A structure simulation analysis method based on mechanical constraint optimization

Abstract

The application discloses a structure simulation analysis method based on mechanical constraint optimization, which comprises the following steps: a CMA-ES algorithm is used to generate a structure parameter population, and a normal sampling mode is used to iteratively update the structure parameter distribution. In the method, a structure simulation model is constructed, static, buckling and modal simulations are performed on each group of structure parameter samples, response data such as displacement, critical load and natural frequency are extracted, an epsilon-constraint modeling method is introduced, a nested level constraint region is constructed by combining performance constraint expressions and tolerance variables, and the optimization search space is dynamically controlled. According to the simulation results and constraint judgment, the sample fitness and violation identification are output, and combined with the optimization convergence condition, a new generation of parameter samples is iteratively generated, and finally a set of structure design parameters meeting the constraint conditions and having the optimal performance is output. The whole process of the application is driven by mechanical simulation data, and has the characteristics of clear structure, closed loop calculation and optimization convergence.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of structure optimization and simulation analysis, and particularly relates to a structure simulation analysis method based on mechanical constraint optimization. BACKGROUND

[0002] With the fusion development of intelligent optimization of engineering structures and multi-physical field simulation, the structure parameter optimization method based on evolutionary algorithm has been widely applied to the design stage of aerospace, civil engineering and high-performance mechanical components. At present, the typical process for constraint structure optimization task mainly includes design variable sampling, performance simulation analysis, target function and constraint function calculation and population evolution update. Common evolutionary optimization methods such as genetic algorithm, particle swarm optimization and covariance matrix adaptive evolution strategy (CMA-ES) have gradually become the mainstream choice in multi-objective optimization.

[0003] The existing structure parameter optimization technology still has significant limitations in constraint processing mechanism and structure performance simulation linkage. On the one hand, the traditional method generally uses hard constraint elimination or penalty function weighting method to handle performance constraints, which is difficult to flexibly control the tolerance range of different constraint items, and cannot realize fine control and dynamic adjustment of multi-level constraint region, resulting in weak convergence ability of optimization search area and insufficient exploration of solution space. On the other hand, the optimization strategy and structure simulation process are loosely coupled, and the structure parameter population generation process lacks iterative update mechanism based on mechanical performance feedback, so the simulation results cannot effectively drive the evolution of structure design parameters, affecting the accuracy of the final optimal solution and the constraint satisfaction rate.

[0004] Therefore, how to provide a structure simulation analysis method based on mechanical constraint optimization is a problem that those skilled in the art need to solve. SUMMARY

[0005] An object of the present application is to provide a structure simulation analysis method based on mechanical constraint optimization. The present application fully integrates structure performance simulation, normal sampling evolutionary algorithm and multi-level constraint expression mechanism, and describes in detail the whole process of structure optimization solution and simulation feedback closed-loop control by constructing a structure parameter population response matrix, a dynamic constraint expression structure and a structure design variable normal sampling model, which has the advantages of strong adaptability, fine constraint regulation and stable convergence effect.

[0006] According to the structure simulation analysis method based on mechanical constraint optimization of the embodiment of the present application, the following steps are included:

[0007] A structure design parameter set is constructed, which includes geometric parameters, material parameters and boundary condition parameters, and a mechanical performance index set is defined, which includes buckling critical load, maximum displacement and first-order natural frequency;

[0008] generate an optimization objective function and a performance constraint set based on the structural design parameter set and the mechanical performance index set;

[0009] introduce adjustable tolerance variables to each constraint item in the performance constraint set by applying an epsilon-constraint modeling method, and generate an optimization problem structure body containing a main objective function and a dynamic constraint expression;

[0010] initialize the CMA-ES algorithm according to the variable range of the structural design parameter set, set the initial mean vector, covariance matrix and step factor, and generate a structural parameter population by normal sampling;

[0011] perform simulation calculation on the structural parameter population input into the structural simulation model to obtain corresponding buckling load, maximum displacement and natural frequency values, and construct a population response matrix;

[0012] jointly calculate the fitness value and constraint satisfaction state of each group of structural design parameters by combining the population response matrix and the optimization problem structure body, and output a fitness ranking table and a violation identification vector;

[0013] update the CMA-ES covariance matrix and mean vector according to the fitness ranking table and the violation identification vector to generate a new generation of structural parameter population, repeat the above simulation and optimization process until the termination condition is met, and output the optimal structural design parameter set.

[0014] Optionally, generating an optimization objective function and a performance constraint set based on the structural design parameter set and the mechanical performance index set includes:

[0015] extract the geometric parameters and material parameters in the structural design parameter set, and construct a structural variable field set, which is used to establish a structural volume calculation path and a material density mapping relationship;

[0016] bind the structural volume calculation path and the material density mapping relationship to generate a structural mass calculation structure body, which is used to construct a structural mass function expression;

[0017] construct an optimization objective function according to the structural mass function expression, which takes the structural variable field set as input and the structural mass calculation structure body as function dependency, forming an optimization objective function that can be used for minimization processing;

[0018] analyze the mechanical performance index set, extract the response calculation paths of the buckling critical load, maximum displacement and first-order natural frequency, and perform parameter binding between the response calculation paths and the structural variable field set to construct a performance index function structure body;

[0019] set the upper and lower limit values of each performance index according to the preset design requirements, establish a comparison relationship between the performance index function structure body and the upper and lower limit parameters, and generate a performance constraint set;

[0020] The optimization objective function is structurally integrated with the performance constraint set to build a target-constraint function set.

[0021] Optionally, the optimization problem structure body includes:

[0022] The target-constraint function set is received, and the target-constraint function set includes a structural mass optimization objective function and a structural performance constraint set, each structural performance constraint expression in the structural performance constraint set establishes a field dependency relationship with a structural variable field set in the structural design parameter set;

[0023] A structural performance tolerance variable is configured for each structural performance constraint expression in the structural performance constraint expression set to form a structural performance tolerance variable set, and the structural performance tolerance variable set and the structural performance constraint set are constructed into a structural performance tolerance mapping index table in a one-to-one correspondence;

[0024] The structural performance tolerance variable set and the structural performance constraint set are combined to build a dynamic structural performance constraint expression set, each expression in the dynamic structural performance constraint expression set is composed of a structural performance constraint expression and a structural performance tolerance variable, and has the following expression structure: g i (x)-ε i ≤0, where g i (x) represents a structural performance constraint expression, and ε i represents a structural performance tolerance variable;

[0025] A nested structural constraint region model is generated based on the dynamic structural performance constraint set, and the nested structural constraint region model contains multiple hierarchical regions, each hierarchical region corresponds to a group of structural performance tolerance variable ranges, and a region hierarchical index relationship is established;

[0026] A nested structural hierarchical control mechanism is built, which receives the current structural parameter population state and the structural performance tolerance variable state, and determines the nested structural constraint hierarchical region to which the structural parameter population belongs based on the region hierarchical index relationship;

[0027] The structural mass optimization objective function, the dynamic structural performance constraint expression set, the structural performance tolerance variable set, the nested structural constraint region model, and the nested structural hierarchical control mechanism are integrated to build the optimization problem structure body.

[0028] Optionally, the generation of the structural parameter population includes:

[0029] A parameter initialization structure of the CMA-ES algorithm is built, the structural variable field set in the structural design parameter set is received, the structural variable dimension information is extracted, and a structural variable dimension index set is generated;

[0030] The structural parameter mean vector is set based on the set of structural variable dimension indices. The structural parameter mean vector is used to define the initial center position of the structural parameter distribution.

[0031] Initialize the structure parameter covariance matrix based on the structure variable dimension index set. The structure parameter covariance matrix is ​​a symmetric positive definite matrix. Define the collaborative relationships between structure variable fields.

[0032] Set the structural parameter step size factor, which is a scalar control variable representing the normal sampling scale of the structural parameters, and form a sampling scale control structure with the structural parameter covariance matrix.

[0033] The mean vector of structural parameters, the covariance matrix of structural parameters, and the step size factor of structural parameters are integrated to construct the CMA-ES structural parameter normal sampling model. The structural parameter normal sampling model is used to generate a set of structural parameter samples in the structural parameter space.

[0034] Set the population size of the structural parameters, call the CMA-ES structural parameter normal sampling model, and perform multiple rounds of structural parameter sampling based on the structural parameter mean vector as the expectation, the structural parameter covariance matrix as the distribution feature, and the structural parameter step size factor as the scaling variable, and output the structural parameter population.

[0035] Optionally, the construction of the structural parameter population response matrix includes:

[0036] A structural simulation model is constructed, which consists of a finite element modeling module, a boundary condition loading module, and a multiphysics field solution module. It is used to receive structural parameter samples from the structural parameter population set and generate structural unit modeling structures.

[0037] The geometric parameter field, material property field and boundary condition field of the structural design parameter set are respectively passed to the finite element modeling module, the material property setting module and the boundary condition loading module to generate the structural simulation input data structure corresponding to each structural parameter sample.

[0038] For each structural parameter sample in the structural parameter population set, the structural simulation model is called to execute the static simulation process, buckling simulation process and modal simulation process in sequence, and the maximum nodal displacement value, buckling critical load value and first natural frequency value corresponding to the current structural parameter sample are output.

[0039] Each set of simulation outputs three mechanical performance data are constructed into a structural performance response field triplet. The structural performance response field triplet includes the maximum nodal displacement field, the critical buckling load field, and the first natural frequency field, and is bound to the structural parameter sample number to form a structural performance response entry.

[0040] The structural parameter sample number is arranged in ascending order, and a structural parameter population response matrix is constructed. The structural parameter population response matrix takes the structural parameter sample number as the row index and takes the structural performance response field as the column index. The matrix dimension is consistent with the structural parameter population set.

[0041] Optionally, the output of the fitness ranking table and the default identification vector includes:

[0042] The structural parameter population response matrix and the optimization problem structure are received. The structural parameter population response matrix includes a plurality of structural performance response field triplets, and the optimization problem structure includes a structural mass optimization objective function and a dynamic structural performance constraint expression set.

[0043] For each structural parameter sample in the structural parameter population response matrix, the structural mass optimization objective function is called to calculate the structural mass objective function value, which is used as the initial fitness value of the structural parameter sample.

[0044] Each structural performance constraint expression in the dynamic structural performance constraint expression set is parsed, and the structural performance response field triplets in the structural parameter population response matrix are respectively judged for constraint. The judgment result forms a structural performance constraint satisfaction state vector of the structural parameter sample.

[0045] The initial fitness value of the structural parameter sample is jointly adjusted according to the structural performance constraint satisfaction state vector to generate the target fitness value of the structural parameter sample.

[0046] All structural performance constraint items that do not meet the conditions in the structural performance constraint satisfaction state vector are set as default items, the number of default items of each structural parameter sample is counted, and a default item number vector of the structural parameter population is constructed.

[0047] The fitness target value set is sorted in descending order, and a fitness ranking table of the structural parameter population is output.

[0048] The default item number vector is binarized to generate a default identification vector of the structural parameter population. Each element in the default identification vector is used to indicate whether the corresponding structural parameter sample violates any structural performance constraint expression.

[0049] Optionally, the output of the optimal structural design parameter set includes:

[0050] The fitness ranking table and the default identification vector of the structural parameter population are received, and the current structural parameter population response matrix and the structural parameter population set are combined to initialize an optimization convergence state identification field.

[0051] The structural parameter population set is sorted based on the fitness ranking table, and the top N structural parameter samples are selected to form an excellent structural sample set of the current optimization round.

[0052] performing a structure parameter vector averaging operation on the excellent structure sample set to generate an updated structure parameter mean vector;

[0053] calculating a structure parameter variance matrix based on the excellent structure sample set, and performing a weighted update in combination with the original structure parameter covariance matrix to generate an updated structure parameter covariance matrix;

[0054] constructing a new structure parameter normal sampling model according to the updated structure parameter mean vector and the structure parameter covariance matrix, performing next-generation structure parameter sample sampling according to a preset structure parameter population size to form a new generation structure parameter population set;

[0055] determining whether the current optimization round reaches a maximum round threshold, or determining whether the change amplitude between the structure parameter mean vector and the historical mean vector is lower than a preset convergence threshold, and if any condition is met, setting an optimization convergence state identifier field to a convergence state;

[0056] if the optimization convergence state identifier field is in the convergence state, selecting all structure parameter samples with a default indicator vector of 0 from the current structure parameter population set, and sorting and extracting a structure parameter sample with an optimal fitness target value according to a fitness sorting table to output a structure design parameter field set corresponding to the structure parameter sample.

[0057] Optionally, the formation of the new generation structure parameter population set comprises:

[0058] receiving the updated structure parameter mean vector and the updated structure parameter covariance matrix, and constructing a structure parameter normal sampling input structure, the structure parameter normal sampling input structure comprising a structure parameter mean vector field and a structure parameter covariance matrix field;

[0059] constructing a structure parameter normal distribution model according to the structure parameter normal sampling input structure, the structure parameter normal distribution model taking the structure parameter mean vector as a distribution center and the structure parameter covariance matrix as a cooperative disturbance relationship to form a distribution definition domain for structure parameter sampling;

[0060] setting a structure parameter population size parameter, the structure parameter population size parameter being a positive integer type control variable for limiting the number of generated structure parameter samples in each round of optimization sampling;

[0061] calling the structure parameter normal distribution model, and performing multiple rounds of structure parameter sample sampling according to the structure parameter population size parameter, each round of sampling generating a structure parameter sample vector;

[0062] Integrate all the structural parameter sample vectors to construct a new generation of structural parameter population set, and the new generation of structural parameter population set is indexed by the structural parameter sample number, the structural variable field is indexed by the column index field, and the current optimization round is marked.

[0063] The beneficial effects of the present application are:

[0064] (1) The present application realizes adaptive sampling and simulation feedback closed-loop control of structural design parameters by constructing a CMA-ES algorithm and an epsilon-constrained modeling structure, effectively improves the adaptability to complex mechanical performance constraints in the structural optimization process, and has a significant advantage in dynamic regulation of constraint level regions in high-dimensional parameter space; at the same time, by jointly constructing a dynamic structural performance constraint expression and a structural response evaluation model, the expression accuracy and solution efficiency of the optimization problem under multi-field coupling conditions are improved.

[0065] (2) The present application integrates static simulation, buckling simulation and modal simulation processes in the structural simulation model, combines the structural performance response matrix and the dynamic constraint judgment mechanism to realize the fitness evaluation and violation screening of the structural sample, and realizes the adaptive termination judgment by the statistical convergence threshold and the historical vector change rate in the optimization convergence judgment and structural parameter updating process, which effectively improves the optimal solution accuracy and feasibility of the structural design parameter set.

[0066] (3) In the updating process of the structural parameter population, the present application constructs a normal sampling model of structural parameters based on the mean vector and covariance matrix of excellent samples, and combines the convergence control mechanism and violation identification vector to jointly constrain, so that the optimization path can approach the structural quality optimal solution while avoiding the structural performance violation region, thereby showing the comprehensive ability superior to the existing method in the feasibility, stability and structural performance guarantee of the optimization result. BRIEF DESCRIPTION OF DRAWINGS

[0067] The accompanying drawings are included to provide a further understanding of the present application, and constitute a part of the specification, which together with the embodiments of the present application, serve to explain the present application, and do not constitute a limitation on the present application. In the drawings:

[0068] Fig. 1 A flowchart of a structural simulation analysis method based on mechanical constraint optimization is proposed for the present application;

[0069] Fig. 2 A structural parameter population generation and simulation process diagram is proposed for the present application;

[0070] Fig. 3 A flowchart of a multi-layer nested structural constraint region construction process based on epsilon-constrained modeling is proposed for the present application. DETAILED DESCRIPTION

[0071] The application will be described in further detail below with reference to the drawings. These drawings are simplified schematic diagrams and only show the basic structure of the application in a schematic manner, and thus only show the components relevant to the application.

[0072] Reference Figs. 1-3 A structure simulation analysis method based on mechanical constraint optimization, comprising the following steps:

[0073] A structure design parameter set is constructed, the structure design parameter set including geometric parameters, material parameters and boundary condition parameters, and a mechanical performance index set is defined, the mechanical performance index set including a buckling critical load, a maximum displacement and a first-order natural frequency;

[0074] An optimization objective function and a performance constraint set are generated based on the structure design parameter set and the mechanical performance index set, the optimization objective function being defined as a structure mass or stability function, and each constraint term in the performance constraint set corresponding to a mechanical performance index;

[0075] An adjustable tolerance variable is introduced into each constraint term in the performance constraint set by using an ε-constraint modeling method, and an optimization problem structure body containing a main objective function and a dynamic constraint expression is generated;

[0076] The CMA-ES algorithm is initialized according to the variable range of the structure design parameter set, an initial mean vector, a covariance matrix and a step factor are set, and a structure parameter population is generated by normal sampling;

[0077] The structure parameter population is input into a structure simulation model to perform simulation calculation, and corresponding buckling load, maximum displacement and natural frequency values are obtained, and a population response matrix is constructed;

[0078] The population response matrix and the optimization problem structure body are jointly calculated to obtain the fitness value and the constraint satisfaction state of each group of structure design parameters, and a fitness ranking table and a violation identification vector are output;

[0079] The CMA-ES covariance matrix and mean vector are updated according to the fitness ranking table and the violation identification vector, a new generation of structure parameter population is generated, and the above simulation and optimization process is repeated until a termination condition is met, and the optimal structure design parameter set is output.

[0080] In this embodiment, generating the optimization objective function and the performance constraint set based on the structure design parameter set and the mechanical performance index set comprises:

[0081] The geometric parameters and the material parameters in the structure design parameter set are extracted, and a structure variable field set is constructed, the structure variable field set being used to establish a structure volume calculation path and a material density mapping relationship;

[0082] The structural volume calculation path is bound to the material density mapping relationship to generate a structural mass calculation structure, which is used to construct a structural mass function expression;

[0083] An optimization objective function is constructed according to the structural mass function expression, the optimization objective function taking the structural variable field set as input and the structural mass calculation structure as function dependency, forming an optimization objective function that can be used for minimization processing;

[0084] A set of mechanical performance indicators is analyzed, response calculation paths of the buckling critical load, maximum displacement and first-order natural frequency are extracted, and the response calculation paths are parameter bound to the structural variable field set to construct a performance indicator function structure;

[0085] Upper and lower limit values of each performance indicator are set according to a predetermined design requirement, a performance constraint set is generated by establishing a comparison relationship between the performance indicator function structure and the upper and lower limit parameters;

[0086] The optimization objective function and the performance constraint set are integrated to construct a target-constraint function set;

[0087] The upper and lower limit values of each performance indicator are set according to the buckling critical load, maximum displacement and first-order natural frequency in the set of mechanical performance indicators, according to the performance limit values defined in the structural use condition, limit bearing capacity, safety specification or industry standard, the constraint upper and lower limit parameters matched with each performance indicator function structure are set respectively, wherein the lower limit value of the buckling critical load constraint is used to ensure that the structure does not locally unstable under compression, the upper limit value of the maximum displacement constraint is used to limit the deformation amplitude of the structure under load, and the lower limit value of the first-order natural frequency constraint is used to avoid the structure frequency entering the environmental excitation resonance interval, all constraint parameters are bound to the corresponding performance indicator function structure as constant fields.

[0088] In this embodiment, generating an optimization problem structure includes:

[0089] The target-constraint function set is received, the target-constraint function set including a structural mass optimization objective function and a set of structural performance constraints, each structural performance constraint expression in the set of structural performance constraints establishing a field dependency relationship with the set of structural variable fields in the set of structural design parameters;

[0090] Each structural performance constraint expression in the set of structural performance constraint expressions is configured with a structural performance tolerance variable to form a set of structural performance tolerance variables, and the set of structural performance tolerance variables and the set of structural performance constraints construct a structural performance tolerance mapping index table in a one-to-one correspondence;

[0091] By performing combined modeling on the set of structural performance tolerance variables and the set of structural performance constraints, a set of dynamic structural performance constraint expressions is constructed. Each expression in the set of dynamic structural performance constraint expressions consists of a structural performance constraint expression and a structural performance tolerance variable, and has the following expression structure: g i (x)-ε i ≤0, where g i (x) represents the structural performance constraint expression, ε i Indicates the structural performance tolerance variable;

[0092] A nested structural constraint region model is generated based on a dynamic set of structural performance constraints. The nested structural constraint region model contains multiple hierarchical regions, each of which corresponds to a set of structural performance tolerance variable ranges, and a region hierarchical index relationship is established.

[0093] A nested structure hierarchical control mechanism is constructed. The nested structure hierarchical control mechanism receives the current state of the structural parameter population and the state of the structural performance tolerance variable, and determines the nested structure constraint hierarchy region to which the structural parameter population belongs based on the region hierarchical index relationship.

[0094] The optimization problem structure is constructed by integrating the structural quality optimization objective function, the set of dynamic structural performance constraint expressions, the set of structural performance tolerance variables, the nested structural constraint region model, and the nested structural hierarchical control mechanism.

[0095] In this embodiment, the generation of the structural parameter population includes:

[0096] Construct the parameter initialization structure for the CMA-ES algorithm, receive the set of structure variable fields from the structure design parameter set, extract the dimension information of the structure variables, and generate a set of structure variable dimension indexes;

[0097] The structural parameter mean vector is set according to the set of structural variable dimension indices. The structural parameter mean vector is used to define the initial center position of the structural parameter distribution and serves as the expected input field of the normal sampling model.

[0098] Initialize the structure parameter covariance matrix based on the structure variable dimension index set. The structure parameter covariance matrix is ​​a symmetric positive definite matrix. Define the collaborative relationships between structure variable fields.

[0099] Set the structural parameter step size factor, which is a scalar control variable representing the normal sampling scale of the structural parameters, and form a sampling scale control structure with the structural parameter covariance matrix.

[0100] The structural parameter mean vector, the structural parameter covariance matrix, and a structural parameter step factor structure are integrated to construct a CMA-ES structural parameter normal sampling model, and the structural parameter normal sampling model is used to generate a structural parameter sample set in a structural parameter space;

[0101] A structural parameter population size is set, the CMA-ES structural parameter normal sampling model is called, the structural parameter mean vector is taken as an expectation, the structural parameter covariance matrix is taken as a distribution characteristic, and the structural parameter step factor is taken as a scale variable, a plurality of rounds of structural parameter sampling are performed, and a structural parameter population is output;

[0102] A mean path tracking operation is performed on the structural parameter population set to construct a structural parameter path tracking vector structure and record a moving trend of the structural parameter mean vector between continuous generations;

[0103] The structural parameter path tracking vector structure, the current structural parameter mean vector, the structural parameter covariance matrix, and the structural parameter step factor are combined to construct a covariance update auxiliary structure for supporting subsequent adaptive adjustment of a structural parameter distribution in a generation;

[0104] The structural parameter population set is output as input structures of a structural simulation calculation module and an optimization problem structure body fitness evaluation module, and the structural parameter path tracking vector structure and the covariance update auxiliary structure are output as input fields of a CMA-ES algorithm iteration control module.

[0105] In this embodiment, the construction of the structural parameter population response matrix includes:

[0106] A structural simulation model is constructed, the structural simulation model is composed of a finite element modeling module, a boundary condition loading module, and a multi-physical field solving module, and is used to receive a structural parameter sample in the structural parameter population set and generate a structural element modeling structure;

[0107] Geometric parameter fields, material attribute fields, and boundary condition fields in the structural design parameter set are respectively transmitted to the finite element modeling module, the material attribute setting module, and the boundary condition loading module to generate a structural simulation input data structure corresponding to each structural parameter sample;

[0108] For each structural parameter sample in the structural parameter population set, the structural simulation model is called to sequentially perform a static simulation process, a buckling simulation process, and a modal simulation process, and output a maximum node displacement value, a buckling critical load value, and a first-order natural frequency value corresponding to the current structural parameter sample;

[0109] The three mechanical performance data of each simulation output are constructed as a structural performance response field triple, the structural performance response field triple includes a node maximum displacement field, a buckling critical load field and a first-order natural frequency field, and is bound with a structural parameter sample number to form a structural performance response entry;

[0110] All structural performance response entries are arranged in ascending order of structural parameter sample numbers to construct a structural parameter population response matrix, the structural parameter population response matrix takes the structural parameter sample number as the row index and the structural performance response field as the column index, and the matrix dimension is consistent with the structural parameter population set;

[0111] The structural parameter population response matrix is transmitted to the optimization problem structure, and the structural parameter population response matrix is used as an input field set of the fitness evaluation module and the performance constraint judgment module;

[0112] The calling structural simulation model sequentially executes a static simulation process, a buckling simulation process and a modal simulation process, which includes that the structural simulation model receives a structural parameter sample in the structural parameter population set as input, and constructs a finite element model, a material parameter mapping structure and a boundary constraint configuration structure respectively; in the static simulation process, the node response displacement is calculated according to the node load configuration, and the maximum node displacement field is extracted; in the buckling simulation process, the critical stability disturbance condition is loaded based on the static simulation result, the minimum eigenvalue is solved, and the corresponding buckling critical load field is extracted; in the modal simulation process, a joint characteristic solving path of the mass matrix and the stiffness matrix is established, the first-order characteristic frequency is calculated, and the first-order natural frequency field is extracted; the above three simulation processes are sequentially executed, and the displacement value, the load value and the frequency value in the simulation output constitute the structural performance response field triple corresponding to the current structural parameter sample.

[0113] In this embodiment, the output of the fitness ranking table and the default identification vector includes:

[0114] Receiving a structural parameter population response matrix and an optimization problem structure, the structural parameter population response matrix including a plurality of structural performance response field triples, and the optimization problem structure including a structural mass optimization objective function and a dynamic structural performance constraint expression set;

[0115] For each structural parameter sample in the structural parameter population response matrix, a structural mass optimization objective function is called to calculate a structural mass objective function value, which is used as the fitness initial value of the structural parameter sample;

[0116] Each structural performance constraint expression in the dynamic structural performance constraint expression set is analyzed, and the structural performance response field triple in the structural parameter population response matrix is judged respectively, and the judgment result forms a structural performance constraint satisfaction state vector of the structural parameter sample;

[0117] According to the structural performance constraint satisfaction state vector, the fitness initial value of the structural parameter sample is jointly adjusted, and the fitness target value of the structural parameter sample is generated, and the fitness target value constitutes the fitness target value set of the structural parameter population;

[0118] All structural performance constraint items that do not meet the conditions in the structural performance constraint satisfaction state vector are set as default items, the number of default items of each structural parameter sample is counted, and the number of default items vector of the structural parameter population is constructed;

[0119] The fitness target value set is sorted in descending order, and the fitness sorting table of the structural parameter population is output;

[0120] The default item number vector is binarized to generate the default item identification vector of the structural parameter population, and each element in the default item identification vector is used to indicate whether the corresponding structural parameter sample violates any structural performance constraint expression;

[0121] The constraint judgment refers to performing logical judgment operation on each set of structural performance response field triplets in the structural parameter population response matrix based on the dynamic structural performance constraint expression set defined in the optimization problem structure, each expression in the dynamic structural performance constraint expression set is composed of a structural performance constraint expression and a structural performance tolerance variable, the structural performance constraint expression is used to describe the numerical range required to be met by the structural performance response field, and the structural performance tolerance variable sets a flexible adjustable boundary for the numerical range. In the constraint judgment process, the system reads the structural performance response field value of the current structural parameter sample, and substitutes it into the corresponding structural performance constraint expression, and compares it with the tolerance range agreed in the expression. If the field value is within the tolerance range, the constraint judgment is "satisfied", otherwise it is "not satisfied". All judgment results are combined in the order of structural performance constraint expressions to form the structural performance constraint satisfaction state vector, which is bound with the structural parameter sample number.

[0122] In the embodiment, the output of the optimal structural design parameter set includes:

[0123] The fitness sorting table and the default item identification vector of the structural parameter population are received, and the current structural parameter population response matrix and the structural parameter population set are combined to initialize the optimization convergence state identification field;

[0124] The structural parameter population set is sorted based on the fitness sorting table, and the top N structural parameter samples are selected to form the excellent structural sample set of the current optimization round;

[0125] The excellent structural sample set is executed to generate the updated structural parameter mean vector;

[0126] Calculate a structure parameter variance matrix based on a set of excellent structure samples, perform weighted update combined with the original structure parameter covariance matrix, and generate an updated structure parameter covariance matrix;

[0127] Construct a new structure parameter normal sampling model according to the updated structure parameter mean vector and the structure parameter covariance matrix, perform next-generation structure parameter sample sampling according to a preset structure parameter population size, and form a new generation of structure parameter population set;

[0128] Determine whether the current optimization round reaches a maximum round threshold, or whether the change amplitude between the structure parameter mean vector and the historical mean vector is lower than a preset convergence threshold, and if any condition is met, set the optimization convergence state identifier field to a convergence state;

[0129] If the optimization convergence state identifier field is in a convergence state, select all structure parameter samples with a default value of 0 from the current structure parameter population set, and sort and extract the structure parameter sample with the optimal fitness target value according to the fitness sorting table, and output the structure design parameter field set corresponding to the structure parameter sample.

[0130] In this embodiment, the formation of the new generation of structure parameter population set includes:

[0131] Receive the updated structure parameter mean vector and the updated structure parameter covariance matrix, and construct a structure parameter normal sampling input structure, which includes a structure parameter mean vector field and a structure parameter covariance matrix field;

[0132] Construct a structure parameter normal distribution model according to the structure parameter normal sampling input structure, which takes the structure parameter mean vector as the distribution center and the structure parameter covariance matrix as the cooperative disturbance relationship, and forms a distribution definition domain for structure parameter sampling;

[0133] Set a structure parameter population size parameter, which is a positive integer type control variable used to limit the number of generated structure parameter samples in each round of optimization sampling;

[0134] Call the structure parameter normal distribution model, perform multiple rounds of structure parameter sample sampling according to the structure parameter population size parameter, and generate one structure parameter sample vector in each round of sampling;

[0135] Integrate all structure parameter sample vectors to construct a new generation of structure parameter population set, which takes the structure parameter sample number as the index field, takes the structure variable field as the column index field, and marks the current optimization round.

[0136] Embodiment 1:

[0137] To verify the feasibility of the application in implementation, the application is applied to the steel structure design optimization task of a certain urban rail transit station, and the project team is responsible for the structural parameter optimization of the upper curved steel truss structure of the station waiting hall. The truss structure has a span of 48 meters, adopts a spatial quadrilateral truss arrangement, and is connected by multiple steel pipe welded nodes. In order to further reduce the self weight and material cost of the steel structure under the premise of meeting the strength and stability requirements, the design unit proposes to carry out multi-objective structural optimization analysis based on mechanical performance constraints.

[0138] In the traditional design method, the designer usually adjusts the size of the truss and the material selection according to experience, and then uses a structural simulation tool to repeatedly calculate and verify. This method not only has low optimization efficiency and blind parameter adjustment, but also is difficult to cover a large-scale parameter combination space, and the final structure result is easily affected by individual experience or local search limit, which has the risk of local optimization. Especially when considering multiple structural performance index constraints such as buckling critical load, maximum node displacement and first order natural frequency, it is difficult to realize closed-loop integration of parameter coordination optimization.

[0139] In view of the above problems, the project team uses a structural simulation analysis method based on mechanical constraint optimization proposed by the application to carry out the optimization process. First, according to the design drawing and construction requirements, the structural design parameter set is constructed, including the length of the rod, the diameter of the cross section, the elastic modulus of the steel, the boundary support condition and the load case setting. According to the engineering target, the structure quality is defined as the optimization objective function, and three key performance constraints are set: the buckling critical load is not less than 120kN, the maximum node displacement is not more than 3.5mm, and the first order natural frequency is not less than 75Hz. The above performance indicators are obtained through the simulation process.

[0140] To support multi-constraint joint optimization, the method first uses the ε-constraint modeling method to introduce tolerance variables to the three performance constraints, and constructs a set of dynamic structural performance constraint expressions. All objective functions and constraint expressions are encapsulated into the optimization problem structure as the core scheduling basis. Then, the CMA-ES algorithm is called to initialize the structure parameter sampling model. By setting the mean vector, covariance matrix and step factor of the structure parameters, a normal sampling structure is constructed, and the population size is set to 50, and the optimization is started.

[0141] In each round of optimization, the system samples a set of structural parameter population from the normal sampling model, and inputs each sample into the self-built structural simulation model. The simulation model is composed of a finite element modeling module, a boundary condition loading module, and a multi-physical field solving module. In the model, the structural geometry is automatically parsed to generate solid meshes, and a constant vertical load is applied through the boundary condition loading module. The static simulation process is used to solve the maximum displacement of each node, the buckling simulation module calculates the critical buckling load based on eigenvalue analysis, and the modal simulation process is used to solve the first few natural frequencies of the structure.

[0142] Each round of simulation output is constructed as a structural parameter population response matrix, containing three fields of maximum node displacement, buckling critical load, and first-order natural frequency corresponding to each structural parameter sample. The response matrix is passed into the fitness evaluation module, the system calls the objective function for each structural sample and judges the violation according to the constraint expression, forming a fitness ranking table and a violation identification vector. The algorithm updates the mean vector and covariance matrix in the current structural parameter sampling model, starts the next generation of sample sampling and simulation, and repeats the above process.

[0143] When the number of optimization iterations reaches 100 rounds, or the change amplitude of the mean vector of the current population and the historical mean vector is less than the set threshold, the system determines convergence. Finally, the optimal value of the fitness value is selected from the structural samples that meet all the constraint conditions, and the corresponding structural design parameter field is output as the optimal structural design parameter set. The following is the comparison result of the structural performance of some samples before and after optimization:

[0144]

[0145] From the "structure simulation optimization performance comparison table" can be seen that the optimization process has made significant improvements in the three key performance indicators of the structure: maximum node displacement, buckling critical load and first order natural frequency. In terms of maximum node displacement, the sample values before optimization are generally between 5.3mm and 6.37mm, which is much higher than the set performance upper limit of 3.5mm, while after optimization, the maximum displacement values of all samples are controlled between 2.39mm and 3.30mm, all meeting the performance constraints, reflecting the effectiveness of the optimization algorithm in structure flexibility control. In terms of buckling critical load, the buckling critical load of the samples before optimization is distributed between 81.65kN and 89.26kN, which fails to meet the design target of 120kN, while after optimization, it is significantly improved to the interval of 126.90kN to 149.45kN, with the highest improvement of about 83%, fully demonstrating that the parameter reconstruction and covariance-guided normal sampling mechanism can systematically improve the stability of the structure. In terms of the first order natural frequency, the sample frequency before optimization is concentrated between 54.14Hz and 64.05Hz, which has the problem of insufficient structural vibration resistance performance, while after optimization, it is generally improved to the interval of 76.75Hz to 88.22Hz, which is significantly higher than the set lower limit of 75Hz, indicating that the optimization algorithm can effectively tap the frequency performance potential under the condition of meeting the stiffness and mass coordination. Combining the data of the three dimensions, it can be seen that the method shows consistency and stability in the multi-objective performance coordinated optimization of the structure, and none of the optimized samples violates the performance constraints, indicating that the optimization path converges well and the results are controllable.

[0146] The above merely describes preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can make equivalent replacements or changes to the technical solutions and inventive concepts of the present application within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A structural simulation analysis method based on mechanical constraint optimization, characterized in that, include: Construct a set of structural design parameters, which includes geometric parameters, material parameters, and boundary condition parameters, and define a set of mechanical performance indicators, which includes the buckling critical load, maximum displacement, and first natural frequency. The optimization objective function and performance constraint set are generated based on the structural design parameter set and mechanical performance index set, specifically including: Extract geometric and material parameters from the structural design parameter set, construct a set of structural variable fields, and use the set of structural variable fields to establish the mapping relationship between the structural volume calculation path and the material density; Bind the structural volume calculation path to the material density mapping relationship to generate a structural mass calculation structure, which is used to construct the structural mass function expression. An optimization objective function is constructed based on the structural quality function expression. The optimization objective function takes the set of structural variable fields as input and the structural quality calculation structure as a functional dependency, thus forming an optimization objective function that can be used for minimization. The mechanical performance index set is analyzed, the response calculation path of buckling critical load, maximum displacement and first natural frequency is extracted, and the response calculation path is parameterized with the set of structural variable fields to construct the performance index function structure; According to the preset design requirements, set upper and lower limits for each performance index, establish a comparison relationship between the performance index function structure and the upper and lower limit parameters, and generate a set of performance constraints. The objective function and the set of performance constraints are structurally integrated to construct an objective-constraint function set. application - The constraint modeling method introduces adjustable tolerance variables into each constraint item in the performance constraint set, generating an optimization problem structure that includes the main objective function and dynamic constraint expressions; Initialize based on the variable range of the structural design parameter set. The algorithm sets an initial mean vector, covariance matrix, and step size factor, and generates a population of structural parameters through normal sampling. Simulation calculations were performed on the structural simulation model with population input of structural parameters to obtain the corresponding buckling load, maximum displacement and natural frequency values, and a population response matrix was constructed. The fitness value and constraint satisfaction state of each set of structural design parameters are calculated jointly by the population response matrix and the optimization problem structure, and the fitness ranking table and default flag vector are output. Execute based on fitness ranking table and default flag vector. The covariance matrix and mean vector are updated to generate a new generation of structural parameter population. The above simulation and optimization process is repeated until the termination condition is met and the optimal structural design parameter set is output.

2. The structural simulation analysis method based on mechanical constraint optimization according to claim 1, characterized in that, The structure for generating the optimization problem includes: Receive the target-constraint function set, which includes the structural quality optimization objective function and the structural performance constraint set. Each structural performance constraint expression in the structural performance constraint set establishes a field dependency relationship with the set of structural variable fields in the structural design parameter set. For each structural performance constraint expression in the set of structural performance constraint expressions, a structural performance tolerance variable is configured to form a set of structural performance tolerance variables. The set of structural performance tolerance variables and the set of structural performance constraints are constructed in a one-to-one correspondence relationship to construct a structural performance tolerance mapping index table. By performing combined modeling on the set of structural performance tolerance variables and the set of structural performance constraints, a set of dynamic structural performance constraint expressions is constructed. Each expression in the set of dynamic structural performance constraint expressions consists of a structural performance constraint expression and a structural performance tolerance variable, and has the following expression structure: ,in This represents the expression for structural performance constraints. Indicates the structural performance tolerance variable; A nested structural constraint region model is generated based on a dynamic set of structural performance constraints. The nested structural constraint region model contains multiple hierarchical regions, each of which corresponds to a set of structural performance tolerance variable ranges, and a region hierarchical index relationship is established. A nested structure hierarchical control mechanism is constructed. The nested structure hierarchical control mechanism receives the current state of the structural parameter population and the state of the structural performance tolerance variable, and determines the nested structure constraint hierarchy region to which the structural parameter population belongs based on the region hierarchical index relationship. The optimization problem structure is constructed by integrating the structural quality optimization objective function, the set of dynamic structural performance constraint expressions, the set of structural performance tolerance variables, the nested structural constraint region model, and the nested structural hierarchical control mechanism.

3. The structural simulation analysis method based on mechanical constraint optimization according to claim 1, characterized in that, The generation of the structural parameter population includes: Build The algorithm initializes the parameter structure by receiving a set of structure variable fields from the structure design parameter set, extracting the dimension information of the structure variables, and generating a set of structure variable dimension indexes. The structural parameter mean vector is set based on the set of structural variable dimension indices. The structural parameter mean vector is used to define the initial center position of the structural parameter distribution. Initialize the structure parameter covariance matrix based on the structure variable dimension index set. The structure parameter covariance matrix is ​​a symmetric positive definite matrix. Define the collaborative relationship between structure variable fields. Set the structural parameter step size factor, which is a scalar control variable representing the normal sampling scale of the structural parameters, and form a sampling scale control structure with the structural parameter covariance matrix. By integrating the structural parameter mean vector, structural parameter covariance matrix, and structural parameter step size factor structure, a construction is constructed. The structural parameter normal sampling model is used to generate a set of structural parameter samples in the structural parameter space. Set the structural parameters and population size, then call... The structural parameter normal sampling model performs multiple rounds of structural parameter sampling based on the structural parameter mean vector as the expectation, the structural parameter covariance matrix as the distribution feature, and the structural parameter step size factor as the scaling variable, and outputs a structural parameter population.

4. The structural simulation analysis method based on mechanical constraint optimization according to claim 1, characterized in that, The construction of the structural parameter population response matrix includes: A structural simulation model is constructed, which consists of a finite element modeling module, a boundary condition loading module, and a multiphysics field solution module. It is used to receive structural parameter samples from the structural parameter population set and generate structural unit modeling structures. The geometric parameter field, material property field and boundary condition field of the structural design parameter set are respectively passed to the finite element modeling module, the material property setting module and the boundary condition loading module to generate the structural simulation input data structure corresponding to each structural parameter sample. For each structural parameter sample in the structural parameter population set, the structural simulation model is called to execute the static simulation process, buckling simulation process and modal simulation process in sequence, and the maximum nodal displacement value, buckling critical load value and first natural frequency value corresponding to the current structural parameter sample are output. Each set of simulation outputs three mechanical performance data are constructed into a structural performance response field triplet. The structural performance response field triplet includes the maximum nodal displacement field, the critical buckling load field, and the first natural frequency field, and is bound to the structural parameter sample number to form a structural performance response entry. All structural performance response entries are sorted in ascending order by structural parameter sample number, and a structural parameter population response matrix is ​​constructed. The structural parameter population response matrix uses the structural parameter sample number as the row index and the structural performance response field as the column index. The matrix dimension is consistent with the structural parameter population set.

5. The structural simulation analysis method based on mechanical constraint optimization according to claim 1, characterized in that, The outputs of the fitness ranking table and the default flag vector include: The system receives a population response matrix of structural parameters and an optimization problem structure. The population response matrix of structural parameters includes multiple triplets of structural performance response fields, and the optimization problem structure includes a set of structural quality optimization objective functions and dynamic structural performance constraint expressions. For each structural parameter sample in the population response matrix of structural parameters, the structural quality optimization objective function is called to calculate the structural quality objective function value, which is used as the initial fitness value of the structural parameter sample. Each structural performance constraint expression in the set of dynamic structural performance constraint expressions is analyzed, and the constraint judgment is performed on the triplet of the structural performance response field in the structural parameter population response matrix. The judgment result forms the structural performance constraint satisfaction state vector of the structural parameter sample. The initial fitness values ​​of the structural parameter samples are jointly adjusted based on the state vector satisfying the structural performance constraints to generate the target fitness values ​​of the structural parameter samples. All structural performance constraint terms that do not meet the conditions in the state vector are set as default terms. The number of default terms for each structural parameter sample is counted, and a vector of the number of default terms for the structural parameter population is constructed. Sort the set of fitness target values ​​in descending order and output the fitness ranking table of the structural parameter population; The vector of the number of default items is binarized to generate a default identifier vector for the structural parameter population. Each element in the default identifier vector indicates whether the corresponding structural parameter sample violates any structural performance constraint expression.

6. The structural simulation analysis method based on mechanical constraint optimization according to claim 1, characterized in that, The output of the optimal structural design parameter set includes: Receive the fitness ranking table and default flag vector of the structural parameter population, combine it with the current structural parameter population response matrix and structural parameter population set, and initialize the optimization convergence state flag field; The population set of structural parameters is sorted based on the fitness ranking table, and the top N structural parameter samples are selected to form the set of excellent structural samples for the current optimization round. Perform a mean operation on the structure parameter vector of the excellent structure sample set to generate an updated mean vector of structure parameters. The structure parameter covariance matrix is ​​calculated based on a set of excellent structure samples. The original structure parameter covariance matrix is ​​then combined with the original structure parameter covariance matrix to perform a weighted update, generating the updated structure parameter covariance matrix. A new structural parameter normal sampling model is constructed based on the updated structural parameter mean vector and structural parameter covariance matrix. Next-generation structural parameter sample sampling is performed according to the preset structural parameter population size to form a new generation structural parameter population set. Determine whether the current optimization round has reached the maximum number of rounds threshold, or determine whether the change between the mean vector of structural parameters and the historical mean vector is lower than the preset convergence threshold. If either condition is met, set the optimization convergence status flag field to convergence status. If the optimization convergence status identifier field is in a convergence state, then all structural parameter samples with a default identifier vector of 0 are selected from the current structural parameter population set, and the structural parameter samples with the best fitness target value are extracted by sorting them according to the fitness sorting table. The set of structural design parameter fields corresponding to the structural parameter samples is then output.

7. The structural simulation analysis method based on mechanical constraint optimization according to claim 6, characterized in that, The formation of a new generation of structural parameter populations includes: Receive the updated structure parameter mean vector and the updated structure parameter covariance matrix, construct the structure parameter normal sampling input structure, which includes the structure parameter mean vector field and the structure parameter covariance matrix field; Based on the normal sampling of structural parameters, a normal distribution model of structural parameters is constructed. The normal distribution model of structural parameters takes the mean vector of structural parameters as the distribution center and the covariance matrix of structural parameters as the cooperative perturbation relationship, forming the distribution domain for structural parameter sampling. Set the structure parameter population size parameter, which is a positive integer type control variable used to limit the number of structure parameter samples generated in each round of optimization sampling; The normal distribution model of structural parameters is invoked, and multiple rounds of structural parameter sampling are performed based on the population size parameter of structural parameters. Each round of sampling generates a structural parameter sample vector. All structural parameter sample vectors are integrated to construct a new generation of structural parameter population set.

Images