Structural simulation analysis method based on mechanical constraint optimization

Abstract

The invention discloses a mechanical constraint optimization-based structure simulation analysis method, which comprises the following steps of: generating a structure parameter population by adopting a CMA-ES algorithm, and iteratively updating structure parameter distribution in a normal sampling mode. The method comprises the following steps: constructing a structure simulation model, performing static, buckling and modal simulation on each group of structure parameter samples, extracting response data such as displacement, critical load and inherent frequency, introducing an epsilon-constraint modeling method, combining a performance constraint expression and a tolerance variable to construct a nested hierarchical constraint region, and dynamically regulating and optimizing a search space. And according to a simulation result and constraint judgment, outputting a sample fitness and a default identifier, iteratively generating a new generation of parameter samples in combination with an optimization convergence condition, and finally outputting a structure design parameter set which meets the constraint condition and has optimal performance. The whole process is driven based on mechanical simulation data, and the method has the characteristics of clear structure, calculation closed loop, optimization convergence and the like.

Description

Technical Field

[0001] This invention relates to the field of structural optimization and simulation analysis technology, and in particular to a structural simulation analysis method based on mechanical constraint optimization. Background Technology

[0002] With the integration of intelligent optimization of engineering structures and multiphysics simulation, structural parameter optimization methods based on evolutionary algorithms have been widely applied in the design phases of aerospace, civil engineering, and high-performance mechanical components. Currently, the typical workflow for constrained structural optimization tasks mainly includes design variable sampling, performance simulation analysis, calculation of objective and constraint functions, and population evolution update. Commonly used evolutionary optimization methods such as genetic algorithms, particle swarm optimization, and covariance matrix adaptive evolution strategy (CMA-ES) are gradually becoming the mainstream choices in multi-objective optimization.

[0003] Existing structural parameter optimization techniques still have significant limitations in terms of the linkage between constraint handling mechanisms and structural performance simulation. On the one hand, traditional methods generally use hard constraint elimination or penalty function weighting to handle performance constraints, making it difficult to flexibly adjust the tolerance range of different constraint terms and achieve fine control and dynamic adjustment of multi-level constraint regions. This results in weak convergence ability of the optimization search region and insufficient exploration of the solution space. On the other hand, the optimization strategy and the structural simulation process are loosely coupled. The generation process of the structural parameter population lacks an iterative update mechanism based on mechanical performance feedback. The simulation results cannot effectively drive the evolution of structural design parameters, affecting the accuracy of the final optimal solution and the constraint satisfaction rate.

[0004] Therefore, how to provide a structural simulation analysis method based on mechanical constraint optimization is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] One objective of this invention is to propose a structural simulation analysis method based on mechanical constraint optimization. This invention fully integrates structural performance simulation, normal sampling evolutionary algorithm and multi-level constraint expression mechanism. It describes in detail the entire process of realizing structural optimization solution and simulation feedback closed-loop control by constructing a population response matrix of structural parameters, a dynamic constraint expression structure and a normal sampling model of structural design variables. It has the advantages of strong adaptability, fine constraint control and stable convergence effect.

[0006] A structural simulation analysis method based on mechanical constraint optimization according to an embodiment of the present invention includes the following steps:

[0007] 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.

[0008] Generate an optimization objective function and a set of performance constraints based on the set of structural design parameters and mechanical performance indicators;

[0009] The ε-constraint modeling method is applied to introduce adjustable tolerance variables into each constraint term in the performance constraint set, generating an optimization problem structure that includes the main objective function and dynamic constraint expressions;

[0010] The CMA-ES algorithm is initialized based on the variable range of the structural design parameter set, and the initial mean vector, covariance matrix and step size factor are set. The structural parameter population is generated through normal sampling.

[0011] Simulation calculations are 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 is ​​constructed.

[0012] 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.

[0013] Based on the fitness ranking table and the default flag vector, the CMA-ES 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.

[0014] Optionally, the optimization objective function and performance constraint set generated based on the structural design parameter set and mechanical performance index set include:

[0015] 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;

[0016] 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;

[0017] 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.

[0018] 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;

[0019] 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.

[0020] The objective function and the set of performance constraints are structurally integrated to construct an objective-constraint function set.

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

[0022] 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.

[0023] 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.

[0024] 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;

[0025] 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.

[0026] 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.

[0027] 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.

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

[0029] 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;

[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] 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.

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

[0042] 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.

[0043] 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.

[0044] 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.

[0045] 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.

[0046] 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.

[0047] Sort the set of fitness target values ​​in descending order and output the fitness ranking table of the structural parameter population;

[0048] The vector of 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.

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

[0050] 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;

[0051] 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.

[0052] Perform a mean operation on the structure parameter vector of the excellent structure sample set to generate an updated mean vector of structure parameters.

[0053] The structure parameter variance matrix is ​​calculated based on a set of excellent structure samples, and a weighted update is performed by combining it with the original structure parameter covariance matrix to generate the updated structure parameter covariance matrix.

[0054] 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 of structural parameter population set.

[0055] Determine whether the current optimization round has reached the maximum number of rounds threshold, or determine whether the change in 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.

[0056] 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.

[0057] Optionally, the formation of a new generation of structural parameter populations includes:

[0058] 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;

[0059] 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.

[0060] 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;

[0061] 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.

[0062] All structural parameter sample vectors are integrated to construct a new generation of structural parameter population set. The new generation of structural parameter population set uses the structural parameter sample number as the index field, the structural variable field as the column index field, and marks the current optimization round.

[0063] The beneficial effects of this invention are:

[0064] (1) By constructing the CMA-ES algorithm and the ε-constraint modeling structure, this invention realizes the adaptive sampling and simulation feedback closed-loop control of structural design parameters, which effectively improves the adaptability of the structural optimization process to complex mechanical performance constraints. In particular, it has significant advantages in the dynamic control of the constraint level region in the high-dimensional parameter space. At the same time, by jointly constructing the dynamic structural performance constraint expression and the structural response evaluation model, the expression accuracy and solution efficiency of the optimization problem under multi-field coupling conditions are improved.

[0065] (2) This invention integrates static simulation, buckling simulation and modal simulation processes into the structural simulation model. By combining the structural performance response matrix and dynamic constraint judgment mechanism, it realizes the fitness evaluation and default screening of structural samples. In the process of optimization convergence judgment and structural parameter update, adaptive termination judgment is realized by statistical convergence threshold and historical vector change rate, which effectively improves the accuracy and feasibility of the optimal solution of the structural design parameter set.

[0066] (3) In the process of updating the structural parameter population, the present invention constructs a normal sampling model of structural parameters based on the mean vector and covariance matrix of excellent samples. Combined with the convergence control mechanism and the joint constraint of the default identification vector, the optimization path can avoid the default region of structural performance while approaching the optimal solution of structural quality. Thus, it shows a comprehensive ability that is superior to the existing methods in terms of the feasibility, stability and structural performance guarantee of the optimization results. Attached Figure Description

[0067] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0068] Figure 1 This is a flowchart of a structural simulation analysis method based on mechanical constraint optimization proposed in this invention;

[0069] Figure 2 This is a schematic diagram of the structural parameter population generation and simulation process proposed in this invention;

[0070] Figure 3 This invention proposes a flowchart for constructing a multi-layered nested structure constraint region based on ε-constraint modeling. Detailed Implementation

[0071] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0072] refer to Figures 1-3 A structural simulation analysis method based on mechanical constraint optimization includes the following steps:

[0073] 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.

[0074] An optimization objective function and a set of performance constraints are generated based on the set of structural design parameters and mechanical performance indicators. The optimization objective function is defined as a structural quality or stability function, and each constraint item in the set of performance constraints corresponds to a mechanical performance indicator.

[0075] The ε-constraint modeling method is applied to introduce adjustable tolerance variables into each constraint term in the performance constraint set, generating an optimization problem structure that includes the main objective function and dynamic constraint expressions;

[0076] The CMA-ES algorithm is initialized based on the variable range of the structural design parameter set, and the initial mean vector, covariance matrix and step size factor are set. The structural parameter population is generated through normal sampling.

[0077] Simulation calculations are 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 is ​​constructed.

[0078] 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.

[0079] Based on the fitness ranking table and the default flag vector, the CMA-ES 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.

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

[0081] 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;

[0082] 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;

[0083] 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.

[0084] 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;

[0085] 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.

[0086] The objective function and the set of performance constraints are structurally integrated to construct an objective-constraint function set.

[0087] The method of setting upper and lower limit values ​​for constraints for each performance index according to preset design requirements is as follows: For the buckling critical load, maximum displacement and first natural frequency in the set of mechanical performance indexes, the upper and lower limit parameters of constraints are set according to the performance limit values ​​defined in the structural service conditions, ultimate bearing capacity, safety specifications or industry standards, respectively, and matched with the structure of each performance index function. The lower limit value of the buckling critical load constraint is used to ensure that the structure does not experience local instability 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 natural frequency constraint is used to prevent the structure frequency from entering the environmental excitation resonance range. All constraint parameters are bound as constant fields to the corresponding performance index function structure.

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

[0089] 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.

[0090] 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.

[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 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.

[0101] 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.

[0102] Perform mean path tracking operation on the population set of structural parameters, construct the structural parameter path tracking vector structure, and record the movement trend of the structural parameter mean vector between consecutive generations;

[0103] The structure parameter path tracking vector structure is combined with the current structure parameter mean vector, structure parameter covariance matrix and structure parameter step size factor to construct a covariance update auxiliary structure, which is used to support the adaptive adjustment of the structure parameter distribution in subsequent generations.

[0104] The output structural parameter clustering structure serves as the input structure for the structural simulation calculation module and the optimization problem structure fitness evaluation module. The structural parameter path tracing vector structure and the covariance update auxiliary structure serve as the input fields for the 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, 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.

[0107] 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.

[0108] 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.

[0109] 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.

[0110] All structural performance response entries are arranged in ascending order by structural parameter sample number. 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.

[0111] The structural parameter population response matrix is ​​passed to the optimization problem structure, and the structural parameter population response matrix serves as the set of input fields for the fitness evaluation module and the performance constraint determination module.

[0112] The process of calling the structural simulation model to sequentially execute static simulation, buckling simulation, and modal simulation involves the structural simulation model receiving structural parameter samples from a set of structural parameter populations as input, and constructing a finite element model, a material parameter mapping structure, and a boundary constraint configuration structure, respectively. In the static simulation process, the nodal response displacements are calculated based on the nodal load configuration, and the maximum nodal displacement field is extracted. In the buckling simulation process, the critical stability perturbation conditions are applied based on the static simulation results, the minimum eigenvalue is solved, and the corresponding buckling critical load field is extracted. In the modal simulation process, a joint feature solution path for the mass matrix and 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 executed sequentially, and the displacement values, load values, and frequency values ​​in the simulation output constitute a triplet of the structural performance response field corresponding to the current structural parameter sample.

[0113] In this embodiment, the outputs of the fitness ranking table and the default flag vector include:

[0114] 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.

[0115] 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.

[0116] 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.

[0117] 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. The target fitness values ​​constitute the set of target fitness values ​​of the structural parameter population.

[0118] 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.

[0119] Sort the set of fitness target values ​​in descending order and output the fitness ranking table of the structural parameter population;

[0120] The vector of number of default items is binarized to generate a default identification vector for the structural parameter population. Each element in the default identification vector indicates whether the corresponding structural parameter sample violates any structural performance constraint expression.

[0121] The constraint judgment refers to performing logical judgment operations on each set of structural performance response field triples in the structural parameter population response matrix based on the set of dynamic structural performance constraint expressions defined in the optimization problem structure. Each expression in the set of dynamic structural performance constraint expressions consists of a structural performance constraint expression and a structural performance tolerance variable. The structural performance constraint expression describes the numerical range that the structural performance response field needs to satisfy, while the structural performance tolerance variable sets flexible and adjustable boundaries for this numerical range. During 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, comparing it with the tolerance range agreed upon 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 arranged in the order of the structural performance constraint expressions to form a structural performance constraint satisfaction state vector, which is then bound to the structural parameter sample number.

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

[0123] 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;

[0124] 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.

[0125] Perform a mean operation on the structure parameter vector of the excellent structure sample set to generate an updated mean vector of structure parameters.

[0126] The structure parameter variance matrix is ​​calculated based on a set of excellent structure samples, and a weighted update is performed by combining it with the original structure parameter covariance matrix to generate the updated structure parameter covariance matrix.

[0127] 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 of structural parameter population set.

[0128] Determine whether the current optimization round has reached the maximum number of rounds threshold, or determine whether the change in 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.

[0129] 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.

[0130] In this embodiment, the formation of the next-generation structural parameter population set includes:

[0131] 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;

[0132] 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.

[0133] 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;

[0134] 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.

[0135] All structural parameter sample vectors are integrated to construct a new generation of structural parameter population set. The new generation of structural parameter population set uses the structural parameter sample number as the index field, the structural variable field as the column index field, and marks the current optimization round.

[0136] Example 1:

[0137] To verify the feasibility of this invention in practice, it was applied to a steel structure design optimization task for an urban rail transit station. The project team was responsible for optimizing the structural parameters of the curved steel truss structure above the station waiting hall. This truss structure has a span of 48 meters, adopts a spatial quadrilateral truss arrangement, and is connected by multiple welded steel pipe nodes. To further reduce the self-weight and material cost of the steel structure while meeting strength and stability requirements, the design unit proposed conducting a multi-objective structural optimization analysis based on mechanical performance constraints.

[0138] Traditional design methods typically rely on designers' experience to adjust truss dimensions and material selection, supplemented by repeated calculations and verifications using structural simulation tools. This approach is not only inefficient and prone to haphazard parameter adjustments, but also struggles to cover a large range of parameter combinations. The final structural results are easily influenced by individual experience or local search limits, posing a risk of local optima. This is especially true when facing constraints from multiple structural performance indicators, such as buckling critical loads, maximum nodal displacements, and first-order natural frequencies, making closed-loop fusion of parameter coordination optimization even more challenging.

[0139] To address the aforementioned issues, the project team employed a structural simulation analysis method based on mechanical constraint optimization proposed in this invention to conduct the optimization process. First, based on the design drawings and construction requirements, a set of structural design parameters was constructed, including member lengths, cross-sectional diameters, steel elastic modulus, boundary support conditions, and load case settings. According to the engineering objectives, structural mass was defined as the optimization objective function, and three key performance constraints were set: a buckling critical load of not less than 120 kN, a maximum nodal displacement of not more than 3.5 mm, and a first-order natural frequency of not less than 75 Hz. All of these performance indicators were obtained through simulation.

[0140] To support multi-constraint joint optimization, the method first utilizes the ε-constraint modeling approach, introducing tolerance variables for each of the three performance constraints and constructing a dynamic set of structural performance constraint expressions. All objective functions and constraint expressions are encapsulated within the optimization problem structure as the core scheduling basis. Subsequently, the CMA-ES algorithm is invoked to initialize the structural parameter sampling model. By setting the mean vector, covariance matrix, and step size factor of the structural parameters, a normal sampling structure is constructed, and the population size is set to 50 before optimization is initiated.

[0141] In each round of optimization, the system samples a population of structural parameters from the normal sampling model and inputs each sample into the self-built structural simulation model. The simulation model consists of a finite element modeling module, a boundary condition loading module, and a multiphysics solution module. Within the model, the structural geometry is automatically analyzed to generate a solid mesh, and a constant vertical load is applied through the boundary condition loading module. The static simulation process is used to solve for the maximum displacement at each node, the buckling simulation module calculates the critical buckling load based on eigenvalue analysis, and the modal simulation process is used to solve for the first few natural frequencies of the structure.

[0142] Each round of simulation output is constructed as a population response matrix of structural parameters, containing three fields: maximum nodal displacement, critical buckling load, and first-order natural frequency for each structural parameter sample. The response matrix is ​​then passed to the fitness evaluation module. The system calls the objective function for each structural sample and performs a violation judgment based on the constraint expression, generating a fitness ranking table and a violation flag vector. The algorithm updates the mean vector and covariance matrix of the current structural parameter sampling model, initiates the next generation of sample sampling and simulation, and repeats the above process.

[0143] The system is considered converged when the number of optimization iterations reaches 100 rounds, or when the change in the mean vector of structural parameters in the current population compared to the historical mean vector is lower than a set threshold. Finally, the system selects the structure with the best fitness value from the samples that satisfy all constraints, and outputs its corresponding structural design parameter fields as the optimal structural design parameter set. The following are comparisons of structural performance before and after optimization for some samples:

[0144]

[0145] The "Performance Comparison Table Before and After Structural Simulation Optimization" shows that the optimization process achieved significant improvements in the three key performance indicators of the structure: maximum nodal displacement, critical buckling load, and first-order natural frequency. Regarding maximum nodal displacement, before optimization, the values ​​of each sample were generally between 5.3 mm and 6.37 mm, far exceeding the set performance upper limit of 3.5 mm. After optimization, the maximum displacement values ​​of all samples were controlled between 2.39 mm and 3.30 mm, fully meeting the performance constraints, demonstrating the effectiveness of the optimization algorithm in controlling structural flexibility. Regarding critical buckling load, before optimization, the critical buckling load of the samples ranged from 81.65 kN to 89.26 kN, failing to meet the design target of 120 kN. After optimization, it significantly improved, reaching the range of 126.90 kN to 149.45 kN, with an improvement of up to approximately 83%. This fully demonstrates that the normal sampling mechanism guided by parameter reconstruction and covariance has a systematic improvement effect on enhancing structural stability. Regarding the first-order natural frequencies, the sample frequencies before optimization were concentrated between 54.14Hz and 64.05Hz, indicating insufficient structural vibration resistance. After optimization, these frequencies generally increased to the range of 76.75Hz to 88.22Hz, significantly higher than the set lower limit of 75Hz. This demonstrates that the optimization algorithm can effectively tap the potential of frequency performance under the condition of satisfying the synergy between stiffness and mass. The data from all three dimensions show that this method exhibits consistency and stability in the coordinated optimization of multi-objective structural performance. None of the optimized samples violated the rules, indicating that the optimization path converged well and the results were controllable.

[0146] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

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. Generate an optimization objective function and a set of performance constraints based on the set of structural design parameters and mechanical performance indicators; The ε-constraint modeling method is applied to introduce adjustable tolerance variables into each constraint term in the performance constraint set, generating an optimization problem structure that includes the main objective function and dynamic constraint expressions; The CMA-ES algorithm is initialized based on the variable range of the structural design parameter set, and the initial mean vector, covariance matrix and step size factor are set. The structural parameter population is generated through normal sampling. Simulation calculations are 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 is ​​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. Based on the fitness ranking table and the default flag vector, the CMA-ES 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 optimization objective function and performance constraint set generated based on the structural design parameter set and mechanical performance index set include: 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.

3. 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: g i (x)-ε i ≤0, where g i (x) represents the structural performance constraint expression, ε i 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.

4. 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: 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; 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 relationships 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. 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. 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.

5. 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.

6. 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 fitness target value set in descending order and output the fitness ranking table of the structural parameter population; The vector of 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.

7. 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, and initialize the optimization convergence state flag field by combining the current structural parameter population response matrix and structural parameter population set; 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 structural parameter variance matrix is ​​calculated based on a set of excellent structural samples. Then, a weighted update is performed by combining the original structural parameter covariance matrix to generate the updated structural 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.

8. The structural simulation analysis method based on mechanical constraint optimization according to claim 7, 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.

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