A method for shape optimization of spatial reticulated shell structure based on genetic algorithm

Abstract

This invention discloses a method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm, relating to the field of data processing technology. The method includes: generating a topological knowledge graph of structural force paths based on node force characteristic data to extract feature vectors representing the integrity and coherence of the main load-bearing paths; using the feature vectors as input and the integrity and coherence of the main load-bearing paths as a reward function to determine the perturbation sequence of key nodes, and encoding the node coordinates using a genetic algorithm; obtaining the optimized positions of structural nodes through population iteration and fitness evaluation; identifying regions of missing non-functional force paths in the structure and updating the digital twin model until the integrity and coherence of the main load-bearing paths meet the optimization threshold, and outputting the optimized geometric shape of the reticulated shell structure. This invention achieves accurate identification and perturbation optimization of key nodes in spatial reticulated shell structures, thereby significantly improving the integrity and coherence of the main load-bearing paths.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and specifically to a method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm. Background Technology

[0002] Space reticulated shell structures possess advantages such as high load-bearing capacity, light weight, large span, and aesthetically pleasing appearance, leading to their widespread application in various large-span public buildings. In practical engineering, space reticulated shell structures often need to withstand complex load combinations, and their structural morphology significantly impacts their overall load-bearing performance and safety. Therefore, effectively optimizing the geometry of reticulated shell structures to improve their load-bearing capacity and economy has long been a crucial issue of concern in the field of engineering design.

[0003] Currently, optimization design methods for space reticulated shell structures are mainly based on traditional static finite element analysis. These methods typically rely on the engineering experience of designers to analyze pre-set load conditions and adjust member dimensions or local shapes accordingly to meet structural safety and economic requirements. This approach struggles to accurately reflect the nodal stiffness sensitivity of reticulated shell structures under complex real loads and lacks a systematic mechanism for identifying sensitive nodes and optimizing critical load-bearing paths. This often results in significant arbitrariness and inefficiency in the structural optimization process. Furthermore, existing technologies fail to deeply consider the dynamic impact of nodal disturbance sequence on the overall structural force path in space reticulated shell structure optimization, and they also fail to establish an effective collaborative optimization mechanism between nodal disturbances and the main load-bearing paths of the structure, making it difficult to obtain a comprehensive structural optimization solution.

[0004] Therefore, existing technologies urgently need a more precise and effective optimization method for space reticulated shell structures that can accurately capture the sensitive characteristics of structural nodes, rationally determine the disturbance sequence of key nodes, and comprehensively consider the integrity and continuity of the main load-bearing path of the structure to achieve comprehensive optimization of the geometric shape of the reticulated shell structure, so as to improve the overall performance and economic benefits of the structure. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the shape of spatial reticulated shell structures based on genetic algorithms, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm, comprising:

[0008] S101: Construct a digital twin model of a spatial reticulated shell structure, simulate the force flow distribution of structural nodes under complex loads in real time, and extract the force characteristic data of the nodes;

[0009] S102: Generate a structural force path topology knowledge graph based on the node force characteristic data, and use a graph embedding algorithm to extract feature vectors that characterize the integrity and coherence of the main load-bearing path of the structure;

[0010] S103: Using the feature vector as input and the integrity and coherence of the main structural bearing path as the reward function, a deep reinforcement learning algorithm is used to determine the perturbation sequence of key nodes;

[0011] S104: Genetic algorithm is used to encode the node coordinates based on the perturbation sequence of key nodes, and the optimal position of the structural nodes is obtained through population iteration and fitness evaluation;

[0012] S105: Real-time monitoring of changes in the structural force path after disturbance, identification of areas where non-functional force paths are lost in the structure, and feedback to update the digital twin model;

[0013] S106: Repeat steps S102 to S105 until the integrity and continuity of the main load-bearing path of the structure meet the optimization threshold, and output the optimized geometries of the reticulated shell structure.

[0014] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0015] This invention uses real-time simulation of the displacement response vector of nodes in a spatial reticulated shell structure under complex loads to accurately extract the node stiffness sensitivity coefficient by applying disturbance loads one by one, and accurately identify the initial main load-bearing node region of the structure. This effectively overcomes the shortcomings of traditional methods, such as inaccurate identification of node sensitive features and difficulty in accurately locating sensitive areas, and significantly improves the accuracy and effectiveness of selecting node disturbance positions during structural optimization.

[0016] This invention constructs a topological knowledge graph of structural force paths and uses a graph embedding algorithm to obtain node feature vectors. The integrity and coherence of the main load-bearing path are quantitatively characterized by the magnitude of the feature vectors and the cosine similarity of the feature vectors between adjacent nodes, respectively. This transforms the feature analysis of the structural force path from a qualitative description to a quantifiable quantitative evaluation, thereby effectively overcoming the lack of quantitative means in the optimization of the main load-bearing path of the structure in the existing technology and improving the scientificity and rigor of the structural optimization process.

[0017] This invention optimizes the perturbation order of key nodes using a deep reinforcement learning algorithm with node feature vectors as state input and the evaluation index of the integrity and coherence of the main bearing path as the reward function. Furthermore, it uses a genetic algorithm to optimize the node coordinate positions, establishing a precise collaborative optimization mechanism between key node perturbation and overall structural morphology optimization. This effectively avoids the blindness and randomness of traditional optimization methods in selecting the node perturbation order, and significantly improves the accuracy, efficiency, and reliability of the overall geometric morphology optimization of the space reticulated shell structure. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0019] Figure 1 This is a flowchart of a spatial reticulated shell structure shape optimization method based on genetic algorithm according to the present invention. Detailed Implementation

[0020] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided to make the description of this application more complete and comprehensive, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The drawings are merely illustrative illustrations of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted.

[0021] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more exemplary embodiments. Numerous specific details are provided in the following description to give a full understanding of the exemplary embodiments disclosed in this application. However, those skilled in the art will recognize that the technical solutions disclosed in this application can be practiced with one or more specific details omitted, or other methods, components, steps, etc., can be employed. In other instances, well-known structures, methods, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of the disclosure of this application.

[0022] Example 1

[0023] like Figure 1 As shown, this embodiment discloses a method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm, including:

[0024] S101: Construct a digital twin model of a spatial reticulated shell structure, simulate the force flow distribution of structural nodes under complex loads in real time, and extract the force characteristic data of the nodes;

[0025] It should be understood that the digital twin model of the aforementioned spatial reticulated shell structure is a simulation analysis model established using the finite element method based on the geometric dimensions, material parameters, and node connection relationships of the actual spatial reticulated shell structure. Specifically, taking a large-span stadium spatial reticulated shell structure as an example, the reticulated shell structure uses steel members, and the elastic modulus of each member is... MPa, the cross-sectional shape of the rod is a circular tube or a rectangular tube, and the cross-sectional moment of inertia parameters (including cross-sectional area, moment of inertia, etc.) are selected according to the actual engineering design; the node connection method of the reticulated shell structure is rigid connection or hinged connection according to the actual design; the digital twin model is established by finite element software such as Ansys or ABAQUS, and the model size strictly corresponds to the actual project.

[0026] In implementation, the real-time simulation of the force flow distribution of structural nodes under complex loads refers to applying complex load conditions formed by a combination of real working conditions such as gravity loads, wind loads, and snow loads to the digital twin model, and solving the displacement response data of the structural nodes and the axial internal forces of the members through the finite element method, thereby clarifying the transmission path distribution of the axial forces of each member; wherein, the axial internal forces of the members are the tensile or compressive forces along the axial direction of the members;

[0027] Furthermore, the nodal displacement response data specifically refers to the displacement values ​​of each node in the global Cartesian coordinate system (i.e., the x, y, and z directions), typically represented as a three-dimensional displacement vector.

[0028]

[0029] In the formula: This represents the displacement response vector of the i-th node; These represent the displacement components of the node in the x, y, and z directions of the global coordinate system, respectively.

[0030] In specific implementation, the method for extracting the node force characteristic data includes:

[0031] In the digital twin model, a first preset load is applied to the spatial reticulated shell structure, and the initial displacement response vector of each node under the first preset load is calculated.

[0032] It should be noted that the first preset load condition can be selected as a typical design combination load of the structure, for example: ;in, The first preset load condition is represented by G; the structure's self-weight (gravity load) is automatically calculated using finite element software; the wind load is obtained through CFD numerical wind tunnel simulation or calculation based on the wind pressure distribution data of the project; and the snow load is calculated using the standard values ​​for the actual project location.

[0033] The initial displacement response vectors of all nodes under the first preset load condition were obtained by finite element analysis. In the formula, These represent the initial displacements of node i along the x, y, and z directions under the first preset load condition.

[0034] Based on the magnitude of the initial displacement response vector of each node, the node region that exceeds the displacement response threshold is determined as the initial main bearing node region;

[0035] Specifically, the magnitude of the initial displacement response vector at each node is calculated as follows:

[0036]

[0037] The displacement response threshold is set according to engineering safety requirements, typically taking the average value of the initial displacement response vector amplitude of the node as a reference, and adjusting it according to the actual situation; nodes exceeding this threshold constitute the initial main load-bearing node region.

[0038] For each node within the initial main bearing node area, the second preset working condition disturbance load is applied one by one, and the disturbance displacement response vector of each node under the action of the second preset working condition disturbance load is calculated respectively.

[0039] Specifically, the method for determining the disturbance displacement response vector includes:

[0040] Determine the set of members directly connected to the target node within the initial main load-bearing node region;

[0041] It should be understood that the set of rods directly connected to the target node is automatically determined by the topological connection relationship between the node and the rod in the finite element model;

[0042] Specifically, the topological connection relationship between nodes and members refers to the connection correspondence between each node and each member in the finite element model. This correspondence is represented by a connection matrix of node numbers and member numbers, called the node-member connection matrix. , where matrix elements This represents the connection between the i-th node and the j-th member; if node i is one of the end nodes of member j, then... If node i is not directly connected to member j, then N represents the total number of nodes in the finite element model, and M represents the total number of members in the finite element model.

[0043] Apply element member disturbance loads along the axial direction of each member in the set of member members connecting the target node, and construct the corresponding member disturbance conditions one by one;

[0044] It should be understood that the element member disturbance load refers to a small axial load applied to the member directly connected to the target node, with its direction along the member's axis. Its value is much smaller than the first preset load condition (typically about 1% to 2% of the first preset load condition, determined by engineering experience), and is used to examine the stiffness sensitivity of the node. The disturbance load is applied at the node at the other end of the member, and is implemented by setting the node load condition in the finite element software.

[0045] Specifically, for the j-th member connected to node i, an application of magnitude is applied to its end furthest from node i. The axial disturbance load forms a member disturbance condition for node i. The direction of the disturbance load is along the axial direction of the member, and the type of load applied is tension or compression (the specific selection depends on the stress state of the member under the first preset working condition load; if the member was originally a tension member, the disturbance load is applied as tension, otherwise it is applied as compression).

[0046] Calculate the element disturbance displacement response vector of the target node under each member disturbance condition, and determine the amplitude of the element disturbance displacement response vector;

[0047] It should be noted that the calculation method for the element disturbance displacement response vector is the same as the calculation method for the initial displacement response vector, that is, it is obtained automatically by the static analysis module using a finite element model under the action of the rod disturbance condition; specifically, taking node i under the rod disturbance condition... The element disturbance displacement response vector is denoted as:

[0048]

[0049] In the formula: This indicates that node i is in the rod disturbance condition. The element displacement response vector under disturbance; These represent node i under the member disturbance condition. Displacement response components along the x, y, z directions of the global coordinate system;

[0050] The calculation method for the magnitude of the element disturbance displacement response vector is the same as that for the initial displacement response vector. For details, please refer to the above text, and it will not be repeated here.

[0051] Select the member disturbance conditions whose amplitude exceeds the element disturbance response threshold, and then superimpose the element disturbance displacement response vectors under the selected member disturbance conditions to form the disturbance displacement response vector of the target node.

[0052] It is understood that the unit disturbance response threshold is a value determined by technicians based on the statistical characteristics of the unit disturbance displacement response vector. Typically, it can be selected as the average or median value of the unit disturbance displacement response vector amplitude under all member disturbance conditions, so as to ensure that member disturbance conditions that have a significant impact on the structure are effectively selected.

[0053] Specifically, assuming that node i selects n element disturbance displacement response vectors from all member disturbance conditions and superimposes them, then the disturbance displacement response vector of node i can be expressed as:

[0054]

[0055] in, Let be the disturbance displacement response vector of node i; This represents the element disturbance displacement response vector of node i under the k-th selected member disturbance condition.

[0056] The node stiffness sensitivity coefficient is determined by the ratio of the amplitude of the disturbance displacement response vector of each node under the second preset working condition disturbance load to the amplitude of the initial displacement response vector of the node, and the stiffness sensitivity coefficient is used as the stress characteristic data of the node.

[0057] Specifically, the formula for calculating the nodal stiffness sensitivity coefficient is as follows:

[0058]

[0059] In the formula: Let be the stiffness sensitivity coefficient of node i.

[0060] S102: Generate a structural force path topology knowledge graph based on the node force characteristic data, and use a graph embedding algorithm to extract feature vectors that characterize the integrity and coherence of the main load-bearing path of the structure;

[0061] In specific implementation, the method for generating the structural force path topology knowledge graph includes:

[0062] Based on the node stiffness sensitivity coefficient, nodes with sensitivity coefficients higher than the sensitivity threshold are identified as graph nodes;

[0063] It should be noted that the sensitivity threshold is... The method for determining it is as follows: In the formula: This represents the arithmetic mean of the stiffness sensitivity coefficients of all nodes in a spatial reticulated shell structure. represents the standard deviation of the stiffness sensitivity coefficients of all nodes in the spatial reticulated shell structure; k is the sensitivity threshold adjustment coefficient, the specific value of which is determined based on the stiffness distribution characteristics of the reticulated shell structure and actual engineering experience.

[0064] Furthermore, when the stiffness sensitivity coefficient of node i satisfies the condition When node i is selected as a graph node.

[0065] Obtain all member connections in the spatial reticulated shell structure, and construct the initial topological connection relationship based on the member connection relationship;

[0066] It should be understood that the connection relationships of the members are determined by the node-member connection matrix provided by the finite element model, and the node-member connection matrix is ​​denoted as . The elements of matrix C are defined as follows:

[0067]

[0068] In the formula, N represents the total number of nodes in the finite element model, M represents the total number of members, and matrix C is automatically generated and exported by the finite element analysis software.

[0069] Specifically, the initial topological connectivity is represented as an undirected, unweighted graph. The node set V includes all nodes in the spatial reticulated shell structure; the edge set E includes all node pairs in the spatial reticulated shell structure that have direct link connections between them; the initial topological connection relationship is obtained directly through the node-link connection matrix C.

[0070] Starting from a graph node, search for valid paths between any two graph nodes one by one according to the initial topological connection relationship;

[0071] It should be noted that the effective path here is defined as: a continuous connection path that starts from any graph node and can be reached from another graph node through the connection of the poles, without repeating intermediate nodes;

[0072] For example, a depth-first search (DFS) algorithm can be used to search for an effective path, as follows:

[0073] With graph nodes As the starting node, the graph node Define the path search function for the target node. ,in

[0074] P represents the current search path; the initial path is... From node Start by searching for adjacent nodes, adding unvisited adjacent nodes to the path set P, and continue the search deeper and deeper until the path reaches the target node. The path is then recorded; if the path cannot be further explored or backtracked to a node... If so, backtrack one step and continue searching for unvisited adjacent nodes;

[0075] Repeat the above DFS process between any two nodes in the graph node set to obtain the set of valid paths between all graph node pairs. .

[0076] A topology graph is generated based on the graph node pairs with valid paths, and each edge of the topology graph is assigned the difference in sensitivity coefficients between the corresponding nodes as the edge weight of the topology graph, thus obtaining the final structural force path topology knowledge graph.

[0077] Specifically, the structural force path topology knowledge graph is represented as an undirected weighted graph. , where: node set The set of graph nodes and the set of edges are defined above. For graph node pairs with direct member connections, specifically a set Adjacent node pairs; set of edge weights The weight of each edge is defined as the absolute value of the difference in stiffness sensitivity coefficients between the two graph nodes connected by that edge. The specific calculation formula is as follows:

[0078]

[0079] In the formula, This represents the edge weight between node i and node j. These are the stiffness sensitivity coefficients of nodes i and j, respectively.

[0080] Furthermore, after generating the structural force path topology knowledge graph, the feature vector of each graph node is extracted using a graph embedding algorithm;

[0081] It should be noted that the feature vectors representing the integrity and coherence of the main load-bearing path of the structure are derived from the topological knowledge graph of the structural force path through graph embedding algorithms (such as the Node2Vec algorithm). The vector obtained after performing feature representation on the nodes in the vector;

[0082] In the specific implementation process, taking the Node2Vec algorithm as an example, firstly, for each node in the structural force path topology knowledge graph G, a random walk is performed according to the set probability rules to obtain a node walk sequence that fully represents the connection relationship between nodes, wherein:

[0083] The typical path length for a single random walk is 80 to 100 steps;

[0084] The number of times each node is repeated as the starting point of the walk is typically 10 to 20.

[0085] The jump probability of a node during a random walk takes into account the neighborhood structure characteristics of the node, so as to balance the local and global connectivity characteristics of the topology graph.

[0086] After obtaining the random walk sequence of nodes, the Skip-Gram model is used to train the sequence to realize the feature vector representation of nodes in the topological graph; the specific training methods include:

[0087] Use the node random walk sequence as the input data for the training samples;

[0088] The Skip-Gram model learns a vectorized representation of a node by maximizing the probability of a node co-occurring with its context nodes.

[0089] The typical width of the context window during Skip-Gram model training is 5 to 10 nodes, in order to better capture the structural relationships between nodes.

[0090] After training, for any node in the topological knowledge graph The corresponding feature vectors are obtained. (d is the vector dimension, typically 128 to 256, determined based on the actual project scale); At this point:

[0091] The magnitude of the node feature vector:

[0092]

[0093] The magnitude of the node feature vector represents the node. The importance of a structure within its main load-bearing path reflects the completeness of that path.

[0094] node Its directly adjacent nodes Cosine similarity of the feature vectors:

[0095]

[0096] Among them, the cosine similarity between the feature vectors of adjacent nodes quantitatively reflects the smoothness of force flow transmission between nodes and embodies the continuity of the main load-bearing path of the structure.

[0097] S103: Using the feature vector as input and the integrity and coherence of the main structural bearing path as the reward function, a deep reinforcement learning algorithm is used to determine the perturbation sequence of key nodes;

[0098] In specific implementation, the method for determining the perturbation sequence of key nodes includes:

[0099] Based on the feature vectors of the structural force path topology knowledge graph, the state space of the intelligent agent is constructed.

[0100] Specifically, the method for constructing the state space includes:

[0101] The magnitude of the node feature vector serves as the node sensitivity coefficient in the current structure, forming a node sensitivity distribution;

[0102] It should be understood that the node sensitivity distribution is based on the magnitude of the node feature vector obtained in step S102. The determination is based on the magnitude of the feature vectors of all nodes; that is, the magnitude of the feature vectors of all nodes is directly used as a quantitative representation of the node sensitivity. Specifically, the larger the value of the node sensitivity, the more significant the influence of the node on the overall stiffness of the structure.

[0103] This results in a distribution of node sensitivity: Where n is the total number of graph nodes, Let i be the feature vector of node i.

[0104] The local topological state of each node is determined by combining the distribution of node sensitivity with the topological connectivity of nodes.

[0105] It is understood that the local topological state of a node described here represents the topological relationship between the node's own sensitivity and the sensitivity of its neighboring nodes, and can be used to effectively distinguish the local structural features of different nodes.

[0106] For example, the local topological state vector of a node can be defined as:

[0107]

[0108] In the formula: Let i be the local topological state of node i;

[0109] The state space of the agent is formed by combining the local topological states of each node.

[0110] It should be noted that the agent's state space S represents the local topological state of the aforementioned nodes. The set, namely: The state space of the agent clearly represents the local topologically sensitive states of each node in the overall structure, which can provide sufficient state information for subsequent reinforcement learning.

[0111] The action space of the intelligent agent is constructed based on the perturbable nodes in the main load-bearing path of the structure.

[0112] Specifically, the method for constructing the action space includes:

[0113] Nodes with higher eigenvector change magnitudes are identified as candidate perturbation nodes;

[0114] It should be noted that a higher magnitude of feature vector change specifically refers to the magnitude of the node feature vector. If the value is greater than the average value of the overall node modulus, it means that the node has a significant impact on the overall stiffness of the structure and is prone to cause significant changes in the structural force path after disturbance.

[0115] In practice, a set of candidate perturbation nodes can be defined. as follows: ,in: The arithmetic mean of the magnitudes of the feature vectors of all nodes; Standard deviation of the magnitude of all node feature vectors; This is an adjustable threshold coefficient, for example, a value of 0.5. The specific value is determined based on engineering experience.

[0116] Based on the topological connectivity path corresponding to the candidate perturbation node, determine the constraints on the perturbation direction of the node;

[0117] It should be understood that the node disturbance direction constraint here refers to the constraint on the range of influence of the node disturbance on adjacent nodes and topological paths, ensuring that the implementation of the disturbance will not destroy the basic topological connectivity of the structure;

[0118] In practice, for any candidate perturbation node The constraint condition for the direction of its disturbance can be defined as:

[0119] Perturbations are only allowed to be applied along the topological path towards neighboring nodes with higher sensitivity.

[0120] If the sensitivity of adjacent nodes is lower than that of the candidate nodes, the direction of the adjacent node with the smallest sensitivity difference is selected to implement the perturbation in order to minimize the risk of local structural failure caused by the perturbation.

[0121] The action space is formed by combining node perturbation actions that satisfy the node perturbation direction constraints.

[0122] The node disturbance action determined by the above constraints is defined as follows: Among them, actions Represents a node to adjacent nodes Implement perturbations; Action set A is the set of feasible perturbation actions for all candidate perturbation nodes, i.e., the action space:

[0123] .

[0124] Based on the state space and action space, perform initial training of the agent's policy network to obtain initial policy network parameters;

[0125] Specifically, the initial training method for the policy network includes:

[0126] In the digital twin model, initial candidate disturbance nodes are selected and disturbed to obtain local displacement response data of the main load-bearing path after disturbance;

[0127] It should be noted that the initial candidate disturbance nodes are selected from a certain proportion (e.g., 20%) of node action pairs randomly selected from the action space, and disturbance simulation is performed one by one in the digital twin model to obtain the displacement response data of the main bearing path node area after each disturbance.

[0128] In practice, disturbance simulation involves applying a predetermined disturbance load along the rod direction of a selected node in a digital twin finite element model, and then solving the displacement response of the node after the disturbance through static analysis.

[0129] Based on the local displacement response data before and after the disturbance, assess the changes in local structural stiffness caused by the nodal disturbance;

[0130] The method for evaluating the change in local structural stiffness caused by nodal disturbances includes:

[0131] Before and after the disturbance node is applied, calculate the change in axial internal force of the directly connected members of the node.

[0132] In practice, axial internal force data for each member before and after the disturbance were obtained using finite element analysis tools:

[0133] The axial internal force of the rod before the disturbance is ;

[0134] The axial internal force of the rod after disturbance is .

[0135] Calculate the axial stiffness variation coefficient of each member based on the variation of axial internal force in the members;

[0136] It should be noted that the coefficient of variation of axial stiffness of the member here is defined as the ratio of the change in axial internal force to the original axial internal force:

[0137]

[0138] In the formula: Let be the coefficient of variation of the axial stiffness of the member 𝑖𝑗; These are the axial internal forces of the rods before and after the disturbance.

[0139] The weighted average of the axial stiffness variation coefficients of the connecting members at the disturbance node is taken as the local stiffness variation of the structure caused by the disturbance node; the specific calculation formula is as follows:

[0140]

[0141] In the formula: The value represents the local structural stiffness variation at node i. Let i be the set of all members directly connected to node i. Here is the axial stiffness coefficient of member 𝑖𝑗: ,in, The elastic modulus of the rod material. Let J be the cross-sectional area of ​​member j. Let j be the length of the rod.

[0142] The reward function value for node perturbation is determined based on the change in local structural stiffness of the perturbed node.

[0143] It is understandable that the reward function value is defined as a function of the change in the local stiffness of the structure, for example, it can be set to be proportional to the change in the local stiffness of the structure: ,in, is the reward function value for node perturbation; is the proportionality coefficient, for example, a value of 0.5, determined by engineering experience.

[0144] The initial value of the reward function is calculated based on the change in local stiffness of the structure, and the initial policy parameters are determined by training the policy network through backpropagation.

[0145] It should be understood that the policy network is a typical deep reinforcement learning network, and its specific structure adopts a policy gradient model based on neural networks. The input is the state vector in the state space, and the output is the probability distribution of each action in the action space.

[0146] Specifically, the initial value of the reward function is the determined reward function value. The policy network training process includes: using the agent's state vector As input to the policy network; the output of the policy network is the selection probability of actions in the action space. , where is the policy network parameter; and the reward function value is... As a goal-oriented approach to network training, the policy gradient algorithm is used for backpropagation updates of network parameters, with the specific optimization objective being to maximize the expected value of the reward function. The policy network parameters φ are updated using the Stochastic Gradient Ascent (SGA) algorithm, with the following specific update rules: Where: 𝛼 is the learning rate, typically ranging from 0.001 to 0.01, determined by model training experience; 𝑎 is the learning rate in state The specific action selected below.

[0147] Using the initial policy network parameters as initial values, an iterative node perturbation policy learning process is executed until the perturbation order of key nodes converges.

[0148] Specifically, the iterative node perturbation strategy learning process includes:

[0149] The agent selects the next perturbation node based on the current policy network parameters, executes the node perturbation, and obtains new structural displacement response data.

[0150] Specifically, the intelligent agent is in a state Below, based on the action probability distribution output by the current policy network. The next node perturbation action is selected using a random sampling method. The perturbation was then applied to the digital twin model to obtain new structural node displacement response data.

[0151] The reward function value is recalculated and updated using the structural displacement response data before and after the disturbance;

[0152] Specifically, the method for updating the reward function value is consistent with the above process, that is, based on the changes in axial internal forces of the connecting members before and after the disturbance, the changes in the local structural stiffness of the disturbed node are recalculated and the reward function value is updated: .

[0153] The agent's policy network parameters are updated using a reinforcement learning algorithm with the new reward function value.

[0154] The method for updating the agent policy network parameters using the reinforcement learning algorithm includes:

[0155] Construct an experience replay sample set containing multiple node perturbation state-action pairs;

[0156] It should be noted that the experience replay sample set D mentioned here is the set of experiences obtained by the agent in multiple perturbation simulation steps, and each experience sample is denoted as a quadruple: ,in: This is the current state; For the agent in state The action to be selected and implemented; To carry out the action The next state after that.

[0157] Randomly extract batch sample data from the experience replay sample set to obtain batch state-action pairs and corresponding reward function values;

[0158] The loss function of the policy network is calculated based on the cross-entropy loss between the action probability distribution output by the policy network and the actual action distribution of the sampled samples.

[0159] It should be understood that the loss function of the policy network here is defined as the cross-entropy loss between the actual action distribution of the batch samples and the output probability distribution of the policy network, that is:

[0160]

[0161] In the formula: Let be the loss function for the policy network parameters φ; For the policy network in state Down Output Action The probability of; State in the sample and The corresponding reward value; This represents the number of samples in the batch.

[0162] The policy network parameters are updated by backpropagation using the loss function until the policy network parameters converge.

[0163] In practice, the loss function is adjusted using a stochastic gradient descent algorithm (such as the Adam algorithm). The backpropagation strategy is executed to update the network parameters 𝜃. The specific update rules are as follows: Where: 𝛼 is the learning rate, determined by network training experience; the update process iterates repeatedly until the loss function converges, that is, the policy network parameter 𝜃 stabilizes within a small range of fluctuations.

[0164] Repeat the above steps of perturbation selection, response evaluation and policy update until the agent policy network parameters converge and the perturbation sequence of key nodes is determined.

[0165] It should be noted that the convergence of the policy network parameters is specifically manifested as follows: after multiple rounds of node perturbation simulation, reward function value update, and backpropagation training, the loss function value of the policy network parameters φ... If the value is less than a preset threshold; after the policy network parameters converge, based on the final parameters of the network, the key node perturbation sequence is determined through the following process: starting from the initial state of the structure, the agent selects perturbation nodes and implements perturbations step by step according to the action probability distribution output by the policy network; the state update after each perturbation is performed in accordance with the aforementioned method until the predetermined number of perturbation steps is met or the structural performance requirements are met; the selected nodes at each step are recorded to form the key node perturbation sequence. ,in: This indicates the node selected for perturbation in step t; T is the total number of perturbation steps, which is determined based on the actual engineering requirements and structural optimization objectives.

[0166] S104: Genetic algorithm is used to encode the node coordinates based on the perturbation sequence of key nodes, and the optimal position of the structural nodes is obtained through population iteration and fitness evaluation;

[0167] In specific implementation, the genetic algorithm encoding method for the node coordinates includes:

[0168] Based on the perturbation sequence of key nodes, determine the initial set of positions of the perturbation nodes;

[0169] In practice, the perturbation node set is composed of all the different nodes in the sequence. And obtain the coordinate position of each node in the initial digital twin finite element model as the initial position set: In the formula: Represents a node The three-dimensional coordinates of the structure in its initial state are typically represented as follows: .

[0170] Based on the initial set of perturbation node positions, a perturbation range constraint is set for the node positions, and the gene sequences of each chromosome in the initial population are randomly generated.

[0171] It should be noted that the gene sequence here refers to the encoding of a single chromosome in the genetic algorithm population, and the coordinates of the gene expression node location;

[0172] In practice, for each node The disturbance location is limited to a given range from the initial location. Typical disturbance range constraints are as follows:

[0173]

[0174]

[0175]

[0176] in: This is the allowable range of disturbance at the node position, typically taken as 1% to 5% of the initial node position, and determined based on engineering experience.

[0177] An initial population is randomly generated within the perturbation range, typically consisting of 20–50 individuals. The gene sequence of each individual (chromosome) is represented as follows:

[0178]

[0179] in, The gene sequence of the j-th chromosome; These represent nodes in the j-th chromosome. The coordinate location of the gene.

[0180] The fitness function value of each chromosome is determined based on the degree of influence of the change in the coordinates of the disturbed nodes on the connectivity of the main load-bearing path of the structure.

[0181] It should be noted that the fitness function here evaluates the impact of the node position change scheme represented by the chromosome on the performance of the main load-bearing path of the structure, specifically evaluating the improvement effect of the node disturbance position on the integrity and coherence of the main load-bearing path of the structure.

[0182] In practice, the fitness function is defined as:

[0183]

[0184] in: Chromosomes The fitness function value; This is an evaluation index for the integrity of the main load-bearing path of the structure, specifically calculated by the change in the stiffness sensitivity coefficient (or the magnitude of the nodal eigenvector) of the structure after nodal disturbance. For example:

[0185]

[0186] In the formula, The magnitude of the feature vector of the node after perturbation. This represents the magnitude of the initial node feature vector; a larger value indicates that the perturbation scheme can improve the integrity of the main bearer path. The primary carrier path continuity evaluation index is defined as: ,in, This refers to the set of edges in the topological knowledge graph of structural force paths. Let i be the feature vector of node i,j.

[0187] Based on the fitness function value, the selection, crossover and mutation operators of the genetic algorithm are used to iterate the population and obtain the final optimized node position;

[0188] The specific implementation includes the following sub-steps: Selecting individuals with high fitness from the current population using a roulette wheel selection or tournament selection method to serve as parents for the next generation; performing a crossover operation on the selected parents, typically using real-number encoded crossover methods such as arithmetic crossover or SBX crossover (simulated binary crossover), determined by engineering experience; performing a mutation operation on the crossover offspring, typically using real-number mutation operations such as uniform mutation or Gaussian mutation; obtaining a new generation population after the crossover and mutation operations, and repeating the above steps to evaluate fitness, select, crossover, and mutate the new population until the maximum number of iterations (e.g., 100 generations) is reached or the fitness function converges to a set threshold range; finally, obtaining the chromosome with the optimal fitness function. The optimal positions of the structural nodes are determined as follows: In the formula: This is the optimized set of coordinate positions of the disturbed nodes; This indicates the optimized coordinates of the node.

[0189] S105: Real-time monitoring of changes in the structural force path after disturbance, identification of areas where non-functional force paths are lost in the structure, and feedback to update the digital twin model;

[0190] In specific implementation, the method for identifying regions where non-functional force paths are lost includes:

[0191] Based on the nodal displacement response vector after disturbance, calculate the nodal displacement response change ratio coefficient;

[0192] It should be noted that the proportionality coefficient of nodal displacement response Defined as the relative change in the magnitude of the nodal displacement vector before and after the disturbance, the specific expression is as follows: ,in: To optimize the displacement response vector magnitude of node i; The magnitude of the displacement response vector of node i before (initial) disturbance;

[0193] Spatial distribution clustering of the proportional coefficients of nodal displacement response changes yields several displacement response change clustering regions;

[0194] In practice, K-means clustering or DBSCAN density clustering algorithm is used, based on the spatial coordinates of the nodes. For the clustering feature space, the displacement response change ratio coefficient The characteristic values ​​for clustering form several spatially distinct cluster regions: .

[0195] Regions in the clustering area whose average displacement response change ratio is lower than a set threshold are identified as initial non-functional regions.

[0196] It should be understood that the aforementioned threshold value... Typically, the smaller of the average of the displacement response scaling factors of all nodes in a cluster region (e.g., values ​​less than or close to 0) is taken, and this region is considered the initial non-functional region.

[0197] In practical implementation, if clustering regions The average displacement response scaling factor of all nodes satisfy: Then the area It is divided into initial non-functional areas (i.e. structurally weak areas).

[0198] Based on the connectivity of the initial non-functional regions in the topological knowledge graph, the final non-functional force path loss regions are extracted and confirmed.

[0199] In specific implementation, based on the initial set of non-functional region nodes, the structural force path topology knowledge graph obtained in step S102 is used. Connectivity analysis is performed: if the initial non-functional region forms a clear independent subgraph or subregion in the topological map, then the subgraph region is the finally determined non-functional force path loss region;

[0200] For example, by using graph connectivity analysis algorithms (such as DFS or BFS search) to determine connected components, the connected subgraph region corresponding to the initial set of non-functional region nodes in the topological graph is determined as the final non-functional force path lost region;

[0201] Once determined, the specific location and extent information of the lost non-functional force path regions are used to update the digital twin model: these regions are marked in the digital twin model as target regions for structural geometry adjustment in the next iteration.

[0202] S106: Repeat steps S102 to S105 until the integrity and continuity of the main load-bearing path of the structure meet the optimization threshold, and output the optimized geometries of the reticulated shell structure.

[0203] Specifically, the optimized geometries of the reticulated shell structure are the set of node coordinates for the optimized geometries, denoted as: ,in: The set of node position coordinates after meeting the optimization objective; N is the total number of nodes in the shell structure.

[0204] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters, weights, and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0205] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired or wireless network. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0206] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm, characterized in that, include: S101: Construct a digital twin model of a spatial reticulated shell structure, simulate the force flow distribution of structural nodes under complex loads in real time, and extract the force characteristic data of the nodes; S102: Generate a structural force path topology knowledge graph based on the node force characteristic data, and use a graph embedding algorithm to extract feature vectors that characterize the integrity and coherence of the main load-bearing path of the structure; S103: Using the aforementioned feature vector as input, and the integrity and coherence of the main structural bearing path as the reward function, a deep reinforcement learning algorithm is employed to determine the perturbation sequence of key nodes; including: Based on the feature vectors of the structural force path topology knowledge graph, the state space of the intelligent agent is constructed. The action space of the intelligent agent is constructed based on the perturbable nodes in the main load-bearing path of the structure. Based on the state space and action space, the agent's policy network is initially trained to obtain initial policy network parameters; including: In the digital twin model, initial candidate disturbance nodes are selected and disturbed to obtain local displacement response data of the main load-bearing path after disturbance; Based on the local displacement response data before and after the disturbance, assess the changes in local structural stiffness caused by the nodal disturbance; including: Before and after the disturbance node is applied, calculate the change in axial internal force of the directly connected members of the node. Calculate the axial stiffness variation coefficient of each member based on the variation of axial internal force in the members; The weighted average of the axial stiffness variation coefficients of the connecting members at the disturbance node is taken as the local stiffness variation value of the structure caused by the disturbance node. The initial value of the reward function is calculated based on the change in local stiffness of the structure, and the initial policy parameters are determined by training the policy network through backpropagation. Using the initial policy network parameters as initial values, an iterative node perturbation policy learning process is executed until the perturbation order of key nodes converges. S104: Genetic algorithm is used to encode the node coordinates based on the perturbation sequence of key nodes, and the optimal position of the structural nodes is obtained through population iteration and fitness evaluation; S105: Real-time monitoring of changes in structural force paths after disturbance, identification of areas where non-functional force paths are lost in the structure, and feedback updates to the digital twin model; including: Based on the nodal displacement response vector after disturbance, calculate the nodal displacement response change ratio coefficient; Spatial distribution clustering of the proportional coefficients of nodal displacement response changes yields several displacement response change clustering regions; Regions in the clustering area whose average displacement response change ratio is lower than a set threshold are identified as initial non-functional regions. Based on the connectivity of the initial non-functional regions in the topological knowledge graph, the final non-functional force path loss regions are extracted and confirmed. S106: Repeat steps S102 to S105 until the integrity and continuity of the main load-bearing path of the structure meet the optimization threshold, and output the optimized geometries of the reticulated shell structure.

2. The method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm according to claim 1, characterized in that, The method for extracting the nodal force characteristic data includes: In the digital twin model, a first preset load is applied to the spatial reticulated shell structure, and the initial displacement response vector of each node under the first preset load is calculated. Based on the magnitude of the initial displacement response vector of each node, the node region that exceeds the displacement response threshold is determined as the initial main bearing node region; For each node within the initial main bearing node area, the second preset working condition disturbance load is applied one by one, and the disturbance displacement response vector of each node under the action of the second preset working condition disturbance load is calculated respectively. The node stiffness sensitivity coefficient is determined by the ratio of the amplitude of the disturbance displacement response vector of each node under the second preset working condition disturbance load to the amplitude of the initial displacement response vector of the node, and the stiffness sensitivity coefficient is used as the stress characteristic data of the node.

3. The method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm according to claim 2, characterized in that, The method for determining the disturbance displacement response vector includes: Determine the set of members directly connected to the target node within the initial main load-bearing node region; Apply element member disturbance loads along the axial direction of each member in the set of member members connecting the target node, and construct the corresponding member disturbance conditions one by one; Calculate the element disturbance displacement response vector of the target node under each member disturbance condition, and determine the amplitude of the element disturbance displacement response vector; Select the member disturbance case whose amplitude exceeds the element disturbance response threshold, and then superimpose the element disturbance displacement response vectors under the selected member disturbance case to form the disturbance displacement response vector of the target node.

4. The spatial reticulated shell structure shape optimization method based on genetic algorithm according to claim 3, characterized in that, The method for generating the structural force path topology knowledge graph includes: Based on the node stiffness sensitivity coefficient, nodes with sensitivity coefficients higher than the sensitivity threshold are identified as graph nodes; Obtain all member connections in the spatial reticulated shell structure, and construct the initial topological connection relationship based on the member connection relationship; Starting from a graph node, search for valid paths between any two graph nodes one by one according to the initial topological connection relationship; A topology graph is generated based on the graph node pairs with valid paths, and each edge of the topology graph is assigned the difference in sensitivity coefficients between the corresponding nodes as the edge weight of the topology graph, thus obtaining the final structural force path topology knowledge graph.

5. The spatial reticulated shell structure shape optimization method based on genetic algorithm according to claim 4, characterized in that, The iterative node perturbation strategy learning process includes: The agent selects the next perturbation node based on the current policy network parameters, executes the node perturbation, and obtains new structural displacement response data. The reward function value is recalculated and updated using the structural displacement response data before and after the disturbance; The agent's policy network parameters are updated using a reinforcement learning algorithm with the new reward function value. Repeatedly execute the perturbation selection, response evaluation, and policy update steps until the agent's policy network parameters converge, thus obtaining a sequence of perturbations for key nodes.

6. The method for optimizing the shape of a spatial reticulated shell structure based on a genetic algorithm according to claim 5, characterized in that, The genetic algorithm encoding method for the node coordinates includes: Based on the perturbation sequence of key nodes, determine the initial set of positions of the perturbation nodes; Based on the initial set of perturbation node positions, a perturbation range constraint is set for the node positions, and the gene sequences of each chromosome in the initial population are randomly generated. The fitness function value of each chromosome is determined based on the degree of influence of the change in the coordinates of the disturbed nodes on the connectivity of the main load-bearing path of the structure. Based on the fitness function value, the selection, crossover and mutation operators of the genetic algorithm are used to iterate the population and obtain the final optimized node position.

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