Balancing crane structure design optimization method based on simulation analysis

Abstract

This invention specifically relates to a simulation-based optimization method for the structural design of a balancing crane, belonging to the field of mechanical structure optimization technology. The method includes: calculating the comprehensive weight scalar value of directed edges based on a topological graph theory model of the balancing crane; extracting a subset of main path nodes and performing a union operation to obtain a set of main path nodes and a set of secondary branch nodes. In this invention, the physical components of the balancing crane are abstracted as nodes, and the assembly relationships are abstracted as directed edges, constructing a topological graph theory model. The main path nodes and secondary branch nodes are automatically separated based on the comprehensive weight scalar value. The initial global stiffness matrix is ​​subjected to block permutation and algebraic dimensionality reduction using the static condensation principle, transforming the equilibrium equations of a large-scale system into low-dimensional equivalent equations containing only the master degrees of freedom for solution, thus avoiding the computational burden of repeatedly solving high-dimensional global stiffness matrices.

Description

Technical Field

[0001] This invention relates to the field of mechanical structure optimization technology, and in particular to a method for optimizing the design of a balance crane structure based on simulation analysis. Background Technology

[0002] Balancing cranes, as common mechanical assistive devices, are widely used in material handling, assembly, and manufacturing. During the structural design of balancing cranes, it is typically necessary to conduct simulation analysis and verification of their load-bearing capacity, motion accuracy, and overall stiffness. In existing technologies, the structural analysis of balancing cranes is mainly based on the finite element method. By establishing a whole-machine finite element model, the equilibrium equations corresponding to the global stiffness matrix are solved to obtain the displacement and stress field distributions of the structure under given working conditions. This method can accurately reflect the structural mechanical behavior and provide a basis for design improvements.

[0003] With the development of structural optimization design technology, simulation-based structural parameter optimization has gradually been introduced into the R&D process of balance cranes. However, balance cranes generally contain multi-link mechanisms and kinematic closed loops, which cause the system stiffness matrix to exhibit certain singularities or ill-conditioned characteristics, requiring additional constraint treatment when solving directly.

[0004] Meanwhile, when iteratively optimizing multiple design variables such as size and shape, repeatedly assembling and solving high-dimensional global stiffness matrices can lead to considerable computational resource consumption. Existing research attempts to reduce model dimensionality using substructure methods or super-element techniques, but automatically identifying the main propagation path and establishing efficient dimensionality reduction equations remains a challenge in practical engineering applications when dealing with non-tree-like topologies determined by assembly relationships.

[0005] Therefore, a method for optimizing the design of a balance crane structure based on simulation analysis is proposed. Summary of the Invention

[0006] The purpose of this invention is to propose a simulation analysis-based optimization method for the design of a balance crane structure in order to solve the above-mentioned problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] The simulation-based optimization method for the structural design of a balance crane includes: Extract the geometric feature information of physical components, abstract the physical components as nodes, construct directed edges based on physical assembly relationships and assign local stiffness matrices, eliminate kinematic loops to obtain the topological graph theory model of the balance crane; Based on the topological graph theory model of the balanced crane, the comprehensive weight scalar value of the directed edge is calculated, the main path node subset is extracted and the union operation is performed to obtain the main path node set and the secondary branch node set. The initial global stiffness matrix is ​​permuted based on the main path node set and the secondary branch node set to obtain the block matrix. The expression of the degree of freedom vector is extracted, the dimension-reduced equilibrium equation is constructed, and the equivalent dimension-reduced stiffness matrix and equivalent dimension-reduced load vector are calculated. Solving the dimension-reduced equilibrium equation yields the principal degree-of-freedom vector, which is then used to inversely derive the secondary degree-of-freedom vector. The global nodal displacement vector is then reconstructed, and the local nodal displacement components are extracted to calculate the stress tensor. The design variable vector is extracted to construct the objective function. The global nodal displacement vector and stress tensor are transformed into inequality constraint functions. The adjoint variable method is used to obtain the analytical gradient. The sequential quadratic programming algorithm is called to iterate the parameters and update the underlying database.

[0009] Preferably, the extraction of geometric feature information of physical components includes: The boundary geometric feature information is extracted from the 3D computer-aided design model file, and the volume, centroid coordinates and mass of the physical component are calculated by Gauss-Legends numerical integration. After initializing the graph data structure in computer memory, the adjacency matrix of the graph data structure is stored in a compressed sparse row format. In computer memory, arrays are maintained to store non-zero element values ​​in row-major order, arrays to store column indices, and arrays to store the starting positions of row offsets. A cache prefetching mechanism with contiguous memory addresses is used to improve data throughput.

[0010] Preferably, the elimination of kinematic loops to obtain the topological graph theory model of the balancing crane includes: A backward edge detection algorithm based on depth-first search is used to identify closed loops composed of node sequences. The nominal internal forces transmitted by each edge in the closed loop are calculated. The edge corresponding to the driven link with the minimum force in the closed loop is identified and disconnected. Two virtual nodes with overlapping spatial positions are generated at the disconnection point. Multi-point constraint equations are introduced between the two virtual nodes to ensure displacement compatibility and force balance at the disconnection point. The Lagrange multiplier method is used to embed the multi-point constraint equations into the system equilibrium equations.

[0011] Preferably, the process of calculating the scalar value of the directed edge comprehensive weight based on the balanced crane topological graph theory model includes: Extract the local stiffness matrix corresponding to the directed edge and calculate the sum of the main diagonal elements of the local stiffness matrix as the trace of the local stiffness matrix. Calculate the Euclidean distance between the connected nodes in the global coordinate system. The formula for calculating the comprehensive weight scalar value of the directed edge based on the trace of the local stiffness matrix and the Euclidean distance is as follows: ; in, Represents a directed edge The comprehensive weight scalar value; Represents a directed edge The trace of the local stiffness matrix; This represents the maximum value of the trace of the local stiffness matrix for all edges in the entire graph; Represents a node and nodes The spatial Euclidean distance between them; This represents the minimum distance between all connected nodes in the entire graph; and Assign coefficients to the weights, and satisfy the following conditions: .

[0012] Preferably, the step of extracting a subset of main path nodes and performing a union operation includes: Set the node representing the end spreader as the starting node and the node representing the base as the target node, and initialize a boolean array to mark the node access status; Push the starting node onto the path stack. Sort the unvisited adjacent nodes in descending order of their comprehensive weight scalar value. Select the node pointed to by the edge with the largest comprehensive weight scalar value and push it onto the path stack. Upon reaching the target node, a backtracking operation is performed. The dynamic weight threshold is set as a specific proportion of the statistical average of the weights of the discovered main path edges. When the cumulative weight of the branch path is lower than the dynamic weight threshold, a pruning operation is performed. Assign binary masks to nodes and perform a union operation on subsets of main path nodes under all typical job conditions using bitwise OR operations.

[0013] Preferably, the process of permuting the initial global stiffness matrix to obtain the block matrix includes: Construct a Boolean permutation matrix in computer memory, and use the permutation matrix to reorder the global node displacement vectors. Arrange the degrees of freedom belonging to the main path node set in the first half of the vector to form the main degree of freedom vector, and arrange the degrees of freedom belonging to the secondary branch node set in the second half of the vector to form the secondary degree of freedom vector. Simultaneously, the permutation matrix is ​​used to perform a permutation operation on the global node load vector to obtain the master node load vector and the slave node load vector; By performing a row and column double permutation operation on the initial global stiffness matrix using the permutation matrix and its transpose, and based on the reciprocity theorem of linear elasticity, it is determined that the cross-coupled stiffness submatrix of the master degree of freedom to the slave degree of freedom is equal to the transpose of the cross-coupled stiffness submatrix of the slave degree of freedom to the master degree of freedom.

[0014] Preferably, the extraction of the degree-of-freedom vector expression and the construction of the dimensionality-reduced equilibrium equation includes: Regularization constants are uniformly superimposed on the main diagonal elements of the self-stiffness submatrix of each degree of freedom. The resulting self-stiffness submatrix is ​​then subjected to Chorsky decomposition, and the product terms are solved using forward and backward substitution algorithms. The formulas for calculating the equivalent reduced-dimensional stiffness matrix and the equivalent reduced-dimensional load vector are as follows: ; ; in, Represents the equivalent reduced-dimensional stiffness matrix; This represents the self-stiffness submatrix between the main degrees of freedom; This represents the cross-coupling stiffness submatrix from the degree of freedom to the master degree of freedom; This represents the inverse matrix of the stiffness submatrix from the degrees of freedom; This represents the cross-coupling stiffness submatrix between the master degree of freedom and the slave degree of freedom; Represents the equivalent dimension-reduced load vector; Represents the master node load vector; This represents the load vector from the node.

[0015] Preferably, the process of solving the dimensionality-reduced equilibrium equation to obtain the master degree of freedom vector includes: The initial guessed solution vector is set to be an all-zero vector and the initial residual vector is calculated. An incomplete Cholsky decomposition is used to construct a preprocessing matrix to improve the eigenvalue distribution of the equivalent dimension-reduced stiffness matrix. The preprocessing conjugate gradient method is combined with the preprocessing matrix to iteratively solve the main degree of freedom vector. The formula for extracting local nodal displacement components to calculate the stress tensor is as follows: ,in Represents the stress tensor of a local region. Represents the elastic constitutive matrix of the material. Represents the geometric strain-displacement matrix. This represents the local nodal displacement components.

[0016] Preferably, the transformation of the stress tensor into an inequality constraint function includes: The stress tensor is converted into a von Mises equivalent stress scalar value. This scalar value is then divided by the allowable stress constant of the material to achieve dimensionless processing, thus constructing an inequality constraint function. The formula for obtaining the analytical gradient using the adjoint variable method is as follows: ; in, Indicates the first The displacement constraint function for the first Partial derivatives of each design variable; Represents the adjoint vector; its superscript Indicates transpose; This represents the partial derivative of the equivalent reduced-dimensional load vector with respect to the design variables; This represents the partial derivative of the equivalent reduced stiffness matrix with respect to the design variables; This represents the main degree of freedom vector.

[0017] Preferably, the step of invoking the sequential quadratic programming algorithm for parameter iteration includes: Construct a Lagrangian function to approximate the nonlinear programming problem as a quadratic programming subproblem to find the search direction vector. Then, use a quasi-Newton method to successively update the Hessian matrix approximation matrix. The update formula is as follows: ; in, This represents the updated approximate Hessian matrix; This represents the approximate Hessian matrix for the current iteration step; This represents the difference vector of the gradients of the Lagrange function; Represents the difference vector of design variables; superscript Indicates the number of iterations; One-dimensional line search technology is used to determine the iteration step size and update the design variable vector. Caro-Kuhn-Tucker convergence judgment is performed. When the relative rate of change of the objective function is less than the preset minimum threshold and the maximum violation of all constraint functions is less than the preset tolerance, the convergence condition is determined to be met.

[0018] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This invention constructs a topological graph theory model by abstracting the physical components of the balance crane as nodes and the assembly relationship as directed edges. It automatically separates the main path nodes and secondary branch nodes based on the comprehensive weight scalar value. It uses the static condensation principle to perform block permutation and algebraic dimensionality reduction on the initial global stiffness matrix, transforming the equilibrium equation of the large-scale system into a low-dimensional equivalent equation containing only the master degree of freedom for solution, thus avoiding the computational burden caused by repeatedly solving the high-dimensional global stiffness matrix.

[0019] 2. This invention obtains the analytical gradient of the constraint function by employing the adjoint variable method during the optimization iteration process, eliminating the need for multiple perturbation simulations for each design variable and further reducing the computational overhead of sensitivity analysis. Furthermore, by covering typical operating conditions through the union operation of subsets of main path nodes, it ensures the good applicability of the dimensionality reduction model under different orientations. While maintaining the accuracy of engineering analysis, it significantly reduces the computational resources and time costs required for structural optimization, strongly supporting multi-round, multi-parameter design iteration processes. Attached Figure Description

[0020] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which: Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0021] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0022] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0023] Example 1 Its specific implementation method is combined with the appendix Figure 1 Please provide a detailed explanation.

[0024] Appendix Figure 1 The flowchart of the simulation analysis-based balanced crane structure design optimization method provided in the embodiments of the present invention shows the complete steps from extracting the geometric feature information of physical components to calling the sequential quadratic programming algorithm to iterate parameters and update the underlying database.

[0025] In this embodiment, it includes: Step 1: Construction of the topological graph theory model of the balancing crane: Extract the geometric feature information of the physical components, abstract the physical components into nodes, construct directed edges according to the physical assembly relationship and assign local stiffness matrices, and eliminate kinematic loops to obtain the topological graph theory model of the balancing crane; The core purpose of this step is to break away from the conventional approach of directly meshing the three-dimensional solid geometric model in traditional finite element analysis, and instead establish an abstract mathematical data structure in computer memory that can accurately map the physical connection relationship and mechanical transmission characteristics of the balancing crane.

[0026] By introducing graph theory, complex mechanical assemblies are transformed into directed acyclic graphs, laying the underlying data foundation for subsequent dimensionality reduction calculations.

[0027] In the specific computer execution process, it is first necessary to collect and analyze the basic structural data of the balance crane in an extremely detailed manner.

[0028] A balance crane typically consists of several physical components, including a base, slewing column, boom, forearm, parallelogram linkage mechanism, counterweight, and end effector. The system reads the 3D computer-aided design (CAD) model files of these components (e.g., STEP or IGES standard format files) and extracts the boundary geometric features of each component. Based on this, the system initializes a graph data structure in memory. ,in The set of nodes in a graph. The set of edges representing a graph.

[0029] The system iterates through all the physical components of the balancer, abstracting each component with independent kinematic characteristics as a node in the graph. ( The node is assigned an integer index number, with values ​​ranging from... (Total number of components).

[0030] To ensure mechanical equivalence, nodes The spatial coordinates are strictly set to the coordinates of the centroid of the corresponding physical component. The computer's underlying layer calculates the component's volume, centroid coordinates, and mass precisely by performing Gauss-Legendary numerical integration on the component's three-dimensional closed geometry.

[0031] In computer memory, a contiguous block of storage is allocated for each node to store its attribute vector. This attribute vector contains not only the node's three-dimensional coordinates in the global Cartesian coordinate system, but also... It also includes lumped mass scalar data for the component. And the moment of inertia tensor data about its three principal axes in its local coordinate system. Moment of inertia tensor It is a 3×3 symmetric matrix containing moments of inertia about three orthogonal axes. and inertial product .

[0032] In this way, the continuous mass distribution is discretized into concentrated inertial properties on the nodes, which greatly reduces the number of parameters required to describe the structure, while fully preserving the dynamic characteristics of the components when they move in space.

[0033] After determining the node set, the system needs to construct the edge set based on the physical assembly relationships between the components of the balance crane. .

[0034] If there is a direct mechanical connection between two physical components (such as a hinged pin connection, a flange bolt rigid connection, or a sliding guide rail connection), then at the corresponding two nodes... and Generate an edge between them .

[0035] To reflect the direction of load transfer, this scheme assigns strict directionality to edges. The direction is defined as: from the end of the load application (i.e., the node where the end-effector is located) to the foundation fixing end (i.e., the node where the base is located). This directionality makes the entire graph structure exhibit a clear hierarchical progression, indicating the search direction for subsequent graph traversal algorithms.

[0036] The system needs to provide each edge Assign a matrix of mechanical properties; Since the connection method of the balance crane is mostly hinged, the system defines a sixth-order local stiffness matrix in the edge properties. .

[0037] This matrix is ​​a 6×6 square matrix, whose diagonal elements represent the stiffness values ​​of the three translational degrees of freedom (X, Y, Z directions) and three rotational degrees of freedom (about the X, Y, Z axes) along the local coordinate system. For an ideal frictionless hinged connection, its rotational stiffness about the hinge axis should theoretically be zero.

[0038] However, when a computer performs matrix inversion or decomposition operations, the presence of absolute zero elements on the diagonal can lead to matrix singularities, which in turn can cause the program to crash.

[0039] Therefore, the system introduces numerical regularization here, setting the stiffness value corresponding to this rotational degree of freedom to a very small non-zero constant. (For example, the value is) Newton-meters per radian.

[0040] This extremely small constant is physically equivalent to introducing a very weak torsional spring, whose effect on the overall mechanical response is negligible. However, at the purely mathematical level, it successfully prevents matrix singularity problems in numerical calculations. The stiffness values ​​of the other five degrees of freedom in the local stiffness matrix are analytically calculated and assigned based on the material's elastic modulus, shear modulus, and geometric dimensions (such as diameter and contact length) of the actual pin.

[0041] Parallelogram linkage mechanisms are widely used in balance crane structures to maintain the stability of the end-end lifting device.

[0042] In graph theory models, this structure forms closed kinematic loops, violating the mathematical properties of directed acyclic graphs and causing subsequent tree traversal algorithms to fail and fall into infinite loops.

[0043] To address this issue, the system introduces a kinematic loop elimination mechanism based on the principle of virtual work when constructing the graphical model.

[0044] When the system identifies a closed loop consisting of a sequence of nodes in the graph using a depth-first search backward edge detection algorithm, the algorithm automatically calculates the nominal internal force transmitted by each edge in the loop and identifies the edge corresponding to the driven link with the minimum force. The system then disconnects this edge in memory and generates two virtual nodes that completely overlap in spatial location at the disconnection point. Subsequently, the system introduces a set of multi-point constraint equations between these two virtual nodes.

[0045] Assume these two virtual nodes are respectively and Their displacement vectors are respectively and Then the multi-point constraint equation can be expressed as During the subsequent assembly of the global stiffness matrix, the system uses the Lagrange multiplier method to embed the constraint equation into the system equilibrium equation.

[0046] The constraint equation mathematically guarantees the displacement compatibility and force balance at the breakpoint, but eliminates physical loops in the graph's topological data structure, making the graph... It strictly satisfies the mathematical definition of a directed acyclic graph.

[0047] To achieve efficient memory access in subsequent calculations, the system resolutely avoids using intuitive but space-consuming two-dimensional arrays to store graph adjacency relationships. For a complex assembly containing thousands of nodes, a two-dimensional array would generate a large number of zero elements, resulting in significant memory waste. This solution employs a highly optimized compressed sparse row format from computer science to store the graph's adjacency matrix. .

[0048] Adjacency matrix elements The definition is as follows: ; in, The adjacency matrix is ​​the first... Line number The element values ​​of the column; Indicates the starting node of a directed edge; This represents the terminating node of a directed edge.

[0049] In compressed sparse line format, the system maintains three one-dimensional arrays in memory: The `values` array stores the values ​​of all non-zero elements in the adjacency matrix in row-major order (all are 1 in this example).

[0050] The `column_indices` array stores the column index of each element in the `values` array in the original adjacency matrix. .

[0051] The row_pointers array stores the starting index of the first non-zero element in each row of the original adjacency matrix in the values ​​array.

[0052] Through this low-level data processing method, the system only records information about the non-zero elements in the matrix. This storage structure not only greatly reduces the memory footprint of the topological model, but also allows the central processing unit (CPU) to achieve extremely high data throughput during graph traversal by utilizing a cache prefetching mechanism with contiguous memory addresses. This enables the computer to complete the construction and resident memory of the topological graph theory model in milliseconds with extremely low memory consumption, even when faced with complex balancing assemblies containing hundreds or thousands of tiny parts.

[0053] Step 2: Identification and extraction of main load transfer path: Based on the topological graph theory model of the balanced crane, calculate the comprehensive weight scalar value of the directed edge, use the depth-first search algorithm to extract the subset of main path nodes and perform the union operation to obtain the set of main path nodes and the set of secondary branch nodes; After constructing the topological graph model of the balancing crane, this step aims to automatically identify the critical paths in the structure that bear the main load transfer tasks using computer algorithms. In complex mechanical systems, not all components participate in load transfer to an equal degree; many auxiliary links, counterweight supports, sensor mounting brackets, or housing decorations bear only minimal internal forces.

[0054] Placing these secondary components at the same level as the main load-bearing components for high-precision finite element calculations would result in a severe waste of computational resources and lead to excessively high dimensionality of the equations. Therefore, this step uses a graph traversal algorithm to divide the structure into "main paths" and "secondary branches," providing clear targets for subsequent degree-of-freedom condensation.

[0055] To quantify the importance of each edge in load transfer, the system first needs to define the graph. Each directed edge in Define a comprehensive weight function .

[0056] The weighting function cannot rely solely on a single geometric parameter; it must comprehensively reflect the mechanical impedance characteristics and spatial distribution features of the structure. The system extracts edges. Corresponding local stiffness matrix The trace of the stiffness matrix is ​​calculated, which is the sum of the elements on the main diagonal. In mechanical terms, the trace of the stiffness matrix represents a comprehensive measure of the connection's ability to resist deformation in each degree of freedom. The larger the trace value, the stronger the connection is, and the more likely it is to become the main channel for load transfer.

[0057] Meanwhile, system computing nodes and nodes Euclidean distance in global coordinate system Edge weight function The core calculation formula is defined as follows: ; in, Represents a directed edge The comprehensive weight scalar value; Representing an edge The trace of the local stiffness matrix; This represents the maximum value of the local stiffness matrix trace of all edges in the entire graph. This parameter is used to perform dimensionless normalization on the stiffness term to ensure that its value range is between 0 and 1. Represents a node and nodes The Euclidean distance between them is calculated using the following formula: ; This represents the minimum distance between all connected nodes in the entire graph, and is used to normalize the distance term. and Let be dimensionless weighting coefficients, and strictly satisfy . .

[0058] These two coefficients are usually set according to the specific working conditions of the balancer. When the focus is on stiffness transfer, they are assigned... Larger values ​​(e.g., 0.7) are assigned Smaller values ​​(e.g., 0.3).

[0059] The physical meaning of this formula is that the side with greater stiffness and shorter spatial distance has a stronger ability to transmit loads, and therefore is given a higher weight value.

[0060] After calculating the weights of all edges, the system uses an improved depth-first search algorithm to extract the main load transfer path.

[0061] Algorithm initialization phase: The system sets the node representing the end effector as the starting node for the search. Set the node representing the base as the target node for the search. .

[0062] Initialize an empty set of main path nodes in computer memory. and an empty set of secondary branch nodes .

[0063] At the same time, a path stack based on the Last-In-First-Out (LIFO) principle is initialized to record the current search trajectory, and a boolean array visited is initialized to mark whether each node has been visited to prevent repeated traversal.

[0064] The iterative execution phases of the algorithm are as follows: The system starts from the starting node To begin, push it onto the path stack and mark it as visited (set to True) in the visited array. The system checks all out-degree adjacent nodes of the current top node in the stack. If there are unvisited adjacent nodes, the system will use the pre-calculated edge weights in memory. ; Traditional depth-first search randomly selects a branch to explore, while this scheme improves upon this by introducing a greedy strategy. The system searches for all feasible adjacent nodes according to their edge weights. The system performs a quicksort from largest to smallest. After sorting, it prioritizes the node pointed to by the edge with the largest weight as the next node to be visited, pushes it onto the path stack, and marks it as visited. This process is repeated until the search reaches the target node. At this point, the node sequence recorded in the path stack constitutes a high-weight load transfer backbone from the lifting device to the base. The system adds all nodes on this path to the main path node set. middle; Upon reaching the target node, the system performs a backtracking operation, popping the top node from the stack, returning to the previous node, and checking if the node has any other unvisited adjacent nodes. During the backtracking and exploration of new branches, the system sets a dynamic weight threshold. This threshold is set as a specific percentage (e.g., 60%) of the statistical average of the weights of all discovered main path edges. If the cumulative weight of a branch path falls below this threshold, the system classifies that branch as a non-critical load transfer path. Nodes on these branches are then categorized into the secondary branch node set. If the branch is not found, further depth searching of that branch is immediately stopped, and a pruning operation is performed. This pruning mechanism greatly improves the efficiency of graph traversal, avoids exhaustive search of large graph structures, and saves a lot of computation time.

[0065] Considering that balance cranes experience various dynamic working conditions such as lifting, slewing, and luffing in actual operation, the direction and magnitude of the load will change significantly, resulting in the main load transmission path not being constant.

[0066] To ensure the extracted paths have comprehensive applicability, the system pre-sets load vectors for multiple typical operating conditions in the computer. For each typical operating condition, the system dynamically adjusts the coefficients in the edge weight function according to the direction of the load vector. and Then, the improved greedy depth-first search algorithm described above is run independently once to obtain the subset of main path nodes under this working condition. .

[0067] Finally, the system performs a mathematical union operation on the subsets of main path nodes obtained under all operating conditions: ; In this formula: This represents the final set of global main path nodes; This represents the total number of typical operating conditions; Indicates the first The main path node subset is extracted under typical working conditions. When implementing the union operation at the computer level, the system uses bitmasking technology. Each node is assigned a bitmask of length... The binary mask of the 1st bit, the 2nd bit A bit value of 1 indicates that the node is in the [number]th position. In this case, it belongs to the main path. Finally, simply perform a bitwise OR operation on the masks of all nodes; as long as the mask is not all zeros, the node is included. .

[0068] This envelope extraction method ensures that all nodes that have undertaken the main load-bearing task under any typical working condition are accurately included in the main path set. Nodes not selected under any working condition are ultimately identified as secondary branch nodes and retained in the main path set. In the collection.

[0069] Thus, through graph theory modeling and algorithmic traversal, the system decouples the complex physical structure of the balancing crane at the logical level into a main path skeleton that undertakes the core mechanical response and secondary branches that play an auxiliary role.

[0070] The results of this data processing are stored in the computer's cache, providing a precise node index mapping table for the next step of condensing the degrees of freedom of non-critical branches. This clears the way for subsequent large-scale matrix dimensionality reduction operations while ensuring computational accuracy.

[0071] Step 3: Non-critical branch degree of freedom aggregation: Based on the set of main path nodes and the set of secondary branch nodes, the initial global stiffness matrix is ​​permuted to obtain the block matrix, the degree of freedom vector expression is extracted, the dimension-reduced equilibrium equation is constructed, and the equivalent dimension-reduced stiffness matrix and equivalent dimension-reduced load vector are calculated. The core objective of this step is to map and condense the mechanical degrees of freedom of the secondary branch node set (i.e., non-critical auxiliary structures) identified in Step Two onto the main path node set (i.e., the core load-bearing skeleton) through rigorous algebraic transformations. In traditional finite element analysis, the degrees of freedom of all nodes participate in the assembly and joint solution of the global stiffness matrix, which leads to an exponential expansion of the matrix dimension and easily causes computer memory overflow.

[0072] This scheme introduces an improved static condensation algorithm to reduce the dimensionality of the system equations in computer memory, thereby significantly reducing the order of the system of algebraic equations to be solved.

[0073] Before performing the condensation operation, the system first needs to assemble the initial global static equilibrium equations in the computer memory.

[0074] This equation can be expressed in standard linear algebraic form: .in, The initial global stiffness matrix, This is the global node displacement vector. This represents the global node payload vector. The system classifies nodes based on the node classification results output in step two (i.e., the main path node set). and secondary branch node set Construct a Boolean permutation matrix in memory. .

[0075] The purpose of this permutation matrix is ​​to apply the global displacement vector. Reordering and partitioning are performed. This is done by performing matrix multiplication. The system extracts the degrees of freedom belonging to the set of main path nodes and arranges them in the first half of the vector to form the main degree of freedom vector. (subscript) (Representing Master); extract the degrees of freedom belonging to the set of secondary branch nodes and arrange them in the latter half of the vector to form the degree-of-freedom vector. (subscript) (Represents Slave). Corresponding to the rearrangement of the displacement vector, the system synchronizes the global nodal load vector in memory. Perform the same permutation operation The master node load vector is obtained. and the load vector from the node .

[0076] The system needs to handle a large initial global stiffness matrix. Perform a double permutation operation of rows and columns, i.e., calculate .

[0077] After rearrangement, the initial static equilibrium equations are transformed into the following second-order block matrix form: ; In this formula: The self-stiffness submatrix represents the stiffness characteristics of the main skeleton itself. The self-stiffness submatrix represents the stiffness characteristics of the attached structure itself. The cross-coupling stiffness submatrix from the degree of freedom to the master degree of freedom reflects the mechanical influence of the auxiliary structure on the main skeleton. This represents the cross-coupling stiffness submatrix of the master degrees of freedom and the slave degrees of freedom. According to the reciprocity theorem of linear elasticity, the matrix... Strictly equal to matrix The transpose of the matrix, i.e. .

[0078] In order to mathematically completely eliminate the vector of degrees of freedom The explicit expression of the above block matrix equation is obtained by performing an algebraic expansion on the second row of the system:

[0079] Through pure algebraic rearrangement and matrix inversion operations, the system extracts the vectors of degrees of freedom from the computer. The parsing expression:

[0080] This Substituting the expression into the first row of the block matrix equation (i.e.) In the process of combining like terms and algebraic simplification, the system is constructed to contain only the main degree of freedom vector. The dimensionality reduction equilibrium equation: ; In this dimensionality-reduced equilibrium equation, the core is the equivalent dimensionality-reduced stiffness matrix. The formula for calculating (known mathematically as Schul complement) is defined as follows: ; Meanwhile, the core equivalent dimensionality reduction load vector The calculation formula is defined as follows: ; The parameters in the two core formulas above are defined as follows: This represents the dimension-reduced stiffness matrix that is equivalently mapped onto the main path node after the degree-of-freedom condensation operation. This represents the reduced-dimensional load vector that is equivalently mapped to the main path node after the degree-of-freedom condensation operation. It represents the inverse matrix of the stiffness submatrix from the degrees of freedom.

[0081] In actual computer execution, the higher-order self-stiffness submatrices of the degrees of freedom are directly processed. Perform the inverse operation (i.e., explicit calculation) This process consumes an extremely large number of CPU clock cycles and, due to the limitations of floating-point precision, is highly prone to accumulating numerical truncation errors. To improve data processing efficiency, the system does not directly calculate the inverse matrix but instead uses the Cholsky decomposition algorithm.

[0082] because Possessing the mathematical property of symmetric positive definiteness, the system decomposes it into a lower triangular matrix. Its transpose The product form, i.e. .

[0083] Subsequently, the system directly solves for the product term using efficient forward and backward substitution algorithms. and The numerical results.

[0084] In order to calculate The system first solves Obtain the intermediate matrix Then solve Get the final .

[0085] This purely algebraic algorithm replacement reduces the computational complexity of the condensation process from... Significantly reduced to level.

[0086] Furthermore, regarding the potential rigid body displacement trends in certain local mechanisms of the balancer (such as unconstrained links), which may lead to... (If the matrix is ​​close to singular and the condition number is too large), the system will perform the Cholsky decomposition beforehand. A very small regularization constant is uniformly superimposed on the main diagonal elements. The strategy for determining the value of this constant is as follows: .

[0087] This tiny numerical perturbation effectively ensures the absolute stability of the matrix decomposition process without affecting the overall mechanical accuracy, thus preventing the computer program from crashing due to division by zero errors.

[0088] Step 4: Calculation of mechanical response of the dimensionality-reduced system: Solve the dimensionality-reduced equilibrium equation to obtain the master degree of freedom vector, inverse the slave degree of freedom vector, reconstruct the global nodal displacement vector, extract the local nodal displacement components and calculate the stress tensor; After the third step of the degree-of-freedom condensation process, the huge balancing crane system, which originally contained hundreds of thousands or even millions of degrees of freedom, was successfully compressed into a compact mathematical model that only retained the degrees of freedom of the core main path nodes.

[0089] This step aims to efficiently solve the algebraic equations for this dimension-reduced system, and then recover the displacement and stress fields of the entire system through an inversion mapping mechanism, thereby completing a comprehensive evaluation of the mechanical response of the balancing crane.

[0090] The system first needs to solve the dimension-reduced equilibrium equation constructed in step three. .

[0091] Due to the dimensionality reduction stiffness matrix The order of the has been significantly reduced, and the distribution of its non-zero elements is more dense. The system calls the preprocessed conjugate gradient solver to perform iterative solution.

[0092] During the initialization phase of iterative solution, the system sets an initial guessed solution vector. Given a vector of all zeros, calculate the initial residual vector. .

[0093] To accelerate convergence, the system employs incomplete Cholsky decomposition to construct the preprocessing matrix. This preprocessing matrix can effectively improve the eigenvalue distribution of the dimensionality-reduced stiffness matrix, reduce its condition number, and make the search direction of the conjugate gradient method more quickly approach the true solution.

[0094] In each iteration, the system calculates the preprocessed residual vector. And update the search direction vector. .

[0095] System calculates step size scalar and update the displacement vector. and the new residual vector .

[0096] The system sets the residual convergence tolerance (e.g., relative residual norm). ).

[0097] When the convergence condition is met, the iteration terminates, and the system can obtain the main degree of freedom vector in a very short computation time. A high-precision numerical solution. This numerical solution represents the spatial displacement response of the main load-bearing frame of the balance crane under the current operating load.

[0098] After obtaining the main degrees of freedom vector Then, the system needs to map the displacement response back to those secondary branch nodes that were condensed.

[0099] The analytical expression derived from the degrees of freedom in step three of the system call: ; Due to the product term and The calculations in step three, which have already been computed and cached in computer memory, mean that the system only needs to perform simple matrix and vector multiplication and vector subtraction operations to extremely quickly invert the vectors of freedom. Numerical solution.

[0100] The system uses the permutation matrix established in the initial stage of step three. The inverse mapping relationship will transform the main degree of freedom vectors and from the vector of degrees of freedom The balance crane was reassembled and reassembled according to its original global node numbering order. This memory reorganization operation restored the complete global node displacement vector. This marks the successful acquisition of the spatial displacement field of the entire system.

[0101] The displacement field is only the basis of the mechanical response. In order to evaluate the strength and safety of the balancing crane structure, the system must further calculate the stress distribution inside each component.

[0102] The system traverses each edge (representing a physical connection or finite element) in the topological graph theory model of the balancing crane and extracts its corresponding local nodal displacement components. Based on the fundamental equations of elasticity, the stress tensor of this local region is calculated systematically. .

[0103] The stress calculation formula is defined as follows: ; In this formula: The stress tensor representing a local region is usually represented by the Voigt notation as a column vector containing normal stress and shear stress components (e.g., a 6×1 column vector in a three-dimensional solid element). The constitutive matrix of the material represents the elastic modulus of the steel used in the balancing crane components. Compared with Poisson Uniquely certain; The geometric strain-displacement matrix is ​​represented by the elements of which are obtained analytically from the spatial coordinates of the local nodes using the partial derivatives of the shape functions. Represents the displacement vector from the global nodes The extracted node displacement column vectors related to the current local region.

[0104] The dimension depends strictly on the number of nodes in the local unit and the number of degrees of freedom of each node; For example, in a commonly used two-node spatial beam element in a balancing lifting linkage mechanism, each node has 6 degrees of freedom. The dimension is a 12×1 column vector; for a four-node tetrahedral solid element, each node has 3 translational degrees of freedom, then... Its dimension is a 12×1 column vector.

[0105] The system will calculate the stress tensor The values ​​are converted to the von Mises equivalent stress scalar values ​​commonly used in engineering. For areas prone to stress concentration in the balanced crane structure, such as the edges of parallelogram connecting rod hinge holes and the variable cross-section area at the root of the boom, the system establishes a dedicated monitoring array in memory to record the peak equivalent stress in these areas in real time.

[0106] In actual operation, balance cranes face a combination of various actions such as hoisting, luffing, and slewing, resulting in a vast array of dynamic working conditions. This is due to the reduced stiffness matrix constructed in step three of this solution. It is only related to the geometry and material properties of the structure, and is completely independent of external loads, thus exhibiting a significant advantage when dealing with multi-condition calculations. The system operates in a multi-threaded parallel processing mode within the computer.

[0107] For each new independent load case, the system only needs to reassemble the global load vector according to the boundary conditions of that load case. And perform a rapid load condensation operation to obtain new Subsequently, each thread independently calls the pre-decomposed dimensionality-reduced stiffness matrix and performs forward substitution and backward replacement operations in parallel, thereby instantly obtaining the main degrees of freedom displacements under all working conditions, and further reproducing the displacement field and stress field of the entire system in parallel.

[0108] Step 5: Iteration and Update of Structural Dimension Parameters: Extract the design variable vector to construct the objective function, transform the global nodal displacement vector and stress tensor into inequality constraint functions, use the adjoint variable method to obtain the analytical gradient, call the sequential quadratic programming algorithm to iterate the parameters and update the underlying database; Based on the high-precision reduced-dimensional mechanical response data obtained in step four, a purely mathematical nonlinear programming model is constructed inside the computer.

[0109] By introducing analytical sensitivity analysis and sequential quadratic programming algorithm, the design variables such as the cross-sectional dimensions and plate thickness of each component of the balance crane are automatically iterated.

[0110] This process completely abandons the trial-and-error method that relies on human experience, and does not require calling any machine learning black box models. Instead, it relies on rigorous calculus and matrix algebra operations to find the target solution that minimizes the overall mass of the balance crane under the premise of satisfying all mechanical strength and stiffness constraints, and finally maps the mathematical solution back to the physical model.

[0111] Design variable extraction and multidimensional mathematical programming model construction: The system first extracts the geometric parameters to be optimized from the topological graph theory model of the balance crane, and defines them as a continuous vector of design variables. .

[0112] in, Indicates the total number of design variables; It can represent geometric dimensions such as the thickness of the steel plate in the box section of the boom, the diameter of the solid cylinder of the parallelogram connecting rod, the width of the base support flange, or the radius of the hinge pin.

[0113] To prevent dimensions from deviating from engineering realities during the iteration process (such as negative thickness, excessive thinness leading to local buckling, or dimensions exceeding the limits of the machining tools), the system sets upper and lower boundary conditions for each design variable: ; in, To design the lower bound column vector of variables, This is the upper limit column vector for design variables.

[0114] The system constructs an objective function oriented towards minimizing the overall mass of the balance crane. .

[0115] The objective function is obtained by traversing all nodes and edges in the graph theory model and accumulating the mass of each component: ; In this formula: This represents the total mass of the balance crane system. This indicates the total number of physical components included in the balancer. Indicates the first The density constant of the material used in each component; Indicates the first The cross-sectional area of ​​each component is a vector of design variables. Analytical functions (e.g., for an outer diameter of...) Inner diameter is The circular tube has the area function as: ); Indicates the first The spatial length corresponding to each component in the graph theory model.

[0116] Simultaneously, the system transforms the mechanical response calculated in step four into inequality constraint functions. These mainly include nodal displacement constraints and element stress constraints. To improve the stability of numerical calculations, the system uniformly performs dimensionless processing on these constraint functions. ; ; In this formula: Indicates the first One stress constraint function; This indicates the extraction of the first [item] in step four. The von Mises equivalent stress scalar values ​​for each monitored area; This represents the allowable stress constant of a material (usually obtained by dividing the material's yield strength by a safety factor). Indicates the total number of stress constraints; Indicates the first One displacement constraint function; This indicates the extraction of the first [item] in step four. The absolute displacement scalar value of a key node (such as the end spreader node); This represents the maximum allowable displacement constant for this node; This indicates the total number of displacement constraints.

[0117] When performing mathematical optimization, the algorithm needs to know the partial derivatives (i.e., gradients or sensitivities) of the objective function and constraint functions with respect to each design variable.

[0118] Traditional finite difference methods require making small perturbations to each variable and resolving the equilibrium equations of the entire system, resulting in an extremely large computational burden when there are many design variables. This approach introduces the adjoint variable method at the computer level, directly obtaining high-precision analytical gradients through pure algebraic derivation.

[0119] Displacement constraints For design variables Taking the partial derivative as an example, the system first defines a Boolean extraction vector. , making (Assuming the displacement of interest is in the master degree of freedom, the element in the extraction vector corresponding to the degree of freedom of interest is 1, and the rest are 0).

[0120] According to the dimensionality reduction equilibrium equation Both sides Differentiation yields: ; The system introduces an adjoint vector in memory. And construct the adjoint equation: ; because It is a symmetric matrix; solving the adjoint equation yields... Then, the analytical sensitivity of the displacement can be directly calculated using the following formula: ; In this formula: Indicates the first The displacement is related to the first Partial derivatives of each design variable; Represents the adjoint vector; its superscript Indicates transpose; This represents the partial derivative of the reduced load vector with respect to the design variables (this term is usually zero when the load is independent of the dimensions). This represents the partial derivative of the dimension-reduced stiffness matrix with respect to the design variables. This matrix can be obtained by differentiating and assembling the stiffness matrices of the local elements. This is the displacement vector of the main degrees of freedom obtained in step four.

[0121] By using the adjoint variable method, the system only needs to solve the adjoint equation once for each constraint to obtain the gradient of the constraint with respect to all design variables, which greatly saves the floating-point operation overhead of the central processing unit.

[0122] After obtaining the gradients of the objective function and constraint functions, the system invokes a sequential quadratic programming algorithm to iterate the parameters. The system then constructs the Lagrangian function in the computer's memory. ; in, and These are the Lagrange multipliers corresponding to stress constraints and displacement constraints, respectively, and it is required that... , In the first In the next iteration (the current design variable is...) The system approximates the original nonlinear programming problem as a quadratic programming subproblem.

[0123] The system calculates the search direction vector. This vector is obtained by solving the following quadratic programming subproblem: ; ; ; In this formula: This represents the transpose of the gradient vector of the objective function at the current iteration point; This represents the search direction vector to be solved; The approximate matrix representing the Hessian matrix of the Lagrange function; and Let represent the transposes of the gradient vectors of the stress constraint and displacement constraint at the current iteration point, respectively. To avoid directly calculating the extremely complex second derivative of the Hessian matrix, the system uses the BFGS quasi-Newton method formula. Update in stages: ; in, Represents the difference vector of design variables; This represents the difference vector of the gradients of the Lagrange function.

[0124] Solve for the search direction Then, the system uses one-dimensional line search techniques (such as the Armijo criterion) to determine the iteration step size. This ensures that the objective function decreases steadily in each iteration. The update formula for the design variables is: ; After each update, the system performs a strict Caro-Kun-Tucker convergence test.

[0125] Convergence conditions include two aspects: First, the relative rate of change of the objective function is less than a preset minimum threshold (e.g.) ); Second, the maximum violation of all constraint functions is less than the preset tolerance (e.g., ).

[0126] If the convergence condition is met, the system determines that the optimization process has ended, and the current... This is the extreme value solution that satisfies the design requirements; if it does not, the system will... As a new starting point, return to perform sensitivity analysis and solve the quadratic programming subproblem until the maximum number of iterations is reached or the convergence condition is met.

[0127] Once the mathematical iterations converge, the system will finally determine the design variable vector. The values ​​in the database are directly overwritten back into the underlying 3D computer-aided design (CAD) database of the balance crane via the application programming interface (API).

[0128] The system-driven geometry kernel regenerates the solid topology based on the new dimensional parameters, thus automating the update of the design scheme.

[0129] Thus, the entire process of designing and optimizing a balance crane structure based on simulation analysis has formed a complete data flow and processing link within the computer.

[0130] 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.

[0131] It should be noted that, in this document, the use of relational terms such as "first" and "second" is merely for distinguishing one entity or operation from another, and does not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0132] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0133] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0134] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for optimizing the structural design of a balance crane based on simulation analysis, characterized in that, include: Extract the geometric feature information of physical components, abstract the physical components as nodes, construct directed edges based on physical assembly relationships and assign local stiffness matrices, eliminate kinematic loops to obtain the topological graph theory model of the balance crane; Based on the topological graph theory model of the balanced crane, the comprehensive weight scalar value of the directed edge is calculated, the main path node subset is extracted and the union operation is performed to obtain the main path node set and the secondary branch node set. The initial global stiffness matrix is ​​permuted based on the main path node set and the secondary branch node set to obtain the block matrix. The expression of the degree of freedom vector is extracted, the dimension-reduced equilibrium equation is constructed, and the equivalent dimension-reduced stiffness matrix and equivalent dimension-reduced load vector are calculated. Solving the dimension-reduced equilibrium equation yields the principal degree-of-freedom vector, which is then used to inversely derive the secondary degree-of-freedom vector. The global nodal displacement vector is then reconstructed, and the local nodal displacement components are extracted to calculate the stress tensor. The design variable vector is extracted to construct the objective function. The global nodal displacement vector and stress tensor are transformed into inequality constraint functions. The adjoint variable method is used to obtain the analytical gradient. The sequential quadratic programming algorithm is called to iterate the parameters and update the underlying database.

2. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, Extracting geometric feature information of physical components includes: The boundary geometric feature information is extracted from the 3D computer-aided design model file, and the volume, centroid coordinates and mass of the physical component are calculated by Gauss-Legends numerical integration. After initializing the graph data structure in computer memory, the adjacency matrix of the graph data structure is stored in a compressed sparse row format. In computer memory, arrays are maintained to store non-zero element values ​​in row-major order, arrays to store column indices, and arrays to store the starting positions of row offsets. A cache prefetching mechanism with contiguous memory addresses is used to improve data throughput.

3. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, Eliminating kinematic loops to obtain the topological graph theory model of the balancing crane includes: A backward edge detection algorithm based on depth-first search is used to identify closed loops composed of node sequences. The nominal internal forces transmitted by each edge in the closed loop are calculated. The edge corresponding to the driven link with the minimum force in the closed loop is identified and disconnected. Two virtual nodes with overlapping spatial positions are generated at the disconnection point. Multi-point constraint equations are introduced between the two virtual nodes to ensure displacement compatibility and force balance at the disconnection point. The Lagrange multiplier method is used to embed the multi-point constraint equations into the system equilibrium equations.

4. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, The process of calculating the scalar value of the comprehensive weight of directed edges based on the topological graph theory model of a balanced crane includes: Extract the local stiffness matrix corresponding to the directed edge and calculate the sum of the main diagonal elements of the local stiffness matrix as the trace of the local stiffness matrix. Calculate the Euclidean distance between the connected nodes in the global coordinate system. The formula for calculating the comprehensive weight scalar value of the directed edge based on the trace of the local stiffness matrix and the Euclidean distance is as follows: ； in, Represents a directed edge The comprehensive weight scalar value; Represents a directed edge The trace of the local stiffness matrix; This represents the maximum value of the trace of the local stiffness matrix for all edges in the entire graph; Represents a node and nodes The spatial Euclidean distance between them; This represents the minimum distance between all connected nodes in the entire graph; and Assign coefficients to the weights, and satisfy the following conditions: .

5. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, Extracting a subset of main path nodes and performing a union operation includes: Set the node representing the end spreader as the starting node and the node representing the base as the target node, and initialize a boolean array to mark the node access status; Push the starting node onto the path stack. Sort the unvisited adjacent nodes in descending order of their comprehensive weight scalar value. Select the node pointed to by the edge with the largest comprehensive weight scalar value and push it onto the path stack. Upon reaching the target node, a backtracking operation is performed. The dynamic weight threshold is set as a specific proportion of the statistical average of the weights of the discovered main path edges. When the cumulative weight of the branch path is lower than the dynamic weight threshold, a pruning operation is performed. Assign binary masks to nodes and perform a union operation on subsets of main path nodes under all typical job conditions using bitwise OR operations.

6. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, The process of permuting the initial global stiffness matrix to obtain the block matrix includes: Construct a Boolean permutation matrix in computer memory, and use the permutation matrix to reorder the global node displacement vectors. Arrange the degrees of freedom belonging to the main path node set in the first half of the vector to form the main degree of freedom vector, and arrange the degrees of freedom belonging to the secondary branch node set in the second half of the vector to form the secondary degree of freedom vector. Simultaneously, the permutation matrix is ​​used to perform a permutation operation on the global node load vector to obtain the master node load vector and the slave node load vector; By performing a row and column double permutation operation on the initial global stiffness matrix using the permutation matrix and its transpose, and based on the reciprocity theorem of linear elasticity, it is determined that the cross-coupled stiffness submatrix of the master degree of freedom to the slave degree of freedom is equal to the transpose of the cross-coupled stiffness submatrix of the slave degree of freedom to the master degree of freedom.

7. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, Extracting the vector expression from the degrees of freedom and constructing the dimensionality-reduced equilibrium equations includes: Regularization constants are uniformly superimposed on the main diagonal elements of the self-stiffness submatrix of each degree of freedom. The resulting self-stiffness submatrix is ​​then subjected to Chorsky decomposition, and the product terms are solved using forward and backward substitution algorithms. The formulas for calculating the equivalent reduced-dimensional stiffness matrix and the equivalent reduced-dimensional load vector are as follows: ； ； in, Represents the equivalent reduced-dimensional stiffness matrix; This represents the self-stiffness submatrix between the main degrees of freedom; This represents the cross-coupling stiffness submatrix from the degree of freedom to the master degree of freedom; This represents the inverse matrix of the stiffness submatrix from the degrees of freedom; This represents the cross-coupling stiffness submatrix between the master degree of freedom and the slave degree of freedom; Represents the equivalent dimension-reduced load vector; Represents the master node load vector; This represents the load vector from the node.

8. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, Solving the dimension-reduced equilibrium equations yields the following main degree-of-freedom vectors: The initial guessed solution vector is set to be an all-zero vector and the initial residual vector is calculated. An incomplete Cholsky decomposition is used to construct a preprocessing matrix to improve the eigenvalue distribution of the equivalent dimension-reduced stiffness matrix. The preprocessing conjugate gradient method is combined with the preprocessing matrix to iteratively solve the main degree of freedom vector. The formula for extracting local nodal displacement components to calculate the stress tensor is as follows: ,in Represents the stress tensor of a local region. Represents the elastic constitutive matrix of the material. Represents the geometric strain-displacement matrix. This represents the local nodal displacement components.

9. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, Transforming the stress tensor into inequality constraint functions includes: The stress tensor is converted into a von Mises equivalent stress scalar value. This scalar value is then divided by the allowable stress constant of the material to achieve dimensionless processing, thus constructing an inequality constraint function. The formula for obtaining the analytical gradient using the adjoint variable method is as follows: ； in, Indicates the first The displacement constraint function for the first Partial derivatives of each design variable; The superscript represents the adjoint vector. Indicates transpose; This represents the partial derivative of the equivalent reduced-dimensional load vector with respect to the design variables; This represents the partial derivative of the equivalent reduced stiffness matrix with respect to the design variables; This represents the main degree of freedom vector.

10. The method for optimizing the design of a balance crane structure based on simulation analysis according to claim 1, characterized in that, The parameter iteration using the sequential quadratic programming algorithm includes: Construct a Lagrangian function to approximate the nonlinear programming problem as a quadratic programming subproblem to find the search direction vector. Then, use a quasi-Newton method to successively update the Hessian matrix approximation matrix. The update formula is as follows: ； in, This represents the updated approximate Hessian matrix; This represents the approximate Hessian matrix for the current iteration step; This represents the difference vector of the gradients of the Lagrange function; Represents the difference vector of design variables; superscript Indicates the number of iterations; One-dimensional line search technology is used to determine the iteration step size and update the design variable vector. Caro-Kuhn-Tucker convergence judgment is performed. When the relative rate of change of the objective function is less than the preset minimum threshold and the maximum violation of all constraint functions is less than the preset tolerance, the convergence condition is determined to be met.

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