A steel tower structure optimization method based on finite element analysis

Abstract

The application discloses a steel tower structure optimization method based on finite element analysis, and relates to the technical field of finite element analysis, which comprises the following steps: defining a parameterized variable set according to the requirements of a steel tower structure, generating an initial geometric model according to the variable set, and constructing a multi-level analysis model system; inputting a candidate scheme into a high-fidelity finite element model to generate a high-fidelity verification result, comparing the high-fidelity verification result with a low-fidelity evaluation result, and calculating the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model; calibrating the low-fidelity evaluation result according to the prediction deviation, and outputting an optimal steel tower scheme when the calibrated low-fidelity evaluation result meets the low-fidelity finite element model and the high-fidelity finite element model at the same time. Through the establishment of a dynamic calibration mechanism based on meta-learning, the deviation between models is quantified as traceable calibration parameters, and real-time precision compensation of rapid evaluation results is realized.

Description

Technical Field

[0001] This invention relates to the field of finite element analysis technology, and in particular to a method for optimizing steel tower structures based on finite element analysis. Background Technology

[0002] With the convergence of computational mechanics and artificial intelligence, structural optimization methods based on finite element analysis have gradually evolved from traditional parametric modeling combined with mathematical programming algorithms to an advanced design paradigm integrating machine learning, surrogate models, and intelligent search algorithms. In recent years, multi-fidelity modeling techniques have provided new ideas for optimizing complex engineering structures by coordinating the computational cost and accuracy of analysis models with different levels of precision. Meanwhile, reinforcement learning has shown potential in handling complex design spaces when solving high-dimensional decision-making problems.

[0003] However, existing structural optimization methods combining reinforcement learning and finite element analysis still struggle to effectively balance the trade-off between exploration efficiency and computational cost. Reinforcement learning agents need to evaluate the performance of numerous candidate solutions during iteration, while traditional single-precision finite element models cannot simultaneously meet the requirements of computational speed and accuracy. This results in either excessive computational time due to the use of high-precision models, or reliance on low-precision models leading to local optima or unreliable design results. This computational bottleneck severely restricts the practical engineering application of this method in the optimization of large steel tower structures. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a steel tower structure optimization method based on finite element analysis to solve the problems of slow optimization convergence speed and low reliability of design results caused by the trade-off between the calculation accuracy and efficiency of the finite element analysis model in the process of steel tower structure optimization.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] This invention provides a method for optimizing steel tower structures based on finite element analysis. The method includes: defining a parameterized set of variables according to the requirements of the steel tower structure; generating an initial geometric model based on the variable set; constructing a multi-level analysis model system; configuring the multi-level analysis model system in a reinforcement learning environment; defining an action space, state space, and reward function for the reinforcement learning agent in the reinforcement learning environment; the reinforcement learning agent executing an exploration strategy to generate steel tower schemes; inputting the steel tower schemes into a low-fidelity finite element model; outputting low-fidelity evaluation results; updating the policy network of the reinforcement learning agent; and outputting new steel tower schemes that meet a preset performance threshold in the low-fidelity evaluation results as candidate schemes; inputting the candidate schemes into a high-fidelity finite element model to generate high-fidelity verification results; comparing the high-fidelity verification results with the low-fidelity evaluation results; calculating the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model; calibrating the low-fidelity evaluation results based on the prediction deviation; and outputting the optimal steel tower scheme when the calibrated low-fidelity evaluation results simultaneously satisfy both the low-fidelity finite element model and the high-fidelity finite element model.

[0008] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the parameterized variable set includes geometric topology variables, cross-sectional dimension variables, and node coordinate variables.

[0009] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the specific steps for generating the initial geometric model based on the variable set are as follows:

[0010] Based on the requirements of the steel tower structure, determine the geometric topological variables of the steel tower structure;

[0011] The geometric topology variables are spatially expanded and coordinates are calculated using a parametric method to generate node coordinate variables and establish the spatial framework of the steel tower structure.

[0012] The spatial frame of the steel tower structure is combined with the cross-sectional dimension variables to perform parametric modeling and generate an initial geometric model.

[0013] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the specific steps for constructing the multi-level analysis model system are as follows:

[0014] The initial geometric model is preprocessed geometrically. The connection areas of the members are automatically identified and geometrically simplified using a feature recognition algorithm to obtain the simplified geometric model.

[0015] Based on the simplified geometric model, a low-fidelity finite element model is established using beam theory analysis and coarse mesh generation.

[0016] Based on the simplified geometric model, a high-fidelity finite element model is established using shell theory analysis and fine mesh generation.

[0017] Establish the displacement mapping relationship between the low-fidelity finite element model and the high-fidelity finite element model, and complete the construction of a multi-level analysis model system.

[0018] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the following steps are taken to define the action space, state space, and reward function for the reinforcement learning agent in the reinforcement learning environment:

[0019] A hierarchical action space architecture is constructed and divided into a macro-topological action layer and a micro-parameter action layer, which serve as the action space for the reinforcement learning agent.

[0020] A multi-scale state representation method is used to extract and fuse state features in the action space to form the state space of the reinforcement learning agent.

[0021] The reward function of the reinforcement learning agent is constructed by weighting the state space through a multi-objective optimization function.

[0022] The reward function and the multi-level analysis model system are dynamically coupled through a data exchange interface, thus completing the configuration of the reinforcement learning environment.

[0023] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the action space includes operations for adding, deleting, and modifying the cross-section of steel tower members;

[0024] The state space includes the geometric topology and mechanical properties of the steel tower structure;

[0025] The reward function includes the steel tower structure weight, stress constraint index, and displacement constraint index.

[0026] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the specific steps for outputting low-fidelity evaluation results are as follows:

[0027] A reinforcement learning agent executes an exploration strategy in a reinforcement learning environment to generate a steel tower design.

[0028] The steel tower scheme is input into a low-fidelity finite element model for performance evaluation, and the low-fidelity evaluation results are output.

[0029] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the steps of updating the policy network of the reinforcement learning agent and outputting new steel tower schemes that meet the preset performance threshold in the low-fidelity evaluation results as candidate schemes are as follows:

[0030] Based on the low-fidelity evaluation results, the policy gradient method with importance sampling and entropy regularization is used to calculate the parameter update of the policy network of the reinforcement learning agent.

[0031] Adjust the parameters of the policy network using the parameter update amount to generate an updated policy network;

[0032] The performance of the steel tower scheme is re-evaluated based on the updated policy network, and new steel tower schemes that simultaneously meet the preset performance thresholds are output as candidate schemes.

[0033] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the specific steps for calculating the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model are as follows:

[0034] The candidate solutions are input into a high-fidelity finite element model for accurate verification, generating high-fidelity verification results.

[0035] The high-fidelity verification results are compared with the low-fidelity evaluation results to generate a residual sequence;

[0036] Based on the residual sequence, the prediction bias between the low-fidelity finite element model and the high-fidelity finite element model is calculated using a dynamic weighted integral algorithm.

[0037] As a preferred embodiment of the steel tower structure optimization method based on finite element analysis described in this invention, the specific steps for outputting the optimal steel tower scheme are as follows:

[0038] Based on the predicted bias, a meta-learning calibration model is constructed by meta-training historical bias patterns, and calibration parameters are generated by forward propagation.

[0039] The low-fidelity evaluation results are corrected by applying calibration parameters to obtain calibrated evaluation results;

[0040] The optimal steel tower scheme is output when the calibrated evaluation results simultaneously meet the rapid performance evaluation criteria of the low-fidelity finite element model and the accurate verification requirements of the high-fidelity finite element model.

[0041] The beneficial effects of this invention are as follows: By establishing a dynamic calibration mechanism based on meta-learning, the deviation between models is quantified into traceable calibration parameters, realizing real-time accuracy compensation for rapid evaluation results; it not only improves the prediction reliability of low-fidelity models in optimization loops, enabling reinforcement learning agents to update policies based on more accurate information, but also effectively suppresses the cumulative amplification effect of errors in the iteration process by constructing a propagation model of prediction deviations. Thus, while ensuring optimization speed, it improves the computational accuracy and engineering feasibility of the output scheme, providing technical support for the efficient and high-precision automated optimization design of large and complex steel tower structures. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart of a steel tower structure optimization method based on finite element analysis.

[0044] Figure 2 A flowchart for constructing a multi-level analysis model system.

[0045] Figure 3 A flowchart for configuring a reinforcement learning environment.

[0046] Figure 4 This is a flowchart for outputting candidate solutions. Detailed Implementation

[0047] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0048] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0049] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0050] Reference Figures 1-4This is one embodiment of the present invention, which provides a method for optimizing steel tower structures based on finite element analysis, including the following steps:

[0051] S1. Based on the requirements of the steel tower structure, define a set of parameterized variables, generate an initial geometric model based on the set of variables, and construct a multi-level analysis model system.

[0052] S1.1: The set of parameterized variables includes geometric topology variables, cross-sectional dimension variables, and node coordinate variables.

[0053] It should be noted that geometric topological variables refer to parameters that control the overall macroscopic shape of the steel tower, such as total height, number of segments, and crossarm arrangement.

[0054] Cross-sectional dimension variables refer to parameters that define the specific specifications of the cross-section of each member in a steel tower, such as the leg width and thickness of angle steel or the outer diameter and wall thickness of steel pipe;

[0055] Node coordinate variables refer to parameters that determine the precise location of all critical connection points of the steel tower structure in three-dimensional space.

[0056] S1.2: Determine the geometric topological variables of the steel tower structure according to the requirements of the steel tower structure;

[0057] Specifically, based on the functional requirements and layout environment of the steel tower in actual engineering, the basic conditions that the overall macroscopic form of the steel tower must meet are clarified, including the total height of the steel tower, the number of segments divided along the height direction, and the arrangement of the crossarms on the tower body; this directly determines the specific range of values ​​and combination of the geometric topological variables of the steel tower structure.

[0058] S1.3: Spatial expansion and coordinate calculation of geometric topological variables are performed using parametric methods to generate node coordinate variables and establish the spatial framework of the steel tower structure;

[0059] Specifically, based on the determined geometric topological variables of the steel tower structure, including the total height, number of segments, and crossarm arrangement, and in accordance with the spatial arrangement rules of the pole system, the macroscopic form described by the geometric topological variables is decomposed layer by layer into the vertical position of each segment and the horizontal extension direction of the crossarm. On this basis, according to the connection relationship and symmetry characteristics of the members, the position of each key connection point in three-dimensional space is determined in turn, forming node coordinate variables. All node coordinate variables together constitute the spatial framework of the steel tower structure.

[0060] It should be noted that the spatial arrangement rules of the rod system structure refer to the spatial arrangement method in which the rods are connected to key nodes along a straight line according to the axial force requirements, based on engineering experience and structural force transmission path, and satisfying geometric stability and structural symmetry.

[0061] S1.4: Combine the spatial frame of the steel tower structure with the cross-sectional dimension variables to perform parametric modeling and generate the initial geometric model.

[0062] Specifically, based on the connection relationship and spatial orientation of each member in the established spatial framework of the steel tower structure, a corresponding cross-sectional dimension variable is assigned to each member. By associating the spatial position of each member with the corresponding cross-sectional dimension variable, a three-dimensional solid representation with complete geometric information is formed, thereby generating the initial geometric model.

[0063] S1.5: Perform geometric preprocessing on the initial geometric model, automatically identify the rod connection area through feature recognition algorithm and perform geometric simplification to obtain the simplified geometric model;

[0064] Specifically, a feature recognition algorithm is used to scan the intersection area of ​​the rods in the initial geometric model to identify the connection node area formed by the intersection of multiple rods. While keeping the overall topological relationship of the rod system unchanged, the complex geometric details in the connection node area are removed or equivalently merged so that the rods intersect at the node in the form of idealized straight line segments. This results in a simplified geometric model that retains the main force path and spatial configuration but reduces geometric complexity.

[0065] It should be noted that complex geometric details refer to the local structural features in the initial geometric model other than the straight segments of the main body of the member, including weld transition zones, connecting plates, stiffening ribs, chamfers, bolt holes, and non-load-bearing auxiliary structures.

[0066] S1.6: Based on the simplified geometric model, a low-fidelity finite element model is established using beam theory analysis and coarse mesh generation;

[0067] Specifically, the simplified geometric model is modeled using beam theory analysis methods, where the member axis represents the spatial position of the member, and the leg width and thickness of the angle steel or the outer diameter and wall thickness of the steel pipe are assigned as cross-sectional attributes based on the corresponding cross-sectional dimension variables. Each member is discretized along its length using a small number of segments to form a sparse mesh layout, and adjacent members are connected at the node coordinate variables defined in the simplified geometric model. This constructs a low-fidelity finite element model that can reflect the overall mechanical behavior of the steel tower but has a small computational scale.

[0068] It should be noted that the beam theory analysis method simplifies the members in a steel tower structure into load-bearing components represented by axes, and describes their bending, axial deformation, and torsional deformation behavior under load based on the plane section assumption and the basic principles of mechanics of materials. It is applicable to slender members with lengths much larger than their cross-sectional dimensions. By defining the spatial orientation of the member's axis, support conditions, and the cross-sectional geometric properties determined by the cross-sectional dimension variables, a mechanical model that can reflect the overall stiffness and load-bearing capacity is established.

[0069] S1.7: Based on the simplified geometric model, a high-fidelity finite element model is established using shell theory analysis and fine mesh generation;

[0070] Specifically, the surface geometry of each member in the simplified geometric model is preserved. Based on the angle steel leg width and thickness or the outer diameter and wall thickness of the steel pipe defined by the cross-sectional dimension variables, a three-dimensional shell surface representation of the member is constructed. A dense mesh is arranged on the surface of the member, with the mesh size much smaller than the characteristic dimensions of the member's cross-section, to fully reflect local geometric changes and stress concentration areas. The connection relationship between members is matched according to the spatial intersection position determined by the node coordinate variables in the simplified geometric model to ensure that the shell surface is continuously closed in the connection area. This forms a high-fidelity finite element model that can accurately describe the local mechanical response of the steel tower structure.

[0071] It should be noted that the shell theory analysis method represents steel tower structural members by their mid-surface and thickness, and considers the combined effects of bending and membrane effects. It is suitable for members with curved or folded plate characteristics and whose thickness is much smaller than the dimensions in the other two directions. By describing the geometry, thickness distribution, and material properties of the mid-surface of the member, it reflects its deformation and internal force state under load. In steel structure modeling, the shell theory analysis method is often used to perform surface geometry modeling of members such as angle steel and steel pipes, and can capture the mechanical behavior of local stress concentration and complex connection areas.

[0072] S1.8: Establish the displacement mapping relationship between the low-fidelity finite element model and the high-fidelity finite element model, and complete the construction of the multi-level analysis model system.

[0073] Specifically, at the same node coordinate variable positions defined in the simplified geometric model, the displacement responses of the corresponding rod endpoints or key connection points in the low-fidelity finite element model and the high-fidelity finite element model are extracted respectively. Based on the consistency of spatial position, the displacement results in the low-fidelity finite element model are matched one-to-one with the displacement results at the same positions in the high-fidelity finite element model to form a displacement mapping relationship based on a common geometric datum. The displacement mapping relationship uses node coordinate variables as a bridge to ensure that the two models with different precisions are comparable and correlated in the overall deformation description of the structure, thereby completing the construction of a multi-level analysis model system.

[0074] S2. Configure the multi-level analysis model system in the reinforcement learning environment, and define the action space, state space and reward function for the reinforcement learning agent in the reinforcement learning environment.

[0075] S2.1: Construct a hierarchical action space architecture, and divide it into a macroscopic topological action layer and a microscopic parameter action layer, as the action space of the reinforcement learning agent;

[0076] Specifically, based on the adjustable geometric topology variables, cross-sectional dimension variables, and node coordinate variables in the steel tower structure optimization, the actions are divided into two categories. One category acts on the overall configuration of the steel tower, including the addition or deletion of members, belonging to the macro-topology action layer; the other category acts on the specific specifications of existing members, including the modification of cross-sectional dimension variables, belonging to the micro-parameter action layer. The operation objects of the macro-topology action layer are the member connection relationships determined by the geometric topology variables, while the operation objects of the micro-parameter action layer are the angle steel leg width and thickness or steel pipe outer diameter and wall thickness defined by the cross-sectional dimension variables. The two layers of actions together constitute a complete action space, supporting the reinforcement learning agent to adjust the steel tower scheme at different scales.

[0077] S2.2: The action space includes operations for adding, deleting, and modifying the cross-section of steel tower members;

[0078] It should be noted that the addition of steel tower members refers to the introduction of new members into the steel tower structure to change its geometric topological variables;

[0079] The deletion operation for steel tower members refers to removing existing members to simplify or adjust the geometric topology variables of the steel tower;

[0080] Modifying the cross-section of steel tower members refers to adjusting the cross-sectional dimension variables of existing members.

[0081] S2.3: Employ a multi-scale state representation method to extract and fuse state features in the action space to form the state space of the reinforcement learning agent;

[0082] Specifically, the overall configuration information reflected by the geometric topological variables of the steel tower structure is extracted at the macro scale, including the total height, number of segments, and crossarm arrangement. At the same time, the member specification information reflected by the cross-sectional dimension variables is extracted at the micro scale, including the leg width and thickness of angle steel or the outer diameter and wall thickness of steel pipe. In addition, the spatial geometry of the structure is described by combining the three-dimensional positions of key connection points determined by the node coordinate variables. The features at different scales are organized and integrated according to the member connection relationships to form a unified state expression that includes geometric topology and mechanical properties, which serves as the state space of the reinforcement learning agent.

[0083] S2.4: The state space includes the geometric topology and mechanical properties of the steel tower structure;

[0084] It should be noted that the geometric topology of a steel tower structure refers to the overall macroscopic morphological information of the steel tower determined by geometric topological variables in the state space, including the total height, number of segments, and crossarm arrangement.

[0085] The mechanical properties of a steel tower structure refer to the physical characteristics in the state space related to the stress behavior of the structure, including the weight of the steel tower structure, stress constraint index, and displacement constraint index.

[0086] S2.5: The reward function of the reinforcement learning agent is constructed by weighting the state space through a multi-objective optimization function;

[0087] Specifically, based on the steel tower structure weight, stress constraint index, and displacement constraint index contained in the state space, corresponding weights are assigned respectively; the steel tower structure weight, stress constraint index, and displacement constraint index are combined according to their corresponding weights to form a single comprehensive evaluation value, which serves as the reward function value, thereby constructing the reward function of the reinforcement learning agent.

[0088] The expression for the reward function is:

[0089] ;

[0090] In the formula, This represents the reward function value. This represents the weighting coefficient for the weight constraint of the steel tower structure. This indicates the total weight of the steel tower structure. This indicates the maximum permissible weight of the steel tower structure. This represents the weighting coefficient for stress constraints in steel tower structures. This indicates the maximum allowable stress of the steel tower structure. This represents the actual stress at a point in the steel tower structure. This represents the weighting coefficient for displacement constraints in the steel tower structure. This indicates the maximum allowable displacement of the steel tower structure. This indicates the actual displacement of a point in the steel tower structure.

[0091] It should be noted that, , and All are dimensionless. and The units of measurement are all kg, then Dimensionless and The dimensions of all are Pa, then Dimensionless and The dimensions of all are m, then Dimensionless, output It is also dimensionless, and all parameters maintain a uniform dimension.

[0092] It should be noted that the weighting coefficient for the steel tower structure weight constraint is mainly determined based on project requirements or user requirements, to establish the priority of lightweighting in the entire optimization process, and to determine the impact of weight on structural safety and function in conjunction with the steel tower's usage scenario and structural stability requirements. An example value for the weighting coefficient of the steel tower structure weight is 0.4, with an adjustable range of [0.3, 0.5]. The value is based on project budget, material costs, transportation requirements, and user requirements regarding the steel tower's self-weight. If the project prioritizes cost and weight reduction, the weighting coefficient will be higher; if structural stability is more important, this weighting may be lowered.

[0093] The weighting coefficient of stress constraint on steel tower structure is set based on the assessment of the maximum load and stress borne by the steel tower in actual use, with reference to relevant engineering safety standards or user safety requirements. The example value of the weighting coefficient of stress constraint on steel tower structure is 0.35, and the adjustable range is [0.3, 0.4]. The value is based on engineering safety standards, historical load test results and user requirements for the load-bearing capacity of steel tower. If the steel tower needs to withstand large wind loads or other external forces, the weighting coefficient of stress constraint on steel tower structure should be increased accordingly.

[0094] The weighting coefficient for displacement constraints of steel tower structures is set based on the analysis of the maximum displacement that the steel tower may produce under different loads, the assessment of its impact on structural stability and function, and the actual use scenario of the steel tower. An exemplary value for the weighting coefficient of displacement constraints of steel tower structures is 0.25, and the adjustable range is [0.2, 0.3]. The value is based on the environmental factors of the steel tower, such as wind load and the precision requirements of the equipment. If the steel tower supports precision equipment or is located in an area with strong winds, the displacement constraints need to be more stringent, thereby increasing the weighting coefficient of displacement constraints of the steel tower structure.

[0095] S2.6: The reward function includes the steel tower structure weight, stress constraint index, and displacement constraint index.

[0096] It should be noted that the weight of the steel tower structure refers to the reward function that gives corresponding rewards and penalties based on the total amount of materials used in the steel tower; the smaller the weight, the higher the reward is usually.

[0097] The stress constraint index refers to the reward function being adjusted based on whether the stress on the member exceeds the allowable strength limit. When the limit is not exceeded, a positive reward is given, and when the limit is exceeded, a penalty is imposed.

[0098] The displacement constraint index refers to the reward function evaluating whether the overall deformation of the steel tower under load meets the allowable deformation range of the project. The reward is increased when the displacement is compliant and decreased when it exceeds the limit.

[0099] S2.7: Achieve dynamic coupling between the reward function and the multi-level analysis model system through the data exchange interface, and complete the configuration of the reinforcement learning environment.

[0100] Specifically, a data exchange interface is preset in the reinforcement learning environment. The data exchange interface defines the types of information that the reward function needs to read, including the weight of the steel tower structure, stress constraint index, and displacement constraint index. When the reinforcement learning agent generates the steel tower scheme and enters the performance evaluation stage, the low-fidelity evaluation results generated by the low-fidelity finite element model are transmitted to the reward function through the data exchange interface. Thus, the connection mechanism between the reward function and the multi-level analysis model system is completed in the environment configuration stage, and the reinforcement learning environment is configured.

[0101] It should be noted that the preset data exchange interface refers to the pre-declaration of the weight and displacement data fields that need to be obtained, which will be automatically matched and filled after the low-fidelity evaluation results are generated.

[0102] S3. The reinforcement learning agent executes an exploration strategy to generate steel tower schemes, inputs the steel tower schemes into a low-fidelity finite element model, outputs low-fidelity evaluation results, updates the policy network of the reinforcement learning agent, and outputs new steel tower schemes that meet the preset performance threshold in the low-fidelity evaluation results as candidate schemes.

[0103] S3.1: The reinforcement learning agent executes an exploration strategy in a reinforcement learning environment to generate a steel tower solution;

[0104] Specifically, the reinforcement learning agent includes a policy network, which, as the core component of the agent, determines which action to take in the action space based on information in the current state space. Based on the geometric topology and mechanical properties of the steel tower structure contained in the state space, the policy network within the agent selects actions. The action space is divided into a macro-topological action layer and a micro-parameter action layer. The macro-topological action layer performs operations to add or delete steel tower members, while the micro-parameter action layer performs operations to modify the cross-sections of the steel tower members. The policy network selects specific action combinations in the action space according to a probability distribution based on the current state characteristics, gradually constructing a complete steel tower scheme.

[0105] It should be noted that the exploration strategy refers to the behavioral rules by which the reinforcement learning agent selects specific action combinations of the macro-topology action layer and the micro-parameter action layer in the action space according to the probability distribution based on the policy network, in order to generate a steel tower scheme that conforms to the definition of geometric topology variables, cross-sectional size variables and node coordinate variables.

[0106] S3.2: Input the steel tower scheme into the low-fidelity finite element model for performance evaluation and output the low-fidelity evaluation results.

[0107] Specifically, the geometric topological variables, cross-sectional dimension variables, and node coordinate variables included in the steel tower scheme are mapped to the rod system representation of the low-fidelity finite element model to determine the spatial axis position, connection relationship, and cross-sectional specifications of each rod. Pre-set load conditions are applied to the low-fidelity finite element model, and based on the basic principles of structural mechanics, the internal force distribution and deformation state of the steel tower under the load conditions are determined. On this basis, the total weight of the steel tower structure is calculated, the location of the maximum stress is identified and it is determined whether it exceeds the allowable limit of the material, and the displacement of the control points is recorded to determine whether it meets the requirements of the engineering specifications, thus forming the low-fidelity evaluation results.

[0108] It should be noted that the low-fidelity finite element model does not require pre-training. The low-fidelity finite element model is a physical simulation model directly constructed based on the simplified geometric model, using beam theory analysis and coarse mesh generation. Its behavior is determined by the basic principles of structural mechanics and does not depend on data-driven or parameter learning processes.

[0109] It should be noted that the preset load conditions refer to the typical external force combinations that are pre-defined in the performance evaluation of steel tower structures to simulate the actual use environment, including wind load, self-weight and operation load.

[0110] The allowable limit for materials refers to the maximum stress value that a member can withstand, determined based on the mechanical properties of steel and the safety factor. Exceeding this value is considered as not meeting the strength requirements.

[0111] Engineering specifications refer to the maximum allowable displacement limits specified in steel structure design standards for the overall or partial deformation of steel towers, which are used to control the stiffness and stability of the structure.

[0112] S3.3: Based on the low-fidelity evaluation results, the parameter update of the policy network of the reinforcement learning agent is calculated using the importance sampling and entropy regularization policy gradient method. The expression is as follows:

[0113] ;

[0114] ;

[0115] In the formula, This represents the parameter update amount of the policy network for the reinforcement learning agent. Indicates the learning rate. Representing state-action pairs Under the current strategy The mathematical expectation, Indicates the network parameters of the policy gradient, Indicates the current strategy In state Select action The logarithm of the probability, Indicates the state Select action Compared to the advantages of the average strategy, The weight coefficients representing the entropy regularization term. Indicates the current strategy The entropy.

[0116] It should be noted that "state" refers to the set of all relevant features of the steel tower structure at a certain moment during the optimization process, including the current configuration and performance indicators of the steel tower defined by variables such as geometric topology, cross-sectional dimensions, and node coordinates.

[0117] Actions refer to the operations that a reinforcement learning agent selects according to a policy in a specific state. In steel tower structure optimization, actions may include adjustments to the geometric topology, cross-sectional dimensions, or node coordinates of the steel tower.

[0118] Average strategy refers to the strategy based on the current strategy Expected return under all possible conditions.

[0119] It should be noted that the weight coefficient of the entropy regularization term is set according to the balance between exploration and exploitation. The example value is 0.01, which is based on the exploration requirements and convergence speed of the task. A larger λ value encourages more exploration, while a smaller λ value tends to exploit the currently known optimal strategy.

[0120] S3.4: Adjust the parameters of the policy network using the parameter update amount to generate the updated policy network;

[0121] Specifically, the parameter update reflects the direction and magnitude of the current policy adjustment in the network parameter space; the parameter update is applied to the original parameters of the policy network to correct the weights within the policy network; the corrected policy network is more inclined to generate steel tower solutions with high rewards in decision-making, while maintaining a certain diversity of actions through entropy regularization to avoid premature convergence to local suboptimal solutions; thus forming the updated policy network.

[0122] S3.5: Re-evaluate the performance of the steel tower scheme based on the updated policy network, and output the new steel tower scheme that simultaneously meets the preset performance threshold as the candidate scheme.

[0123] Specifically, the updated policy network generates new steel tower designs in a reinforcement learning environment; the new steel tower designs are then fed into a low-fidelity finite element model for rapid performance evaluation, obtaining low-fidelity evaluation results that include the steel tower structure weight, stress constraint index, and displacement constraint index; the steel tower structure weight, stress constraint index, and displacement constraint index are compared with preset performance thresholds, including weight threshold, stress threshold, and displacement threshold; when the steel tower structure weight does not exceed the weight threshold, the actual stress does not exceed the stress threshold, and the actual displacement does not exceed the displacement threshold, the new steel tower design is deemed to meet the requirements and is retained as a candidate design.

[0124] It should be noted that the weight threshold is set based on the project's material cost control objectives, transportation and hoisting capacity limitations, and structural lightweighting requirements; the value range is 80% to 120% of the weight of similar steel tower structures in the past; the basis includes the user's explicit requirements for the steel tower's self-weight, the foundation bearing capacity design margin, and economic indicators; if the steel tower structure weight is less than 80%, although it is beneficial to reduce costs, it may lead to insufficient structural stiffness or low redundancy, affecting overall stability; if it is higher than 120%, it will increase material consumption and construction difficulty, exceeding the bearing capacity of transportation or installation equipment;

[0125] The stress threshold is determined based on the yield strength of the steel used; the value ranges from 60% to 90% of the steel's yield strength to ensure sufficient safety margin under extreme loads; it is based on industry standards, steel grade performance parameters, and user requirements for structural safety levels; if it is below 60%, it indicates that the material strength is not fully utilized, there is over-design, and waste occurs; if it exceeds 90%, the members may undergo plastic deformation or even instability and failure, endangering structural safety;

[0126] The displacement threshold is set based on the steel tower's function, the accuracy requirements of auxiliary equipment, and the requirements for wind vibration control; the value range is 1 / 100 to 1 / 75 of the total height of the steel tower; the basis includes the restrictions on tower top deflection in the transmission line design code, the equipment's tolerance to tower sway, and the user's requirements for operational reliability; if it is less than 1 / 100, it indicates that the structural stiffness is too large, which may be accompanied by unnecessary material addition; if it exceeds 1 / 75, it will affect conductor sag control, insulator offset, or normal equipment operation, and in severe cases, it may cause safety accidents.

[0127] S4. Input the candidate scheme into the high-fidelity finite element model to generate high-fidelity verification results. Compare the high-fidelity verification results with the low-fidelity evaluation results and calculate the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model.

[0128] S4.1: Input the candidate solutions into the high-fidelity finite element model for accurate verification and generate high-fidelity verification results;

[0129] Specifically, the geometric topological variables, cross-sectional dimension variables, and node coordinate variables contained in the candidate schemes are mapped to the shell geometry of the high-fidelity finite element model to ensure that the shape of the members, connection structure, and spatial position are consistent with the original scheme. The same preset load conditions as the low-fidelity finite element model are applied. The steel tower structure is simulated in detail using the high-fidelity finite element model to capture the stress concentration effect in local areas of the members (such as the angle steel limb tips, weld transition zone, and bolt hole perimeter) and the three-dimensional deformation behavior of complex connection nodes. Based on this, the maximum stress value and its location, the control point displacement value, and the total weight of all components are extracted throughout the tower to form a high-fidelity verification result containing more realistic mechanical response details.

[0130] It should be noted that the high-fidelity finite element model does not require pre-training. The high-fidelity finite element model is a physical simulation model directly constructed based on the simplified geometric model, using shell theory analysis and fine mesh generation. Its behavior is determined by the basic principles of structural mechanics and does not depend on data-driven or parameter learning processes.

[0131] S4.2: Compare the high-fidelity verification results with the low-fidelity evaluation results to generate a residual sequence;

[0132] Specifically, a one-to-one correspondence is established between the same physical quantities in the high-fidelity verification results and the low-fidelity evaluation results, including the weight of the steel tower structure, actual stress, and actual displacement. Under the same load conditions and geometric reference, the values ​​of each index in the high-fidelity verification results are compared with the corresponding values ​​in the low-fidelity evaluation results item by item. For each index, the difference between the two is recorded to form deviation data organized by index type. The deviation data is arranged in a preset order to form a residual sequence.

[0133] It should be noted that the preset order refers to organizing the various deviation data according to a fixed arrangement of the steel tower structure weight, stress constraint index, and displacement constraint index.

[0134] S4.3: Based on the residual sequence, the prediction bias between the low-fidelity finite element model and the high-fidelity finite element model is calculated using a dynamic weighted integral algorithm. The expression is as follows:

[0135] ;

[0136] In the formula, This represents the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model. This represents the total number of physical quantities in the residual sequence. Indicates the physical quantity index. Indicates the first The weighting coefficients of each physical quantity satisfy the following conditions: =1, Indicates the first The absolute value of the residual of each physical quantity Indicates the first Standardized benchmark values ​​for physical quantities.

[0137] It should be noted that the first The standardized benchmark value of a physical quantity refers to the reference value used for the residual of a dimensionless physical quantity. It is usually taken as the allowable value, design limit, target value or historical statistical characteristics (such as standard deviation) to reflect the relative size of the error.

[0138] It should be noted that the first The weighting coefficient of each physical quantity is determined by the relative importance of the physical quantity to the design objectives (such as structural safety, stability, etc.). The example value is 0.4, which is based on the influence of a certain physical quantity (such as stress, displacement, etc.) on the structural reliability in steel tower structure design. Physical quantities with larger weights have higher weighting coefficients.

[0139] S5. The low-fidelity evaluation results are calibrated based on the prediction deviation. When the calibrated low-fidelity evaluation results simultaneously satisfy both the low-fidelity finite element model and the high-fidelity finite element model, the optimal steel tower scheme is output.

[0140] S5.1: Based on the predicted bias, a meta-learning calibration model is constructed through meta-training historical bias patterns, and calibration parameters are generated by forward propagation.

[0141] Specifically, historically accumulated prediction deviation instances are integrated, covering deviation records under various steel tower structure working conditions, forming a historical deviation pattern set. Using a meta-learning framework, the historical deviation pattern set is used for model training. The training process focuses on learning the mapping relationship between predicted deviations and ideal calibration, thereby constructing a meta-learning calibration model. The meta-learning calibration model has the ability to adapt to new deviation patterns. After training, for new predicted deviations, the forward propagation mechanism of the meta-learning calibration model is directly applied. The forward propagation mechanism generates corresponding calibration parameters based on the parameter weights already learned within the meta-learning calibration model.

[0142] It should be noted that the meta-learning calibration model adopts a lightweight multi-layer neural network structure, which is in a feedforward form. The multi-layer neural network receives vectors reflecting the deviations of various performance indicators between the low-fidelity finite element model and the high-fidelity finite element model as input, and outputs a set of calibration parameters for adjusting the behavior of the low-fidelity finite element model. The multi-layer neural network contains two intermediate hidden layers, each with a moderate number of neurons, and uses non-linear activation functions to enhance expressive power while maintaining computational efficiency, making it easy to call quickly in the optimization loop.

[0143] The training process of the meta-learning calibration model is based on high-fidelity and low-fidelity simulation comparison data accumulated from a large number of historical steel tower design cases. Each training sample corresponds to a typical working condition, including the deviation characteristics between the low-fidelity finite element model prediction results and the high-fidelity benchmark under the typical working condition, as well as the optimal calibration parameters obtained through offline optimization. The training process updates the network weights by minimizing the comprehensive error between the low-fidelity and high-fidelity results after calibration. The standard stochastic gradient optimization method is adopted. The training data is divided into layers according to tower type and working condition. A portion is reserved for validation to prevent overfitting. An early stopping mechanism is set to automatically terminate the training when the performance of the meta-learning calibration model no longer improves, thus obtaining a well-trained meta-learning calibration model.

[0144] The expression for generating calibration parameters is:

[0145] ;

[0146] In the formula, Indicates calibration parameters, This represents the total amount of historical prediction deviation. Index representing historical prediction deviation. Indicates the first The weighting coefficients for each historical prediction deviation Indicates the first The absolute value of the historical prediction deviation. Indicates the first A standardized baseline value for the historical prediction deviation.

[0147] It should be noted that the first The weight coefficient of each historical prediction deviation is derived from the meta-learning calibration model's assessment of the matching degree between the historical deviation pattern and the current steel tower structure in terms of load conditions and topological characteristics. The example value is 0.6, which is based on the fact that the structural type (such as transmission tower) and load conditions (such as wind load dominance) corresponding to the historical deviation pattern are highly consistent with the current optimization task.

[0148] S5.2: Apply calibration parameters to correct the low-fidelity evaluation results to obtain calibrated evaluation results;

[0149] Specifically, the calibration parameters are correlated with the actual structural weight, actual stress, and actual displacement. The calibration parameters consist of a scaling factor and an offset. The scaling factor is used to adjust the magnitude of the actual structural weight, actual stress, and actual displacement values, while the offset is used to adjust the position of the adjusted actual structural weight, actual stress, and actual displacement values. After the adjustment is completed, the calibrated actual structural weight, actual stress, and actual displacement values ​​are formed and combined into the calibrated evaluation result.

[0150] S5.3: When the calibrated evaluation results simultaneously meet the rapid performance evaluation criteria of the low-fidelity finite element model and the accurate verification requirements of the high-fidelity finite element model, the optimal steel tower scheme is output.

[0151] Specifically, the calibrated evaluation results are compared with preset performance thresholds. If the calibrated steel tower structure weight does not exceed the weight threshold, the calibrated actual stress does not exceed the stress threshold, and the calibrated actual displacement does not exceed the displacement threshold, then the calibrated evaluation results are determined to simultaneously meet the computational efficiency requirements of the low-fidelity finite element model and the accurate verification requirements of the high-fidelity finite element model. The corresponding steel tower scheme is then determined as the optimal steel tower scheme.

[0152] It should be noted that if the evaluation result of a certain steel tower scheme after calibration does not simultaneously meet the rapid performance evaluation criteria of the low-fidelity finite element model and the accurate verification requirements of the high-fidelity finite element model, it will return to the policy network of the reinforcement learning agent for updating. The updated policy network will execute a new exploration strategy in the reinforcement learning environment to generate an improved steel tower scheme.

[0153] In summary, this invention establishes a dynamic calibration mechanism based on meta-learning, quantifying the deviations between models into traceable calibration parameters to achieve real-time accuracy compensation for rapid evaluation results. This not only improves the predictive reliability of low-fidelity models in optimization loops, enabling reinforcement learning agents to update policies based on more accurate information, but also effectively suppresses the cumulative amplification effect of errors during iteration by constructing a propagation model for prediction deviations. Thus, while ensuring optimization speed, it improves the computational accuracy and engineering feasibility of the output scheme, providing technical support for the efficient and high-precision automated optimization design of large and complex steel tower structures.

[0154] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing steel tower structures based on finite element analysis, characterized in that: include, Based on the requirements of the steel tower structure, a parameterized set of variables is defined. An initial geometric model is generated based on this set of variables, and a multi-level analysis model system is constructed. The specific steps are as follows. The initial geometric model is geometrically preprocessed, and the connection areas of the rods are automatically identified and geometrically simplified using a feature recognition algorithm to obtain a simplified geometric model. Based on the simplified geometric model, a low-fidelity finite element model is established using beam theory analysis and coarse mesh generation. Based on the simplified geometric model, a high-fidelity finite element model is established using shell theory analysis and fine mesh generation. Establish the displacement mapping relationship between the low-fidelity finite element model and the high-fidelity finite element model, and complete the construction of a multi-level analysis model system; The multi-level analysis model is configured in the reinforcement learning environment, defining the action space, state space, and reward function for the reinforcement learning agent in the environment. The specific steps are as follows. A hierarchical action space architecture is constructed and divided into a macroscopic topological action layer and a microscopic parameter action layer, which serve as the action space for the reinforcement learning agent. A multi-scale state representation method is used to extract and fuse state features in the action space to form the state space of the reinforcement learning agent. The reward function of the reinforcement learning agent is constructed by weighting the state space through a multi-objective optimization function. The reward function and the multi-level analysis model system are dynamically coupled through a data exchange interface to complete the configuration of the reinforcement learning environment; The reinforcement learning agent executes an exploration strategy to generate steel tower schemes, inputs the steel tower schemes into a low-fidelity finite element model, outputs low-fidelity evaluation results, updates the policy network of the reinforcement learning agent, and outputs new steel tower schemes that meet the preset performance threshold in the low-fidelity evaluation results as candidate schemes. The candidate scheme is input into the high-fidelity finite element model to generate high-fidelity verification results. The high-fidelity verification results are compared with the low-fidelity evaluation results, and the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model is calculated. The low-fidelity evaluation results are calibrated based on the prediction deviation. When the calibrated low-fidelity evaluation results simultaneously satisfy both the low-fidelity finite element model and the high-fidelity finite element model, the optimal steel tower scheme is output.

2. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The parameterized set of variables includes geometric topology variables, cross-sectional dimension variables, and node coordinate variables.

3. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The specific steps for generating the initial geometric model based on the set of variables are as follows. Based on the requirements of the steel tower structure, determine the geometric topological variables of the steel tower structure; The geometric topology variables are spatially expanded and coordinates are calculated using a parametric method to generate node coordinate variables and establish the spatial framework of the steel tower structure. The spatial frame of the steel tower structure is combined with the cross-sectional dimension variables to perform parametric modeling and generate an initial geometric model.

4. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The action space includes operations for adding, deleting, and modifying the cross-section of steel tower members; The state space includes the geometric topology and mechanical properties of the steel tower structure; The reward function includes the steel tower structure weight, stress constraint index, and displacement constraint index.

5. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The specific steps for outputting the low-fidelity evaluation result are as follows. A reinforcement learning agent executes an exploration strategy in a reinforcement learning environment to generate a steel tower design. The steel tower scheme is input into a low-fidelity finite element model for performance evaluation, and the low-fidelity evaluation results are output.

6. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The policy network of the updated reinforcement learning agent is then used to output new steel tower schemes that meet a preset performance threshold in the low-fidelity evaluation results as candidate schemes. The specific steps are as follows. Based on the low-fidelity evaluation results, the policy gradient method with importance sampling and entropy regularization is used to calculate the parameter update of the policy network of the reinforcement learning agent. Adjust the parameters of the policy network using the parameter update amount to generate an updated policy network; The performance of the steel tower scheme is re-evaluated based on the updated policy network, and new steel tower schemes that simultaneously meet the preset performance thresholds are output as candidate schemes.

7. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The specific steps for calculating the prediction deviation between the low-fidelity finite element model and the high-fidelity finite element model are as follows. The candidate solutions are input into a high-fidelity finite element model for accurate verification, generating high-fidelity verification results. The high-fidelity verification results are compared with the low-fidelity evaluation results to generate a residual sequence; Based on the residual sequence, the prediction bias between the low-fidelity finite element model and the high-fidelity finite element model is calculated using a dynamic weighted integral algorithm.

8. The steel tower structure optimization method based on finite element analysis as described in claim 1, characterized in that: The specific steps for outputting the optimal steel tower scheme are as follows. Based on the predicted bias, a meta-learning calibration model is constructed by meta-training historical bias patterns, and calibration parameters are generated by forward propagation. The low-fidelity evaluation results are corrected by applying calibration parameters to obtain calibrated evaluation results; The optimal steel tower scheme is output when the calibrated evaluation results simultaneously meet the rapid performance evaluation criteria of the low-fidelity finite element model and the accurate verification requirements of the high-fidelity finite element model.

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