Structure optimization design method based on particle swarm optimization

Abstract

The invention discloses a structure optimization design method based on a particle swarm optimization algorithm, aiming at a super high-rise building, an initial structure parameter matrix is generated by establishing an optimization model, setting a target function and taking structure layer displacement, an inter-layer displacement angle and top layer peak resultant acceleration as constraint conditions; a wind vibration response characteristic matrix is obtained by adopting a frequency domain calculation method in combination with structural dynamic characteristics and a wind tunnel test result, and an equivalent static wind load matrix and an acceleration response matrix are calculated. A combined algorithm of an optimization criterion method and a particle swarm algorithm is used for performing multiple iterations, wind load and acceleration response data are recalculated by initializing and updating related parameters of a particle swarm, calculating a fitness value, iteratively updating a position and a speed matrix, and finally an optimal solution matrix is output according to convergence judgment. Therefore, a final design scheme of the structure is determined, and comprehensive optimization of wind resistance and economic benefits of the structure is realized.

Description

Technical Field

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

[0002] In the prior art, traditional structural optimization methods, such as genetic algorithms and simulated annealing algorithms, are usually 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 and wind tunnel test results. Traditional methods mostly rely on design and analysis based on static mechanics, and often use approximate models for estimation when calculating wind loads and acceleration responses. In addition, some optimization methods have certain limitations in calculation efficiency and accuracy when dealing with structural dynamic characteristics.

[0003] In the existing technology, a common problem is that the optimization effect is not ideal. Especially when dealing with complex wind vibration effects, traditional optimization algorithms are difficult to strike a balance between global search capabilities and local convergence. At the same time, the existing algorithms are easily affected by local optimal solutions in terms of constraint processing and objective function fitness calculation, resulting in poor stability and feasibility of the optimization results. In addition, these methods are not adaptable enough in multi-objective optimization scenarios, and it is difficult to simultaneously meet the wind resistance and economic requirements of the structure.

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

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

[0006] The present application provides a structural optimization design method based on a particle swarm algorithm, comprising:

[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 synthetic acceleration as constraint conditions, 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 wind vibration response is calculated using a frequency domain calculation method to obtain a 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 combined optimization algorithm of the optimization criterion method and the particle swarm algorithm is used to perform the following iterative calculation:

[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 pros and cons 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 particle swarms;

[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 the acceleration response matrix Acc are recalculated to update the wind vibration response data during the optimization process;

[0016] P106: According to 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 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 criteria method and the particle swarm algorithm, 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 a stronger global search capability 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 synthetic 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 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 optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It 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] Many specific details are described in the following description to facilitate a full 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 connotation of the present application, so the present application is not limited by the specific implementation disclosed below.

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

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

[0024] The specific implementation of step S101 is to establish an optimization model for the design of super high-rise building structure. The core of the model is to determine the objective function and constraint conditions and generate the initial structural parameter matrix X.

[0025] First, in the process of model building, the structural design of super high-rise buildings usually involves complex multi-objective optimization. To this end, it is necessary to define an objective function suitable for this type of building. The objective function should include multiple factors that affect the cost and performance of structural design, such as material cost, construction cost, structural weight, etc. Specifically, the objective function can be comprehensively defined based on factors such as the material, geometric dimensions, and structural form of the building. The objective function should reflect the trade-off between economy and performance in the design as much as possible, for example, by minimizing the cost or total weight to achieve the optimal design.

[0026] Secondly, in order to ensure the safety and performance of the structure, constraints must be introduced in 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 an initial structural parameter matrix X. The generation of this matrix needs to be initialized in combination with the range of values ​​of the design variables. The design variables may include the column section size, beam section size, 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 random distribution, Latin hypercube sampling (LHS) and other methods 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 allowed range of values ​​to avoid unreasonable design parameters from entering the subsequent optimization calculations.

[0028] In the process of generating the initial structural parameter matrix, preliminary adjustments are also required according to the dynamic characteristics of the building. This adjustment is to make the initial parameter matrix better adaptable to the subsequent particle swarm optimization process on the basis of satisfying the basic structural performance. 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 basis for subsequent particle swarm optimization calculations by establishing an optimization model, setting objective functions and constraints, and generating an initial structural parameter matrix. This step ensures the economic and performance requirements in 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 layer displacement; θ i represents the interlayer displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle; a top represents the synthetic acceleration of the top layer; a max Indicates the maximum permissible 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 the 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 so as 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 obtained by comprehensively evaluating multiple performance indicators of the building structure. Each term in the formula represents a specific design goal or constraint, and the overall performance of the structure is optimized by multiple objectives. In this module, each term in the formula is explained in detail, and how to obtain these data from the actual structural response.

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

[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 obtained by combining the unit price of the material. The cost of all components is added up to get C. mat .

[0037] C const Indicates the total construction cost of the structure. This part covers the various expenses required during the construction of the building structure, including labor, equipment, site rental, etc. The calculation method of the total construction cost is usually based on the construction process, time and resource requirements, and can be obtained by adding up the various expenses.

[0038] It is an item in the objective function, which is mainly used to measure the layer displacement of the structure. i is the layer displacement of the i-th layer, obtained by 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 It represents the maximum permissible story displacement, which is usually set according to the building code or design standard. A logarithmic term is introduced in the calculation of this term to enhance the effect on fitness when the story displacement is small, thereby encouraging the design solution to better meet the story displacement constraint.

[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 allowable inter-story drift angle specified, which is set based on the code and design standard. The exponential term is used to increase the penalty when the inter-story drift angle approaches the maximum allowable value, so as to avoid the design scheme being too close to the safety margin.

[0040] Represents the constraint on the top-level composite acceleration. top It is the synthetic 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 vibration response. max is the maximum allowed top floor resultant acceleration, set by code or design requirements. The logarithmic part of this term increases its fitness at smaller accelerations to encourage design solutions to be optimized in the lower acceleration range, thereby improving the comfort of the building.

[0041] Reflects the change of equivalent static wind load. 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 It is the equivalent static wind load of the i-th layer in the previous iteration, and records the result of the previous iteration. The absolute value of this item indicates the variation of wind load in different iterations, and its purpose is to control the stability of the design scheme during the optimization process and avoid excessive load fluctuations.

[0042] Indicates the change in acceleration response. Acc i 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 the i-th layer in the previous iteration, reflecting the response in the previous iteration. The absolute value of this term is used to control the stability of the acceleration response in different iterations, ensuring that the optimization process can gradually converge without unreasonable acceleration fluctuations.

[0043] All items in the objective function F are balanced with different weight coefficients α, β, γ, δ, η. These coefficients can be adjusted according to specific design requirements to find a suitable trade-off between different optimization objectives. The data acquisition and analysis module 101 continuously collects and updates all the above parameters to provide an accurate data basis 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, the wind vibration response is calculated using a frequency domain calculation method to obtain a response characteristic matrix R.

[0045] The specific implementation of step S102 is based on the initial structural parameter matrix X, combined with the dynamic characteristics of the structure and the wind tunnel test results, using the frequency domain calculation method to calculate the wind vibration response, and finally obtain the response characteristic matrix R. The purpose of this step is to accurately evaluate the dynamic response of the building under wind load, so as to provide reliable data support for subsequent structural optimization.

[0046] First, step S102 needs to analyze 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 dynamic response of the structure and can be calculated by 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, because these vibration modes have an important contribution to the wind vibration response. The modal parameters obtained by analysis will be used for subsequent wind 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 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 power spectrum density of the wind load, it is necessary to establish the transfer function of wind load-structural response. The transfer function describes the transformation relationship of wind load to structural response through structural dynamic characteristics. The establishment of the transfer function is usually 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, especially the combined calculation of the contribution of each vibration mode. Through the transfer function, the frequency domain characteristics of the wind load can be converted into the frequency domain response characteristics of the structure.

[0049] After establishing the transfer function of wind load-structural response, the frequency domain calculation of wind vibration response is performed based on random vibration theory. This calculation process obtains the power spectrum density (PSD) of the structural response by multiplying the wind load PSD with the transfer function. The response PSD can reflect the response energy distribution of the structure at different frequencies and can accurately describe the dynamic response characteristics of the building structure under wind load, such as acceleration, layer displacement, and inter-layer displacement angle.

[0050] Finally, by integrating the response PSD, the response characteristic matrix R of the structure under wind load can be obtained. The response characteristic matrix R contains information such as the acceleration response, layer displacement, and inter-layer displacement angle of the structure on each floor. This matrix will serve as the basic data 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 the wind tunnel test results to ensure the accuracy and reliability of the wind vibration response evaluation.

[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 transfer function of wind load-structural response;

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

[0057] In this embodiment, the frequency domain calculation method is used to accurately evaluate the wind 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 vibration mode eigenvalues ​​and eigenvectors can be extracted. The vibration mode eigenvalue usually represents the natural frequency of the structure, which is the frequency of free vibration of the structure without damping and external loads; the eigenvector describes the vibration mode 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 in an actual wind environment. In the test, a scaled-down building model is placed in a wind tunnel for testing. By setting different wind speeds and wind directions, the wind pressure history at different locations on the model surface can be measured. The wind pressure history is a curve of the wind load changing over time, which is usually measured at various surface locations of the model by pressure sensors. The wind pressure history data can truly reflect the stress changes of the building under the actual wind load, 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 loads 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 the transfer function of the wind load-structural response. The transfer function is an important concept in the dynamic analysis of the structure, which is used to describe the relationship between the amplitude and phase changes of the structure's response to the external load. The establishment of the transfer function is usually based on the 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. The wind load PSD can be used as input and processed by the transfer function to obtain the corresponding structural response PSD. 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 the 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 vibration analysis because wind load is essentially a random process and its frequency domain response is usually expressed in the form of power spectrum density. When calculating the structural response, the power spectrum density of the wind load is multiplied by the transfer function to obtain the power spectrum density of the structural response. By integrating the response power spectrum density, the acceleration response, layer displacement, inter-layer displacement angle and other parameters 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 on each floor and is the 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 vibration response characteristics into equivalent static wind load and acceleration response, so as to provide 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 comfort of high-rise buildings. In order to obtain the acceleration response matrix, it is necessary to calculate based on the random vibration theory using the acceleration components in the response characteristic matrix R. 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 magnitude of different floors of the structure under wind loads.

[0069] Through this calculation method, step S103 can accurately obtain the equivalent static wind load matrix and acceleration response matrix, which are indispensable basic data in the optimization process. This step of 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 part in the present embodiment calculates the equivalent static wind load matrix W and the acceleration response matrix Acc based on the response characteristic matrix R to accurately reflect the force and response characteristics of the structure under the wind load. In order 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 contribution 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 take the square root of 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, takes 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 magnitude of acceleration on a specific floor, which is a key parameter reflecting the vibration intensity of the building under wind load.

[0078] In the whole calculation process, the equivalent static wind load matrix W and the acceleration response matrix Acc are important outputs of the wind vibration response analysis, which are used to evaluate the stress state and dynamic performance of the structure respectively. The accurate calculation of these matrices is crucial for the subsequent structural optimization, because they not only provide basic data for the optimization objective function, but also directly affect 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: According to the equivalent static wind load matrix W and the acceleration response matrix Acc, a combined optimization algorithm of the optimization criterion method and the particle swarm algorithm is used to perform the following iterative calculation:

[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 pros and cons 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 particle swarms;

[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 the acceleration response matrix Acc are recalculated to update the wind vibration response data during the optimization process;

[0086] P106: According to 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] The specific implementation of step S104 is to perform 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 algorithm, with the aim of achieving 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 value matrix A of each particle is calculated to evaluate the pros and cons of the current design scheme. The fitness value is the core indicator for evaluating the pros and cons of the solution in the particle swarm algorithm. The fitness value matrix A contains the fitness value of each particle. The higher the fitness of the particle, the closer its corresponding design scheme is to the optimization goal. The calculation of the objective function combines multiple constraints, such as structural layer displacement, interlayer displacement angle, and top floor acceleration, so that the optimization results can comprehensively reflect the wind resistance and economic benefits of the structure.

[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. best; At 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 update the particle position matrix P and velocity matrix V. During the velocity update process, factors such as inertia weight, learning factor and random disturbance are considered, so that the movement of particles in the solution space has a balance between global search and local optimization. The updated position matrix P′ and velocity matrix V′ are obtained through the new position and new velocity of each particle. These updated values ​​will be 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 acceleration response matrix Acc need to be recalculated based on it to ensure the dynamic update of wind vibration response data. In this way, the optimization process can adapt to the changes of design variables in each iteration and keep synchronization with the actual wind load.

[0093] After each round of iteration, it is necessary to determine whether the change in the position matrix meets the convergence condition based on the preset convergence accuracy ε. Specifically, the difference norm between the updated position matrix P′ and the previous round position matrix P is calculated. If the norm is less than ε, it is considered that the optimization has met the expected accuracy requirements and the optimal solution matrix Opt is output; if the convergence condition is not met, the updated position matrix P′ is assigned to P and returns to the fitness calculation stage of the next round of 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 random values ​​between -10% and +10% of the position matrix.

[0099] In the optimization design process of the particle swarm algorithm of this embodiment, the particle swarm is initialized based on the response characteristic matrix R, which is crucial for the accuracy and efficiency of the optimization process. The relevant parameters of the initialized particle swarm need to provide a good starting point for the global search and local optimization of the particle swarm on the basis of maintaining diversity. In order to ensure that the particle swarm can fully explore in 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. The present invention recommends setting 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 result in insufficient coverage of the solution space and may 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 better 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 for 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, which 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 moving speed of each particle in the solution space, and is a key parameter for controlling the direction and amplitude of particle movement in the particle swarm algorithm. During the initialization process, 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 value of the velocity 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 initial iteration, while avoiding excessive solution jumps caused by excessive velocity or slow convergence caused by too small velocity. In addition, the selection of this random range can maintain a certain degree of randomness and flexibility in the early stage of the particle swarm, which helps to explore the potential optimal solution 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 the subsequent fitness evaluation and iterative update. The rationality of the initialization step 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 accurately controlled during the specific implementation process, thereby improving 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 ith 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 interlayer displacement angle of the i-th layer; θ max Represents the maximum allowable inter-story displacement angle; R i,j Is a random number.

[0107] In the implementation of the particle swarm algorithm of 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 layer displacement and interlayer displacement angle of the structure, 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) It represents the initial velocity of the jth dimension of the ith particle, which 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 base initial velocity of the jth dimension is a preset velocity value, which is usually set according to the range of the design variable. Specifically, during initialization, an initial velocity range is specified for each dimension, such as the upper and lower limits of the structural cross-sectional size change. The base initial velocity is used to set the upper limit of the initial velocity of each particle to ensure that the initial search has a certain directionality and amplitude.

[0112] Δ iRepresents the layer displacement of the i-th floor, which is the horizontal displacement response of the structure under wind load or other external loads. This value can be obtained through finite element analysis or other structural analysis methods. Specifically, by simulating the dynamic response of the building under wind load, the displacement response values ​​of different floors can be obtained. The displacement response directly reflects the deformation state of the structure and is a parameter that needs to be considered in the optimization process.

[0113] Δ max It represents the maximum allowable floor displacement, which is a value set according to building design specifications or standards to limit the maximum deformation of the structure under external forces. This value usually depends on the building's use 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 It is a normalized layer displacement factor, which is used to indicate the relative degree of the current displacement to the maximum allowed displacement. Its purpose is to adjust the velocity so that the particles are subject to greater velocity adjustment when they are close to the maximum displacement constraint, so as to encourage the particles to conduct a more detailed search near the displacement constraint.

[0115] θ i The inter-story displacement angle of the i-th floor is the ratio of the relative displacement between two adjacent floors to the floor height. This is an important parameter that reflects the stiffness and lateral displacement resistance of the structure. It can be obtained by calculating the relative displacement of adjacent floors and dividing it by the floor height. Similar to the floor displacement, the inter-story displacement angle is also obtained through structural dynamic analysis and is usually used to evaluate the lateral displacement state of the structure under wind load or seismic load.

[0116] θ max It is the maximum allowable inter-story displacement angle, which is the upper limit value set according to the building design specifications. Its function is to limit the relative deformation of the building under lateral loads to ensure the stability and safety of the structure. This value is specified by the building specifications and is usually related to the type, structural system and use function of the building.

[0117] In formula (2), the term is a normalized interlayer displacement angle factor, whose purpose is to adjust the velocity according to the relative magnitude of the current interlayer displacement angle. In this way, when the interlayer displacement angle is close to its maximum allowable value, the velocity adjustment amplitude will become larger to strengthen the control of this constraint, thereby guiding the particle swarm to pay more attention to the limitation of the interlayer displacement angle during the optimization process.

[0118] R (i,j)is a random number used to introduce randomness and diversity to particle speed. Random numbers are usually in the range of [0,1]. By adding random numbers, the exploration ability of the particle swarm can be increased to prevent the algorithm from falling into the local optimum. The introduction of random numbers makes the particle speed have a certain degree of randomness, which helps to balance the relationship between global search and local search during the optimization process.

[0119] From the above description, it can be seen that each item 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 global search ability and convergence efficiency of the algorithm. 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 pay more attention to the key performance constraints of the structure while maintaining the search diversity. This initialization method can effectively improve the applicability and efficiency of the particle swarm algorithm in structural optimization, thereby better realizing the 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, so as to better find the optimal solution for structural optimization.

[0126] First, the fitness matrix A is needed 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 solution under the premise of meeting the constraints. For comparison, first extract the fitness value of each particle and compare it with the individual optimal position matrix P. bestCompare with the historical optimal fitness value 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 All fitness values ​​in the swarm are traversed and compared. By comparison, the particle with the highest fitness value can be found, that is, the optimal position of the best performing individual in the current swarm of particles can be found. This optimal position represents the currently known optimal solution of the swarm of particles in the global scope and is a candidate solution for the global optimal position.

[0129] Finally, the optimal position matrix G of the group is updated with the selected optimal fitness value. 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 toward 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 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 ith particle; V′ i,jrepresents the updated velocity of the jth dimension of the ith particle; P i,j represents the position of the jth dimension of the ith particle; P′ i,j represents the updated position of the jth dimension of the ith particle; c 1 ,c 2 represents the learning factor, which is used to control the influence of individual optimality and group optimality on speed update; r 1 ,r 2 is a random number in the interval [0,1], used to increase the randomness of particle motion; P best,i,j represents the individual optimal position of the jth dimension of the ith 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 the structural optimization design. In step P104, the position matrix P and the velocity matrix V of the particle swarm are updated by formula (3) and formula (4), which not only ensures the dynamic search ability of the particle swarm in the solution space, but also can effectively balance the optimization objectives of the wind load and acceleration response of the structure.

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

[0137]

[0138] First, V′ (i,j) The updated speed of the jth dimension of the ith particle is the new speed value obtained by the combined effect of multiple factors in the current iteration. Speed ​​update is the most critical step in the particle swarm algorithm, which determines the next movement direction and stride of the particle.

[0139] ω max Represents the initial inertia weight, which is a parameter that controls the continuity of particle velocity. The inertia weight is used to balance the global search and local search capabilities: a larger inertia weight helps the global search, while a smaller inertia weight helps the local search. In order to gradually increase the weight of the local search during the optimization process, the inertia weight is usually designed to decrease with the number of iterations, which is achieved through an exponential decrease factor exp(-λ·t), where λ is the decrease coefficient, which is used to control the decrease speed of the inertia weight. t is the current iteration number. As the number of iterations increases, the inertia weight decreases gradually, prompting the particles to concentrate on the local optimal solution.

[0140] V (i,j)Indicates the current speed of the jth dimension of the ith particle, which is the speed value of the particle before this round of iteration. The function of this item is to adjust the inertia weight so that the movement of the particle can maintain a certain continuity and stability, avoiding excessive jumps that lead to unstable search.

[0141] c 1 ·r 1 ·(P best,i,j -P (i,j) ) is the individual learning term, which reflects the motivation of the particle to move toward its historical optimal position. 1 is the individual learning factor, which is used to adjust the influence of the individual optimal position on the speed update. 1 The value will enhance the individual's attraction to its optimal solution, making the particle more inclined to search for its own historical optimal solution. 1 is a random number in the interval [0,1], which is used to increase the randomness and diversity of individual searches and ensure that different particles do not tend to the same direction during the search process. best,i,j is the individual optimal position of the jth dimension of the ith 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] c 2 ·r 2 ·(G best,j -P (i,j) ) is the group learning term, which reflects the motivation of particles to move toward the global optimal position. 2 is the group learning factor, which is used to adjust the effect of the group's optimal position on the speed update. 2 The value will enhance the attraction of particles to the group optimal solution, making the particles tend to move towards the global optimal solution. 2 is another random number in the interval [0,1] used to increase the population The randomness of the search. best,j It is the optimal position of the group, representing the global optimal solution of the entire particle group in the current iteration.

[0143] is the acceleration adjustment item, which is used to balance the influence of wind load and acceleration response. Where, φ is the acceleration adjustment factor, which is used to control the influence of wind load and acceleration response on velocity update. It is a normalized process of layer displacement and nonlinear mapping through hyperbolic tangent function. This mapping method can enhance the regulation of velocity when the displacement is small, and gradually weaken it when the displacement is close to 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 item is to adjust the velocity according to the difference between layer displacement, wind load and acceleration response, so as to make 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 the 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]

[0151] Among them, W′ i represents 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 interlayer displacement angle of the i-th layer; θ max Represents the maximum allowable inter-story drift angle.

[0152] 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 load and response. The detailed implementation of formulas (5) and (6) is described below.

[0153] The form of formula (5) is:

[0154]

[0155] Among them, W′ i Represents the updated equivalent static wind load, which is the adjusted load value of the i-th layer in the current iteration. The updated load value is calculated to better reflect the dynamic response changes of the structure under wind load, ensuring that the optimization process can accurately adjust the impact of wind load on the structure.

[0156] W i is the equivalent static wind load before updating, obtained through the wind 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.

[0157] μ is a regulating factor used to control the dynamic adjustment range of wind load. The setting of this factor depends on the specific optimization goal and the characteristics of the structure, and can be adjusted according to the optimization effect in the experiment. A larger μ value will increase the adjustment range of the load, thereby enhancing the sensitivity of the optimization process to changes in wind load.

[0158] 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 It represents the maximum allowable layer displacement, which is the upper limit value set according to the building design code or standard. It is the maximum deformation allowed by the structure under the action of wind load and is used to limit the horizontal displacement of the structure. The introduction of the hyperbolic tangent function makes the influence of layer displacement present nonlinear characteristics in the updating process. This means that when the layer displacement is small, the amplitude of load adjustment is small; when the layer displacement is close to the maximum allowable value, the amplitude of load adjustment will increase significantly, thereby better guiding the structural optimization to develop in a safe direction.

[0159] The form of formula (6) is:

[0160]

[0161] Among them, Acc′ i represents the updated acceleration response, which 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. iis the acceleration response before the update, usually obtained through wind vibration response analysis, representing the acceleration response of the i-th layer under wind load in the last iteration. ν is the adjustment factor, which is used to control the dynamic adjustment amplitude of the acceleration response. The setting of this factor is similar to μ, and is also adjusted through experiments and optimization effects. A larger ν value will make the adjustment of the acceleration response more significant, thereby increasing the sensitivity to structural acceleration.

[0162] It is the normalization of the interlayer displacement angle and increases the nonlinear weight through square operation. i θ represents the inter-story displacement 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 lateral displacement resistance. max is the maximum allowable inter-story displacement angle, which is the upper limit set according to the design specification and is used to limit the relative deformation of the structure. The square operation of the inter-story displacement angle allows the acceleration response to have a larger adjustment range at a larger displacement angle. This nonlinear enhancement enables the optimization process to better cope with the situation of larger displacement angles and ensure the stability and safety of the structure.

[0163] During the implementation process, 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 in 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 can achieve comprehensive optimization of wind load and acceleration response while meeting safety and comfort requirements. This sophisticated dynamic adjustment method makes the structural optimization process more accurate and reliable.

[0164] Step S105: Based on the output optimal solution matrix Opt, determine the final design solution S of the structure to achieve the optimal design of the wind resistance performance and economic benefits of the structure.

[0165] The implementation of step S105 is based on the output optimal solution matrix Opt to determine the final design solution S of the structure to achieve the comprehensive optimal design of the wind resistance and economic benefits of the structure. The purpose of this step is to convert the optimal solution obtained through multiple iterations of optimization into a practical building structure design solution.

[0166] First, the final values ​​of each design variable need to be extracted from the optimal solution matrix Opt. The optimal solution matrix Opt is the optimal solution obtained during the iteration of the particle swarm algorithm, in which each element represents a specific structural design parameter. These design parameters may include the cross-sectional dimensions of beams and columns of the building, the thickness of the floor slab, the strength grade of the structural material, etc. Therefore, during the implementation process, the design variable values ​​in the optimal solution matrix need to be read one by one and used in the subsequent design plan formulation.

[0167] After extracting the design variable values, these values ​​need to be rounded or standardized to meet the actual construction requirements of the project. In building structure design, some design parameters may need to match the standard specifications of the construction industry, such as steel bar size or concrete strength grade. The purpose of this rounding or standardization is to ensure that the optimal design parameters can be implemented in the actual project without affecting the overall performance of the building structure. In this process, appropriate adjustments or corrections can be made according to relevant engineering standards or specifications to ensure the feasibility of the design parameters.

[0168] 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 comprehensively evaluate the safety, stability and performance of the structure before determining the final design solution 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 solution and ensure that it meets all constraints and design objectives.

[0169] After the verification is completed, the final structural design solution S can be determined. This solution will contain the design parameters, dimensions, material types and other relevant information of all components, and is a structural design drawing and specification that can be used for actual construction. This solution should be able to optimize economic benefits while ensuring structural safety and user comfort. The determination of the final design solution marks the completion of the optimization process and is the result of the application of particle swarm algorithm in building structure design.

[0170] 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.

[0171] Furthermore, the final design solution S of the structure is determined based on the output optimal solution matrix Opt, including:

[0172] Extract the values ​​of each design variable in the optimal solution matrix Opt;

[0173] Round the design variables to the actual specifications and dimensions that can be adopted in the project;

[0174] Conduct structural finite element analysis verification to ensure that all constraints are met;

[0175] Output the final design parameters of each structural component to form a design solution S.

[0176] In the particle swarm algorithm optimization design method of this embodiment, the final design solution S of the structure is determined by the optimal solution matrix Opt. This process is a key part of the entire optimization process, involving converting the calculation results into a practical engineering design solution. In order to ensure the accuracy and feasibility of this step, each link is described in detail below.

[0177] First, it is necessary to extract the values ​​of each design variable in the optimal solution matrix Opt. The optimal solution matrix Opt is the result matrix obtained after the particle swarm algorithm completes all iterations, which contains the optimal values ​​of all design variables. These design variable values ​​are the global optimal solutions obtained after fitness evaluation and multiple iterative optimizations, representing 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 section size, material strength, floor height, etc. These variable values ​​are an important basis for the final design of the structure and will be directly used in engineering design implementation.

[0178] Next, the design variables need to be rounded to the actual specifications that can be used in the project. Since the optimization results of the particle swarm algorithm are usually 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, steel bar diameter, and plate thickness must meet 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 meet the actual specifications that can be used in the project. This conversion process can be completed by searching and matching the standard size library to ensure that the design solution not only meets the optimization goals, but can also be actually applied in construction.

[0179] 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 build 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 show 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.

[0180] After completing the finite element analysis verification and ensuring that all constraints are met, the final design parameters of each structural component need to be output to form the structural design plan S. The final design plan should include detailed design parameters of each structural component, including beam and column sections, floor thickness, material type, steel bar configuration, etc. These parameters will serve as the basis for construction drawings and project implementation to ensure that the structural optimization design can be applied and implemented in actual projects.

[0181] Through the above steps, this embodiment can generate a final design solution S that meets the actual needs of the project from the optimal solution matrix Opt. This process not only realizes the transformation of the optimization results, but also ensures the feasibility and safety of the structural design, providing a reliable design basis for engineering construction.

[0182] A second embodiment of the present application provides an electronic device, the electronic device comprising:

[0183] processor;

[0184] The memory is used to store a program, and when the program is read and executed by the processor, the structure optimization design method based on the particle swarm algorithm provided in the first embodiment of the present application is executed.

[0185] The third embodiment of the present application provides a computer-readable storage medium on which a computer program is stored. 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.

[0186] Although the present application is disclosed as above in the form of a preferred embodiment, it is not intended to limit the present application. Any technical personnel in this field 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 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 synthetic acceleration as constraint conditions, 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 wind vibration response is calculated using a frequency domain calculation method to obtain a response characteristic matrix R; Based on the response characteristic matrix R, the equivalent static wind load matrix W and the 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 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 pros and cons 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 particle swarms; 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 the acceleration response matrix Ac c , thereby updating the wind vibration response data during the optimization process; P106: According to 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 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 structure optimization design method based on particle swarm algorithm according to claim 1 is 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 layer displacement; θ i represents the interlayer displacement angle of the i-th layer; θ max Indicates the maximum allowable inter-story displacement angle; a top represents the composite acceleration of the top layer; a max Indicates the maximum permissible 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 the 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 structure optimization design method based on particle swarm algorithm according to claim 1 is characterized in that: The frequency domain calculation method is used to calculate the wind vibration response to obtain the response characteristic matrix R, including: 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 transfer function of wind load-structural response; Based on the random vibration theory, the structural response is calculated in the frequency domain and the response characteristic matrix R is obtained.

4. The structure optimization design method based on particle swarm algorithm 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 structure optimization design method based on particle swarm algorithm 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 random values ​​between -10% and +10% of the position matrix.

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

7. The structure optimization design method based on particle swarm algorithm according to claim 1 is 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 structure optimization design method based on particle swarm algorithm 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 V represents the velocity of the jth dimension of the ith particle; i ′ ,j represents the updated velocity of the jth dimension of the ith particle; P i,j represents the position of the jth dimension of the ith particle; P i ′ ,j represents the updated position of the jth dimension of the ith 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 ith 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 structure optimization design method based on particle swarm algorithm according to claim 1, characterized in that: 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: Among them, W i ′ Represents 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 interlayer displacement angle of the i-th layer; θ max Represents the maximum allowable inter-story drift angle.

10. The structure optimization design method based on particle swarm algorithm 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 dimensions 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 a design solution S.

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