is intended to cover all such substitutions, modifications and variations that fall within the broad scope of all embodiments. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present invention should be included in the scope of protection of this disclosure.

Claims

1. A structural reliability optimization design method based on uncertainty measurement, characterized in that: The method comprises: Determining performance parameters of a structure, and constructing a limit state function of the structure under epistemic uncertainty based on uncertain variables affecting the performance parameters, wherein the uncertain variables obey a continuous or regular uncertainty distribution; According to the limit state function combined with uncertainty distribution or uncertain inverse distribution, a reliability measurement model of the structure based on uncertainty measurement is constructed; Determine the structural optimization design objective function, and establish a design optimization model with the structural performance reliability constraint and the objective function in combination with the reliability measurement model; An equivalent analytical solution model of the design optimization model is constructed, and the optimal design variables are obtained in combination with the boundary conditions of the design variables.

2. The method according to claim 1, characterized in that The step of constructing a reliability measurement model of the structure based on uncertainty measurement according to the limit state function and uncertainty distribution includes: According to the limit state function, the reliability of the structure based on the uncertainty measure is calculated through the uncertainty distribution of the uncertain variables The reliability measurement model of the structure based on uncertainty measurement is obtained: Where τ is the uncertainty vector τ = (τ1, τ2, ..., τ n ) T ,τ1,τ2,…,τ n is an uncertain variable, which obeys the continuous uncertain distribution γ1, γ2, …, γ n , the limit state function g(τ1, τ2, …, τ n ) about τ1, τ2, …, τ m is strictly monotonically increasing, and about τ m+1 , τ m+2 ,…,τ n Strictly monotonically decreasing, is the confidence of the failure event, and sup represents the upper bound.

3. The method according to claim 1, characterized in that The step of constructing a reliability measurement model of the structure based on uncertainty measurement according to the limit state function combined with uncertain inverse distribution includes: According to the limit state function, the uncertainty inverse distribution is used to solve the reliability measurement model of the structure based on uncertainty measurement: Among them, τ1, τ2, …, τ n is an uncertain variable, which obeys the regular uncertain distribution γ1, γ2, …, γ n , the failure reliability of the structure α is the solution of the equation, the reliability based on the uncertainty measure is 1-α, and the limit state function g(τ1, τ2, …, τ n ) about the uncertain variables τ1, τ2, ..., τ m Strictly monotonically increasing, and with respect to the uncertain variable τ m+1 , τ m+2 ,…,τ n Strictly monotonically decreasing.

4. The method according to claim 1, characterized in that: The determining of the structural optimization design objective function comprises: If the structure needs to satisfy multiple mutually constrained optimization objective functions, a corresponding weight factor is assigned according to the importance of each objective function; A weighted sum is performed on the multiple objective functions to obtain the total objective function of the structure.

5. The method according to claim 1, characterized in that The determining of the structural optimization design objective function and establishing a design optimization model having the structural performance reliability constraint and the objective function in combination with the reliability measurement model also include: For any of the limit state functions, obtaining a performance reliability value of the structure according to the reliability measurement model based on uncertainty measurement; According to the overall objective function and performance reliability value of the structure, a reliability design optimization model of the structure that meets the corresponding expected reliability value is established.

6. The method according to claim 1, characterized in that The input variables of the structure include design variables and uncertain non-design variables, the design variables include: deterministic design variables and uncertain design variables, the uncertain design variables and the uncertain non-design variables are uncertain variables, the determined structure optimization design objective function, combined with the reliability measurement model to establish a design optimization model with the structural performance reliability constraint and the objective function, and also include: According to the objective function and the reliability constraint conditions determined based on the reliability measurement model combined with the boundary conditions of the design variables in the structure, a reliability-based design optimization model is constructed: Solving for {d, x} Satisfy: reliability constraints, Boundary conditions, d Lower ≤d≤d Upper , x Lower ≤x≤x Upper , j = 1, 2, ..., N g Among them, d, x, τ are the vectors composed of deterministic design variables, uncertain design variables and uncertain non-design variables, respectively, and f i (d, x, τ), ω i are the i-th objective function and the corresponding weight factor, N f is the total number of objective functions, g j (d, x, τ), are the reliability, limit state function and expected reliability value of the jth reliability constraint condition, respectively. g is the number of reliability constraints, d Lower and d Upper are the upper and lower bound vectors of the deterministic design variables, x Lower and x Upper are the upper and lower bound vectors of the uncertain design variables respectively; The reliability-based design optimization model is solved to obtain optimal design variables that meet the reliability constraints of the structure.

7. The method according to claim 6, characterized in that The equivalent analytical solution model of the design optimization model is constructed, and the optimal design variables are obtained in combination with the boundary conditions of the design variables, including: The reliability-based design optimization model is subjected to equivalent planning analysis to convert the reliability-based design optimization model into the following clear equivalent planning model: Solving for {d, x} Satisfy: reliability constraints, Boundary conditions, d Lower ≤d≤d Upper , x Lower ≤x≤x Upper , j = 1, 2, ..., N g ; The clear equivalent programming model is solved to obtain the optimal design variables that meet the reliability constraint conditions of the structure.

8. A structural reliability optimization design device based on uncertainty measurement, characterized in that: The device comprises: A limit state function acquisition unit, used for determining performance parameters of the structure, and constructing a limit state function of the structure under epistemic uncertainty according to uncertain variables affecting the performance parameters, wherein the uncertain variables obey a continuous or regular uncertainty distribution; A reliability analysis acquisition unit, used to construct a reliability measurement model of the structure based on uncertainty measurement according to the limit state function combined with uncertainty distribution or uncertain inverse distribution; A design optimization model acquisition unit is used to determine the structural optimization design objective function, and to establish a design optimization model having the structural performance reliability constraint and the objective function in combination with the reliability measurement model; The design optimization solution unit is used to construct an equivalent analytical solution model of the design optimization model and obtain the optimal design variables in combination with the boundary conditions of the design variables.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

10. A computer storage medium, characterized in that: The storage medium stores at least one executable instruction, and the executable instruction enables the processor to execute the method as described in any one of claims 1-7.

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