A Multi-Level Structure Discrete Optimization Method Based on Mechanical Sensitivity

Abstract

This invention discloses a multi-level structural discrete optimization method based on mechanical sensitivity. It includes using variable topology parameters as outer traversal variables, performing a three-level progressive discrete parameter optimization process on a fixed topology structure: rapid approximation of the feasible region, redundancy pruning, and perturbation and repair. It relies on physical response sensitivity to guide iteration and combines an automated mechanical evaluation engine to complete fitness assessment, achieving lightweight optimization of strongly constrained discrete variable structures. This invention utilizes the sensitivity mapping of structural mechanical response to discrete variables to determine the evolution direction of discrete parameters to locate the feasible region. By actively avoiding ineffective evaluations of infeasible solutions, it significantly reduces the number of calls to the underlying evaluation engine (such as finite element calculation) in a single optimization iteration.

Description

Technical Field

[0001] This invention relates to the fields of engineering structure optimization design and computer-aided engineering technology, specifically a multi-level structural discrete optimization method based on mechanical sensitivity guidance. Background Technology

[0002] In modern structural engineering practice, there are numerous non-standard structures that require highly customized design based on terrain, function, and load. These structural systems are widely used in engineering fields such as large-span spatial grid structures, high-rise building steel frames, modular prefabricated buildings, deep-sea pressure hulls, and aerospace trusses. Their design and optimization processes typically face many prominent challenges, as follows: First, the geometric configuration of the structure is constrained by a set of discrete topological parameters, such as column spacing and inter-joint length, and the cross-sections of the structural components must be selected from a standard industrial profile library of discrete values. Changes in the topological parameters can directly lead to abrupt changes in the number and location of structural components, which in turn can cause nonlinear steps in the structural stiffness matrix and mechanical response, bringing fundamental constraints and challenges to structural optimization.

[0003] Secondly, in current engineering practice, the optimization of such structures often involves manual calculations and adjustments of cross-sections using finite element analysis (FEA) software to meet relevant engineering specifications. This traditional optimization method is not only time-consuming and labor-intensive, but also inefficient. Furthermore, it makes it difficult to achieve precise control over material usage, resulting in conservative design schemes with excessive material redundancy, significantly increasing construction costs and failing to meet the requirements for lightweight structural design.

[0004] Finally, when facing such strongly constrained mixed discrete variable optimization problems, commonly used metaheuristic algorithms in existing technologies, such as genetic algorithms (GA) and particle swarm optimization (PSO), while possessing global nonlinear search capabilities, often treat the physical system as a "black box," ignoring the mechanical force transmission laws within the structure. Because these algorithms rely on large-scale population mutation and massive finite element analysis (FEM) trials, they struggle to achieve convergence within limited computational budgets in engineering problems where single FEM analysis computations are expensive, resulting in extremely poor timeliness and failing to meet the high-efficiency requirements of practical engineering design.

[0005] In summary, existing structural optimization methods suffer from drawbacks such as high computational cost, low convergence efficiency, large material redundancy, and difficulty in adapting to strongly constrained discrete variable structures. Therefore, there is an urgent need for a new structural optimization method that can both integrate prior mechanical knowledge to greatly reduce computational consumption and break through the local extremum trap of traditional optimization, so as to achieve accurate optimization and lightweighting of discrete variables of variable topology structures while ensuring that the structural strength and stiffness strictly meet the specifications. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-level structure discrete optimization method based on mechanical sensitivity, which aims to improve the problems of high computational cost and difficulty in approximating the optimal solution under strong constraint discrete boundaries in existing traditional random search methods without physical guidance.

[0007] This invention is implemented as follows: A multi-level structural discrete optimization method based on mechanical sensitivity guidance includes using variable topology parameters as outer traversal variables, performing three-level progressive discrete parameter optimization on a fixed topology structure: rapid approximation of the feasible region, redundancy pruning, and perturbation and repair. Iterative optimization is guided by physical response sensitivity, and fitness assessment is completed using an automated mechanical evaluation engine, achieving lightweight optimization of strongly constrained discrete variable structures. The specific steps are as follows: 1) First stage: Rapid approximation of the feasible region, guiding design variables from the infeasible region to the feasible region based on the sensitivity of structural mechanical response; 2) Second stage: Redundancy pruning, identifying and eliminating shallow structural safety redundancies; 3) Third stage: Disturbance and repair, actively reconstructing the load transfer path to achieve global deep optimization and escape local optima.

[0008] Preferably, the feasible region fast approximation stage includes: Initialization: Assign critical or minimum specification attributes from the discrete parameter library to the component to be optimized; Calculate the normalized constraint violation degree η k , which serves as the maximum critical approximation rate envelope value of the component under engineering constraints of strength, stiffness, and stability; Sensitivity-guided update: when η k When the value is greater than 1, the sensitivity of the constraints to the generalized physical characteristic parameters of the design variables is extracted. Along the steepest descent or the direction with the highest sensitivity, the discrete parameter combination that satisfies the physical lower bound and minimizes the increase in weight / cost is selected to complete the update and generate the initial feasible solution.

[0009] Preferably, the redundant pruning stage includes: Set a global pruning threshold T less than 1. prune ; Non-minimum specification components are classified according to η k Sort in ascending order for η k ≤T prune The components were downgraded by one level in cross-section and then verified using finite element analysis. Adaptive rollback: If batch degradation does not meet the constraints, rollback occurs, only for η. k The lowest possible single component degradation trial; Termination conditions: If the single most conservative component is downgraded beyond its limit or the utilization rate of all components exceeds the threshold, shallow redundancy is determined to be exhausted.

[0010] Preferably, the disturbance and repair phase includes: Locate the disturbance source: Weight reduction benefit ΔW according to degradation theory saving Arrange in descending order, and demote the component with the highest profit level by one tier. Internal force redistribution determination: If the over-limit position shifts, the internal force redistribution is determined to be successful, and the repair process begins; if the over-limit is concentrated at the disturbance source, the suboptimal disturbance source is switched. Net Income Assessment: Calculate the increased weight cost ΔW for the progressive upgrade and repair of the oversized components. cost Only when ΔW cost <ΔW saving The new solution is accepted only if the structure satisfies all constraints; Deep optimization loop: After successful perturbation-repair, return to the redundant pruning stage to form a pruning-perturbation-re-pruning closed loop.

[0011] Preferably, the generalized physical characteristic parameters include generalized section characteristic parameters that determine structural strength and generalized inertial characteristic parameters that determine structural stiffness.

[0012] Preferably, redundancy pruning is used to eliminate shallow safety redundancy in statically indeterminate structures caused by stiffness coupling or rapid approximation of the feasible region.

[0013] Preferably, the disturbance and repair utilize the multi-path force transmission characteristics of the statically indeterminate structure to reconstruct the load transmission path in order to escape the local optimum.

[0014] Preferably, the optimization method is applicable to variable topology discrete variable structural systems such as large-span spatial grid structures, high-rise building steel frames, modular prefabricated buildings, deep-sea pressure hulls, and aerospace trusses.

[0015] Preferably, the goal is to minimize the consumption of structural materials, manufacturing costs, or comprehensive economic indicators, and the constraints include generalized stress field limits, generalized displacement field limits, and overall stability limits.

[0016] Preferably, the automated mechanical evaluation engine is an automated finite element analysis platform used for structural mechanical response calculation and constraint verification.

[0017] Compared with the prior art, the beneficial effects of the present invention are: 1. This method utilizes the sensitivity mapping of structural mechanical response to discrete variables to determine the evolution direction of discrete parameters and thus locate the feasible region. By actively avoiding invalid evaluations of infeasible solutions, it significantly reduces the number of calls to the underlying evaluation engine (such as finite element calculation) for a single optimization.

[0018] 2. The algorithm of this invention has extremely strong physical adaptability. By introducing the internal force redistribution physical mechanism of "pruning-perturbation-re-pruning", the algorithm can effectively handle two typical topological convergence modes: "incremental deep optimization" and "fast boundary locking", and accurately escape the local optimal solution trap in the discrete variable space.

[0019] 3. Under the premise of ensuring that the service performance of the structure, such as strength and stiffness, strictly meets the engineering specifications (such as the maximum Von Mises stress and maximum deflection ratio limit), this method can accurately select the most economical section combination from the discrete profile library, significantly reducing the material redundancy of traditional conservative design. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the first stage of the present invention; Figure 3 This is a schematic diagram of the second stage of the present invention; Figure 4 This is a schematic diagram of the third stage of the present invention. Detailed implementation method: In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0021] The following description, in conjunction with the accompanying drawings and specific embodiments, provides further details: A multi-level structure discrete optimization method based on mechanical sensitivity is characterized by using variable topology parameters as outer-layer traversal variables and performing discrete parameter optimization with the following three progressive steps on a given inner-layer topology: 1. First stage: Rapid approximation of the feasible region.

[0022] This stage aims to utilize the sensitivity of the structure's linear or weakly nonlinear mechanical response to guide design variables to quickly transition from the infeasible region to the feasible region.

[0023] (1) Initialization: Assign critical (or minimum) specification attributes from the discrete parameter library to all components to be optimized in the structural system.

[0024] (2) Calculate the generalized performance evaluation index: Extract the response results of mechanical calculations, and for the k-th type of component, calculate its normalized constraint violation degree η. k This index is defined as the maximum critical approximation envelope value of the component under all given engineering constraints (such as strength, stiffness, stability, etc.).

[0025] (3) Sensitivity-oriented update: When the assessment finds ηk When the value is greater than 1 (i.e., there is a risk of failure or exceeding the limit), the sensitivity of this constraint to the generalized physical characteristic parameters of the structural variables to be optimized is extracted. A traversal is performed in the given discrete parameter library, prioritizing the selection of discrete parameter combinations that simultaneously satisfy the physical lower bound and minimize the increase in the objective function (e.g., weight, cost) along the steepest descent or highest sensitivity direction for updating. This mechanism generates a high-quality initial feasible solution.

[0026] 2. Second stage: Redundancy pruning.

[0027] This step aims to identify and eliminate shallow safety redundancies in statically indeterminate or complex structural systems caused by stiffness coupling or the rapid approximation in the previous step.

[0028] (1) Set a degradation threshold: All non-minimum specification components are classified according to the normalized constraint violation degree η. k Sort in ascending order. Set the global pruning threshold T. prune The threshold is a preset safety margin constant that is less than 1.

[0029] (2) Batch parallel pruning: Prune all η k ≤ T prune The component's section level in the discrete library is simultaneously downgraded by one level and submitted to the evaluation engine for finite element verification.

[0030] (3) Adaptive rollback mechanism: If the structure after batch downgrading still satisfies all constraints, the modification is accepted and a new round of batch pruning is started; if a constraint violation occurs, it indicates that the step size is too large, the system triggers a rollback, and switches to selecting only η in the global range. k The lowest (i.e. most conservative) single component type is used for downgrading.

[0031] (4) Termination conditions: When the degradation of a single most conservative component still leads to exceeding the limit, or when the utilization rate of all components is higher than the set threshold, the shallow redundancy is determined to be exhausted, and this stage is terminated.

[0032] 3. The third stage: Disturbance and repair.

[0033] This stage utilizes the multi-path force transmission characteristics of statically indeterminate structures to achieve global depth search by actively reconstructing the load transfer path, thus escaping local extrema.

[0034] (1) Locate the disturbance source: Traverse the components that are not currently at the minimum specification, and determine the theoretical target gain (such as weight reduction gain ΔW) that can be obtained by parameter downgrading. saving Sort the components in descending order. Force the component with the greatest benefit (i.e., the "disturbance source") to be downgraded by one level, temporarily ignoring the current constraint out-of-bounds error it caused.

[0035] (2) Determination of internal force redistribution: Recalculate the system response. If the excessive internal force is still concentrated in the disturbance source itself, the response path is determined to be physically infeasible, and the system is switched to the suboptimal disturbance source; if the location of the excessive force changes, it indicates that the system has successfully redistributed internal forces and enters the repair process.

[0036] (3) Net income assessment closed loop: Implement step-by-step upgrade and repair for newly emerging oversized components, and calculate the cumulative repair weight increase cost ΔW. cost Introducing the net benefit criterion: Only when the cost of correcting the weight gain is less than the benefit of the weight loss due to the disturbance (i.e., ΔW) cost <ΔW saving The new topology scheme will only be accepted if the structure satisfies all constraints again.

[0037] (4) Deep optimization loop: Once the disturbance-repair is successful, the system will revert to the "second stage: redundancy pruning" to eliminate the secondary redundancy caused by the change of internal force path, and finally form a deep optimization closed loop of "pruning-disturbance-re-pruning".

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below in conjunction with specific application scenarios.

[0039] This embodiment uses a modular pressurized structure (MPS) for high-altitude applications as the engineering structure to be optimized. This structure needs to meet stringent mechanical specifications and achieve the lightest possible design while maintaining a long-term internal air pressure load of 20–40 kPa.

[0040] In this embodiment, the "minimization of structural material consumption, manufacturing cost, or comprehensive economic indicators" specifically means minimizing the total weight of the MPS main steel frame; when considering manufacturing factors, component material costs, node processing costs, and installation costs can be converted into comprehensive economic indicators.

[0041] In this embodiment, the "generalized stress field limit" corresponds to the maximum Von Mises equivalent stress yield limit of the component, the "generalized displacement field limit" corresponds to the maximum deflection of the component or node, and the "overall stability limit" corresponds to the critical load limit of the component under compression buckling.

[0042] In the beam-column member system of this embodiment, the "generalized section characteristic parameters" specifically refer to the cross-sectional area A and section modulus W that determine strength; the "generalized inertia characteristic parameters" specifically refer to the section moment of inertia I that determines stiffness.

[0043] For this MPS structure, with the goal of minimizing total steel consumption, the column spacing S is used as the outer layer traversal variable, and a three-step inner layer optimization based on physical response sensitivity is performed: Phase 1: The system sets all beam and column members as the minimum cross-sections in the discrete library. The calculated ratio of the maximum Von Mises stress to the maximum deflection is extracted, and this ratio is used to calculate the normalized constraint violation rate (overall utilization η). k ). Regarding η k For components with a strength greater than 1, extract the sensitivity requirements of the bending and tensile stiffness properties of structural mechanics (i.e., the theoretically required cross-sectional area A, section modulus W, and moment of inertia I). ​​In the section library, select the section that satisfies these three geometric lower bounds and has the minimum linear density in a jump-like manner for updating, and quickly obtain the initial feasible solution.

[0044] The envelope update strategy in this embodiment is as follows: calculate the normalized approximation rates of stress, displacement, and stability constraints respectively, and take the maximum value ηk as the control envelope. When ηk... k When the value is greater than 1, the required physical lower bounds such as A, W, and I are derived from the control constraints, and then the section that simultaneously satisfies the lower bounds and minimizes the increase in weight or cost is selected from the discrete profile library. This strategy updates parameters directly with physical boundaries, rather than relying on repeated trials of random mutations.

[0045] Phase 2: Setting the pruning threshold T prune = 0.9. η is identified. k For components with a cross-sectional area ≤ 0.9 that exceed safety limits, downgrade their cross-section by one level in the library. If verification passes, continue; if stress or deflection exceeds limits, adaptively roll back and downgrade only η. k Start with the smallest single component, and work your way up until all components are fully utilized.

[0046] The third stage: To escape the local stress concentration trap caused by the downgrading of a single component in a statically indeterminate frame, the system proactively downgrades the component with the greatest theoretical weight reduction benefit (i.e., the heaviest) by one level as a "disturbance source." The structural response after stress redistribution is calculated, and newly emerging over-limit components are upgraded and repaired. As long as the weight increase from repair is less than the weight reduction from the disturbance, the new topology scheme is accepted, and the system returns to the second stage for secondary pruning. Verification through the above embodiments shows that, under strict computational constraints, the method of this invention only requires dozens of finite element method calls to lock in the global optimum. Its optimization efficiency and accuracy far exceed traditional genetic algorithms and particle swarm optimization algorithms, significantly reducing the engineering material redundancy of such complex discrete structures.

[0047] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-level structural discrete optimization method based on mechanical sensitivity guidance, characterized in that, For structural systems with discrete variable characteristics, a three-level progressive discrete parameter optimization process is performed, including fast approximation of the feasible region, redundancy pruning, and perturbation and repair. Iteration is guided by the sensitivity of the structural physical response, and fitness assessment is completed using an automated mechanical evaluation engine, achieving lightweight optimization of strongly constrained discrete variable structures. The specific steps are as follows: 1) First stage: Rapid approximation of the feasible region, guiding design variables from the infeasible region to the feasible region based on the sensitivity of structural mechanical response; 2) Second stage: Redundancy pruning, identifying and eliminating shallow structural safety redundancies; 3) Third stage: Disturbance and repair, actively reconstructing the load transfer path to achieve global deep optimization and escape local optima.

2. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 1, characterized in that, The feasible region fast approximation stage includes: Initialization: Assign critical or minimum specification attributes from the discrete parameter library to the component to be optimized; Calculate the normalized constraint violation degree η k , which serves as the maximum critical approximation rate envelope value of the component under engineering constraints of strength, stiffness, and stability; Envelope update criterion: when η k When the value is greater than 1, the sensitivity of the constraints to the generalized physical characteristic parameters of the design variables is extracted. Based on the envelope update strategy of the full stress design criterion, the lower bound of the cross-sectional geometric parameters required by the theory is calculated. The discrete parameter combination that satisfies the physical lower bound and has the smallest increase in weight / cost is selected to complete the update and generate the initial feasible solution.

3. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 1, characterized in that, The redundant pruning phase includes: Set a global pruning threshold T less than 1. prune ; Non-minimum specification components are classified according to η k Sort in ascending order for η k ≤T prune The components were downgraded by one level in cross-section and then verified using finite element analysis. Adaptive rollback: If batch degradation does not meet the constraints, rollback occurs, only for η. k The lowest possible single component degradation trial; Termination conditions: If the single most conservative component is downgraded beyond its limit or the utilization rate of all components exceeds the threshold, shallow redundancy is determined to be exhausted.

4. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 1, characterized in that, The disturbance and repair phase includes: Locate the disturbance source: Weight reduction benefit ΔW according to degradation theory saving Arrange in descending order, and demote the component with the highest profit level by one tier. Internal force redistribution determination: If the over-limit position shifts, the internal force redistribution is determined to be successful, and the repair process begins; if the over-limit is concentrated at the disturbance source, the suboptimal disturbance source is switched. Net Income Assessment: Calculate the increased weight cost ΔW for the progressive upgrade and repair of the oversized components. cost Only when ΔW cost <ΔW saving The new solution is accepted only if the structure satisfies all constraints; Deep optimization loop: After successful perturbation-repair, return to the redundant pruning stage to form a pruning-perturbation-re-pruning closed loop.

5. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 2, characterized in that, The generalized physical characteristic parameters include generalized section characteristic parameters that determine structural strength and generalized inertial characteristic parameters that determine structural stiffness.

6. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 3, characterized in that, The redundancy pruning is used to eliminate shallow safety redundancy in statically indeterminate structures caused by stiffness coupling or rapid approximation of the feasible region.

7. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 4, characterized in that, The disturbance and repair utilize the multi-path force transmission characteristics of statically indeterminate structures to reconstruct the load transmission path in order to escape the local optimum.

8. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 1, characterized in that, The optimization method is applicable to variable topology discrete variable structural systems such as large-span spatial grid structures, high-rise building steel frames, modular prefabricated buildings, deep-sea pressure hulls, and aerospace trusses.

9. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 1, characterized in that, With the goal of minimizing structural material consumption, manufacturing costs, or overall economic indicators, the constraints include generalized stress field limits, generalized displacement field limits, and overall stability limits.

10. The multi-level structure discrete optimization method based on mechanical sensitivity guidance according to claim 1, characterized in that, The automated mechanical evaluation engine is an automated finite element analysis platform used for structural mechanical response calculation and constraint verification.

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