A truss size optimization design method based on minimum cut set correlation

Abstract

The application discloses a truss size optimization design method based on minimum cut set correlation. The method comprises the following steps: establishing a balance matrix of the truss structure, using a zero space method to obtain a minimum cut set database of failure modes; constructing a joint failure model of the database, and then obtaining a failure probability under the consistency of the cut set edge probability space and establishing a reliability constraint optimization model; inputting the material density and length of each rod of the truss structure into the model, and outputting the optimized total weight and the cross-sectional area of each rod after processing, so as to perform size optimization design of the truss structure. The application solves the problems of failure mode combination explosion, insufficient correlation modeling and missing reliability constraints in the reliability analysis of the truss structure, can significantly reduce the complexity of the truss size optimization design, improve the structure failure probability evaluation precision, realize efficient and accurate system reliability evaluation and lightweight design, and has good computability and engineering applicability while ensuring the precision.

Description

TECHNICAL FIELD

[0001] The present application relates to a truss size optimization design method, in particular to a truss size optimization design method based on minimum cut set correlation. BACKGROUND

[0002] Truss structures are widely used in large-span bridges, stadiums, high-rise buildings, aerospace and other fields due to their clear stress, light weight, high material utilization and other advantages. In practical engineering, truss structures often bear random loads such as wind load, earthquake action, and vehicle load, and their safety is crucial. Therefore, accurate reliability evaluation and optimization design of their safety are the core links to ensure engineering safety and prevent catastrophic accidents.

[0003] Traditional truss structure reliability analysis and design methods have some limitations, and face the problem of combinatorial explosion of failure paths. Especially for high-dimensional structures, the number of failure combinations may lead to an unbearable calculation load. Although methods such as beta-unzipping attempt to search for key sequences through heuristic search to alleviate this problem, the search process still relies on a large amount of sorting and screening, which is low in computational efficiency and difficult to ensure that key failure modes are not missed. In addition, current designs are mostly focused on deterministic optimization or component-level reliability optimization. Deterministic optimization is based on the safety factor specified in the specification and cannot truly reflect the failure risk of the structure under actual random loads. While component-level reliability optimization can ensure the reliability of a single rod, the overall failure mechanism of the truss system is complex, and the safety of a single component does not equal the safety of the system. Although some studies attempt to incorporate system reliability into the optimization model, due to the computational bottleneck of system reliability analysis, they often have to use simplified system failure models or computationally expensive nested Monte Carlo simulations, which makes the optimization process either inaccurate or computationally expensive, making it difficult to be widely applied in engineering practice. SUMMARY

[0004] To solve the problems in the background art, the present application provides a truss size optimization design method based on minimum cut set correlation.

[0005] The technical scheme adopted by the present application is:

[0006] The truss size optimization design method based on minimum cut set correlation of the present application comprises:

[0007] Step S1: Establish the balance matrix of the truss structure based on the geometric information and boundary conditions of the truss structure, and obtain the minimum cut set database of the failure modes of the truss structure using the null space method based on the geometric invariance criterion of the structure according to the balance matrix.

[0008] Step S2: Construct a joint failure model of the minimum cut set database, and then obtain the failure probability of the truss structure while maintaining the consistency of the probability space of the cut set edge.

[0009] Step S3: Establish a reliability constraint optimization model based on the failure probability of the truss structure. Input the material density and length of each member of the truss structure into the reliability constraint optimization model. After processing, output the total weight of the optimized truss structure and the cross-sectional area of ​​each member to meet the reliability requirements, so as to optimize the size design of the truss structure.

[0010] The specific steps of S1 are as follows:

[0011] Step S11: Based on the geometry of the truss structure, establish the equilibrium matrix A, which includes the direction cosine components of each node between each member in the global coordinate direction.

[0012] Step S12: After processing the balanced matrix A with Singular Value Decomposition (SVD), construct the singular matrix. Singular Matrix Including the left singular matrix U and the singular value matrix And right singular matrix Singular value matrix Let be a diagonal matrix containing several singular values, and the right singular matrix. This includes the intrinsic directions of the axial forces in each member of the truss structure.

[0013] Step S13: Convert the singular value matrix Medium to small singular value threshold The singular values ​​are taken as zero, thereby extracting the null space basis vectors in the right singular matrix V. Null space basis vectors Each row vector is the null space row vector of each member of the truss structure.

[0014] Step S14: Based on null space basis vectors Perform a minimum cut set search on the truss structure to obtain a minimum cut set database M of the truss structure's failure modes.

[0015] In step S14, in the null space basis vectors First, a single-member cut set determination is performed. For each member of the truss structure, when the zero-space basis vector... If the null space row vector of the current member is 0, then deleting the current member will cause the truss structure to fail. The member corresponding to the null space row vector of the current matrix is ​​taken as the minimum cut set unit. Then, a multi-member cut set determination is performed, based on the null space basis vectors... Remove one of the null space row vectors that is the smallest cut set unit to form a new null space basis vector. No single member is removed, so the original matrix remains unchanged. Random selection is made within the truss structure. Root members constitute the candidate set In the new null space basis vectors Extract candidate set The null space row vectors of each member form a submatrix When rank( )< rank() is The size of the rank of the candidate set If the null space row vectors of each member are linearly dependent, then the candidate set... It is a cut set; then the cut set is determined. Whether it is a minimal cut set depends on the cut set. Each proper subset in When satisfied , For a true subset If the null space basis vectors are given, then the cut set... For minimal cut sets; the minimal cut sets are used to form a minimal cut set database M of the failure modes of the truss structure, M = {C1, C2, ..., C...} θ}, C1, C2, ..., C θ It is the 1st, 2nd, ..., θth minimal cut set.

[0016] The specific steps of S2 are as follows:

[0017] Step S21: Obtain the discrete correlation coefficients of every two minimal cut sets in the minimal cut set database, and then construct a joint failure model from the discrete correlation coefficients. .

[0018] Step S22: Combine the failure model Each discrete correlation coefficient in the model is mapped to a uniform spatial correlation coefficient using a Copula probability model. Then, the uniform spatial correlation coefficients are mapped to normal spatial correlation coefficients using a Gaussian distribution. Finally, a normal correlation matrix is ​​constructed from the various normal spatial correlation coefficients. .

[0019] Step S23: Based on the normal correlation matrix Generate a relevant sample Z, and obtain the number of sample failures based on the relevant sample Z.

[0020] Step S24: Obtain the failure probability of the truss structure by calculating the number of failed samples in the correlation sample Z. .

[0021] In step S23, based on the normal correlation matrix Decompose the lower triangular element matrix L, , and perform matrix Cholesky decomposition to generate independent normal samples Then generate the correlation sample Z, Then determine the critical state of the correlation sample Z as follows:

[0022]

[0023]

[0024] wherein, is the critical state of the ith sample in the correlation sample Z, that is, the failure state of the minimum cut set of the ith independent normal sample ; is the ith state function, is the standard normal distribution function; is the failure probability of the cut set i.

[0025] Finally, the number of sample failures of each independent normal sample is as follows:

[0026]

[0027] wherein, is the number of sample failures of the kth independent normal sample ; is the system failure of the kth normal sample; is whether the kth normal sample Y triggers the failure event of the ith minimum cut set .

[0028] In step S24, under independent repeated sampling, the failure probability of the truss structure is as follows:

[0029]

[0030] wherein, is the total number of independent normal samples ; is the number of sample failures of the kth independent normal sample .

[0031] In step S3, the reliability constraint optimization model is specifically as follows:

[0032]

[0033] wherein, 、 and are the optimization design variable vector and its upper and lower limit constraints of the truss structure respectively, the lower limit and the upper limit of the design variable represent the cross-sectional size range required by manufacturing or specification, , are the cross-sectional areas of the 1st, 2nd, …, i, …, b bars respectively, b is the total number of bars; is the total weight of the truss structure; is the material density of the i-th bar; is the length of the i-th bar; is the failure probability of the truss structure, i.e., the structure reliability index; is the preset upper limit of the failure probability target.

[0034] The particle swarm algorithm is used to solve the reliability constraint optimization model, and the optimized optimal truss structure optimization design variable is obtained to perform size optimization design on the truss structure.

[0035] The truss size optimization design system based on the minimum cut set correlation of the application comprises:

[0036] The database establishment module establishes the balance matrix of the truss structure based on the geometric information and boundary conditions of the truss structure, and obtains the minimum cut set database of the failure mode of the truss structure by using the null space method according to the balance matrix based on the geometric invariance criterion of the structure.

[0037] The failure probability acquisition module constructs a joint failure model of the minimum cut set database, and then obtains the failure probability of the truss structure under the condition of maintaining the consistency of the cut set edge probability space.

[0038] The size optimization design module establishes a reliability constraint optimization model based on the failure probability of the truss structure, inputs the material density and length of each bar of the truss structure into the reliability constraint optimization model, and outputs the total weight and cross-sectional area of each bar of the optimized truss structure that meets the reliability requirement after processing, so as to perform size optimization design on the truss structure.

[0039] The electronic device of the application comprises a memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the method as described above.

[0040] The computer readable storage medium of the application has program data stored thereon, and the program data is executed by a processor to implement the method as described above.

[0041] The present application is directed to different dimension truss structure, first construct the mathematical balance matrix of truss and identify the critical condition of geometric invariance or variability based on zero space criterion, introduce singular value decomposition and minimum advance discrimination to efficiently obtain the minimum cut set (key failure combination); on this basis, the system failure event is expressed as the minimum cut set failure event, the edge failure probability model of cut set is uniformly established, the correlation matrix of cut set is constructed and Copula is adopted to ensure the consistency of edge probability, so as to accurately estimate the system failure probability; further, the reliability constraint optimization model is constructed with the minimum structure weight as the target and the system reliability index as the constraint, and the particle swarm algorithm is adopted to solve to obtain the optimal design parameters of truss structure size and shape meeting the reliability requirements and design the truss structure.

[0042] The beneficial effects of the present application are:

[0043] The present application solves the problems of failure mode combination explosion, insufficient correlation modeling in reliability analysis of existing truss structure, and missing system level reliability constraint in optimization design. By introducing minimum cut set to represent system failure, Copula theory to model cut set correlation, and particle swarm algorithm to solve reliability constraint optimization problem, efficient and accurate system reliability evaluation and lightweight design are realized. The present application does not need to exhaust the failure sequence, significantly reduces the calculation complexity of truss size optimization design; the independence assumption deviation is corrected by cut set correlation modeling, the accuracy of structure failure probability evaluation is improved; while ensuring accuracy, good computability and engineering applicability are possessed. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 The flowchart of the method of the present application is shown;

[0045] Figure 2 The truss structure balance matrix and failure combination extraction diagram of the present application is shown;

[0046] Figure 3 The correlation mapping flowchart in reliability evaluation of the present application is shown;

[0047] Figure 4 The particle swarm algorithm optimization process flowchart of the present application is shown;

[0048] Figure 5 The simulation structure and numerical structure verification diagram of the present application is shown. DETAILED DESCRIPTION

[0049] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0050] As shown in Figure 1 The truss size optimization design method based on minimum cut set correlation of the present application is as follows:

[0051] Step A:

[0052] (1) Establish the geometric model of the truss structure, input the node coordinates, the topological connection relationship of the members and the support constraints, and perform discretization matrix modeling on the target truss structure. Assume that the truss structure has n nodes and b members, and the node set is: , where each node Spatial coordinates are The set of rods is defined as: Each rod The two nodes it connects Definition; for any bar Calculate its length, defined as: ,in, and They are nodes and nodes The coordinate vector.

[0053] To reflect the geometric constraints of the truss structure, an equilibrium matrix A is established based on the geometric information and boundary conditions of the truss structure. Equilibrium matrix A includes the direction cosine components of each member with respect to each node in the global coordinate direction. The number of columns is equal to the number of members ε, and the number of rows represents the system's degrees of freedom. .

[0054] For any member, calculate the direction cosine vector in the global coordinate system. The definition is as follows:

[0055]

[0056] Direction cosine vector It is row vectors ( (This represents the total degrees of freedom of the structure), and its elements are filled according to the following rules:

[0057] In the corresponding node The translational degrees of freedom positions are filled in with the following components:

[0058]

[0059] In the corresponding node The translational degrees of freedom positions are filled with the following components:

[0060]

[0061] The remaining positions are 0.

[0062] Based on its connection relationship with the node degrees of freedom, it is expanded into a global row vector. :

[0063]

[0064] i.e. fill in the corresponding degree of freedom position of node with , fill in the position of node with , and fill in 0 for the rest of the positions.

[0065] The truss structure is built by a plurality of members, and the connection point between two members is a node; the coordinates of the node i of the truss are or , respectively, the member set , the node set , the member connection relationship and the structure boundary condition are obtained to obtain the geometric information of the truss, and for any member , the length is . According to the directional quantity as the matrix element, it is defined as follows:

[0066]

[0067] wherein is the directional cosine component of the member k in the global coordinate direction.

[0068] The row vectors of all members are stacked in order to construct the balance matrix :

[0069]

[0070] The balance matrix describes the balance relationship between the member force and the node force in the truss structure, and is the basis for the geometric invariance determination; based on the above component method, the core mathematical model of the structure stress balance, the balance matrix A, is constructed. The balance matrix A generated by taking an 11-member truss as an example is as follows:

[0071]

[0072] (2) Next, the geometric stability determination and singular value decomposition of the balance matrix A are carried out to extract the null space. First, the static balance relationship between the member internal force vector and the node external force vector is established: .

[0073] The null space of the equilibrium matrix A contains all the internal force vectors t of the members satisfying At = 0. These vectors represent the "self-stress" modes that enable the structure to self-equilibrium under no external loads. The dimension of the null space (i.e., the number of self-stress modes) is directly related to the static indeterminacy degree of the structure. More importantly, the basis vectors of the null space provide crucial information for determining the geometric stability of the structure.

[0074] Then, based on the geometric invariance criterion of the structure, a minimum cut set database of failure modes of the truss structure is obtained using the null space method according to the equilibrium matrix. To robustly solve the null space, singular value decomposition (SVD) is performed on the equilibrium matrix A. Based on the mechanism motion criterion established by null space theory, linear algebraic analysis is performed on the equilibrium matrix A, and potential mechanism motion modes of the structure are identified by solving its null space. By applying Singular Value Decomposition (SVD) to the equilibrium matrix A to sparsify and robusten matrix operations, three singular matrices are formed. The singular matrices of the equilibrium matrix A are defined as follows: Singular Matrix Including the left singular matrix U and the singular value matrix And right singular matrix Singular value matrix The left singular matrix U is a diagonal matrix containing several singular values. The column vectors of the left singular matrix U describe the principal directions of the structural node displacements; the singular value matrix... , These are the 1st, 2nd, ..., rth singular values, and the singular values ​​on their diagonal. Arranged in descending order, among which... It is a sequence of singular values, with a size of , The singular value matrix represents the sum of the degrees of freedom of each node in the truss structure in the translational directions in space. The number of non-zero singular values ​​in each singular value is the rank of the balance matrix A. It equals the number of independent equilibrium equations of the structure. Based on singular value decomposition, numerical robustness is achieved to avoid numerical noise interference from different singular value matrices generated for different truss structures, using the diagonal matrix... Set the singularity tolerance threshold The specific form is, ,in, Let τ be the smallest of the non-zero singular values, and let τ be the numerical tolerance threshold used to distinguish between true zero singular values ​​and pseudo-zero values ​​generated by numerical errors. Values ​​smaller than this threshold will be excluded. The singular values ​​are treated as zero, thus robustly extracting the null space basis vectors. Right singular matrix Including the eigendirections of the axial forces in each member of the truss structure, and the right singular matrix. , each row vector of the right singular matrix V represents each member of the truss structure, and each column vector represents the distribution characteristics of the member axial force of the truss structure in the self-stress mode, each column corresponding to a self-stress state that can be formed by the structure under the condition of no external force; the right singular matrix V is divided into , wherein , the non-zero singular values of the singular value matrix correspond to the singular values of the singular value matrix , s = b-r(A) is the dimension of the null space, i.e. the static indeterminacy; the singular value matrix has the same number of columns as the right singular matrix V.

[0075] The singular value matrix is obtained by singular value decomposition of the equilibrium matrix A, and the singular values less than the singular value threshold are regarded as zero, so as to extract the null space basis vector in the right singular matrix V; each row vector of the null space basis vector is the null space row vector of each member of the truss structure; if an element on the singular value matrix is 0, the corresponding current column element in the right singular matrix V can be extracted, so as to obtain the null space basis vector ; in a specific implementation, the null space basis vector of the 11-member truss is as follows:

[0076]

[0077] Based on the null space basis vector , the minimum cut set search of the truss structure is performed, so as to obtain the minimum cut set database M of the failure mode of the truss structure. Since the minimum cut set is defined as the minimum member combination leading to the mechanism of the structure, if a group of members (members) is removed at the same time, the truss changes from a static state to a movable state, i.e. at least one motion mechanism appears, and the group of members can become a cut set.

[0078] The construction of the equilibrium matrix, the solution of the null space and the combination judgment process are modularized and separated, and a new matrix When the SVD decomposition is performed, the rank of the matrix is obtained, which leads to the excessive consumption of computing resources. Therefore, by separating the matrix solution and combination determination module, the repeated operation of large-scale matrix in the search process is avoided, and the minimum cut set identification process is decoupled into three logically independent calculation modules: 1) matrix decomposition module, used for performing one-time singular value decomposition on the balanced matrix, and outputting the null space basis vector matrix; 2) combination generation module, used for systematically generating candidate member combinations according to the search strategy; 3) combination determination module, which receives the null space basis vector matrix and the candidate member combination, and completes the cut set determination by checking the rank condition and minimality condition of the sub-matrix corresponding to the combination. The output of the matrix decomposition module is repeatedly called by the combination determination module, avoiding repeated decomposition of the balanced matrix in the search process; significantly improving the calculation efficiency of high-dimensional truss structures; and finally outputting all the identified minimum cut sets to form the minimum cut set database M of failure modes for system reliability analysis.

[0079] (3) On the basis of the structural geometric model, all possible member failure combinations are generated. To reduce the amount of calculation, the order of the candidate combination does not exceed the static indeterminacy of the system. Based on this theorem, the minimum cut sets are systematically searched and determined according to the following criteria:

[0080] In the null space basis vector , first, single-member cut set determination is performed. For each member of the truss structure, when the null space row vector of the current member in the null space basis vector is 0, the current member is deleted, which causes the truss structure to fail. The member corresponding to the null space row vector of the current matrix is regarded as a minimum cut set unit. Deleting the member will immediately cause the truss structure to be geometrically deformable, so the member k is a "necessary member" of the structure and constitutes a single-element minimum cut set. Then, multiple-member cut set determination is performed. In the null space basis vector , one of the null space row vectors that is a minimum cut set unit is deleted to form a new null space basis vector . Without removing single members, the original matrix remains unchanged. In the truss structure, randomly selected members form a candidate set , >1, the null space row vectors of the members in the candidate set are extracted from the new null space basis vector to form a sub-matrix . When rank( )< , rank( ) is the rank of , the null space row vectors of the members in the candidate set are linearly dependent, indicating that the set There is a set of members, which are self-stressed and constrained by each other, and cannot change independently. When and only when the condition is met, the set is deleted The rank of the equilibrium matrix will decrease, and the truss structure will change from a geometrically stable system to a geometrically deformable system. Then the candidate set is a cut set; then determine whether the cut set is a minimal cut set. For each proper subset of the cut set , if the condition is met, the proper subset is a cut set . is a proper subset of the cut set , and the null space basis vector of the cut set , delete the entire set . If deleting any one member of the cut set will not lead to geometric deformation, the cut set is a minimal cut set; form the minimal cut set database M of the failure modes of the truss structure by each minimal cut set. M = {C1, C2, …, C θ}, C1, C2, …, C θ are the first, second, …, θ minimal cut sets.

[0081] In the implementation, single-member cut set search: traverse each member , and check its row vector V k in the matrix k . If V C = 0, the member k does not participate in any self-stressed mode and is a key member that maintains stability, and itself constitutes a minimal cut set .

[0082] Multi-member cut set search: for to (the static indeterminacy number), enumerate all combinations of members with a size of . Since s = b - r = 11 - 8 = 3 for the 11-member structure, the number of members contained in a minimal cut set does not exceed 3. Cut set determination: calculate , where

[0083] is the submatrix in the matrix corresponding to the members. If it is less than , the cut set is a minimal cut set. After searching for the cut sets based on the above two criteria, further minimalness determination is required: to avoid repeated calculations and interference from non-minimal combinations, the minimalness of the candidate set is verified. Define the set , and delete the member member

[0084] in the set from the set .Subsequently, if the structure remains geometrically stable (the resulting new matrix) (It will no longer cause a rank decrease) if and only if the following condition is met:

[0085]

[0086] at this time It is a set of minimal cut sets.

[0087] (4) Generation and output of the minimal cut set database: All minimal cut sets identified through the above process are generated and output. Collect, organize, and store, such as Figure 2 As shown, a structured minimal cut set database is formed. :

[0088]

[0089] An 11-bar truss has a total of 36 minimal cut sets. Based on the number of members it contains, they can be divided into two categories:

[0090] Results of 11-bar example: A total of 36 minimum cut sets were obtained, which were divided into the following two categories: Binary minimum cut sets (16): {3,5}, {3,7}, {3,10}, {3,11}, {4,6}, {4,8}, {4,9}, {5,7}, {5,10}, {5,11}, {6,8}, {6,9}, {7,10}, {7,11}, {8,9}, {10,11}.

[0091] Triple minimal cut sets (20 sets): {2,3,4}, {2,3,6}, {2,3,8}, {2,3,9}, {2,4,5}, {2,4,7}, {2,4,10}, {2,4,11}, {2,5,6}, {2,5,8}, {2,5,9}, {2,6,7}, {2,6,10}, {2,6,11}, {2,7,8}, {2,7,9}, {2,8,10}, {2,8,11}, {2,9,10}, {2,9,11}.

[0092] The minimal cut set database comprehensively describes all potential system-level failure modes of the truss structure. Each minimal cut set is a "critical failure unit" leading to system failure. This database will serve as the fundamental basis for subsequent system reliability analysis, achieving a dimensionality reduction mapping from the intractable "failure sequence" space to a finite, essential "failure state" space, thus laying the foundation for the computational efficiency of the entire method.

[0093] Step B:

[0094] like Figure 3 As shown, the minimal cut set database obtained in step A This study conducts system-level reliability assessments of truss structures, constructs a joint failure model based on a minimal cutset database, and obtains the failure probability of the truss structure while maintaining the consistency of the cutset edge probability space. Its core innovation lies in abandoning the unrealistic strong assumption of independent cutset failure events in traditional analysis. Instead, it uses Copula theory to accurately model the statistical correlation between different minimal cutset failure events, thereby significantly improving the accuracy of system failure probability calculation.

[0095] (1) First, calculate the failure probability of the cut set edge:

[0096] For minimal cut set data Each minimal cut set in Calculate its edge failure probability This probability represents the probability that all members included in the cut set will simultaneously be in a failure state under the influence of uncertain factors such as random loads and material strength. The discrete correlation coefficients of every two minimal cut sets in the minimal cut set database are obtained, and these discrete correlation coefficients are then used to construct a joint failure model. The minimal cut set database M serves as the basis for defining each cut set. Calculate cut sets Edge failure probability as follows:

[0097]

[0098] in, For the first The limit state function of a minimum cut set It is a structured random parameter vector.

[0099] Given a function: for a bar Establish its limit state function The stress-intensity function model is typically used, and its specific expression is as follows:

[0100]

[0101] in, For the resistance of the rod, The actual internal forces acting on the member. Let be the cross-sectional area of ​​the i-th rod. This represents the allowable stress for the member. For the internal forces of the rod.

[0102] when When, explain The member fails; when At that time, the rod is safe.

[0103] It is essential to accurately solve the internal forces of the truss. In the face of such a large-scale situation, the mechanical equilibrium equation is used:

[0104] AN=F

[0105] where F is the node load vector, and the internal forces of the truss are solved. First, the stiffness matrix of the single-bar element needs to be established. For each bar in the truss structure, the stiffness matrix in the local coordinate system can be derived from the basic principles of material mechanics. Take bar i as an example. The bar connects nodes m and n, and its stiffness matrix in the local coordinate system is:

[0106]

[0107] where E is the elastic modulus of the material, A is the cross-sectional area of the bar, L is the length of the bar. This matrix describes the balance relationship of the axial forces at both ends of the bar and reflects the stiffness characteristics of the bar under axial load. In the local coordinate system, only axial deformation is considered, and lateral deformation and other complex effects are ignored. This is based on the fact that truss structures mainly bear axial forces, which is consistent with the basic assumptions in engineering practice.

[0108] Since the directions of the bars in the truss structure are different, the stiffness matrix in the local coordinate system needs to be converted to the global coordinate system for overall structural analysis. Coordinate transformation is achieved through rotation matrix T. Through the connection of nodes m and n, in the corresponding columns of the matrix in the balance equation, the rows corresponding to the x and y degrees of freedom of node m are filled with the direction cosines and sines, while the rows corresponding to the x and y degrees of freedom of node n are filled with the opposite direction cosines and sines, to reflect the reaction forces generated by the bar at the nodes. The direction cosines are c = cos θ and s = sin θ, and the rotation matrix T is which is expressed as follows:

[0109]

[0110] The role of the rotation matrix T is to convert the stiffness matrix of the bar in the local coordinate system to the global coordinate system, ensuring that the forces and displacements of the bar can be correctly projected in the global coordinate system, thereby achieving the overall structural balance. The stiffness matrix in the global coordinate system is then constructed by:

[0111]

[0112] After obtaining the overall stiffness matrix K and the node load vector F, the node displacement vector is calculated by numerical methods. According to this idea, to verify the accuracy of solving the internal forces of the truss, the stiffness matrix of all elements is assembled to establish the mechanical equilibrium equation as follows:

[0113]

[0114] in, For the overall stiffness matrix, Let be the nodal displacement vector. This is the node load vector.

[0115] The displacement vectors obtained from the mechanical equations and simulation results in ANSYS software were compared and verified. The nodal displacements were then calculated. To verify the accuracy of the calculated nodal displacements, ANSYS software was used for finite element analysis, and the ANSYS solver was used for static analysis to obtain the displacement distribution of each member node. After ensuring consistency between the numerical calculation and simulation results, the axial force of the unit was calculated based on the nodal displacements. :

[0116]

[0117] in, This refers to the change in axial length of a member after it is subjected to force.

[0118] Minimum cut set Failure event It is the intersection of all member failure events it contains, that is:

[0119]

[0120] If the failure scenarios of a member at a given sample point include or exceed any cut set, then that sample point is defined as a failure sample point. The marginal failure probability of each cut set is obtained by statistically analyzing the ratio of the number of failure sample points to the total number of samples. .

[0121] Next, we need to find the case where any two cut sets fail simultaneously, i.e., we need to perform second-order failure analysis to find it. Define any two cut sets , The joint probability of simultaneous failure is:

[0122]

[0123] in, and These are the i-th and j-th minimum cut sets, respectively.

[0124] Establish a correlation model among the failure events of each cut set.

[0125] (2) Cut-set correlation modeling and quantification: Different minimal cut-sets may share the same member or be affected by the same group of random loads, and there exists significant statistical correlation between their failure events. Ignoring this correlation will lead to a serious deviation in the system failure probability estimation.

[0126] By constructing the cut-set correlation coefficient between all pairs of minimal cut-sets , the statistical correlation between the failure events of the cut-sets is quantified, and the system failure probability is calculated by establishing a joint probability model. To reduce the computational load and obtain a more accurate system failure profile, the correlation coefficient is mapped in the normal space, i.e., the correlation coefficient in the normal space is solved .

[0127] First, according to the calculated failure probability of the cut-set and the joint failure probability , because the failure state of the cut-set in the structure is only two (failure / safety), not in the continuous normal space, the discrete state (only two failure states) is gradually converted to the continuous state.

[0128] Construct a discrete correlation matrix : First, according to the marginal failure probability and the joint failure probability of the cut-set , the discrete correlation coefficient of any two cut-sets is defined as:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] where represents the covariance, which measures the relationship between two variables; and are the failure probabilities of cut-sets i and j, which are the same as the failure probability of the cut-set mentioned above; is the variance of the variable.

[0135] The range of discrete correlation coefficient is [-1, 1], which reflects the linear dependence degree of cut set failure events. The correlation coefficients of all cut set pairs are combined to form a discrete correlation matrix, and the correlation between all cut sets is Filled in, which constitutes a discrete correlation matrix (based on 36 cut sets Matrix construction):

[0136]

[0137] Since is only a second-order statistic (linear correlation matrix). It describes the trend of the failure of the two cut sets, but it cannot uniquely determine the joint failure probability distribution of the entire system. The system failure probability is the union probability of all minimal cut set failures. To calculate this union probability, the joint distribution of cut set failure events needs to be known, and to effectively characterize these correlations and introduce a reliable calculation framework, the minimal cut sets need to be mapped from the event set perspective to the variable space perspective.

[0138] Then each discrete correlation coefficient in the joint failure model is mapped to a uniform space correlation coefficient by a Copula probability model, and then the uniform space correlation coefficient is mapped to a normal space correlation coefficient by a Gaussian distribution, and each normal space correlation coefficient is constructed into a normal correlation matrix .

[0139] Define each cut set as a Bernoulli random variable , which represents whether the cut set fails. For each Bernoulli variable , its value is 0 or 1, and the corresponding probability is , and its cumulative distribution function CDF (Cumulative Probability Distribution Function) is :

[0140]

[0141] When performing system reliability analysis of truss structures, the ultimate goal is to solve the high-order joint failure probability:

[0142]

[0143] Where is the kth minimal cut set failure event. If the variable is not independent, the joint distribution of the variable However, given Bernoulli's marginal distribution, in discrete space, a joint distribution that simultaneously satisfies all marginal probabilities and the required correlation structure is almost nonexistent, especially for high-dimensional cut-set systems. Constructing a distribution that satisfies the specified... The joint probability table is a nondeterministic problem with polynomial complexity.

[0144] (3) Furthermore, using the probability space consistency mapping method, discrete variables are mapped to continuous space using the Gaussian Copula method, Nataf transform, and other tools to convert the correlation coefficients of discrete Bernoulli variables. The correlation problem is transformed into the correlation coefficient in normal space. Correlation analysis.

[0145] Discrete correlation coefficient Mapping to a continuous probability space forms continuous correlation coefficients. This is achieved by defining each cutset as a Bernoulli random variable. , indicating whether the cut set is invalid. For each Bernoulli variable Its value is either 0 or 1, corresponding to the probabilities of safety or failure, respectively. .because It cannot be directly mapped to the normal space to obtain Therefore, it is necessary to separate discrete variables. Mapping to continuous variables Continuity is assigned while maintaining the marginal probability unchanged; from the Bernoulli variable Mapped to variables conforming to Uniform(0,1). By mapping using the Copula probability model, Convert to standard uniform distribution variable Construct a random variable with boundary [0,1].

[0146] First, Bernoulli discrete variables cannot be directly transformed into normal distributions for calculation because Bernoulli variables are discrete, and their cumulative distribution function... It is a jump, and cannot satisfy the one-to-one probability integral transformation condition. It needs to be mapped to a normal copula, which requires the input variables to be continuous.

[0147] Mapped using the Copula probability model, Convert to standard uniform distribution variable Construct a random variable with boundary [0,1]. The specific expression is as follows:

[0148]

[0149] Constructing the uniformity condition of marginal edges , This transformation ensures uniform distribution on the interval, thus maintaining statistical properties consistent with . To make subsequent Nataf transformation more robust, the discrete Bernoulli correlation coefficient is transformed into the equivalent correlation coefficient in the standard uniform distribution space , where a set of variables is defined in the standard normal space as follows:

[0150]

[0151] is a set of randomly generated variables. The transformation of this set of variables in the uniform space maps back to a two-element uniform random quantity by setting thresholds , The specific expression is as follows:

[0152]

[0153]

[0154] Thus, the Bernoulli variable is obtained = probability consistency, obtaining the variable in the uniform space.

[0155] The above joint probability is brought into the Bernoulli variable correlation coefficient to construct the objective function , which is transformed into the uniform space to construct the solution objective function of the uniform space correlation coefficient as follows:

[0156]

[0157] The root of is solved by numerical method, obtaining the uniform space correlation coefficient . In the solving process, the clipping mechanism is used to handle abnormal values beyond the Fréchet boundary. The function is strictly monotonically increasing on (-1, 1), and there is a unique root in (-1, 1).

[0158] To further utilize the advantages of Gaussian distribution tools, the uniform space correlation coefficient needs to be mapped to the normal space correlation coefficient . Based on the Nataf transformation theory, for a pair of uniform variables , Uniform(0,1) with correlation . Define the standard normal variable with correlation . The relationship between the uniform variable and the normal variable is defined by the probability integral transform:

[0159]

[0160] where is the standard normal distribution function.

[0161] Define , is the normal threshold corresponding to the marginal probability. It can be known that corresponds to , corresponds to , which ensures that the marginal distribution of U is still consistent with the probability of the Bernoulli variable. For , the joint tail probability of the two variables is:

[0162]

[0163] where is the correlation coefficient between the assumed normal variable , , which is used to construct the binary joint distribution; is the two-dimensional standard normal density function; , is the equivalent threshold of the failure quantile of the cut set i, j in the standard normal space.

[0164] In specific implementation, the correlation mapping is constructed by the Nataf theory, and the conversion equation defines the correlation relationship of the two uniform variables as:

[0165]

[0166] where is the standard deviation of the standard uniform variable, , is the cumulative distribution function CDF of the standard normal distribution; is the binary standard normal joint probability density function PDF (Probability Density Function):

[0167]

[0168] The integral expression reflects the correlation coefficient between the variable pairs in the normal space. is the only control quantity that can accurately adjust the cooperation of the variables after mapping.

[0169] Further explanation, select a candidate correlation coefficient , the objective function constructed is:

[0170]

[0171] When =0, the normal space correlation coefficient can make the transformed uniform variable , match the target correlation , get the normal space correlation coefficient .

[0172] By determining all and unique , to carry out the normal correlation matrix construction, further assembled into the normal correlation matrix , used to express the pair-wise correlation relationship between all cut-set variables in the system, the specific form is as follows:

[0173]

[0174] This system reliability analysis framework based on the zero space method of cut-set identification and correlation correction not only guarantees the calculation accuracy, but also effectively avoids the high-dimensional combination explosion problem of traditional failure sequence method, and lays a foundation for subsequent introduction of reliability constraints in optimization problems.

[0175] (4) Based on the normal correlation matrix , the correlation sample Z is generated, and the sample failure number is obtained according to the correlation sample Z; then the failure probability of the truss structure is obtained by solving based on the number of failure samples in the correlation sample Z . After the construction of the normal correlation matrix , in order to generate a multivariate correlation sample matched in the standard normal space, the scheme of Cholesky decomposition + linear transformation is adopted again to realize the dependency modeling of high-dimensional normal variables.

[0176] According to the correlation coefficient matrix , which satisfies the positive definite symmetric condition of matrix, through Cholesky decomposition , the is decomposed into a triangular element matrix L, and the original m×m correlation matrix is compressed into a lower triangular element matrix L. Further, the sample without correlation is converted into the sample with correlation, and the lower triangular element matrix L is subjected to matrix Cholesky decomposition to generate independent normal samples , and then sampling is carried out, that is I is the covariance matrix, and the Cholesky decomposition of the matrix is a unique reversible, stable and minimum computational positive definite matrix, which generates independent standard normal vector samples, and the essence of Y is a random vector with independent standard normal distribution, which is each element , and and are independent of each other, so that only in the case of input independent normal distribution, the output covariance structure can be completely determined by L, and by generating correlation sample Z:

[0177] ,

[0178] that is, generate samples Z, get the correlation standard normal vector of length m , let the ith minimum cut set The failure probability is According to the standard normal space, the threshold value is established:

[0179]

[0180] The purpose is to calculate the corresponding threshold value for each cut set , and ensure that each group of Cholesky generated samples If , then .

[0181] Then judge the critical state of the correlation sample Z, and threshold the discrete failure variable as follows:

[0182]

[0183] where, is the critical state of the ith sample in the correlation sample Z, that is, the failure state of the minimum cut set of the ith independent normal sample ; is the ith state function, is the standard normal distribution function; is the failure probability of cut set i; in this way, the Bernoulli variable is converted into a continuous latent normal value, and then becomes the state under Bernoulli, and satisfies the initial statistical marginal failure probability.

[0184] After that, through the sample failure judgment mechanism, the failure number of the sample function is determined to determine the failure number of the sample number, and finally the independent normal sample The number of sample failures is as follows:

[0185]

[0186] in, For the k-th independent normal sample The number of sample failures; The system failure occurs for the k-th normal sample; Does the k-th normal sample Y trigger the i-th minimum cut set? Failure event.

[0187] That is, as long as there exists a certain i such that Then there will be ;otherwise .

[0188] In independent repetition Under the second sampling, the failure probability of the truss structure is finally obtained by solving the problem. as follows:

[0189]

[0190] in, Independent normal samples The total number; For the k-th independent normal sample The number of sample failures.

[0191] Step C:

[0192] A reliability-constrained optimization model is established based on the failure probability of truss structures. The material density and length of each member of the truss structure are input into the model, and the output, after processing, is the optimized total weight of the truss structure and the cross-sectional area of ​​each member, satisfying reliability requirements. This allows for dimensional optimization design of the truss structure. The goal is to find the lightest truss dimensional optimization design scheme that meets system-level reliability requirements. It creatively incorporates the aforementioned accurate system failure probability assessment results as constraints into a highly efficient optimization framework, resolving the contradiction that traditional deterministic optimization or component-level reliability optimization cannot guarantee system safety, while traditional system reliability optimization involves enormous computational costs.

[0193] Here, the cross-sectional area of ​​the truss structure and the ordinates of some nodes are used as design variables, formalizing the optimization design problem of the truss structure into a standard constrained optimization problem. The objective function is set as minimizing the total weight of the truss structure while satisfying performance and safety constraints, i.e., a reliability-constrained optimization model:

[0194]

[0195] in, , and are the upper and lower limit constraints of the optimization design variable vector of the truss structure, the lower limit and upper limit of the design variable represent the cross-sectional size range required by manufacturing or specification, , are the cross-sectional areas of the first, second, …, i, …, b bars, and b is the total number of bars; is the total weight of the truss structure; is the material density of the i-th bar; is the length of the i-th bar; is the failure probability of the truss structure, i.e., the structure reliability index; is the upper limit of the preset failure probability target.

[0196] Due to the highly coupled nonlinear structure optimization problem formed by the influence of the geometric parameters of the structure on the bar length, load path, internal force distribution, and failure combination, that is, as the failure analysis defined in the constraint of the objective function, the system failure probability needs to meet the pre-set target reliability index.

[0197] The optimization of the truss structure is realized by minimizing the total mass under the premise of meeting the system reliability constraint, and a reliability constraint optimization model is established by taking the minimization of the total weight of the truss structure as the optimization objective and the system-level reliability requirement as the core constraint.

[0198] The particle swarm algorithm is used to solve the reliability constraint optimization model to obtain the optimal design variables of the optimized truss structure, and the optimal design parameters d that meet the system reliability requirement searched by the particle swarm algorithm are output, the final truss structure shape characteristics can be obtained, and the optimal structure weight W, system failure probability and key failure mode information corresponding to the design are output; and then the size optimization design of the truss structure is performed.

[0199] As Figure 4As shown, first, the initial particle position is randomly generated according to the upper and lower bounds of the design variables, and a random speed is given to each particle to form an initial population. Then, the particle position and speed are preliminarily updated according to the current speed of the particle and the PSO update formula, to prepare the candidate solution for subsequent fitness evaluation. Then, the position of each particle is analyzed and the reliability is calculated to obtain the target function value (weight) and form the particle fitness in combination with the system reliability constraint. This process is used to judge the pros and cons of the current solution of the particle. Then, the fitness of the current particle is compared with its historical best fitness, and if the current one is better, the new individual optimal value pbest is updated. The pbest of all particles is compared, and the best one is selected as the global optimal solution gbest. The gbest will guide the motion direction of all particles in the next iteration. Then, the optimal solution is output when the maximum number of iterations is reached, otherwise the next step is continued, and it is checked whether the updated particle is out of the design space boundary, and if it is out, it is truncated or reflected, etc. to ensure that the particle is always located in the feasible region. Finally, the particle is reinitialized with a preset probability P C determine whether the crazy jump mechanism is triggered, and for the particle triggering the crazy jump mechanism, the speed or position thereof is reinitialized according to a random strategy, so that the particle re-explores the design space, and if the particle does not perform the jump, the updated state thereof is maintained to enter the next iteration. The velocity updating, position updating and fitness evaluation steps are repeated until the termination condition is met.

[0200] Under the above conditions and targets, the optimization target based on the particle swarm optimization PSO (Particle Swarm Optimization) is improved, and the specific optimization function is as follows:

[0201]

[0202] wherein, represents the total weight of the structure, and represents the penalty term for violation of the system reliability constraint and the local stress constraint, respectively; is the system target failure probability.

[0203] The particle swarm optimization algorithm adopted by the present application is efficient and robust for solving, and the improvements mainly lie in the following aspects:

[0204] 1. Adaptive disturbance mechanism: In order to avoid the particle swarm from losing diversity and stagnating in the later search stage, an adaptive disturbance strategy is introduced. The strategy applies a random disturbance term to the speed of the particle . The improved velocity updating formula is:

[0205]

[0206] in, Inertial weights are used to adjust the continuity of particle velocity and achieve a smooth transition from global exploration to local development. For the first The particle in the first The velocity vector of the generation; and These are the individual learning factor and the group learning factor, which determine the particle's trajectory toward its historical best value. The degree to which it approaches the global optimum, gbest; , These are random numbers in the interval [0,1], used to enhance the randomness and diversity of the search. This is the particle's current position; For the adaptive perturbation term, in probability Random activation is used to prevent the particle swarm from getting trapped in local optima in the later stages of the search.

[0207] Perturbation mechanism: based on a preset probability Apply random perturbation to the particle velocity To prevent the particle swarm from getting trapped in a local optimum too early, the perturbation term... Defined as:

[0208]

[0209] in, A coefficient used to control the amplitude of the disturbance; The maximum permissible speed; The sign function ensures that the perturbation direction is random. and All Random numbers within the interval. This mechanism allows particles to escape the current local optimum with a certain probability, enhancing global exploration capabilities.

[0210] 2. Adaptive Parameter Strategy: The inertia weight w and / or learning factors c1 and c2 are dynamically adjusted according to the iteration process, enhancing global exploration capability in the early stages of optimization and local exploitation capability in the later stages. To balance exploration and local exploitation at different stages of optimization, a dynamic parameter adjustment strategy is adopted. Inertia weight... and learning factors Adaptive changes as the iteration process progresses:

[0211]

[0212]

[0213]

[0214]

[0215] where, is the time ratio; is the maximum time; and respectively represent the value of inertia weight at the initial and final stage of optimization, and its linear decrease can achieve the smooth transition from global exploration to local exploitation; and respectively are the starting and ending values of individual learning factor; and respectively are the starting and ending values of group learning factor.

[0216] At the initial stage of optimization, a higher and , and a lower are set, in order to let the particles carry out extensive global exploration. With the optimization proceeding, and gradually decrease, while gradually increases, so that the search behavior smoothly transitions from global exploration to the exploration of the discovered excellent solution region.

[0217] 3. Feasibility priority constraint processing mechanism: In order to effectively process reliability constraints, a feasibility priority criterion is introduced in the algorithm. When comparing the pros and cons of particles, solutions that meet all constraints (feasible solutions) are always superior to solutions that violate any constraints (infeasible solutions). In the process of particle updating and optimal solution selection, the design scheme that meets all constraint conditions is preferentially selected; for the scheme that violates the constraints, the penalty function method based on constraint violation degree is adopted to adjust its objective function value, in order to guide the population to converge to the feasible region.

[0218] For infeasible solutions, a dynamic penalty function method is adopted, and its penalty term is positively related to the degree of violation of system reliability constraints, and is adaptively enhanced with the iteration number, guiding the population to migrate to the feasible region.

[0219]

[0220]

[0221] where, is the equivalent objective function after constraint penalty; and are the penalty coefficients; is the constraint violation degree; is the system target failure probability.

[0222] 4. Diversity Preservation Strategy: During iteration, when the population diversity is detected to be below a threshold or convergence stagnation occurs, some particles are reset or reinitialized to maintain the global search capability of the population. When the population diversity is detected to be below a threshold or convergence stagnation occurs, an elite reset mechanism is activated. Particles with poor fitness in the population are replaced with newly initialized particles within the search space, or elite solution information from the previous optimization run is introduced to maintain the vitality of the population.

[0223] Through iterative search using the improved particle swarm optimization algorithm described above, the optimal design variable point d that has converged is finally output. The optimal design solutions for the 11-bar truss are shown in Table 1 below:

[0224] Table 1

[0225]

[0226] The above design scheme minimizes the total structural weight while satisfying system reliability constraints and all other engineering constraints. Furthermore, the output includes the system failure probability corresponding to this optimal design, the final cross-sectional dimensions of each member, and the importance ranking of key failure modes, providing comprehensive decision support for engineering design and reinforcement.

[0227] like Figure 5 As shown, truss structures with 10, 25, and 120 members were built in ANAYS software and simulated under the same working conditions. The displacement results and contour plots of the nodes were output. The displacement results were obtained by numerical calculation in the equilibrium equations established with the stiffness matrix. To verify whether the results of the members are consistent, the axial internal forces are calculated. .

[0228] This invention also designs a truss size optimization design system based on minimum cut set correlation. The system includes a database establishment module, a failure probability acquisition module, and a size optimization design module. The database establishment module establishes the equilibrium matrix of the truss structure based on the geometric information and boundary conditions of the truss structure, and obtains the minimum cut set database of the failure modes of the truss structure using the null space method based on the geometric invariance criteria of the structure. The failure probability acquisition module constructs a joint failure model of the minimum cut set database, and then obtains the failure probability of the truss structure while maintaining the consistency of the cut set edge probability space. The size optimization design module establishes a reliability constraint optimization model based on the failure probability of the truss structure, inputs the material density and length of each member of the truss structure into the reliability constraint optimization model, and outputs the total weight of the optimized truss structure and the cross-sectional area of ​​each member after processing to meet the reliability requirements, so as to perform size optimization design of the truss structure.

[0229] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the same. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A truss size optimization design method based on minimum cut set correlation, characterized by, The application relates to a method for designing a truss structure, comprising the following steps: Step S1: establishing a balance matrix of the truss structure, and obtaining a minimum cut set database of failure modes of the truss structure by using a zero space method according to the balance matrix; Step S2: constructing a joint failure model of the minimum cut set database, and further obtaining a failure probability of the truss structure under the condition of keeping the consistency of the edge probability space of the cut set; Step S3: establishing a reliability constraint optimization model based on the failure probability of the truss structure, inputting the material density and length of each rod of the truss structure into the reliability constraint optimization model, and outputting the total weight and the cross-sectional area of each rod of the optimized truss structure after processing, so as to perform size optimization design on the truss structure; The step S1 is specifically as follows: Step S11: establishing a balance matrix A based on the geometric shape of the truss structure, wherein the balance matrix A comprises directional cosine components of each rod to each node between the rods; Step S12: singular matrix is constructed after singular value decomposition (SVD) is processed on the balance matrix A , the singular matrix includes singular value matrix and right singular matrix , the singular value matrix is a diagonal matrix including several singular values, and the right singular matrix includes the eigen direction of the axial force of each member of the truss structure; Step S13: Singular value matrix whose singular values are smaller than a singular value threshold are regarded as zero, thereby extracting zero space basis vectors in the right singular matrix V Each row vector of the zero space basis vectors is a zero space row vector of each member of the truss structure Step S14: Based on the null space basis vectors A minimum cut set search of the truss structure is performed to obtain a minimum cut set database M of failure modes of the truss structure.

2. The truss size optimization design method based on the minimum cut set correlation according to claim 1, characterized in that: In step S14, in the null space basis vectors First, a single-member cut set determination is performed. For each member of the truss structure, when the zero-space basis vector... If the null space row vector of the current member is 0, then deleting the current member will cause the truss structure to fail. The member corresponding to the null space row vector of the current matrix is ​​taken as the minimum cut set unit. Then, a multi-member cut set determination is performed, based on the null space basis vectors... Remove one of the null space row vectors that is the smallest cut set unit to form a new null space basis vector. Randomly selected in the truss structure Root members constitute the candidate set In the new null space basis vectors Extract candidate set The null space row vectors of each member form a submatrix When rank( )< rank() is The size of the rank of the candidate set If the null space row vectors of each member are linearly dependent, then the candidate set... It is a cut set; then the cut set is determined. Whether it is a minimal cut set depends on the cut set. Each proper subset in When satisfied , For a true subset If the null space basis vectors are given, then the cut set... For minimal cut sets; the minimal cut sets are used to form a minimal cut set database M of the failure modes of the truss structure, M = {C1, C2, ..., C...} θ }, C1, C2, ..., C θ It is the 1st, 2nd, ..., θth minimal cut set.

3. The method of claim 1, wherein: The step S2 is specifically as follows: Step S21: obtaining discrete correlation coefficients of each two minimal cut sets in the minimal cut set database, so as to construct each discrete correlation coefficient as a joint failure model ; Step S22: mapping each discrete correlation coefficient in the joint failure model to a uniform space correlation coefficient by a Copula probability model, and then mapping the uniform space correlation coefficient to a normal space correlation coefficient by a Gaussian distribution, and constructing each normal space correlation coefficient into a normal correlation matrix ; Step S23: based on the normal correlation matrix The correlation sample Z is generated, and the sample failure number is obtained according to the correlation sample Z. Step S24: solving the failure probability of the truss structure based on the number of failure samples in the correlation sample Z .

4. The method of claim 3, wherein: In step S23, the critical state of the correlation sample Z is judged based on the normal correlation matrix The lower triangular element matrix L is decomposed, The lower triangular element matrix L is decomposed by matrix Cholesky to generate The independent normal sample Then the correlation sample Z is generated, Then the critical state of the correlation sample Z is judged as follows: ； ； where, is the critical state of the ith sample in the correlation sample Z, i.e., the minimal cut set of the ith independent normal sample is the failure state of the minimal cut set is the ith state function, is the standard normal distribution function; is the failure probability of the cut set i;​​ The final number of samples for each independent normal sample The number of sample failures is as follows: ； wherein, is the number of failures of the kth independent normal sample ; is the system failure of the kth normal sample is the failure event of the kth normal sample Y triggering the ith minimal cut set .

5. The method of claim 3, wherein: In the step S24, the failure probability of the truss structure As follows: ； wherein, is the total number of independent normal samples . is the number of failed samples of the kth independent normal sample .

6. The method of claim 1, wherein: In the step S3, the reliability constraint optimization model is specifically as follows: ； wherein, , and are the optimization design variable vector and its upper and lower limit constraints of the truss structure, respectively, , are the cross-sectional areas of the 1st, 2nd, …, i-th, …, b-th member, b is the total number of members; is the total weight of the truss structure; is the material density of the i-th member; is the length of the i-th member; is the failure probability of the truss structure; is the preset upper limit of the failure probability target; The particle swarm algorithm is used to solve the reliability constraint optimization model, and the optimal design variable of the optimized truss structure is obtained, so as to perform size optimization design on the truss structure.

7. An electronic device, comprising: The application further relates to a computer readable storage medium, comprising: A memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the method according to any one of claims 1-6.

8. A computer readable storage medium having stored thereon program data, wherein, The program data is executed by the processor to implement the method according to any one of claims 1-6.

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