Method and system for optimizing size of spanning frame structure based on firefly algorithm

Abstract

The invention discloses a spanning frame structure size optimization method and system based on a firefly algorithm, and relates to the technical field of electric power engineering construction, and the method comprises the steps: firstly building a parameterized finite element model, implementing normalized hierarchical loading, obtaining a tangent stiffness matrix evolved along with a load, calculating the modal participation degree of a component, and constructing a dynamic participation degree track; and according to the quantitative trajectory smoothing index, the modal dominance and the key component suppression index, constructing a brightness function with coupled rigidity and trajectory features. The firefly attraction degree is corrected by means of trajectory similarity based on modal energy fingerprints, and nonlinear search is executed through a characteristic resonance mechanism. The method solves the problem that traditional static optimization neglects geometric nonlinear evolution to cause modal abrupt change, and the dynamic stability and evolution robustness of the spanning frame in the full stress process are remarkably improved while the structural light weight is achieved.

Description

A Method and System for Optimizing the Dimensions of a Flying Frame Structure Based on the Firefly Algorithm Technical Field

[0001] This invention relates to the field of power engineering construction technology, and in particular to a method and system for optimizing the dimensions of a cross-passage structure based on the firefly algorithm. Background Technology

[0002] In the construction of high-voltage transmission lines that need to cross natural obstacles such as rivers, railways, and urban areas, the role of crossing frames is not only to support the power lines, but also to ensure the stability and safety of the structure during construction and subsequent use. Engineers typically set parameters based on experience and verify them using finite element analysis. This design approach can yield a preliminary solution, but it cannot quickly cope with various complex load variations. When encountering multiple loads such as wind loads, conductor tension, and icing loads, it is not only inefficient but also prone to redundant design and material waste.

[0003] With the continuous development of computer technology, intelligent optimization algorithms have been gradually introduced into structural design. Adaptive optimization improves design efficiency and reduces manual intervention. Current high-voltage transmission line construction mainly focuses on static optimization, with optimization objectives typically including minimizing weight or optimizing stress distribution. While this provides some improvement in structural performance under static loads, it doesn't adequately consider the dynamic response and modal changes of crossing frames under multiple working conditions or loads, failing to fully reflect their performance under actual working conditions. Summary of the Invention

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

[0005] Therefore, this invention provides a method for optimizing the structural dimensions of a gantry structure based on the firefly algorithm. This solves the problems of existing gantry structure size design methods, which are difficult to characterize the evolution of structural dynamic characteristics under multi-condition loading, lack quantitative constraints on the risk of stress concentration in key components, and have the evaluation function in the swarm intelligence optimization process being disconnected from the actual stable state of the structure, making it difficult for the size optimization results to take into account the overall lightweight, modal stability and safety margin of key components.

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

[0007] In a first aspect, the present invention provides a method for optimizing the structural dimensions of a straddle frame based on the firefly algorithm, which includes: establishing a finite element model based on the geometric dimensions, material parameters and working load of the straddle frame; generating an overall mass matrix and an initial stiffness matrix; implementing normalized graded loading; and considering the structural geometric nonlinear effects under each loading level to update and generate the corresponding tangent stiffness matrix.

[0008] Based on the overall mass matrix and the tangent stiffness matrix corresponding to each loading level, the characteristic equation is solved to obtain the mode shape that evolves with the loading level, and the modal participation of each component under the current loading level is calculated based on the overall mass matrix.

[0009] Modal engagement is concatenated into engagement trajectories according to loading levels, and trajectory smoothing index, modal dominance, and key component suppression index are calculated.

[0010] The overall mass, key displacement, maximum stress, and stability coefficient are used as physical constraints, and the trajectory smoothing index and key component suppression index are used as evolutionary constraints to jointly construct the firefly brightness function. The trajectory similarity is calculated using the modal dominance, and the attraction between individual fireflies is corrected based on the trajectory similarity to perform a search. The rod diameter, thickness, and support angle that match the evolutionary constraints are output as the optimal dimensions, and the finite element model is updated to convergence.

[0011] As a preferred embodiment of the cross-frame structure size optimization method based on the firefly algorithm described in this invention, the establishment of the finite element model includes: obtaining the geometric dimensions and spatial positional relationships of the main columns, crossbeams and supporting components based on the cross-frame design drawings and site layout data; determining the density and elastic parameters according to the material specifications; discretizing the main columns and crossbeams using three-dimensional beam elements; discretizing the supporting components using three-dimensional rod elements; setting the node connection relationships and basic constraints; and generating the cross-frame finite element model.

[0012] The generation of the overall mass matrix and the initial stiffness matrix includes, in the finite element model, constructing the element mass matrix of each element according to the geometric dimensions and material density of each element, and assembling them to form the overall mass matrix; calculating the element stiffness according to the cross-sectional properties and material elastic parameters of each element and summing them to form the overall stiffness matrix.

[0013] As a preferred embodiment of the cross-frame structure size optimization method based on the firefly algorithm described in this invention, the implementation of normalized graded loading includes: forming a load combination based on conductor tension, wind load, icing load, and structural self-weight to obtain an extreme load vector; introducing a normalized loading variable with a value between zero and one; discretizing the extreme load into multiple loading levels proportionally and applying them to the cross-frame finite element model to induce the stress stiffening effect of the structure; and calculating and outputting the tangent stiffness matrix for each loading level.

[0014] As a preferred embodiment of the cross-frame structure size optimization method based on the firefly algorithm described in this invention, the solution of the characteristic equation includes: for each discrete loading level, taking the tangent stiffness matrix and the overall mass matrix contained in the current loading level as input, calling the numerical eigenvalue extraction algorithm to solve the generalized characteristic equation, obtaining the characteristic frequency set and the corresponding modal shape vector set that evolve with the loading level, and performing normalization processing on the modal shape vector with respect to the overall mass matrix to unify the comparison benchmark of each mode;

[0015] The calculation of the modal participation of each component under the current loading level includes: extracting local mode shape sub-vectors containing only the degrees of freedom of specific components from the normalized mode shape vectors; calculating the modal kinetic energy of the component based on the local mode shape sub-vectors and the element mass matrix corresponding to the component; and defining the ratio of the modal kinetic energy of the component to the overall modal kinetic energy of the structure as the modal participation of the component under the current loading level and current mode.

[0016] As a preferred embodiment of the cross-frame structure size optimization method based on the firefly algorithm described in this invention, the calculation of the trajectory smoothing index, modal dominance, and key component suppression index includes: arranging the modal participation of each component in each modal according to the loading level order to form a modal participation sequence covering all loading levels; using the modal participation sequence as the participation trajectory of the corresponding component and the corresponding mode; calculating the rate of change of modal participation between adjacent loading levels on the participation trajectory; and accumulating the square of the rate of change over the entire loading process to obtain the trajectory smoothing index.

[0017] The modal participation of each component in the same mode is summed within each loading level, and the squares of the summation results are accumulated across all loading levels to obtain the modal dominance.

[0018] Based on predetermined key components, the modal participation degree of the key components at each loading level and each modal order is multiplied and weighted with the corresponding modal dominance degree, and the weighted result is accumulated throughout the entire loading process to obtain the key component suppression index.

[0019] As a preferred embodiment of the cross-frame structure size optimization method based on the firefly algorithm described in this invention, the construction of the firefly brightness function includes: during the implementation of normalized graded loading, detecting whether the tangent stiffness matrix exhibits singularity or non-positive definiteness, recording the corresponding normalized loading variable value, defining the normalized loading variable value as the critical stability coefficient, and constructing a stiffness risk factor using the difference between the maximum loading level and the critical stability coefficient;

[0020] The trajectory smoothing index and the key component suppression index are summed to construct the trajectory evolution factor;

[0021] Using the reciprocal of the overall mass of the traverse frame as a benchmark term, a monotonically decreasing mapping factor is constructed by multiplying the stiffness risk factor and the trajectory evolution factor. The benchmark term is multiplied by the function value corresponding to the monotonically decreasing mapping factor to obtain the firefly brightness function that couples stiffness and trajectory features. The modal dominance degrees of each order corresponding to two firefly individuals are extracted, and modal dominance degree vectors composed of each order of modal dominance degree are constructed respectively. The cosine similarity between the two modal dominance degree vectors is calculated.

[0022] Calculate the absolute value of the difference in trajectory smoothness index between two individual fireflies, and construct a smoothness difference attenuation term using the absolute value of the difference; multiply the cosine similarity by the smoothness difference attenuation term to obtain the trajectory similarity.

[0023] As a preferred embodiment of the cross-frame structure size optimization method based on the firefly algorithm described in this invention, the following steps are taken: the difference between the trajectory similarity and the preset resonance threshold is calculated, and the difference is input into a preset bias-type nonlinear mapping function for mapping to generate a resonance adjustment coefficient between zero and one.

[0024] When calculating the attraction of fireflies, a basic attenuation term based on Euclidean distance is constructed, and the basic attenuation term is multiplied by the resonance adjustment coefficient to obtain the corrected attraction.

[0025] When the trajectory similarity between two individual fireflies is greater than the resonance threshold, the high gain value output by the resonance adjustment coefficient is used to enhance the attraction and trigger the structural feature resonance search; when the trajectory similarity is less than the resonance threshold, the low gain value or zero value output by the resonance adjustment coefficient is used to cut off the attraction and achieve subpopulation isolation.

[0026] The modified attraction is used to drive individual fireflies to move toward the target individual to perform position updates, generating a new generation of size design schemes that include rod diameter, thickness and support angle. The new generation of size design schemes is fed back to reconstruct the finite element model and it is determined whether the brightness function meets the convergence condition. If it does not meet the condition, the next iteration is carried out based on the reconstructed finite element model. If it does meet the condition, the current design scheme is output as the optimal size.

[0027] Secondly, the present invention provides a cross-frame structure size optimization system based on the firefly algorithm, including: a finite element module, which establishes a finite element model based on the cross-frame geometry, material parameters and working load, generates an overall mass matrix and an initial stiffness matrix, and implements normalized graded loading, considering the structural geometric nonlinear effects under each loading level to update and generate the corresponding tangent stiffness matrix.

[0028] The participation module solves the characteristic equations based on the overall mass matrix and the tangent stiffness matrix corresponding to each loading level to obtain the mode shape that evolves with the loading level, and calculates the modal participation of each component under the current loading level based on the overall mass matrix.

[0029] The metrics module concatenates modal participation into a participation trajectory according to loading level, and calculates the trajectory smoothing index, modal dominance, and key component suppression index.

[0030] The execution module uses the overall mass, key displacement, maximum stress, and stability coefficient as physical constraints, and the trajectory smoothing index and key component suppression index as evolutionary constraints to jointly construct the firefly brightness function. It calculates the trajectory similarity using the modal dominance and performs a search based on the trajectory similarity to correct the attraction between individual fireflies. It outputs the rod diameter, thickness, and support angle that match the evolutionary constraints as the optimal dimensions and updates the finite element model until convergence.

[0031] Thirdly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, wherein: when the computer program is executed by the processor, it implements any step of the method for optimizing the size of a straddle structure based on the firefly algorithm as described in the first aspect of the present invention.

[0032] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein: when the computer program is executed by a processor, it implements any step of the method for optimizing the size of a straddle structure based on the firefly algorithm as described in the first aspect of the present invention.

[0033] The beneficial effects of this invention are as follows: By introducing a graded loading mechanism to construct a tangential stiffness matrix and solve the structural mode shapes in conjunction, the dynamic response variation law of the straddle frame during the load evolution process can be characterized. Based on the overall mass matrix, the participation degree of each component under different modes can be quantified, forming a participation degree trajectory that reflects the stress evolution state of the components. By combining the participation degree trajectory calculation trajectory smoothing index, modal dominance degree and key component suppression index, the risk of modal mutation and the stress concentration trend of key components can be simultaneously constrained, so that the search process automatically avoids potential unstable configurations. By constructing a brightness function that includes stiffness risk factors and trajectory evolution factors, and correcting the attraction relationship between individuals with the similarity of modal dominance degree vectors, a swarm intelligent search driven by structural dynamic characteristics can be realized, obtaining a lightweight size combination under the premise of ensuring safety margin and stability. The overall process realizes the synergistic optimization of dimensional parameters, mechanical performance and dynamic behavior, improves the design convergence speed and result reliability, reduces the amount of manual correction, and enhances the safety control capability of the straddle frame structure under complex working conditions. Attached Figure Description

[0034] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 is a flowchart of the method for optimizing the size of the strut structure based on the firefly algorithm. Detailed Implementation

[0036] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0037] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0038] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0039] Referring to Figure 1, an embodiment of the present invention is provided, which offers a method for optimizing the dimensions of a straddle frame structure based on the firefly algorithm, comprising the following steps:

[0040] S1: Based on the geometric dimensions, material parameters and working load of the strut, a finite element model is established to generate the initial mass matrix and initial stiffness matrix. Normalized graded loading is then implemented, and the structural geometric nonlinear effects are considered under each loading level to update and generate the corresponding tangent stiffness matrix.

[0041] First, based on the original design drawings, on-site survey data, and construction layout information of the crossing frame, the topological information of the crossing frame is extracted, including the geometric lengths, cross-sectional dimensions, and spatial relationships between the main columns, crossbeams, and supporting components. Simultaneously, based on the material specifications of the selected steel, the physical property parameters of the material are determined, mainly including material density, elastic modulus, and Poisson's ratio.

[0042] Next, a parametric model is established using finite element analysis software. To balance computational accuracy and iterative optimization efficiency, this embodiment employs a discretization modeling strategy: for major load-bearing components such as main columns and crossbeams, three-dimensional beam elements are used for discretization to accurately simulate their axial and bending deformation capabilities; for supporting components (such as diagonal web members), three-dimensional rod elements or three-dimensional beam elements are used for discretization; based on the actual engineering conditions, rigid or hinged connections between nodes are set, and full or elastic support constraints are applied to the bottom nodes of the bridging frame, thereby generating a complete finite element model of the bridging frame.

[0043] Based on the established finite element model, the system automatically executes the matrix assembly program: mass matrix generation: the mass of each element is calculated according to the geometric volume and material density of each element, and the mass of all elements is assembled into the global coordinate system in the form of an element mass matrix to form the overall mass matrix of the structure.

[0044] Based on the cross-sectional area, moment of inertia and elastic modulus of each element, the elastic stiffness of each element in the unstressed state is calculated, and they are assembled to form the overall initial stiffness matrix of the structure.

[0045] To obtain the dynamic characteristics of the structure under load, this step does not perform a single static calculation, but instead implements graded loading: First, based on relevant design specifications, considering conductor tension, wind load, icing load, and the structure's self-weight, the extreme load vector that the truss may withstand is calculated using load combination coefficients. A dimensionless normalized loading variable with a value between zero and one is defined to control the load application progress. Starting from zero, this variable is gradually increased to one in a preset step size, thus numerically discretizing the above extreme load vector into multiple consecutive loading levels (e.g., 10%, 20%, ... 100%). The load vector corresponding to each loading level is sequentially applied to the finite element model. Since the truss is a tall, flexible structure, when subjected to large axial forces (such as conductor tension), the axial forces inside the structure will significantly change the lateral stiffness of the components. This phenomenon is called the "stress stiffening effect" or "geometric nonlinear effect." For each specific loading level, the finite element solver updates and calculates the current structural stiffness based on the aforementioned geometric nonlinear effects, generating a tangent stiffness matrix specific to that loading level.

[0046] Establishing a parametric finite element model and implementing normalized graded loading can solve the technical challenge of traditional linear analysis failing to capture the stiffness drift of the gantry under high stress. The gantry is a tall, flexible steel structure that undergoes significant geometric deformation under large loads such as conductor tension, leading to changes in its structural configuration. By defining the member dimensions as variable variables through parametric modeling and introducing a normalized loading process, the finite element system can capture the geometric nonlinear effects caused by axial forces in real time at each small load increment step, i.e., stress stiffening or softening phenomena.

[0047] Updating the tangent stiffness matrix at each loading level is a key technique for transitioning from static analysis to dynamic evolution analysis. Traditional methods typically use only the initial elastic stiffness matrix for calculations, neglecting the correction effect of loads on structural stiffness, leading to significant deviations between the calculated results and the actual stress state. By employing a hierarchical update strategy, the solver is forced to reassemble the stiffness matrix at each load step, inheriting the geometric deformation and internal force state from the previous step into the stiffness matrix of the current step. This yields a series of realistic physical stiffness data that dynamically change with the load magnitude.

[0048] This method of constructing an evolutionary sequence based on the tangent stiffness matrix fundamentally eliminates the applicability of the linear superposition principle, providing an accurate input source containing nonlinear characteristics for subsequent modal analysis. Only by obtaining the tangent stiffness containing geometric nonlinear information can the subsequently calculated frequency drift and mode distortion have physical meaning. This approach ensures that numerical simulations can accurately reproduce the gradual transition of a structure from stability to instability under extreme conditions, eliminating the blind spots in safety assessment caused by stiffness indeterminacy.

[0049] S2: Solve the characteristic equations based on the mass matrix and the tangent stiffness matrix corresponding to each loading level to obtain the mode shape that evolves with the loading level, and calculate the modal participation of each component under the current loading level based on the mass matrix.

[0050] For each loading level, the system automatically invokes the BlockLanczos algorithm to solve for the generalized eigenvalues ​​that evolve with the loading level, generating the tangent stiffness matrix that contains geometric nonlinear information for that loading level. With the overall quality matrix As input, the generalized characteristic equation is solved. The BlockLanczos algorithm was chosen because of its extremely high convergence efficiency when dealing with large sparse matrices. In this process, the following mathematical model is calculated:

[0051]

[0052] in, For the first The tangent stiffness matrix corresponding to each loading level; For the overall quality matrix; To solve the first Load level The angular frequency of the first mode; This is the corresponding mode shape vector.

[0053] Modal mode mass normalization is necessary to ensure that subsequent calculated indices have a unified comparison benchmark. Perform normalization on the overall quality matrix to ensure orthogonality:

[0054]

[0055] Among them, superscript This represents the vector transpose. After this step, the overall modal kinetic energy of the structure is normalized to a unit value of 1, ensuring that the participation rate in subsequent calculations is a strictly defined dimensionless ratio.

[0056] Quantifying the modal kinetic energy participation of components is a key interface connecting "finite element analysis" and "trajectory optimization innovation." The system starts from the normalized global vibration modes. In the middle, the extraction only contains the first Local mode vectors of the degrees of freedom of a component (such as a numbered brace). And combined with the element mass matrix of the component Perform calculations. Component modal participation. The calculation formula is as follows:

[0057]

[0058] in, Indicates the first The component in the first Loading level and 1 Modal participation in the first mode; This represents the local modal kinetic energy of the component; This represents the overall modal kinetic energy of the structure.

[0059] Solving the generalized characteristic equation based on a sequence of tangent stiffness matrices transforms modal analysis from a single static snapshot to a full-process dynamic cinematography. By using the tangent stiffness matrix, which incorporates stress stiffening effects, as input, the calculated characteristic frequencies and mode shapes are no longer fixed constants but rather variables that evolve with the load level. This approach can keenly capture sharp frequency drops caused by column instability or frequency increases caused by cable tensioning, thus revealing potential dynamic bifurcation points in the structure and solving the problem of predicting modal transitions during loading, which is difficult to achieve with traditional methods.

[0060] By normalizing the modal vibrations with respect to the overall mass matrix and calculating the modal kinetic energy participation of the components, a quantitative mapping channel from macroscopic overall vibration to microscopic component response is established. By extracting local mode shape sub-vectors containing only the degrees of freedom of specific components and combining them with the corresponding element mass matrix, the kinetic energy proportion of each member in a specific modal vibration can be accurately calculated. This energy-based quantitative method avoids the limitations of judging component importance solely based on displacement or stress, directly identifying the energy source that contributes the most to the overall structural vibration.

[0061] Constructing a multidimensional data array of component modal participation evolving with loading levels provides the unique data foundation for subsequent trajectory smoothness analysis. Traditional modal analysis often stops at obtaining the overall vibration mode, ignoring the changing patterns of component-level contributions. By continuously recording the proportion of component kinetic energy at each loading step, the transfer process of the core load-bearing path within the structure can be clearly depicted as the external load increases. This data structure allows the optimization algorithm to no longer blindly adjust all members, but rather to accurately identify and adjust those key components that play a dominant role in dangerous modes based on the kinetic energy flow direction.

[0062] S3: Concatenate the modal participation degrees according to the loading level to form a participation degree trajectory, and calculate the trajectory smoothness index, modal dominance degree and key component suppression index.

[0063] To accurately capture the evolution characteristics of the structure throughout the loading process, the system first defines continuous normalized loading variables for continuous fitting of the component modal participation trajectory. For each component and each mode The discrete participation sequence calculated by S2 As control points, a cubic spline interpolation algorithm is used for fitting to generate a continuous dynamic participation trajectory function. .

[0064] Trajectory smoothing index The calculations are used to quantify the stability of the modal characteristics of the structure during stress. The system's trajectory function... The first derivative (i.e., the rate of change) is squared and integrated to penalize any unexpected modal shifts. The calculation formula is as follows:

[0065]

[0066] in, For trajectory smoothing index; This represents the total modal order. The total number of components; Represents the instantaneous rate at which participation changes with load; Indicates the component's index number; Indicates the order index of the mode; This represents a continuous normalized load variable with a value range of [0, 1]. Indicates the first The component in the first Mode following A continuously changing dynamic participation trajectory function; Indicates; the The component in the first First mode, first Discrete modal engagement values ​​under each loading level; This represents the maximum number of indices for a discrete load level; This indicates continuously normalized loaded variables.

[0067] Modal dominance This index is used to identify which mode dominates the overall energy distribution of the structure throughout the entire operating process. The system at each instant... Summing the participation of all components and integrating the square of the sum over the entire domain:

[0068]

[0069] in, For the first The dominance of the first mode. By integrating the square of the sum of the participation of all components, the system can screen out the mode that is energy dominant throughout the process. This index will be directly used for the "trajectory similarity" calculation in the subsequent firefly algorithm.

[0070] Key component suppression index To protect the core load-bearing components (such as the main columns) in the spanning frame and prevent them from bearing excessive energy in the dominant mode, the system is based on a pre-defined set of key components. Calculate the weighted product of the participation trajectories and modal dominance of these key components:

[0071]

[0072] in, As a key component suppression index; A set of key component indexes specified for designers. This formula is obtained through... The product coupling mechanism forces the optimization algorithm to reduce the energy proportion of key components under the strong dominant mode, thereby achieving directional protection.

[0073] A cubic spline interpolation algorithm is used to fit discrete modal participation sequences into continuous trajectories, and a trajectory smoothing index is calculated, overcoming the technical limitation that discrete data points cannot characterize the abrupt changes in structural evolution. Structures often undergo drastic modal transformations near critical instability states, and simple discrete point comparisons easily miss these high-risk abrupt changes. By constructing a continuously differentiable trajectory function and integrating or accumulating the square of the rate of change, a penalty mechanism highly sensitive to modal abrupt changes is built, forcing the optimization direction to avoid solutions that, while satisfying static strength requirements, exhibit drastic fluctuations in dynamic evolution.

[0074] By calculating modal dominance and combining it with global integration, a macroscopic control of the energy distribution characteristics of the structure throughout its entire lifespan is achieved. Unlike traditional methods that only focus on the principal modes at the moment of maximum load, modal dominance is achieved by summing the squares of the participation of all components throughout the entire loading domain, thus filtering out those persistent modes that consistently dominate throughout the entire loading cycle. This global integration evaluation mechanism ensures that the optimization algorithm can identify and suppress potentially dangerous modes that are hidden in the low-load stage but erupt in the high-load stage, thereby improving the dynamic robustness of the structure throughout its entire life cycle.

[0075] A key component suppression index was constructed, and a product-coupling mechanism was used to achieve directional dynamic protection of the core load-bearing components. The participation trajectory of the key component was weighted and accumulated with the modal dominance, meaning that a high penalty value was only generated when a certain mode was both the dominant mode and the key component had a high participation in that mode. This design forces the optimization algorithm to automatically adjust the structural stiffness distribution, transferring the vibration energy of the dominant mode from key components such as the main columns to secondary components, thereby significantly reducing the probability of dynamic failure of the core components without increasing the overall material usage.

[0076] S4: Using the overall mass, key displacement, maximum stress, and stability coefficient as physical constraints, and the trajectory smoothing index and key component suppression index as evolutionary constraints, a firefly brightness function is constructed. The trajectory similarity is calculated using the modal dominance, and the attraction between individual fireflies is corrected based on the trajectory similarity to perform a search. The rod diameter, thickness, and support angle that match the evolutionary constraints are output as the optimal dimensions, and the finite element model is updated to convergence.

[0077] First, trace back the normalized graded loading process in step S1 and check the tangent stiffness matrix. Does a singularity or nondefinite state occur? Record the normalized loading variable value when such a state occurs, and define it as the critical stability coefficient. (If the entire process is stable, then) A stiffness risk factor is constructed using the difference between the maximum loading level (i.e., value 1) and the critical stability coefficient. Simultaneously, the trajectory smoothing index output in step S3 is summed with the key component suppression index to construct a trajectory evolution factor. Next, the reciprocal of the overall mass of the bridging frame is used as a baseline term. A monotonically decreasing mapping factor is constructed using the product of the stiffness risk factor and the trajectory evolution factor (in this embodiment, the monotonically decreasing mapping factor is implemented using an exponentially decreasing function). The baseline term is multiplied by the function value corresponding to the monotonically decreasing mapping factor to obtain the final brightness function.

[0078] The final brightness function calculation model is as follows:

[0079]

[0080] in, The overall mass of the gantry crane is the total weight of the gantry crane structure, which is obtained by adding up the masses of each unit. The adjustment coefficient is used; this formula utilizes a product coupling mechanism to ensure that the adjustment is applied only when the structural stiffness reserve is sufficient. Approaching 1, and the evolutionary trajectory is smooth. and When the value approaches 0, an individual can achieve high brightness, thereby automatically eliminating potential unstable solutions.

[0081] To quantify the essential differences in physical configuration among different design schemes, the system first extracts the modal dominance degrees calculated in step S3, and constructs modal dominance degree vectors composed of the modal dominance degrees of each order. Next, calculate the individual fireflies. and The cosine similarity of the modal dominance vectors between the two models is calculated; simultaneously, the absolute value of the difference between their trajectory smoothness indices is calculated, and a smoothness difference attenuation term is constructed using this absolute value. The trajectory similarity is then obtained by multiplying the cosine similarity by the smoothness difference attenuation term. The calculation formula is as follows:

[0082]

[0083] in, Indicates individual fireflies The modal dominance vector; Indicates individual fireflies The modal dominance vector; Indicates the sensitivity coefficient for evolutionary differences; Represents an individual The trajectory smoothing index; Represents an individual The trajectory smoothing index.

[0084] Using the above trajectory similarity A non-linear correction is applied to the attraction factor of the firefly algorithm to achieve sub-population isolation. First, the trajectory similarity is calculated. With preset resonance threshold The difference is then input into a preset bias-type nonlinear mapping function (the Sigmoid function is used in this embodiment) for mapping, generating a resonance adjustment coefficient between zero and one. Next, when calculating the firefly's attraction, a basic attenuation term based on Euclidean distance is constructed, and this basic attenuation term is multiplied by the resonance adjustment coefficient to obtain the corrected attraction. .

[0085] The calculation model for corrected attractiveness is as follows:

[0086]

[0087] in, This indicates a correction to the attractiveness level; Indicates maximum attraction; Indicates the light absorption coefficient; Represents Euclidean distance, individual fireflies and Geometric distance in the design space (dimensional variables); This represents the resonance modulation coefficient, which controls the slope of the Sigmoid activation function and determines the initial sensitivity. This represents the resonance threshold, a preset criterion used to distinguish whether a resonance search has been triggered.

[0088] Driven by the above mechanism:

[0089] When the trajectory similarity is greater than the resonance threshold, the resonance adjustment coefficient outputs a high gain value, enhancing attraction and triggering structural feature resonance search; when the trajectory similarity is less than the resonance threshold, the resonance adjustment coefficient outputs a low gain value or zero value, cutting off attraction and achieving subpopulation isolation. The corrected attraction is used to drive individual fireflies to move towards the target individual to perform position updates, generating a new generation of dimensional design schemes including rod diameter, thickness, and support angle. This new generation of dimensional design schemes is fed back to step S1 to reconstruct the parametric finite element model, and it is determined whether the brightness function meets the convergence condition. If not, the next iteration is performed based on the reconstructed finite element model; if so, the current design scheme is output as the optimal size.

[0090] A brightness function coupled with the product of stiffness risk factor and trajectory evolution factor is constructed, establishing a nonlinear multi-gating screening mechanism. The critical stability coefficient characterizes the stiffness degradation risk, and the smoothness index characterizes evolutionary stability. Both are placed in an exponential decay term, ensuring that any single-dimensional defect leads to a drastic decrease in individual brightness. This product-coupling logic completely eliminates the trade-off effect of traditional linear weighting, ensuring that only design schemes that simultaneously satisfy sufficient stiffness reserve and smooth evolutionary trajectory are selected by the algorithm, effectively eliminating pseudo-optimal solutions.

[0091] By calculating trajectory similarity based on modal energy fingerprints, the algorithm's search metric space is expanded from geometric dimension space to physical configuration space. By calculating the cosine similarity of modal dominance vectors and combining it with smoothness difference decay, the algorithm can identify whether two design schemes belong to the same class in terms of dynamics. This physical similarity metric avoids the error of misjudging two structures with drastically different force modes as similar individuals simply because the member dimensions are similar, ensuring the physical effectiveness of subsequent search strategies.

[0092] By introducing a resonance threshold and a nonlinear activation function to implement feature resonance search and subpopulation isolation, the premature convergence and blind oscillation problems commonly encountered in high-dimensional nonlinear optimization are solved. When the trajectory similarity is higher than the threshold, a high gain coefficient is used to enhance the attraction, prompting individuals with similar physical configurations to conduct refined resonance searches locally. When the similarity is lower than the threshold, the attraction path is cut off to prevent solutions with different force modes from interfering with each other. This adaptive isolation mechanism based on physical features enables the Firefly algorithm to automatically form multiple subpopulations attached to specific physical configurations in a complex solution space, significantly improving the efficiency and accuracy of finding the global optimum.

[0093] This embodiment also provides a straddle frame structure size optimization system based on the firefly algorithm, including:

[0094] The finite element module establishes a finite element model based on the geometry, material parameters, and load conditions of the strut, generates the overall mass matrix and initial stiffness matrix, and implements normalized graded loading. Under each loading level, the structural geometric nonlinear effects are considered to update and generate the corresponding tangent stiffness matrix.

[0095] The participation module solves the characteristic equations based on the overall mass matrix and the tangent stiffness matrix corresponding to each loading level to obtain the mode shape that evolves with the loading level, and calculates the modal participation of each component under the current loading level based on the overall mass matrix.

[0096] The metrics module concatenates modal participation into a participation trajectory according to loading level, and calculates the trajectory smoothness index, modal dominance index, and key component suppression index.

[0097] The execution module uses the overall mass, key displacement, maximum stress, and stability coefficient as physical constraints, and the trajectory smoothing index and key component suppression index as evolutionary constraints to jointly construct the firefly brightness function. It calculates the trajectory similarity using the modal dominance and performs a search based on the trajectory similarity to correct the attraction between individual fireflies. It outputs the rod diameter, thickness, and support angle that match the evolutionary constraints as the optimal dimensions and updates the finite element model until convergence.

[0098] This embodiment also provides a computer device applicable to the method for optimizing the size of a scaffold structure based on the firefly algorithm, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the method for optimizing the size of a scaffold structure based on the firefly algorithm as proposed in the above embodiment.

[0099] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0100] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the method for optimizing the size of a straddle structure based on the firefly algorithm as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0101] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the dimensions of a straddle-type structure based on the firefly algorithm, characterized in that, include: A finite element model is established based on the geometric dimensions, material parameters, and load conditions of the strut. An overall mass matrix and an initial stiffness matrix are generated, and normalized graded loading is implemented. At each loading level, the structural geometric nonlinearity is considered to update the corresponding tangent stiffness matrix. Based on the overall mass matrix and the tangent stiffness matrices corresponding to each loading level, characteristic equations are solved to obtain the mode shapes evolving with each loading level. The modal participation of each component at the current loading level is calculated based on the overall mass matrix. The modal participation is then pieced together by loading level to form a participation trajectory, and trajectory smoothing index, modal dominance, and key component suppression index are calculated. The overall mass, key displacement, maximum stress, and stability coefficient are used as physical constraints, and the trajectory smoothing index and key component suppression index are used as evolutionary constraints to jointly construct a firefly brightness function. The modal dominance is used to calculate trajectory similarity, and the attraction between individual firefly individuals is corrected based on trajectory similarity to perform a search. The diameter, thickness, and support angle of the members matching the evolutionary constraints are output as optimal dimensions, and the finite element model is updated until convergence.

2. The method for optimizing the dimensions of a straddle-shaped structure based on the firefly algorithm as described in claim 1, characterized in that: The establishment of the finite element model includes obtaining the geometric dimensions and spatial relationships of the main columns, beams, and supporting components based on the design drawings and site layout data of the truss frame; determining the density and elastic parameters according to the material specifications; discretizing the main columns and beams using three-dimensional beam elements; discretizing the supporting components using three-dimensional rod elements; setting node connection relationships and foundation constraints; and generating the finite element model of the truss frame. The generation of the overall mass matrix and initial stiffness matrix includes constructing the element mass matrix of each element based on its geometric dimensions and material density in the finite element model, and assembling it to form the overall mass matrix; calculating the element stiffness based on the cross-sectional properties and material elastic parameters of each element, and summarizing them to form the overall stiffness matrix.

3. The method for optimizing the dimensions of a straddle frame structure based on the firefly algorithm as described in claim 2, characterized in that: The implementation of normalized graded loading includes forming a load combination based on conductor tension, wind load, icing load, and structural self-weight to obtain an extreme load vector. A normalized loading variable with a value between zero and one is introduced, and the extreme load is discretized into multiple loading levels proportionally and applied to the finite element model of the strut, thereby stimulating the stress stiffening effect of the structure. The tangent stiffness matrix is ​​then calculated and output for each loading level.

4. The method for optimizing the dimensions of a straddle-shaped structure based on the firefly algorithm as described in claim 3, characterized in that: The solution of the characteristic equation includes, for each discrete loading level, taking the tangent stiffness matrix and the global mass matrix contained in the current loading level as input, calling the numerical eigenvalue extraction algorithm to solve the generalized characteristic equation, obtaining the characteristic frequency set and the corresponding modal shape vector set that evolve with the loading level, and performing normalization processing on the modal shape vector with respect to the global mass matrix to unify the comparison benchmark of each order of modes; the calculation of the modal participation of each component in the current loading level includes, from the normalized modal shape vector, extracting local mode shape sub-vectors that contain only the degrees of freedom of specific components, calculating the modal kinetic energy of the component based on the local mode shape sub-vectors and the element mass matrix corresponding to the component, and defining the ratio of the modal kinetic energy of the component to the overall modal kinetic energy of the structure as the modal participation of the component in the current loading level and the current mode.

5. The method for optimizing the dimensions of a straddle-shaped structure based on the firefly algorithm as described in claim 4, characterized in that: The computational trajectory smoothing index, modal dominance, and key component suppression index include arranging the modal participation of each component in each modal according to the loading level order to form a modal participation sequence covering all loading levels, and using the modal participation sequence as the participation trajectory of the corresponding component and the corresponding mode. On the participation trajectory, the rate of change of modal participation between adjacent loading levels is calculated, and the square of the rate of change is accumulated over the entire loading process to obtain the trajectory smoothing index; within each loading level, the modal participation of each component under the same mode is summed, and the square of the summation result is accumulated over all loading levels to obtain the modal dominance. Based on predetermined key components, the modal participation degree of the key components at each loading level and each modal order is multiplied and weighted with the corresponding modal dominance degree, and the weighted result is accumulated throughout the entire loading process to obtain the key component suppression index.

6. The method for optimizing the dimensions of a straddle-shaped structure based on the firefly algorithm as described in claim 5, characterized in that: The construction of the firefly brightness function includes, during the implementation of normalized graded loading, detecting whether the tangent stiffness matrix exhibits singularity or non-positive definiteness, recording the corresponding normalized loading variable values, defining the normalized loading variable values ​​as critical stability coefficients, and constructing a stiffness risk factor using the difference between the maximum loading level and the critical stability coefficients. The trajectory smoothing index and the key component suppression index are summed to construct the trajectory evolution factor. The reciprocal of the overall mass of the traverse frame is used as a benchmark term. A monotonically decreasing mapping factor is constructed using the product of the stiffness risk factor and the trajectory evolution factor. The benchmark term is multiplied by the function value corresponding to the monotonically decreasing mapping factor to obtain the firefly brightness function coupling stiffness and trajectory characteristics. The modal dominance degrees of each order corresponding to two firefly individuals are extracted, and modal dominance degree vectors composed of each order of modal dominance degree are constructed respectively. The cosine similarity between the two modal dominance degree vectors is calculated. The absolute value of the difference in the trajectory smoothing index between two firefly individuals is calculated, and a smoothness difference attenuation term is constructed using the absolute value of the difference. The cosine similarity is multiplied by the smoothness difference attenuation term to obtain the trajectory similarity.

7. The method for optimizing the dimensions of a straddle-shaped structure based on the firefly algorithm as described in claim 6, characterized in that: The difference between the trajectory similarity and the preset resonance threshold is calculated, and the difference is input into a preset bias-type nonlinear mapping function for mapping to generate a resonance adjustment coefficient between zero and one; when calculating the attraction of fireflies, a basic attenuation term based on Euclidean distance is constructed, and the basic attenuation term is multiplied by the resonance adjustment coefficient to obtain the corrected attraction. When the trajectory similarity of two individual fireflies is greater than the resonance threshold, the high gain value output by the resonance adjustment coefficient is used to enhance the attraction and trigger the structural feature resonance search. When the trajectory similarity is less than the resonance threshold, the attraction is cut off by using the low gain value or zero value output by the resonance adjustment coefficient to achieve subpopulation isolation; the modified attraction is used to drive firefly individuals to move towards the target individual to perform position updates, generating a new generation of size design schemes that include rod diameter, thickness and support angle. The new generation size design scheme is fed back to reconstruct the finite element model, and it is determined whether the brightness function meets the convergence condition: if it does not meet the condition, the next iteration is carried out based on the reconstructed finite element model; if it does meet the condition, the current design scheme is output as the optimal size.

8. A scaffolding structure size optimization system based on the firefly algorithm, wherein the scaffolding structure size optimization method based on the firefly algorithm as described in any one of claims 1 to 7 is characterized in that: The finite element module establishes a finite element model based on the geometric dimensions, material parameters, and working loads of the strut, generates the overall mass matrix and initial stiffness matrix, and implements normalized graded loading. Under each loading level, the structural geometric nonlinear effects are considered to update and generate the corresponding tangent stiffness matrix. The participation module solves the characteristic equations based on the overall mass matrix and the tangent stiffness matrix corresponding to each loading level to obtain the mode shapes that evolve with the loading level, and calculates the modal participation of each component under the current loading level based on the overall mass matrix. The index module splices the modal participation into a participation trajectory according to the loading level, and calculates the trajectory smoothing index, modal dominance, and key component suppression index. The execution module uses the overall mass, key displacement, maximum stress, and stability coefficient as physical constraints, and the trajectory smoothing index and key component suppression index as evolutionary constraints to jointly construct the firefly brightness function. It uses the modal dominance to calculate the trajectory similarity, and performs a search based on the trajectory similarity to correct the attraction between individual fireflies. It outputs the rod diameter, thickness, and support angle that match the evolutionary constraints as the optimal dimensions, and updates the finite element model until convergence.

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