A structural optimization design method based on particle swarm optimization algorithm

Abstract

The present invention discloses a structural optimization design method based on a particle swarm algorithm. For super high-rise buildings, an optimization model is established, an objective function is set, and the structural layer displacement, inter-layer displacement angle, and top-floor peak composite acceleration are used as constraints to generate an initial structural parameter matrix. Combining the structural dynamic characteristics and wind tunnel test results, a frequency domain calculation method is used to obtain the wind vibration response characteristic matrix, and the equivalent static wind load matrix and acceleration response matrix are calculated. Multiple iterations are performed using a combined algorithm of the optimization criterion method and the particle swarm algorithm. By initializing and updating the relevant parameters of the particle swarm, calculating the fitness value, iteratively updating the position and velocity matrix, and recalculating the wind load and acceleration response data, the optimal solution matrix is ​​finally output based on the convergence judgment, thereby determining the final design scheme of the structure and achieving comprehensive optimization of the structural wind resistance and economic benefits.

Description

Technical Field

[0001] The present invention relates to the technical field of wind resistance performance optimization design of super high-rise buildings, and in particular to a structure optimization design method based on particle swarm algorithm. Background Art

[0002] In existing technologies, traditional structural optimization methods, such as genetic algorithms and simulated annealing, are commonly used for the structural design of super-high-rise buildings. These methods optimize structural parameters by establishing objective functions and constraints, combining the dynamic characteristics of the building structure with wind tunnel test results. Traditional methods often rely on design and analysis based on static mechanics, often using approximate models to estimate wind loads and acceleration responses. Furthermore, some optimization methods have limitations in computational efficiency and accuracy when dealing with structural dynamic characteristics.

[0003] A common problem with existing technologies is suboptimal optimization results. Traditional optimization algorithms struggle to strike a balance between global search capabilities and local convergence, particularly when dealing with complex wind-induced vibrations. Furthermore, existing algorithms are susceptible to local optimal solutions in terms of constraint handling and objective function fitness calculations, resulting in poor stability and feasibility of optimization results. Furthermore, these methods are insufficiently adaptable in multi-objective optimization scenarios, making it difficult to simultaneously meet both wind resistance and economic requirements.

[0004] Therefore, it is urgent to develop a new structural optimization design method based on particle swarm optimization algorithm. Summary of the Invention

[0005] This application provides a structural optimization design method based on particle swarm optimization to improve the accuracy and stability of optimization results.

[0006] This application provides a structural optimization design method based on particle swarm optimization, including:

[0007] By establishing an optimization model for super high-rise building structures, setting the objective function, and setting the structural layer displacement, inter-layer displacement angle and top-floor peak composite acceleration as constraints, the initial structural parameter matrix X is generated.

[0008] Based on the initial structural parameter matrix X, combined with the dynamic characteristics of the structure and the wind tunnel test results, the frequency domain calculation method is used to calculate the wind vibration response to obtain the response characteristic matrix R;

[0009] Based on the response characteristic matrix R, the equivalent static wind load matrix W and the acceleration response matrix Acc are calculated;

[0010] According to the equivalent static wind load matrix W and the acceleration response matrix Acc, the following iterative calculation is performed using the combined optimization algorithm of the optimization criterion method and the particle swarm algorithm:

[0011] P101: According to the response characteristic matrix R, initialize the relevant parameters of the particle swarm, including the position matrix P and the velocity matrix V, and set the initial individual optimal position matrix P best and the group optimal position matrix G best ;

[0012] P102: Substitute the position matrix P into the objective function and calculate the fitness value matrix A of each particle to evaluate the quality of the current design scheme;

[0013] P103: Update the individual optimal position matrix P according to the fitness value matrix A best and the group optimal position matrix G best , to improve the global and local search capabilities of the particle swarm;

[0014] P104: Based on the optimization criterion method, combined with the updated individual optimal position matrix P best and the group optimal position matrix G best , iteratively update the position matrix P and velocity matrix V of the particle swarm to obtain the updated position matrix P' and velocity matrix V';

[0015] P105: Based on the updated position matrix P', the equivalent static wind load matrix W and acceleration response matrix Acc are recalculated to update the wind-induced vibration response data during the optimization process.

[0016] P106: Based on the preset convergence accuracy ε, determine whether the norm of the difference between the updated position matrix P' and the previous position matrix P is less than ε; if less than ε, output the optimal solution matrix Opt; if greater than or equal to ε, assign P' to P and return to step P102 for further iteration;

[0017] Based on the output optimal solution matrix Opt, the final design scheme S of the structure is determined to achieve the optimal design of the structural wind resistance and economic benefits.

[0018] The beneficial effects of the technical solution provided by this application include:

[0019] (1) By combining the optimization criterion method and the particle swarm algorithm for combined optimization, the present invention continuously updates the equivalent static wind load and acceleration response matrix during the optimization process, thereby dynamically adjusting the wind vibration response during the calculation process, and improving the accuracy and stability of the optimization results. (2) The particle swarm algorithm has strong adaptability in global search and local optimization. By setting a dynamic update mechanism for individual optimal positions and group optimal positions, the algorithm has stronger global search capabilities in the early stage, and can quickly achieve local convergence in the later stage, thereby improving the overall optimization effect. (3) The present invention introduces multiple constraints such as structural layer displacement, inter-layer displacement angle and top-layer composite acceleration into the objective function, so that the optimization process can take into account both wind resistance and structural economy, ensuring the effectiveness and feasibility of the multi-objective optimization results. (4) The present invention adopts a frequency domain calculation method to quickly obtain the wind vibration response characteristic matrix, combined with efficient fitness evaluation and optimization iteration strategy, effectively reducing calculation time and resource consumption, and improving the efficiency and practicality of the optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flowchart of a structure optimization design method based on particle swarm algorithm provided in the first embodiment of the present application. DETAILED DESCRIPTION

[0021] The following description sets forth many specific details to facilitate a thorough understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar generalizations without violating the scope of the present application. Therefore, the present application is not limited to the specific implementations disclosed below.

[0022] The first embodiment of the present application provides a structural optimization design method based on particle swarm optimization. Figure 1 , which is a schematic diagram of the first embodiment of this application. Figure 1 A structural optimization design method based on a particle swarm algorithm is described in detail for the first embodiment of the present application.

[0023] Step S101: By establishing an optimization model for the super high-rise building structure, setting the objective function, and setting the structural layer displacement, inter-layer displacement angle and top-floor peak composite acceleration as constraints, an initial structural parameter matrix X is generated.

[0024] Step S101 is specifically implemented by establishing an optimization model for the design of super high-rise building structures. The core of the model is to determine the objective function and constraints and generate an initial structural parameter matrix x.

[0025] First, during the modeling process, the structural design of supertall buildings often involves complex multi-objective optimization. To this end, it is necessary to define an objective function appropriate for this type of building. This objective function should include multiple factors that influence structural design cost and performance, such as material cost, construction cost, and structural weight. Specifically, the objective function can be comprehensively defined based on factors such as the building's materials, geometry, and structural form. The objective function should reflect the trade-offs between economics and performance in the design, for example, by minimizing cost or total weight to achieve an optimal design.

[0026] Secondly, in order to ensure the safety and performance of the structure, constraints must be introduced into the optimization model. In step S101, the constraints mainly include factors such as structural layer displacement, inter-layer displacement angle and top-floor peak composite acceleration. Specifically, the layer displacement constraint is to ensure the stability of the structure by limiting the horizontal displacement of each floor under the action of wind load to no more than the specified value; the inter-layer displacement angle constraint is used to limit the relative displacement angle between adjacent floors to ensure the overall stiffness and lateral resistance of the structure; the top-floor peak composite acceleration constraint is used to control the acceleration response of high-rise buildings under wind vibration to ensure the comfort and safety of users. These constraints can be obtained by analyzing the dynamic characteristics of the building structure and set according to engineering specifications or design standards.

[0027] After the objective function and constraints are clear, step S101 then generates the initial structural parameter matrix x. The generation of this matrix needs to be initialized in combination with the value range of the design variables. The design variables may include the column cross-sectional dimensions, beam cross-sectional dimensions, floor thickness, structural material strength grade, etc. of the building. Each element of the matrix x represents a design parameter in the structure, and its initial value can be generated by methods such as random distribution and Latin hypercube sampling (LHS) to ensure diversity and global search capabilities during the optimization process. When generating the initial parameter matrix, it is necessary to ensure that each design variable in the matrix is ​​within its allowable value range to avoid unreasonable design parameters from entering the subsequent optimization calculations.

[0028] During the generation of the initial structural parameter matrix, preliminary adjustments are required based on the building's dynamic characteristics. This adjustment ensures that the initial parameter matrix, while still meeting basic structural performance requirements, is better suited for the subsequent particle swarm optimization process. This preliminary adjustment may involve specific offsets or corrections to certain key design parameters in the matrix, such as weighting the design parameters of the top structure to improve wind resistance.

[0029] In summary, step S101 provides an initial foundation for subsequent particle swarm optimization calculations by establishing an optimization model, setting the objective function and constraints, and generating an initial structural parameter matrix. This step ensures the economic and performance requirements of the structural design and provides a reasonable starting point for the subsequent optimization process.

[0030] Furthermore, the objective function adopts the following formula 1:

[0031]

[0032] Among them, F represents the fitness value; n represents the total number of layers of the structure; Δ i represents the layer displacement of the i-th layer; Δ max represents the maximum permissible story displacement; θ i represents the inter-story displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle; a top represents the resultant acceleration of the top layer; A max Indicates the maximum allowable top composite acceleration; C mat Indicates the total material cost of the structure; C const represents the total construction cost of the structure; α, β, γ, δ, η are balance coefficients; W i is the equivalent static wind load of the i-th layer calculated in the current iteration; W i,prev is the equivalent static wind load of the i-th layer calculated in the previous iteration; Acc i is the acceleration response of the i-th layer calculated in the current iteration; Acc i,prev is the acceleration response of the i-th layer calculated in the previous iteration.

[0033] The specific implementation of the data acquisition and analysis module 101 involves acquiring, processing and analyzing various data in the objective function formula in order to accurately calculate the objective function value F and use it in the optimization process of the particle swarm algorithm.

[0034] The objective function F is derived by comprehensively evaluating multiple performance indicators of the building structure. Each term in the formula represents a specific design goal or constraint, resulting in a multi-objective optimization of the overall structural performance. This module explains each term in detail and how to derive this data from actual structural responses.

[0035] First, the objective function F is an evaluation index of the fitness value, reflecting the pros and cons of the current design scheme. This objective function consists of multiple parts, each corresponding to a specific structural performance indicator:

[0036] C matIndicates the total material cost of the structure. This is calculated by counting the types and quantities of materials used in each structural component. Specifically, the volume of the material can be calculated based on the design size and material density of each component, and then the cost of each component can be calculated by combining the unit price of the material. The cost of all components is added together to get C mat .

[0037] C const This represents the total construction cost of the structure. This section covers all expenses incurred during the construction of the structure, including labor, equipment, and site rental. The total construction cost is typically calculated based on the construction process, time, and resource requirements, and can be calculated by adding up the various expenses.

[0038] It is an item in the objective function, mainly used to measure the layer displacement of the structure. i is the story displacement of the i-th floor, obtained through structural analysis, usually based on finite element model calculations. It can be determined by analyzing the displacement response under wind load or other loads. max This represents the maximum permitted story displacement, typically set by a building code or design standard. A logarithmic term is included in the calculation of this term to enhance the effect on fitness when story displacements are small, thereby encouraging designs to better meet story displacement constraints.

[0039] Represents the constraint condition of the inter-story displacement angle. i θ is the inter-story displacement angle of the i-th floor, which can be calculated by the ratio of the relative displacement of two adjacent floors and the floor height, and is usually obtained through structural dynamic analysis under wind load. max is the maximum permissible inter-story drift angle, set based on specifications and design standards. The exponential term is used to impose a penalty when the inter-story drift angle approaches the maximum permissible value, thus preventing the design from approaching the safety margin too closely.

[0040] Represents the constraint on the top-level composite acceleration. top It is the resultant acceleration of the top floor, obtained through the dynamic response analysis of the structure, usually calculated based on the power spectral density (PSD) of the wind-induced vibration response. max is the specified maximum allowable resultant top-floor acceleration, set by code or design requirements. The logarithmic portion of this term increases its adaptability at lower accelerations, encouraging designs to optimize within the lower acceleration range, thereby improving building comfort.

[0041] Reflects the change of equivalent static wind load. W iis the equivalent static wind load of the i-th layer in the current iteration, which is calculated by wind load and structural response analysis and is usually combined with wind load characteristics during structural analysis. i,prev is the equivalent static wind load for the i-th floor in the previous iteration, recording the result of the previous iteration. The absolute value of this term represents the magnitude of the wind load change between iterations. The purpose is to control the stability of the design during the optimization process and avoid excessive load fluctuations.

[0042] Indicates the change in acceleration response. Acc i Acc is the acceleration response of the i-th layer in the current iteration, obtained through wind-induced vibration response analysis, usually calculated based on the dynamic characteristics of the structure and the wind load characteristics. i,prev is the acceleration response of layer i in the previous iteration, reflecting the response in the previous iteration. The absolute value of this term is used to control the smoothness of the acceleration response across iterations, ensuring that the optimization process converges gradually without unreasonable acceleration fluctuations.

[0043] All terms in the objective function F are balanced using different weight coefficients α, β, γ, δ, and η. These coefficients can be adjusted based on specific design requirements to find the appropriate trade-off between different optimization objectives. The data acquisition and analysis module 101 continuously collects and updates all of the above parameters, providing an accurate data foundation for the calculation of the objective function, thereby ensuring the stability and feasibility of the optimization process.

[0044] Step S102: Based on the initial structural parameter matrix X, combined with the dynamic characteristics of the structure and the wind tunnel test results, a frequency domain calculation method is used to calculate the wind vibration response to obtain a response characteristic matrix R.

[0045] Step S102 is implemented by using the frequency domain method to calculate the wind-induced vibration response based on the initial structural parameter matrix X, combined with the structure's dynamic characteristics and wind tunnel test results, and ultimately obtaining the response characteristic matrix R. The purpose of this step is to accurately assess the building's dynamic response under wind loads, thereby providing reliable data support for subsequent structural optimization.

[0046] First, step S102 requires analyzing the dynamic characteristics of the super high-rise building structure. This includes modal analysis of the structure to extract its modal parameters, such as vibration mode, natural frequency, and damping ratio. These modal parameters are the basis of the structural dynamic response and can be calculated using finite element analysis software. During the modal analysis process, at least the first few vibration modes of the structure (for example, the first 30 modes) should be extracted, as these vibration modes make an important contribution to the wind-induced vibration response. The modal parameters obtained through analysis will be used for subsequent wind-induced vibration response calculations.

[0047] Secondly, in step S102, the wind tunnel test results are another key input. These test results usually include wind pressure time history data on the building surface, which reflects the stress conditions of the structure under different wind speeds and wind directions. The wind pressure time history data can be obtained through wind tunnel model tests or estimated through numerical simulations. The wind pressure time history data needs to be preprocessed to ensure that it is suitable for frequency domain calculations. During the preprocessing process, the original time domain data needs to be converted into frequency domain data through fast Fourier transform (FFT) to obtain the wind load power spectral density (PSD). The wind load PSD describes the energy distribution of the wind load at different frequencies and is the basic data for calculating the wind vibration response.

[0048] After obtaining the wind load power spectral density, a wind load-to-structural response transfer function must be established. This transfer function describes the transformation of wind loads through the structural dynamic characteristics into structural responses. This transfer function is typically based on random vibration theory, combining the wind load PSD with the structural modal parameters for calculation. Specifically, the transfer function should consider the frequency response characteristics of the structure, specifically combining the contributions of each mode shape. This transfer function can be used to convert the frequency domain characteristics of the wind load into the frequency domain response characteristics of the structure.

[0049] After establishing the wind load-structural response transfer function, frequency-domain calculations of the wind-induced vibration response are performed based on random vibration theory. This calculation multiplies the wind load PSD by the transfer function to obtain the power spectral density (PSD) of the structural response. The response PSD reflects the structure's response energy distribution at different frequencies and accurately describes the building's dynamic response characteristics under wind loads, including acceleration, story displacement, and interstory displacement angle.

[0050] Finally, by integrating the response PSD, we can obtain the structural response characteristic matrix R under wind load. This matrix contains information such as the structural acceleration response, story displacement, and interstory displacement angle at each floor. This matrix will serve as the basis for calculating the equivalent static wind load matrix W and the acceleration response matrix Acc in subsequent steps. All calculations in step S102 should be based on the actual dynamic characteristics of the structure and wind tunnel test results to ensure the accuracy and reliability of the wind-induced vibration response assessment.

[0051] Furthermore, the frequency domain calculation method is used to calculate the wind vibration response to obtain the response characteristic matrix R, including:

[0052] Perform structural modal analysis and extract the eigenvalues ​​and eigenvectors of the first 30 vibration modes;

[0053] Obtain the wind pressure time history on the structure surface through wind tunnel tests;

[0054] Perform fast Fourier transform on the wind pressure time history to obtain the wind load power spectrum density;

[0055] Establish the wind load-structural response transfer function;

[0056] Based on random vibration theory, the structural response is calculated in the frequency domain and the response characteristic matrix R is obtained.

[0057] In this embodiment, a frequency domain calculation method is used to accurately evaluate the wind-induced vibration response and obtain the response characteristic matrix R. This method is particularly important in structural dynamics analysis, especially in the design optimization of high-rise buildings, because wind loads have a significant impact on the structural performance of super-high-rise buildings.

[0058] First, a structural modal analysis is required. Modal analysis is a basic step in structural dynamics analysis, which is used to determine the vibration characteristics of a building structure under wind loads or other dynamic loads. Specifically, by establishing a finite element model of the building structure and performing a modal analysis on the structure, the first 30-order mode shape eigenvalues ​​and eigenvectors can be extracted. The mode shape eigenvalue usually represents the natural frequency of the structure, which is the frequency of the structure's free vibration without damping and external loads; while the eigenvector describes the mode shape of the structure at each natural frequency, that is, the relative displacement mode of each node of the structure. These modal parameters are the basis of wind vibration response analysis and will be used to construct the dynamic characteristics of the structure in subsequent frequency domain calculations.

[0059] After the modal analysis is completed, a wind tunnel test is required to obtain the wind pressure history on the surface of the structure. Wind tunnel testing is an effective method to simulate the stress conditions on the building surface under actual wind conditions. In the test, a scaled-down building model is placed in a wind tunnel for testing. By setting different wind speeds and directions, the wind pressure history at different locations on the model surface can be measured. The wind pressure history is a curve showing the change of wind load over time, which is usually measured at various surface locations of the model using pressure sensors. The wind pressure history data can truly reflect the stress changes of the building under actual wind loads and is an indispensable input in the calculation of wind-induced vibration response.

[0060] Next, the obtained wind pressure time history data is subjected to a fast Fourier transform (FFT) to convert the time domain signal into a frequency domain signal. The purpose of this step is to obtain the power spectral density (PSD) of the wind load. Power spectral density is an important indicator that describes the energy distribution of wind load at different frequencies. Through FFT, the time domain information in the wind pressure time history can be converted into frequency domain information. Specifically, FFT decomposes the wind pressure time history into a superposition of different frequency components, and calculates the amplitude and phase of each frequency component, thereby obtaining the frequency spectrum characteristics of the wind load. The power spectral density can not only describe the amplitude changes of the wind load at different frequencies, but also reflect the random characteristics of the wind load, providing a basis for subsequent frequency domain response calculations.

[0061] After obtaining the power spectral density of the wind load, it is necessary to establish a transfer function for the wind load-structural response. The transfer function is an important concept in structural dynamic analysis, which is used to describe the relationship between the amplitude and phase changes of the structure's response to external loads. The establishment of the transfer function is usually based on random vibration theory, combining the wind load power spectral density with the structural modal parameters to describe the response characteristics of the structure at different frequencies. The transfer function is a function that contains frequency variables. By taking the wind load PSD as input and processing it with the transfer function, the corresponding structural response PSD can be obtained. This process can be understood as converting the frequency domain characteristics of the wind load into the frequency domain response characteristics of the structure.

[0062] Finally, based on random vibration theory, the structural response is calculated in the frequency domain to obtain the response characteristic matrix R. Random vibration theory plays an important role in wind-induced vibration analysis because wind loads are essentially a random process, and their frequency domain response is usually expressed in the form of power spectral density. When calculating the structural response, the power spectral density of the wind load is multiplied by the transfer function to obtain the power spectral density of the structural response. By integrating the response power spectral density, parameters such as the acceleration response, story displacement, and inter-story displacement angle of the structure can be obtained. These parameters are expressed in matrix form to form the response characteristic matrix R. The response characteristic matrix R contains the dynamic response information of the structure at each floor and is key data in the optimization process.

[0063] Through the above process, the use of frequency domain calculation method can not only improve the accuracy of wind-induced vibration response analysis, but also more comprehensively reflect the dynamic characteristics of the structure under wind load, providing a scientific basis and data support for subsequent structural optimization.

[0064] Step S103: Based on the response characteristic matrix R, the equivalent static wind load matrix W and the acceleration response matrix Acc are calculated.

[0065] The specific implementation of step S103 is to calculate the equivalent static wind load matrix W and the acceleration response matrix Acc based on the response characteristic matrix R. The purpose of this step is to convert the wind-induced vibration response characteristics into equivalent static wind loads and acceleration responses, thereby providing key parameter support for the subsequent structural optimization process.

[0066] First of all, the calculation of the equivalent static wind load matrix W needs to comprehensively consider the contribution of different vibration modes to the structural response. In structural dynamics, each order vibration mode has different effects on the response of the structure, so it is necessary to use the modal superposition method to combine the responses. In the specific implementation, the square root of the sum of squares (SRSS) method is used for modal combination, which can effectively superimpose the contribution of each order vibration mode. Specifically, it is first necessary to sum the response of each mode according to the modal response values ​​of each order in the response characteristic matrix R, and then calculate the square root of the sum of squares of these modal responses to obtain the combined response. The calculation result of this step is a matrix reflecting the total response of the structure, which contains the comprehensive contribution of all modes to the structural response.

[0067] After obtaining the comprehensive response, it needs to be converted into an equivalent static wind load matrix W. To this end, the inverse method can be used to determine the wind load distribution that is equivalent to the comprehensive response under static conditions. In specific implementation, it is necessary to first establish a static model, and calculate the corresponding equivalent static wind load by taking the comprehensive response matrix as input and setting the stiffness parameters and deformation relationship of the structure. Each element in the equivalent static wind load matrix W represents the equivalent wind load intensity of the structure at a specific location. The matrix is ​​used to simulate the static effect of wind loads during the optimization process, so that the optimization results can better reflect the response characteristics of the structure under actual wind loads.

[0068] The calculation of the acceleration response matrix Acc focuses on the vibration acceleration of the structure. Acceleration response is a key indicator for evaluating the wind resistance and user comfort of high-rise buildings. In order to obtain the acceleration response matrix, it is necessary to use the acceleration components in the response characteristic matrix R for calculation based on random vibration theory. Specifically, the acceleration response values ​​of each floor of the structure can be obtained by extracting the acceleration-related part of the response characteristic matrix and performing random vibration integration on it. Each element in the acceleration response matrix Acc corresponds to the acceleration value of the structure at a specific floor. These values ​​can reflect the vibration acceleration of different floors of the structure under wind load.

[0069] Through this calculation method, step S103 accurately obtains the equivalent static wind load matrix and acceleration response matrix, which are essential foundational data for the optimization process. This calculation ensures that the optimization model can truly reflect the response characteristics of the structure under wind load in subsequent iterations, thereby improving the reliability and accuracy of the overall optimization.

[0070] Furthermore, the calculation of the equivalent static wind load matrix W and the acceleration response matrix Acc based on the response characteristic matrix R includes:

[0071] Based on the response characteristic matrix r, the SRSS method is used to combine the contributions of each mode;

[0072] The equivalent static wind load matrix w with the same effect is calculated by the inverse method;

[0073] The wind-induced acceleration calculation method is used to obtain the acceleration response of each layer of the structure and form the acceleration response matrix Acc.

[0074] This section of the present embodiment calculates the equivalent static wind load matrix W and the acceleration response matrix Acc based on the response characteristic matrix R, accurately reflecting the force and response characteristics of the structure under wind load. To ensure that the calculation of these matrices is technically reasonable, accurate, and feasible, the implementation process is described in detail below.

[0075] First, based on the response characteristic matrix R, the square root of the sum of squares (SRSS) method is needed to combine the contributions of each mode to the structural response. The SRSS method is widely used in modal combination in structural dynamics because it can effectively superimpose responses of different vibration modes. Specifically, the response characteristic matrix R contains the response values ​​of each mode, and the response of each mode is the response of the structure to the wind load under the corresponding vibration mode. In order to obtain the overall response, these modal responses need to be combined. The basic principle of the SRSS method is to perform a square sum operation on the response values ​​of each mode and square the result to obtain the total response after combination. In this way, the SRSS method can reflect the nonlinear superposition effect between different modes and avoid the deviation of excessive or too small response caused by direct addition.

[0076] After obtaining the combined response, the next step is to calculate the equivalent static wind load matrix W through the inverse method. The inverse method is a calculation method based on the force-displacement relationship, which is used to determine the static load distribution equivalent to the dynamic response. In actual operation, it is first necessary to determine the displacement and internal force distribution of the structure on each floor based on the combined response, and then inversely deduce the equivalent wind load that can produce the same response under static action. Specifically, this step establishes the stiffness matrix and static model of the structure, uses the combined response as the displacement input, and calculates the equivalent static load based on the stiffness relationship of the structure, thereby obtaining the equivalent static wind load matrix W. Each element in the equivalent static wind load matrix represents the static load that needs to be applied on a specific floor or node to produce the same structural response as under actual wind load.

[0077] Next, the wind-induced acceleration calculation method is used to obtain the acceleration response of each layer of the structure and form the acceleration response matrix Acc. Wind-induced acceleration is a key response indicator of a building under wind load. Especially in the design of high-rise buildings, acceleration has an important impact on the comfort and safety of the structure. Specifically, the calculation of wind-induced acceleration is based on random vibration theory. The acceleration component in the response characteristic matrix R is extracted and analyzed in combination with the modal parameters of the structure and the power spectrum density of the wind load. By calculating the acceleration response of each layer, a matrix Acc describing the acceleration response of different floors can be obtained. Each element in the matrix represents the acceleration magnitude on a specific floor and is a key parameter reflecting the vibration intensity of the building under wind load.

[0078] Throughout the calculation process, the equivalent static wind load matrix W and the acceleration response matrix Acc are important outputs of the wind-induced vibration response analysis, used to assess the structural stress state and dynamic performance, respectively. The accurate calculation of these matrices is crucial for subsequent structural optimization because they not only provide basic data for the optimization objective function but also directly influence the fitness evaluation and iteration process of the particle swarm algorithm.

[0079] Through the above steps, this embodiment can accurately calculate the static wind load and acceleration response equivalent to the wind vibration response, thereby providing a scientific and reasonable numerical basis for structural optimization design.

[0080] Step S104: Based on the equivalent static wind load matrix W and the acceleration response matrix Acc, the following iterative calculation is performed using a combined optimization algorithm of the optimization criterion method and the particle swarm algorithm:

[0081] P101: According to the response characteristic matrix R, initialize the relevant parameters of the particle swarm, including the position matrix P and the velocity matrix V, and set the initial individual optimal position matrix P best and the group optimal position matrix G best ;

[0082] P102: Substitute the position matrix P into the objective function and calculate the fitness value matrix A of each particle to evaluate the quality of the current design scheme;

[0083] P103: Update the individual optimal position matrix P according to the fitness value matrix A best and the group optimal position matrix G best , to improve the global and local search capabilities of the particle swarm;

[0084] P104: Based on the optimization criterion method, combined with the updated individual optimal position matrix P best and the group optimal position matrix G best, iteratively update the position matrix P and velocity matrix V of the particle swarm to obtain the updated position matrix P' and velocity matrix V';

[0085] P105: Based on the updated position matrix P', the equivalent static wind load matrix W and acceleration response matrix Acc are recalculated to update the wind-induced vibration response data during the optimization process.

[0086] P106: Based on the preset convergence accuracy ε, determine whether the norm of the difference between the updated position matrix P' and the position matrix P of the previous round is less than ε; if it is less than ε, output the optimal solution matrix Opt; if it is greater than or equal to ε, assign P' to P and return to step P102 for further iteration.

[0087] Step S104 is specifically implemented by performing multiple iterative calculations based on the equivalent static wind load matrix W and the acceleration response matrix Acc, using a combined optimization algorithm of the optimization criterion method and the particle swarm optimization algorithm. The goal is to achieve global optimization of the structural design under multi-objective constraints.

[0088] In this process, the particle swarm needs to be initialized first. According to the response characteristic matrix R, the relevant parameters of the particle swarm are initialized, including the position matrix P and the velocity matrix V. The position matrix P represents the current value of the structural design variable and is a specific representation of the design parameters; the velocity matrix V reflects the movement speed of the particles in the search space. In order to improve the diversity of the search, the initial values ​​of the position and velocity are randomly generated within the allowable range. In addition, the initial individual optimal position matrix P is set best and the group optimal position matrix G best , which are used to record the historical optimal position of each particle and the historical optimal position of the entire particle group.

[0089] After initialization, the position matrix P is substituted into the objective function, and the fitness matrix A for each particle is calculated to evaluate the current design. Fitness is the core metric for evaluating solutions in the particle swarm algorithm. The fitness matrix A contains the fitness of each particle, and particles with higher fitness indicate that their corresponding design approaches the optimization goal. The objective function calculation incorporates multiple constraints, such as structural layer displacement, inter-layer displacement angle, and top-floor acceleration, enabling the optimization results to comprehensively reflect the structure's wind resistance and economic benefits.

[0090] After the fitness value matrix A is calculated, the individual optimal position matrix P needs to be updated according to the fitness value. best and the group optimal position matrix G best For each particle, if its current fitness value is better than the historical optimal fitness value, the individual optimal position matrix P is updated bestAt the same time, the particle position with the highest fitness is selected from all individual optimal positions as the group optimal position matrix G best , in order to improve the global and local search capabilities of the particle swarm.

[0091] After completing the optimal position update, according to the optimization criterion method, combined with the updated individual optimal position matrix P best and the group optimal position matrix G best , iteratively updating the particle's position matrix P and velocity matrix V. During the velocity update process, factors such as inertia weight, learning factor, and random perturbations are taken into account, ensuring that the particle's motion within the solution space achieves a balance between global search and local optimization. The updated position matrix P' and velocity matrix V' are obtained by calculating the new position and velocity of each particle. These updated values ​​are used for the next round of fitness calculation and optimal position update.

[0092] After obtaining the updated position matrix P', the equivalent static wind load matrix W and the acceleration response matrix Acc need to be recalculated based on this to ensure the dynamic update of the wind-induced vibration response data. In this way, the optimization process can adapt to the changes in the design variables in each iteration and maintain synchronization with the actual wind load.

[0093] After each iteration, the position matrix changes must be determined based on the preset convergence accuracy ε to determine whether they have met the convergence criteria. Specifically, the difference norm between the updated position matrix P' and the previous position matrix P is calculated. If this norm is less than ε, the optimization is considered to have met the expected accuracy requirements and the optimal solution matrix Opt is output. If the convergence criteria are not met, the updated position matrix P' is assigned to P and the process returns to the fitness calculation phase of the next iteration for further optimization.

[0094] This optimization process will continue until the convergence accuracy is met, ensuring that the output optimal solution matrix Opt can achieve the comprehensive optimal design of the structural wind resistance and economic benefits.

[0095] Furthermore, the initialization of relevant parameters of the particle swarm according to the response characteristic matrix R includes:

[0096] Set the particle swarm size to 30-50 particles;

[0097] Randomly generate the initial position matrix P within the allowable range of the design variables;

[0098] Set the initial velocity matrix V to a random value between -10% and +10% of the position matrix.

[0099] In the optimization design process of the particle swarm algorithm in this embodiment, the particle swarm is initialized based on the response characteristic matrix R. This step is crucial to the accuracy and efficiency of the optimization process. The relevant parameters of the particle swarm need to be initialized while maintaining diversity, providing a good starting point for the global search and local optimization of the particle swarm. In order to ensure that the particle swarm can fully explore the solution space and quickly converge to the optimal solution, the implementation process is described in detail below.

[0100] First, the size of the particle swarm needs to be set. The size of the particle swarm refers to the number of particles involved in the search during the optimization process. In this invention, it is recommended to set it to 30-50 particles. The selection of the particle swarm size requires a balance between computational efficiency and search effect: a smaller particle swarm may lead to insufficient coverage of the solution space and easily fall into a local optimum; while a larger particle swarm may increase the amount of computation and convergence time. Within the range of 30-50 particles, the size of the particle swarm can achieve a good balance in actual engineering applications, ensuring global search capabilities without causing excessive consumption of computing resources.

[0101] Next, the initial position matrix P needs to be randomly generated within the allowable range of the design variables. The position matrix P is the core parameter in the particle swarm algorithm, which represents the specific position of each particle in the solution space. The current position of each particle is composed of multidimensional design variables. Specifically in structural optimization, these design variables can include the cross-sectional dimensions of beams and columns, the thickness of floor slabs, the strength of structural materials, etc. In order to achieve initialization, it is first necessary to determine the upper and lower limits of each design variable. These ranges are usually set based on structural design specifications or engineering experience. Then, within these allowable ranges, random number generation technology is used to assign initial values ​​to each design variable to generate the initial position matrix P. This random generation method can ensure that the initial position of the particle swarm has a sufficient distribution range in the solution space, which helps to fully cover the entire solution space at the beginning of the global search and improve the diversity of the algorithm.

[0102] After generating the initial position matrix P, the initial velocity matrix V needs to be set. The velocity matrix V represents the speed at which each particle moves in the solution space and is a key parameter in the particle swarm algorithm that controls the direction and amplitude of particle motion. During initialization, the value of the initial velocity matrix is ​​set to a random value between -10% and +10% of the position matrix. Specifically, for each particle and each design variable, the initial velocity value is generated by multiplying the corresponding element of the position matrix by a random number between -0.1 and 0.1. This velocity initialization method can provide a certain degree of exploration for the particle swarm in the early iterations, while avoiding excessive solution jumps caused by excessive velocity or slow convergence caused by excessive velocity. In addition, the selection of this random range can maintain a certain degree of randomness and flexibility in the early stages of the particle swarm, which helps to explore potential optimal solutions in the solution space.

[0103] Through the above initialization steps, the relevant parameters of the particle swarm are effectively set, laying a good foundation for subsequent fitness evaluation and iterative updates. The rationality of the initialization steps directly affects the optimization effect and convergence speed of the particle swarm algorithm. Therefore, it is necessary to ensure that the generation range and randomness of each parameter are precisely controlled during the specific implementation process to improve the performance and efficiency of the entire structural optimization design process.

[0104] Furthermore, when the velocity matrix V of the particle swarm is initialized in step P101, the following formula 2 is used:

[0105]

[0106] Among them, V i,j represents the initial velocity of the jth dimension of the i-th particle; V init,j represents the baseline initial velocity of the jth dimension; Δ i represents the layer displacement of the i-th layer; Δ max represents the maximum allowable layer displacement; θ i represents the inter-story displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle; R i,j is a random number.

[0107] In the implementation of the particle swarm algorithm in this embodiment, the initialization of the velocity matrix V is crucial. By using formula (2), it can be ensured that the initial value of the velocity matrix can reflect key parameters such as the structure's story displacement and interstory displacement angle, thereby providing reasonable initial conditions for the optimization process.

[0108] The basic form of formula (2) is:

[0109]

[0110] In this formula, V (i,j) The initial velocity of the jth dimension of the i-th particle is the specific velocity component of each particle in the structural optimization design. The velocity of the particle is the key factor in controlling the search direction and amplitude in the particle swarm algorithm.

[0111] V init,j The baseline initial velocity for the jth dimension is a preset velocity value, typically set based on the range of the design variables. Specifically, during initialization, an initial velocity range is assigned to each dimension, such as the upper and lower limits of a structure's cross-sectional dimensions. The baseline initial velocity sets an upper limit for each particle's initial velocity, ensuring a consistent directionality and amplitude during the initial search.

[0112] Δ iThe displacement of the i-th floor is the horizontal displacement response of the structure under wind loads or other external loads. This value can be obtained through finite element analysis or other structural analysis methods. Specifically, by simulating the building's dynamic response under wind loads, the displacement response values ​​of different floors can be derived. The displacement response directly reflects the deformation state of the structure and is a key parameter to consider during the optimization process.

[0113] Δ max The maximum allowable story displacement is a value set by building design codes or standards to limit the maximum deformation of a structure under external forces. This value is typically determined by the building's function, safety requirements, and design standards, such as the maximum allowable displacement of a high-rise building under earthquake or wind loads.

[0114] In formula (2), the term is a normalized layer displacement factor that represents the relative degree of the current displacement relative to the maximum allowed displacement. Its purpose is to adjust the velocity so that particles are subject to greater velocity regulation when approaching the maximum displacement constraint, prompting particles to conduct more detailed searches near the displacement constraint.

[0115] θ i The inter-story drift angle represents the i-th floor and is the ratio of the relative displacement between two adjacent floors to the floor height. This parameter reflects the structural stiffness and lateral drift resistance and is calculated by calculating the relative displacement between adjacent floors and dividing it by the floor height. Similar to story drift, the inter-story drift angle is obtained through structural dynamic analysis and is typically used to assess the lateral drift behavior of a structure under wind or seismic loads.

[0116] θ max The maximum allowable inter-story drift angle is an upper limit set by building design codes. Its purpose is to limit the relative deformation of a building under lateral loads to ensure structural stability and safety. This value is regulated by building codes and is generally related to the building type, structural system, and intended use.

[0117] In formula (2), the term is a normalized inter-story displacement angle factor whose purpose is to adjust the velocity based on the relative magnitude of the current inter-story displacement angle. In this way, as the inter-story displacement angle approaches its maximum allowable value, the velocity adjustment amplitude becomes larger to strengthen the control of this constraint, thus guiding the particle swarm to pay more attention to the inter-story displacement angle constraint during the optimization process.

[0118] R (i,j)is a random number used to introduce randomness and diversity to particle velocities. Random numbers typically range from [0, 1]. The inclusion of random numbers enhances the swarm's exploration capabilities and prevents the algorithm from falling into local optima. The introduction of random numbers imparts a degree of randomness to particle velocities, helping to balance global and local search during the optimization process.

[0119] From the above explanation, it can be seen that each term in formula (2) plays an important role in the velocity initialization process. The velocity initialization not only affects the search direction and speed of the particle swarm algorithm, but also directly affects the algorithm's global search capability and convergence efficiency. By combining the normalization factors of displacement and inter-story displacement angle with the benchmark velocity and random number, the initial value of the velocity can maintain search diversity while paying more attention to the key performance constraints of the structure. This initialization method can effectively improve the applicability and efficiency of the particle swarm algorithm in structural optimization, thereby better achieving comprehensive optimization of building structures.

[0120] Furthermore, according to the fitness value matrix A, the individual optimal position matrix P is updated. best and the group optimal position matrix G best ,include:

[0121] Determine whether the current particle's fitness value is better than its historical optimal value;

[0122] If it is better than the historical optimal value, the individual optimal position matrix P is updated with the current position best ;

[0123] Select the optimal fitness value from the individual optimal positions of all particles;

[0124] Update the group optimal position matrix G with the selected optimal value best .

[0125] In the implementation process of the particle swarm algorithm of this embodiment, the individual optimal position matrix P is updated based on the fitness value matrix A. best and the group optimal position matrix G best This process aims to improve the global and local search capabilities of the algorithm, thereby better finding the optimal solution for structural optimization.

[0126] First, the fitness matrix A is used to determine the comparison between the current fitness value of each particle and its historical optimal value. The fitness value is an indicator used to evaluate the quality of the particle's current position in the solution space. The higher the fitness value of the particle position, the better the objective function performance of the design scheme under the premise of meeting the constraints. For comparison, the fitness value of each particle is first extracted and compared with the individual optimal position matrix P. bestCompare with the historical optimal fitness values ​​recorded in .

[0127] If the current fitness value of a particle is better than its historical optimal value, the current position of the particle needs to be used to update the individual optimal position matrix P best When the current fitness value exceeds the historical optimal value, the corresponding position value in the current position matrix P is assigned to P best This updating method ensures that each particle can retain the historically optimal solution in the solution space, thus providing a better local search reference in subsequent iterations.

[0128] Next, we need to select the optimal fitness value from the individual optimal positions of all particles. This process involves the individual optimal position matrix p best By traversing and comparing all fitness values ​​in the swarm, we can find the particle with the highest fitness value, that is, the optimal position of the best performing individual in the current swarm. This optimal position represents the currently known best solution for the swarm and is a candidate for the global optimal position.

[0129] Finally, the selected optimal fitness value is used to update the group optimal position matrix G best . Group optimal position matrix G best Each element in corresponds to the global optimal position of the particle swarm in a certain dimension. When the optimal position of the individual with the highest fitness is found, it is necessary to move the iteration of this position towards the global optimal solution.

[0130] This updating process can not only improve the global search capability of the particle swarm algorithm, but also ensure the accuracy and stability of the individual optimal position. best and the group optimal position matrix G best ,The particle swarm optimization algorithm can better balance the relationship between ,global search and local search in the solution space, thereby achieving ,the comprehensive optimal design of structural optimization.

[0131] Furthermore, in step P104, the position matrix p and velocity matrix V of the particle swarm are iteratively updated using the following formulas 3 and 4:

[0132]

[0133] P' i,j =P i,j +V' i,j (4)

[0134] Among them, ω max represents the initial inertia weight; λ is the decreasing coefficient; t represents the current number of iterations; V i,j represents the velocity of the jth dimension of the i-th particle; V' i,jrepresents the updated velocity of the jth dimension of the i-th particle; P i,j represents the position of the jth dimension of the i-th particle; P' i,j represents the updated position of the jth dimension of the i-th particle; c1, c2 represent learning factors, which are used to control the influence of individual optimality and group optimality on speed update; r1, r2 are random numbers in the interval [0, 1], which are used to increase the randomness of particle motion; P best,i,j represents the individual optimal position of the jth dimension of the i-th particle; G best,j represents the optimal position of the group in the jth dimension; φ is the acceleration adjustment factor, which is used to balance the influence of wind load and acceleration response; W i is the equivalent static wind load of the i-th layer; Acc i is the acceleration response of the i-th layer.

[0135] In this embodiment, the iterative update of the particle swarm algorithm is one of the core processes of structural optimization design. In step P104, the particle swarm's position matrix P and velocity matrix V are updated using equations (3) and (4). This not only ensures the particle swarm's dynamic search capability in the solution space but also effectively balances the optimization objectives of the structure's wind load and acceleration response.

[0136] The form of formula (3) is:

[0137]

[0138] First, V' (i,j) The updated velocity of the jth dimension of the i-th particle is the new velocity value obtained through the interaction of multiple factors in the current iteration. Velocity update is the most critical step in the particle swarm algorithm, which determines the next direction and stride of the particle.

[0139] ω max represents the initial inertia weight, a parameter that controls the continuity of particle velocity. The inertia weight is used to balance global and local search capabilities: a larger inertia weight favors global search, while a smaller inertia weight favors local search. To gradually increase the weight of local search during optimization, the inertia weight is typically designed to decrease with the number of iterations. This is achieved using an exponential decrease factor, exp(-λ·t), where λ is the coefficient that controls the rate at which the inertia weight decreases. t is the current iteration number. As the number of iterations increases, the inertia weight decreases, encouraging particles to converge on the local optimal solution.

[0140] V (i,j)The current velocity of the jth dimension of the i-th particle is the velocity of the particle before the current iteration. This item is used to adjust the inertia weight to ensure that the particle's motion maintains a certain degree of continuity and stability, avoiding excessive jumps that may cause search instability.

[0141] c1·r1·(P best,i,j -P (i,j) ) is the individual learning term, which reflects the motivation of the particle to move towards its historical optimal position. Among them, c1 is the individual learning factor, which is used to adjust the influence of the individual optimal position on the speed update. A larger c1 value will increase the individual's attraction to its optimal solution, making the particle more inclined to search for its own historical optimal solution. r1 is a random number in the interval [0,1], which is used to increase the randomness and diversity of the individual search and ensure that different particles do not move in exactly the same direction during the search process. best,i,j is the individual optimal position of the jth dimension of the i-th particle, representing the best solution of the particle in the historical iteration. (i,j) is the current particle position, and the difference between it and the individual optimal position is used to guide the particle to move closer to the individual optimal position.

[0142] c2·r2·(G best,j -P (i,j) ) is the group learning term, which reflects the motivation of particles to move towards the global optimal position. Among them, c2 is the group learning factor, which is used to adjust the influence of the group optimal position on the speed update. A larger c2 value will enhance the attraction of particles to the group optimal solution, making particles tend to move towards the global optimal solution. r2 is another random number in the range [0,1] used to increase the group Randomness of the search. best,j is the optimal position of the group, representing the global optimal solution of the entire particle swarm in the current iteration.

[0143] is the acceleration adjustment term, which is used to balance the effects of wind load and acceleration response. Where φ is the acceleration adjustment factor, which is used to control the effects of wind load and acceleration response on velocity update. It is a normalized process for layer displacement and nonlinear mapping through hyperbolic tangent function. This mapping method can enhance the speed regulation when the displacement is small, and gradually weaken it when the displacement approaches the maximum allowable value. i is the equivalent static wind load of the i-th layer, which is the static load obtained through wind vibration response analysis. i is the acceleration response of the i-th layer, reflecting the vibration intensity of the structure under wind load. The overall effect of this term is to adjust the velocity based on the differences between layer displacement, wind load, and acceleration response, so that the particles move closer to the optimal solution in the solution space.

[0144] Formula (4) is used to update the particle position matrix:

[0145] P' (i,j) =P (i,j) +V' (i,j)

[0146] Among them, P' (i,j) is the updated position of the jth dimension of the ith particle, which is obtained by adding the updated velocity to the current particle position. This formula reflects the position change of the particle in the current iteration and is the most basic displacement update mechanism in the particle swarm algorithm.

[0147] Through the iterative update of formulas (3) and (4), the particle swarm can dynamically adjust its speed and position in the solution space, so that the search process finds a balance between global and local optimality, thereby achieving the comprehensive goal of structural optimization design.

[0148] Furthermore, in step P105, the recalculation of the equivalent static wind load matrix W and the acceleration response matrix Acc is implemented using the following formulas 5 and 6:

[0149]

[0150] Among them, W' i Indicates the updated equivalent static wind load; Acc' i represents the updated acceleration response; W i Indicates the equivalent static wind load before updating; Acc i represents the acceleration response before updating; μ,v is the adjustment factor used to enhance the dynamic adjustment of load and response; Δ i represents the layer displacement of the i-th layer; Δ max represents the maximum allowable layer displacement; θ i represents the inter-story displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle.

[0151] In the particle swarm optimization process of this embodiment, step P105 involves recalculating the equivalent static wind load matrix W and the acceleration response matrix Acc. This process is crucial because it further improves the optimization effect of the structure by dynamically adjusting the loads and responses. The following describes the detailed implementation of equations (5) and (6).

[0152] The form of formula (5) is:

[0153]

[0154] Among them, W' irepresents the updated equivalent static wind load, which is the adjusted load value for layer i in the current iteration. The updated load value is calculated to better reflect the dynamic response of the structure under wind loads, ensuring that the optimization process accurately adjusts for the effects of wind loads on the structure.

[0155] W i is the equivalent static wind load before the update, obtained from the wind-induced vibration response analysis of the previous iteration. It represents the equivalent static load on the i-th layer in the previous iteration and is used to simulate the effect of wind load.

[0156] μ is a modulating factor that controls the dynamic adjustment range of the wind load. The setting of this factor depends on the specific optimization goal and the characteristics of the structure, and can be adjusted during the experiment based on the optimization results. A larger μ value increases the load adjustment range, thereby increasing the optimization process's sensitivity to wind load changes.

[0157] It is a nonlinear mapping of the layer displacement after normalization through the hyperbolic tangent function. i Represents the layer displacement of the i-th layer, which is the horizontal displacement of the structure calculated under the current load. This value is usually obtained through finite element analysis or structural dynamics analysis and is an important parameter reflecting the deformation state of the structure. max The maximum allowable story displacement is an upper limit set by building design codes or standards. It represents the maximum allowable deformation of a structure under wind loads and is used to limit its horizontal displacement. The introduction of the hyperbolic tangent function makes the influence of story displacements nonlinear during the update process. This means that when story displacements are small, the load adjustment is small; however, as story displacements approach the maximum allowable value, the load adjustment increases significantly, thereby better guiding structural optimization towards safety.

[0158] The form of formula (6) is:

[0159]

[0160] Among them, Acc' i The updated acceleration response is the adjusted acceleration value of the i-th layer in the current iteration. The updated acceleration response reflects the response adjustment of the structure to wind vibration during the optimization process and is a key parameter for controlling the comfort and safety of the structure. i is the acceleration response before the update, typically obtained through wind-induced vibration analysis. It represents the acceleration response of the i-th floor under wind loads during the previous iteration. v is a control factor that controls the dynamic adjustment of the acceleration response. This factor, similar to μ, is also adjusted through experimentation and optimization. Larger v values ​​result in more significant adjustments to the acceleration response, thereby increasing the sensitivity of the structure to acceleration.

[0161] It is the normalization of the inter-story displacement angle and increases the nonlinear weight through square operation. i θ represents the inter-story drift angle of the i-th floor, which is obtained by calculating the ratio of the relative displacement of two adjacent floors to the floor height. This parameter is an important indicator for measuring the structural stiffness and anti-lateral drift performance. max is the maximum allowable inter-story drift angle, an upper limit set by design specifications to limit the relative deformation of the structure. Squaring the inter-story drift angle results in a greater adjustment of the acceleration response at larger displacement angles. This nonlinear enhancement allows the optimization process to better handle large displacement angles, ensuring structural stability and safety.

[0162] During implementation, the dynamic adjustment mechanism of formulas (5) and (6) can update the equivalent static wind load and acceleration response in real time based on the current wind load and acceleration response changes during each iteration of the particle swarm algorithm. This adjustment mechanism not only improves the flexibility of the optimization but also ensures that the optimization results meet safety and comfort requirements while achieving comprehensive optimization of wind load and acceleration response. This sophisticated dynamic adjustment method makes the structural optimization process more accurate and reliable.

[0163] Step S105: Based on the output optimal solution matrix Opt, a final design solution S of the structure is determined to achieve an optimal design for the wind resistance performance and economic benefits of the structure.

[0164] Step S105 determines the final structural design S based on the output optimal solution matrix Opt, achieving a comprehensive optimal design for both wind resistance and economic efficiency. The goal of this step is to transform the optimal solution, obtained through multiple iterations of optimization, into a practical, implementable building structural design.

[0165] First, the final values ​​of each design variable need to be extracted from the optimal solution matrix Opt. This matrix represents the optimal solution obtained during the particle swarm algorithm's iterations. Each element in the matrix represents a specific structural design parameter. These design parameters may include the cross-sectional dimensions of beams and columns, floor slab thickness, and the strength grade of the structural material. Therefore, during implementation, the design variable values ​​in the optimal solution matrix must be read one by one and used in the subsequent design plan formulation.

[0166] After extracting the design variable values, they need to be rounded or normalized to meet the actual construction requirements of the project. In building structural design, some design parameters may need to match standard specifications in the construction industry, such as rebar size or concrete strength grade. The purpose of this rounding or normalization is to ensure that the optimal design parameters can be implemented in the actual project without affecting the overall performance of the building structure. During this process, appropriate adjustments or corrections can be made according to relevant project standards or specifications to ensure the feasibility of the design parameters.

[0167] Next, it is necessary to perform finite element analysis verification of the structure based on the extracted design variable values. The purpose of finite element analysis is to conduct a comprehensive evaluation of the safety, stability and performance of the structure before determining the final design scheme S. Specifically, by taking the optimal design parameters as input, a complete structural finite element model is established, and force analysis, stability analysis and dynamic response analysis are performed on it. Force analysis is used to evaluate the stress and deformation of the structure under static loads; stability analysis is used to check the structure's ability to resist lateral displacement under lateral loads (such as wind loads); dynamic response analysis is used to evaluate the acceleration response and inter-story displacement angle of the structure under wind vibration. These analysis results can help engineers judge the rationality and feasibility of the optimal design scheme, ensuring that it meets all constraints and design objectives.

[0168] After verification is complete, the final structural design solution S can be determined. This solution will include the design parameters, dimensions, material types, and other relevant information for all components, and will serve as the structural design drawings and specifications for actual construction. This solution should optimize economic benefits while ensuring structural safety and user comfort. The final design solution marks the completion of the optimization process and is the result of the application of the particle swarm algorithm to building structural design.

[0169] Through the above steps, step S105 converts the output optimal solution matrix Opt into a detailed and implementable structural design solution S, ensuring the practical application value of the structural optimization results while meeting the technical requirements in engineering practice.

[0170] Furthermore, the final design solution S of the structure is determined based on the output optimal solution matrix Opt, including:

[0171] Extract the values ​​of each design variable in the optimal solution matrix Opt;

[0172] Round the design variables to the actual specifications and sizes that can be adopted in the project;

[0173] Conduct structural finite element analysis verification to ensure that all constraints are met;

[0174] Output the final design parameters of each structural component to form the design scheme S.

[0175] In the particle swarm optimization design method of this embodiment, the final structural design solution S is determined by using the optimal solution matrix Opt. This process is a key part of the entire optimization process, involving the conversion of the calculation results into a practical and feasible engineering design solution. To ensure the accuracy and feasibility of this step, each link is described in detail below.

[0176] First, it is necessary to extract the values ​​of each design variable from the optimal solution matrix Opt. The optimal solution matrix Opt is the result matrix obtained after the particle swarm algorithm completes all iterations and contains the optimal values ​​of all design variables. These design variable values ​​are the global optimal solution obtained through fitness evaluation and multiple iterative optimizations. They represent the best design solution for the structure while satisfying the constraints and optimization objectives. During the extraction process, it is necessary to separate the specific values ​​of each design variable from the optimal solution matrix, such as structural cross-sectional dimensions, material strength, and floor height. These variable values ​​are an important basis for the final design of the structure and will be directly used in the engineering design implementation.

[0177] Next, the design variables need to be rounded to actual project specifications. While the optimization results of a particle swarm algorithm are typically continuous values, the design variables used in actual projects are often discrete, standard specifications. For example, variables such as beam and column cross-sectional dimensions, rebar diameter, and plate thickness must conform to existing standard specifications or material supply requirements in engineering design. Therefore, in this step, the design variables in the optimal solution need to be rounded or approximately adjusted to conform to the actual project specifications. This conversion process can be accomplished by searching and matching a standard dimension library, ensuring that the design solution not only meets the optimization objectives but can also be applied in construction.

[0178] After obtaining the design variables that meet the actual specifications, the design scheme needs to be verified by structural finite element analysis. Finite element analysis is a common method to verify the rationality and safety of structural design, and can simulate the response of the structure under different loads. In this verification step, the rounded design variables need to be used as input to construct a finite element model of the structure. By simulating the load conditions, support conditions and boundary conditions of the structure, the displacement, stress and deformation of the structure can be calculated. The focus of the verification is to ensure that the structure can meet the specified strength, stability and deformation requirements under wind loads, seismic loads or other design loads. If the results of the finite element analysis indicate that the design scheme does not meet the constraints, the design scheme needs to be appropriately adjusted to ensure that all design variables can meet the safety and optimization goals at the same time.

[0179] After completing the finite element analysis and verifying that all constraints are met, the final design parameters of each structural component must be output, thus forming the structural design solution S. The final design solution should include detailed design parameters for each structural component, including beam and column cross-sections, floor slab thickness, material type, and reinforcement configuration. These parameters will serve as the basis for construction drawings and project implementation, ensuring that the optimized structural design can be applied and implemented in the actual project.

[0180] Through the above steps, this embodiment can generate a final design solution S that meets the actual needs of the project based on the optimal solution matrix Opt. This process not only realizes the transformation of optimization results, but also ensures the feasibility and safety of the structural design, providing a reliable design foundation for engineering construction.

[0181] A second embodiment of the present application provides an electronic device, comprising:

[0182] processor;

[0183] The memory is used to store a program, which, when read and executed by the processor, executes the structure optimization design method based on the particle swarm algorithm provided in the first embodiment of the present application.

[0184] The third embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the structure optimization design method based on the particle swarm algorithm provided in the first embodiment of the present application is executed.

[0185] Although the present application is disclosed as above with the preferred embodiments, it is not intended to limit the present application. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be based on the scope defined by the claims of the present application.

Claims

1. A structural optimization design method based on particle swarm optimization algorithm, characterized in that: include: By establishing an optimization model for super high-rise building structures, setting the objective function, and setting the structural layer displacement, inter-layer displacement angle and top-floor peak composite acceleration as constraints, the initial structural parameter matrix X is generated. Based on the initial structural parameter matrix X, combined with the dynamic characteristics of the structure and the wind tunnel test results, the frequency domain calculation method is used to calculate the wind vibration response to obtain the response characteristic matrix R; Based on the response characteristic matrix R, the equivalent static wind load matrix W and acceleration response matrix Ac are calculated. c ; According to the equivalent static wind load matrix W and acceleration response matrix Ac c , the combined optimization algorithm of the optimization criterion method and the particle swarm optimization algorithm is used to perform the following iterative calculations: P101: According to the response characteristic matrix R, initialize the relevant parameters of the particle swarm, including the position matrix P and the velocity matrix V, and set the initial individual optimal position matrix P best and the group optimal position matrix G best ; P102: Substitute the position matrix P into the objective function and calculate the fitness value matrix A of each particle to evaluate the quality of the current design scheme; P103: Update the individual optimal position matrix P according to the fitness value matrix A best and the group optimal position matrix G best , to improve the global and local search capabilities of the particle swarm; P104: Based on the optimization criterion method, combined with the updated individual optimal position matrix P best and the group optimal position matrix G best , iteratively update the position matrix P and velocity matrix V of the particle swarm to obtain the updated position matrix P′ and velocity matrix V′; P105: Based on the updated position matrix P′, recalculate the equivalent static wind load matrix W and acceleration response matrix Ac. c , thereby updating the wind-induced vibration response data during the optimization process; P106: Based on the preset convergence accuracy ε, determine whether the norm of the difference between the updated position matrix P′ and the previous position matrix P is less than ε; if less than ε, output the optimal solution matrix Opt; if greater than or equal to ε, assign P′ to P and return to step P102 for further iteration; Based on the output optimal solution matrix Opt, the final design scheme S of the structure is determined to achieve the optimal design of the structural wind resistance and economic benefits.

2. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: The objective function adopts the following formula 1: Among them, F represents the fitness value; n represents the total number of layers of the structure; Δ i represents the layer displacement of the i-th layer; Δ max represents the maximum permissible story displacement; θ i represents the inter-story displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle; a top represents the resultant acceleration of the top layer; a max Indicates the maximum allowable top composite acceleration; C mat Indicates the total material cost of the structure; C const represents the total construction cost of the structure; α, β, γ, δ, η are balance coefficients; W i is the equivalent static wind load of the i-th layer calculated in the current iteration; W i,prev is the equivalent static wind load of the i-th layer calculated in the previous iteration; Acc i is the acceleration response of the i-th layer calculated in the current iteration; Acc i,prev is the acceleration response of the i-th layer calculated in the previous iteration.

3. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: The frequency domain calculation method is used to calculate the wind vibration response to obtain the response characteristic matrix R, which includes: Perform structural modal analysis and extract the eigenvalues ​​and eigenvectors of the first 30 vibration modes; Obtain the wind pressure time history on the structure surface through wind tunnel tests; Perform fast Fourier transform on the wind pressure time history to obtain the wind load power spectrum density; Establish the wind load-structural response transfer function; Based on random vibration theory, the structural response is calculated in the frequency domain and the response characteristic matrix R is obtained.

4. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: The calculation of the equivalent static wind load matrix W and the acceleration response matrix Acc based on the response characteristic matrix R includes: Based on the response characteristic matrix R, the SRSS method is used to combine the contributions of each mode; The equivalent static wind load matrix W with the same effect is calculated by the inverse method; The wind-induced acceleration calculation method is used to obtain the acceleration response of each layer of the structure and form the acceleration response matrix Acc.

5. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: Initializing the relevant parameters of the particle swarm according to the response characteristic matrix R includes: Set the particle swarm size to 30-50 particles; Randomly generate the initial position matrix P within the allowable range of the design variables; Set the initial velocity matrix V to a random value between -10% and +10% of the position matrix.

6. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: When initializing the velocity matrix V of the particle swarm in step P101, the following formula 2 is used: Among them, V i,j represents the initial velocity of the jth dimension of the i-th particle; V init,j represents the baseline initial velocity of the jth dimension; Δ i represents the layer displacement of the i-th layer; Δ max represents the maximum allowable layer displacement; θ i represents the inter-story displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle; R i,j is a random number.

7. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: According to the fitness value matrix A, the individual optimal position matrix P is updated best and the group optimal position matrix G best ,include: Determine whether the current particle's fitness value is better than its historical optimal value; If it is better than the historical optimal value, the individual optimal position matrix P is updated with the current position best ; Select the optimal fitness value from the individual optimal positions of all particles; Update the group optimal position matrix G with the selected optimal value best .

8. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: In step P104, the position matrix P and velocity matrix V of the particle swarm are iteratively updated using the following formulas 3 and 4: P′ i,j =P i,j +V′ i,j (4) Among them, ω max represents the initial inertia weight; λ is the decreasing coefficient; t represents the current number of iterations; V i,j represents the velocity of the jth dimension of the i-th particle; V i ′ ,j represents the updated velocity of the jth dimension of the i-th particle; P i,j represents the position of the jth dimension of the i-th particle; P i ′ ,j represents the updated position of the jth dimension of the i-th particle; c1, c2 represent learning factors, which are used to control the influence of individual optimality and group optimality on speed update; r1, r2 are random numbers in the interval [0, 1], which are used to increase the randomness of particle motion; P best,i,j represents the individual optimal position of the jth dimension of the i-th particle; G best,j represents the optimal position of the group in the jth dimension; φ is the acceleration adjustment factor, which is used to balance the influence of wind load and acceleration response; W i is the equivalent static wind load of the i-th layer; Acc i is the acceleration response of the i-th layer.

9. The structural optimization design method based on particle swarm optimization algorithm according to claim 1, characterized in that: In step P105, the equivalent static wind load matrix W and the acceleration response matrix Acc are recalculated using the following formulas 5 and 6: Among them, W i ′ Indicates the updated equivalent static wind load; Acc i ′ represents the updated acceleration response; W i Indicates the equivalent static wind load before updating; Acc i represents the acceleration response before updating; μ,v is the adjustment factor used to enhance the dynamic adjustment of load and response; Δ i represents the layer displacement of the i-th layer; Δ max represents the maximum allowable layer displacement; θ i represents the inter-story displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle.

10. The structural optimization design method based on particle swarm optimization according to claim 1, characterized in that: The final design solution S of the structure is determined based on the output optimal solution matrix Opt, including: Extract the values ​​of each design variable in the optimal solution matrix Opt; Round the design variables to the actual specifications and sizes that can be adopted in the project; Conduct structural finite element analysis verification to ensure that all constraints are met; Output the final design parameters of each structural component to form the design scheme S.

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