An optimization method and system of a branched cable support prestressed column structure system

Abstract

The application discloses a kind of branch type cable support prestressed column structure system optimization method and system, the problem that only part of structure is optimized in prior art is solved, with the beneficial effect of optimizing overall structure, improving overall stability, specific scheme is as follows: a kind of branch type cable support prestressed column structure system optimization method, with the height of the end of bracing bar and center column in branch type cable support prestressed column, the angle between bracing bar and center column as optimization variable, with the maximum linear buckling load of structure as optimization goal, construct branch type cable support prestressed column optimization equation;Branch type cable support prestressed column optimization equation is iteratively solved using neighborhood random gradient method, randomly select perturbation point in the neighborhood of each iteration point, and calculate the gradient at perturbation point;With the perturbation point gradient calculated by neighborhood random gradient method as search direction, linear search is carried out with iteration point as base point, until linear search meets constraint condition.

Description

Technical Field

[0001] This invention relates to the field of building engineering technology, and in particular to an optimization method and system for a branched cable-supported prestressed column structure system. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Cable-supported prestressed columns are structural members that significantly improve the stability and load-bearing capacity of ordinary compression columns by introducing a cable-support system consisting of struts and cables. Due to their high stability and slender shape, they are particularly suitable for structures with large column spacing and high bracing. When the struts are paired and not perpendicular to the central column, they are called branched cable-supported prestressed columns. Existing engineering and research results show that a reasonable arrangement of the cable-support system can significantly improve the stability and load-bearing capacity of compression columns, with branched systems showing a better improvement in the load-bearing capacity of the central column compared to vertical struts. Optimizing the arrangement of struts is beneficial to improving the stability of cable-supported prestressed columns; however, current technologies only optimize parts of the structure according to load optimization design schemes, without considering factors such as strut position and angle, or disturbance factors of the overall structure, resulting in ineffective control of building material usage during construction. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide an optimization method for branched cable-supported prestressed column structure system, which can optimize various types of cable-supported prestressed columns, improve their stability performance, reduce the length of the struts, and save materials and costs.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution: An optimization method for a branched cable-supported prestressed column structure system includes the following: Using the height of the connection between the strut and the central column in the branched cable-supported prestressed column and the angle between the strut and the central column as optimization variables, and taking the maximum linear buckling load of the structure as the optimization objective, an optimization equation for the branched cable-supported prestressed column is constructed. The neighborhood stochastic gradient method is used to iteratively solve the optimization equation of the branched cable-supported prestressed column. In each iteration step, a disturbance point is randomly selected in the neighborhood of the iteration point, and the gradient at the disturbance point is calculated. The perturbation point gradient calculated by the neighborhood stochastic gradient method is used as the search direction, and the iteration point is used as the base point to perform a line search until the line search satisfies the constraint conditions. Update the optimization variables and judge the convergence of the optimization. If the convergence condition is not met, enter a new iteration step and update the iteration point. Repeat the neighborhood stochastic gradient method for the new iteration step until the optimization meets the convergence condition.

[0006] The optimization method for a branched cable-supported prestressed column structural system described above, wherein the expression for the optimization equation of the branched cable-supported prestressed column is as follows:

[0007] in, This represents the negative value of the lowest-order buckling load calculated based on finite element analysis. The independent variables for optimization include the height of the connection between the strut and the central column, and the angle between the strut and the central column. This represents the feasible region of the independent variable, and the number of independent variables is... n .

[0008] The optimization method for a branched cable-supported prestressed column structure system, as described above, involves iteratively solving the optimization equation of the branched cable-supported prestressed column using the neighborhood stochastic gradient method. In each iteration step, a disturbance point is randomly selected within the neighborhood of the iteration point. This includes the following: The perturbation point is calculated using a dimensionless sphere uniform perturbation method. The perturbation direction of the perturbation point is obtained, and the perturbation step size is calculated. The perturbation step size is based on the... t The neighborhood radius coefficient of the step and the number randomly selected with equal probability in [0,1] are determined; Calculate the dimensionless disturbance offset based on the disturbance direction and disturbance step size of the disturbance point; The calculated dimensionless perturbation offset is transformed into a dimensional perturbation, and the perturbation point is calculated based on the iteration point.

[0009] The optimization method for a branched cable-supported prestressed column structure system described above, after obtaining the disturbance point, also requires further optimization of the first... t The neighborhood radius coefficients of the step are adjusted, and the gradient direction of the current step is determined, including the following: Calculate the basic annealing neighborhood radius coefficient; To determine whether the optimization objective of the current step has decreased, first calculate the difference between the optimization objective of the previous step and the current step; According to the adaptive multiplier, for the th t The neighborhood radius coefficient of the step is adjusted; According to the adjusted number t The neighborhood radius coefficient of the step is calculated, multiple independent random perturbation points are calculated, the gradient is calculated independently for each perturbation point, and the average value is used as the gradient direction of the current step.

[0010] The optimization method for a branched cable-supported prestressed column structure system described above calculates the basic annealing neighborhood radius coefficient based on the initial neighborhood radius coefficient, the number of iterations, and the annealing rate exponent. The first is determined based on the adaptive multiplier and the basic annealing neighborhood radius coefficient.t The neighborhood radius coefficient of the step.

[0011] The optimization method for a branched cable-supported prestressed column structure system described above, wherein obtaining the relationship between the coordinates of the nodes at both ends of the strut and the independent variables in the global coordinate system includes the following: The finite element calculation process for linear buckling load is given, and the derivative process for linear buckling load is derived based on the finite element calculation process for linear load. The gradient of the optimization objective is derived, and the gradient of the optimization equation is expressed as:

[0012] in, The gradient of the negative of the linear buckling load of the structure with respect to the optimization variables; Based on finite element analysis and the geometric relationship of branched cable-supported prestressed steel columns, the stiffness matrix is ​​differentiated. Based on the geometric relationship of the struts of the branched cable-stayed steel column, the relationship between the coordinates of the nodes at both ends of the strut and the independent variable in the global coordinate system is derived.

[0013] The optimization method for a branched cable-supported prestressed column structure system, as described above, provides the finite element calculation process for linear buckling load. Based on the finite element calculation process for linear load, the derivative process for linear buckling load is derived, including the following: The finite element calculation process for linear buckling load is given, considering that the cable-supported steel column is subjected to a given external load, and the structural load vector is calculated. pass Calculate the buckling coefficients and corresponding buckling modes for each order, where, Represents the linear stiffness matrix of the structure. Under load The stress stiffness matrix of the structure under action, and Then they are respectively the first q The first buckling coefficient and the corresponding buckling mode; Command Take the first-order coefficients and modes, and let both ends of them be relative to the independent variable. Taking the derivative, we get the formula:

[0014] Normalizing the first-order buckling mode and simplifying the derivative formula, we get:

[0015] in, It is a linear stiffness matrix. Here is the stress stiffness matrix.

[0016] The optimization method for a branched cable-supported prestressed column structure system, as described above, involves differentiating the stiffness matrix based on finite element analysis and the geometric relationship of the branched cable-supported prestressed steel column, and includes the following: Obtain the linear stiffness matrix and stress stiffness matrix, and then perform differentiation; The element linear stiffness matrix and stress stiffness matrix in the global coordinate system are calculated from the stiffness matrix in the element coordinate system through coordinate transformation, and the derivatives of the element linear stiffness matrix and stress stiffness matrix are then obtained. Calculate the derivative of the overall structural displacement vector with respect to the independent variable under linear static analysis, extract the derivative of the element displacement vector in the global coordinate system, and calculate the derivative of the element internal force with respect to the independent variable.

[0017] The optimization method for a branched cable-supported prestressed column structure system, as described above, involves deriving the relationship between the coordinates of the nodes at both ends of the strut and the independent variable in the global coordinate system based on the geometric relationship of the strut. This includes the following: Taking the first set of struts as an example, determine the height coordinates of the intersection point between the strut and the central column; Determine the coordinates of the upper and lower intersection points of the struts with the central column in the first group of struts, as well as the coordinates of the outward extension points. The coordinates of the intersection point of the first set of struts and the central column are obtained by differentiating the coordinates with respect to the height, the angle, and the distance between the connection points of the two struts and the central column. The coordinates of the extended end node of the first set of struts (referring to the end of the strut away from the central column) are also obtained by differentiating the coordinates with respect to the height, the angle, and the distance between the connection points of the two struts and the central column.

[0018] Secondly, the present invention provides an optimization system for a branched cable-supported prestressed column structure system, including a computing device configured to: Using the height of the connection between the strut and the central column in the branched cable-supported prestressed column and the angle between the strut and the central column as optimization variables, and taking the maximum linear buckling load of the structure as the optimization objective, an optimization equation for the branched cable-supported prestressed column is constructed. The neighborhood stochastic gradient method is used to iteratively solve the optimization equation of the branched cable-supported prestressed column. In each iteration step, a disturbance point is randomly selected in the neighborhood of the iteration point, and the gradient at the disturbance point is calculated. The perturbation point gradient calculated by the neighborhood stochastic gradient method is used as the search direction, and the iteration point is used as the base point to perform a line search until the line search satisfies the constraint conditions. Update the optimization variables and judge the convergence of the optimization. If the convergence condition is not met, enter a new iteration step and update the iteration point. Repeat the neighborhood stochastic gradient method for the new iteration step until the optimization meets the convergence condition.

[0019] The beneficial effects of the present invention are as follows: 1) This invention provides an optimization method that takes the maximum minimum buckling load of the branched cable-supported prestressed steel column as the optimization objective and the height and angle of the strut of the cable-supported prestressed steel column as optimization variables. By introducing a neighborhood random disturbance mechanism for independent variables in the gradient method, it can optimize various types of cable-supported prestressed steel columns, improve their stability performance, reduce strut length, and save materials and costs.

[0020] 2) In this invention, the neighborhood stochastic gradient method is used to iteratively solve the optimization equation of the branched cable-supported prestressed column. One or more disturbance points are randomly selected in the neighborhood of the current iteration point to calculate the gradient and average it to obtain the descent direction of the relative local region. An adaptive annealing mechanism is introduced to dynamically adjust the neighborhood radius based on the calculation results of each step.

[0021] 3) This invention normalizes the range of variable perturbations of different dimensions and orders of magnitude to a sphere, ensuring that the perturbation direction is uniformly distributed on a unit sphere; calculates the neighborhood radius coefficient, and then calculates the perturbation step size, and ensures that the probability of the perturbation point being selected in the sense of the volume inside the sphere is equal; calculates the dimensionless perturbation offset according to the perturbation direction and perturbation radius, and maps and transforms it into a dimensional perturbation, and then calculates the perturbation point. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0023] Figure 1 This is a flowchart of an optimization method for a branched cable-supported prestressed column structure system according to one or more embodiments of the present invention.

[0024] Figure 2 This is a structural model parameter diagram of an optimization method for a branched cable-supported prestressed column structure system according to one or more embodiments of the present invention.

[0025] Figure 3 This is a schematic diagram of a branched cable-supported prestressed steel column structure in an optimization method for a branched cable-supported prestressed column structure system according to one or more embodiments of the present invention.

[0026] The diagram exaggerates the spacing or dimensions between parts to show their positions; the diagram is for illustrative purposes only. Detailed Implementation

[0027] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0028] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless otherwise expressly indicated by the invention, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. As described in the background section, there are problems in the prior art. In order to solve the above-mentioned technical problems, this invention proposes an optimization method for a branched cable-supported prestressed column structure system.

[0029] Example 1 In a typical embodiment of the present invention, reference is made to Figure 1 As shown, an optimization method for a branched cable-supported prestressed column structure system is presented. The optimization objective is to maximize the linear buckling load of the structure. The height and angle of the struts are used as optimization variables, the feasible region of the optimization variables is used as the optimization constraint, and the neighborhood stochastic gradient method is used as the solution algorithm. The branched cable-supported prestressed column structure is shown in the figure. Figure 2 As shown, there are two sets of symmetrically arranged branch-type struts, with the center point heights of the branch-type struts being respectively... h 1 and h 2. The included angle between the struts in a branched strut system, i.e., the angle between the strut and the central column, is as follows: θ 1 and θ 2. The distances between the connection points of the two struts and the central column in each group of branch struts are respectively... d 1 and d 2. The upper end of the central column is subjected to a vertical downward pressure, and both ends are simply supported, including the following: S1. Based on the determined optimization objective and optimization variables, establish the optimization equation for the cable-supported prestressed column, the expression of which is: (1) in, This represents the negative value of the lowest-order buckling load calculated based on finite element analysis. The independent variables for optimization include the height of the connection between the strut and the central column, and the angle between the strut and the central column. This represents the feasible region of the independent variable, and the number of independent variables is... n .

[0030] S2. The neighborhood stochastic gradient method is used for iterative solution. The initial step does not calculate the perturbation point, but each subsequent step requires calculating the perturbation point within the neighborhood of the current iteration point. In this example, the perturbation point is calculated in the neighborhood of the current iteration point. t Take the step as an example.

[0031] S2.1.1 The perturbation point is calculated using a dimensionless, uniform perturbation method within a sphere. Let the number of independent variables be... n (In this embodiment) n =6, considering the generality of the expression, we will still use... n Generate random perturbation vectors The vector follows n The perturbation direction is obtained by normalizing the multivariate normal distribution, where each element is an independent standard normal random number (i.e., mean 0, variance 1), and the components are independent of each other. (2) in, This indicates the normalized descent direction. Since the independent variables have different dimensions and feasible regions, this method normalizes the perturbation ranges of variables with different dimensions and orders of magnitude to a sphere, ensuring that the perturbation direction is uniformly distributed on a unit sphere.

[0032] S2.1.2 To ensure that the probability of selecting a perturbation point is equal at all points within the sphere, the perturbation radius (i.e., the perturbation step size) is calculated using the following formula: (3) in, Indicates the perturbation step size. Indicates the first t The neighborhood radius coefficient of the step is calculated by the adaptive annealing algorithm. The numbers are randomly selected with equal probability within the range [0,1]. This method ensures that the probability of selecting a perturbation point is equal in terms of the volume within the sphere.

[0033] S2.1.3. Based on the disturbance direction and disturbance step size, the dimensionless disturbance offset is calculated using equation (4): (4) in, This represents the dimensionless perturbation offset.

[0034] S2.1.4. Transform the above dimensionless space perturbation mapping into a dimensional perturbation, and calculate the perturbation point based on the iteration point: (5) in, Indicates the first t The perturbation point of the step, Indicates the first t The iteration point of the step. The dimension is n The feasible domain vector of the independent variable, symbol This indicates that the elements at corresponding positions are multiplied one by one.

[0035] S2.2, Adaptive annealing algorithm is used to adjust the neighborhood radius coefficient. Update it and adjust it adaptively to ensure optimized convergence and convergence speed.

[0036] S2.2.1 Calculate the basic annealing neighborhood radius coefficient: (6) in, For the first t The neighborhood radius coefficient of the basic annealing step. This is the initial neighborhood radius coefficient, which can be set to 0.05; t This indicates the number of iterations, with an initial step count of 0. This represents the annealing rate index; the larger the value, the faster the radius decays, and the smaller the value, the slower the radius decays.

[0037] S2.2.2 Determine if the optimization objective of the current step has decreased. First, calculate the difference between the optimization objective of the previous step and the current step: (7) like The target was determined to be declining. Then it is determined that the target has not decreased.

[0038] Based on the above judgment, an adaptive multiplier is introduced. If the first is determined by equation (7), t If the step is to descend towards the target, then by... The reduction factor, if the first t If the step determines that the target has not descended, then proceed... Magnification factor and These represent the scaling-down and scaling-up ratios of the coefficients, respectively, and the adaptive multiplier ranges from [0.2, 5].

[0039] S2.2.3. Adjust the perturbation coefficients according to the adaptive multiplier: (8) in, For the determined first t The neighborhood radius coefficient is limited to the range of [0.001, 0.1]. If it exceeds the upper or lower limit, the corresponding boundary limit value is used directly.

[0040] S2.3 Calculate multiple independent random disturbance points The gradient is calculated independently for each perturbation point. And use its average value as the gradient direction for this step.

[0041] S3. Based on finite element calculation and the geometric relationship of branched cable-supported prestressed columns, the stiffness matrix is ​​differentiated to facilitate subsequent gradient calculation.

[0042] S3.1 The overall linear stiffness matrix and stress stiffness matrix of the structure are obtained by assembling the element stiffness matrices in the global coordinate system, that is: (9) (10) in, and They represent the first j The linear stiffness matrix and stress stiffness matrix of each element in the global coordinate system. j Indicates the unit number. m This represents the total number of units. Differentiating both sides, we get: (11) (12) S3.2 The element linear stiffness matrix and stress stiffness matrix in the global coordinate system are calculated from the stiffness matrix in the element coordinate system through coordinate transformation: (13) (14) in, and These represent the element transformation matrix and its transpose, respectively.

[0043] Differentiating equations (13) and (14), we get: (15) (16) S3.3 In this embodiment, the classic Euler-Bernoulli beam element is used to simulate the central column and strut, and the bar element, which has only axial stiffness after the beam element degenerates, is used to simulate the cable. Therefore, the specific form of the element stiffness matrix will not be described in detail.

[0044] If we differentiate the element linear stiffness matrix in the element coordinate system with respect to the independent variable, and only the element length is affected by the independent variable while other parameters are independent, then... The derivative formula can be written as: (17) Differentiating the element stress-stiffness matrix in the element coordinate system with respect to the independent variables reveals that only the element internal forces and element length are affected by the independent variables; all other parameters are independent of the independent variables. The derivative formula can be written as: (18) in, For the internal forces of an element, their derivatives with respect to the independent variable can be calculated using the following process: First, calculate the derivative of the overall structural displacement vector with respect to the independent variable under linear static analysis: (19) Extract the derivative of the element displacement vector in the global coordinate system, and calculate the derivative of the element internal force with respect to the independent variable using the following formula: (20) (twenty one) in, and This indicates that the element displacement vectors in the element coordinate system and the global coordinate system are obtained through linear static analysis, where The derivative can be directly extracted from the overall structural displacement calculated in equation (19).

[0045] S4. After determining the neighborhood perturbation points, calculate the gradient of the optimization objective based on the perturbation points: S4.1 First, the finite element calculation process for linear buckling load is given. Considering that the cable-supported steel column is subjected to a given external load (such as axial pressure at the top), the linear static response of the structure is calculated by the following formula: (twenty two) in, Represents the linear stiffness matrix of the structure. Represents the structural displacement vector. This represents the structural load vector.

[0046] Furthermore, by performing eigenvalue analysis on the following formula, the buckling coefficients of each order and the corresponding modes are calculated.

[0047] (twenty three) in, Under load The stress stiffness matrix of the structure under action, and Then they are respectively the first q The first buckling coefficient and the corresponding buckling mode. When q is 1. The lowest order buckling load factor, its corresponding For the first-order buckling mode, the linear buckling load is calculated from the lowest-order buckling load factor: (twenty four) S4.2 Based on the above finite element calculation process of linear load, derive the derivative process of linear buckling load.

[0048] Let equation (23) take the first-order coefficients and modes, and let both sides of it be relative to the independent variable. Taking the derivative, we get: (25) Normalizing the first-order buckling mode, we have: (26) Multiply both sides of equation (25) on the left We can obtain: (27) Simplifying equation (27) using the normalization formula and rearranging it, we get: (28) because and Let be the first-order buckling coefficient and the mode, respectively. By using equation (23), the second term on the right side of the equation can be eliminated, and the above equation can be further simplified to: (29) Differentiating both sides of equation (24), and taking into account Given an external load, rather than a variable, the derivative of the linear buckling load can be obtained: (30) As can be seen from equation (29), the key to calculating the derivative of linear buckling load is to calculate the linear stiffness matrix. and stress stiffness matrix The derivative with respect to the independent variable is obtained by formula (25) because the external load F is constant. Therefore, the derivative of the buckling load with respect to the independent variable is transformed into the derivative of the first buckling coefficient with respect to the independent variable.

[0049] S4.3. The gradient of the optimization objective is derived. The gradient of the optimization equation is expressed as: (31) in, The gradient of the negative linear buckling load of the structure with respect to the optimization variables can be expressed by equation (32): (32) in, This represents the linear buckling load of the structure. Indicates the first i There are several independent variables. This embodiment, based on the eigenvalue analysis method of finite element simulation, presents the process of differentiating the linear buckling load of the structure with respect to the independent variables.

[0050] S5. Since the length of an element is determined by the coordinates of the nodes at both ends of the element, it is necessary to derive the relationship between the coordinates of the nodes at both ends of the strut and the independent variable in the global coordinate system based on the geometric relationship of the strut of the branched cable-stayed steel column.

[0051] S5.1, Taking the first set of struts as an example, from Figure 2 It can be seen that the height coordinate of the intersection point of the strut and the central column can be calculated by the following formula: (33) (34) in, and These are the height coordinates of the intersection point of the first set of struts and the central column. The horizontal coordinate of the outward extension end of the first set of struts can be calculated by the following formula: (35) S5.2 Therefore, the coordinates of the upper and lower intersection points of the first set of struts with the central column are respectively... and The coordinates of the extended endpoint are .

[0052] The derivatives of the coordinates of the intersection point of the first set of struts and the central column with respect to height are as follows: and The derivatives with respect to the angle are respectively and The derivatives with respect to the distance between the connection points of the upper and lower struts and the central column are as follows: and The derivative of the first set of strut extension nodes with respect to height is: The derivative with respect to the angle is The derivative of the distance between the connection points of the upper and lower struts and the central column is: .

[0053] S5.3 Similarly, the derivative expressions for the coordinates of the upper and lower intersection points and the extended ends of the second set of struts can be derived.

[0054] Through the above content, by transforming the strut length and angle with the overall coordinate system of the cable-supported prestressed column, the purpose of differentiation is to convert the natural structural parameters such as strut length and angle into parameters in the overall coordinate system during programming calculations.

[0055] S6. The golden section search method is adopted, with the iteration point as the base point and the gradient direction as the search direction, until the set conditions are met.

[0056] S7. Update the optimization variables and proceed to the next iteration, repeating processes S2-S6. Check the convergence of the calculations in each iteration. If the convergence condition is met, the optimization is considered complete. The condition is that after 5 consecutive iterations, the convergence is achieved. ,in As the tolerance value for error, it can be set as follows: ; S8. Output the optimization results.

[0057] The optimization method provided in this application takes maximizing the lowest-order buckling load of the branched cable-supported prestressed steel column as the optimization objective and the height and angle of the strut of the cable-supported prestressed steel column as optimization variables. It introduces a neighborhood random disturbance mechanism for independent variables in the gradient method, which can optimize various types of cable-supported prestressed steel columns, improve their stability performance, reduce strut length, and save materials and costs.

[0058] Example 2 This embodiment discloses an optimization system for a branched cable-supported prestressed column structure system, including a computing device configured as follows: Using the height of the connection between the strut and the central column in the branched cable-supported prestressed column and the angle between the strut and the central column as optimization variables, and taking the maximum linear buckling load of the structure as the optimization objective, an optimization equation for the branched cable-supported prestressed column is constructed. The neighborhood stochastic gradient method is used to iteratively solve the optimization equation of the branched cable-supported prestressed column. In each iteration step, a disturbance point is randomly selected in the neighborhood of the iteration point, and the gradient at the disturbance point is calculated. Based on finite element linear buckling analysis, the derivative formulas of the linear buckling load of the structure with respect to each optimization variable are calculated. The perturbation point gradient calculated by the neighborhood stochastic gradient method is used as the search direction, and the iteration point is used as the base point to perform a line search until the line search satisfies the constraint conditions. Update the optimization variables and judge the convergence of the optimization. If the convergence condition is not met, enter a new iteration step and update the iteration point. Repeat the neighborhood stochastic gradient method for the new iteration step until the optimization meets the convergence condition.

[0059] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimization method for a branched cable-supported prestressed column structural system, characterized in that, Includes the following: Using the height of the connection between the strut and the central column in the branched cable-supported prestressed column and the angle between the strut and the central column as optimization variables, and taking the maximum linear buckling load of the structure as the optimization objective, an optimization equation for the branched cable-supported prestressed column is constructed. The neighborhood stochastic gradient method is used to iteratively solve the optimization equation of the branched cable-supported prestressed column. In each iteration step, a disturbance point is randomly selected in the neighborhood of the iteration point, and the gradient at the disturbance point is calculated. The perturbation point gradient calculated by the neighborhood stochastic gradient method is used as the search direction, and the iteration point is used as the base point to perform a line search until the line search satisfies the constraint conditions. Update the optimization variables and judge the convergence of the optimization. If the convergence condition is not met, enter a new iteration step and update the iteration point. Repeat the neighborhood stochastic gradient method for the new iteration step until the optimization meets the convergence condition.

2. The optimization method for a branched cable-supported prestressed column structure system according to claim 1, characterized in that, The expression for the optimization equation of the branched cable-supported prestressed column is as follows: in, This represents the negative value of the lowest-order buckling load calculated based on finite element analysis. The independent variables for optimization include the height of the connection between the strut and the central column, and the angle between the strut and the central column. This represents the feasible region of the independent variable, and the number of independent variables is... n .

3. The optimization method for a branched cable-supported prestressed column structure system according to claim 2, characterized in that, The optimization equation for branched cable-stayed prestressed columns is solved iteratively using the neighborhood stochastic gradient method. In each iteration step, a disturbance point is randomly selected within the neighborhood of the iteration point, including the following: The perturbation point is calculated using a dimensionless sphere uniform perturbation method. The perturbation direction of the perturbation point is obtained, and the perturbation step size is calculated. The perturbation step size is based on the... t The neighborhood radius coefficient of the step and the number randomly selected with equal probability in [0,1] are determined; Calculate the dimensionless disturbance offset based on the disturbance direction and disturbance step size of the disturbance point; The calculated dimensionless perturbation offset is transformed into a dimensional perturbation, and the perturbation point is calculated based on the iteration point.

4. The optimization method for a branched cable-supported prestressed column structural system according to claim 3, characterized in that, After obtaining the disturbance point, it is also necessary to further investigate the first disturbance point. t The neighborhood radius coefficients of the step are adjusted, and the gradient direction of the current step is determined, including the following: Calculate the basic annealing neighborhood radius coefficient; To determine whether the optimization objective of the current step has decreased, first calculate the difference between the optimization objective of the previous step and the current step; According to the adaptive multiplier, for the th t The neighborhood radius coefficient of the step is adjusted; According to the adjusted number t The neighborhood radius coefficient of the step is calculated, multiple independent random perturbation points are calculated, the gradient is calculated independently for each perturbation point, and the average value is used as the gradient direction of the current step.

5. The optimization method for a branched cable-supported prestressed column structural system according to claim 4, characterized in that, The basic annealing neighborhood radius coefficient is calculated based on the initial neighborhood radius coefficient, the number of iterations, and the annealing rate exponent. The first is determined based on the adaptive multiplier and the basic annealing neighborhood radius coefficient. t The neighborhood radius coefficient of the step.

6. The optimization method for a branched cable-supported prestressed column structural system according to claim 1, characterized in that, The gradient of the perturbation point is obtained, including the following: Based on finite element calculations and the geometric relationship of branched cable-supported prestressed steel columns, the stiffness matrix is ​​differentiated. Based on finite element linear buckling analysis, the derivative formulas of the linear buckling load of the structure with respect to each optimization variable are calculated. The gradient of the optimization objective is obtained by differentiating the linear buckling load of the structure with respect to each optimization variable. The gradient of the optimization objective, i.e., the optimization equation, is expressed as: in, The gradient of the negative of the linear buckling load of the structure with respect to the optimization variables; Based on the geometric relationship of the struts of the branched cable-stayed steel column, the relationship between the coordinates of the nodes at both ends of the strut and the independent variable in the global coordinate system is derived.

7. The optimization method for a branched cable-supported prestressed column structural system according to claim 6, characterized in that, The formula for calculating the derivative of the linear buckling load of the structure with respect to each optimization variable based on finite element linear buckling analysis includes the following: The finite element calculation process for linear buckling load is given, considering that the cable-supported steel column is subjected to a given external load, and the structural load vector is calculated. pass Calculate the buckling coefficients and corresponding buckling modes for each order, where, Represents the linear stiffness matrix of the structure. Under load The stress stiffness matrix of the structure under action, and Then they are respectively the first q The first buckling coefficient and the corresponding buckling mode; Command Take the first-order coefficients and modes, and let both ends of them be relative to the independent variable. Taking the derivative, we get the formula: Normalizing the first-order buckling mode and simplifying the derivative formula, we get: in, It is a linear stiffness matrix. Here is the stress stiffness matrix.

8. The optimization method for a branched cable-supported prestressed column structural system according to claim 6, characterized in that, The method for differentiating the stiffness matrix based on finite element analysis and the geometric relationship of branched cable-stayed prestressed steel columns includes the following: Obtain the linear stiffness matrix and stress stiffness matrix, and then perform differentiation; The element linear stiffness matrix and stress stiffness matrix in the global coordinate system are calculated from the stiffness matrix in the element coordinate system through coordinate transformation, and the derivatives of the element linear stiffness matrix and stress stiffness matrix are then obtained. Calculate the derivative of the overall structural displacement vector with respect to the independent variable under linear static analysis, extract the derivative of the element displacement vector in the global coordinate system, and calculate the derivative of the element internal force with respect to the independent variable.

9. The optimization method for a branched cable-supported prestressed column structural system according to claim 6, characterized in that, The derivation of the relationship between the coordinates of the nodes at both ends of the strut and the independent variable in the global coordinate system based on the geometric relationship of the branched cable-supported steel column strut includes the following: Taking the first set of struts as an example, determine the height coordinates of the intersection point between the strut and the central column; Determine the coordinates of the upper and lower intersection points of the struts with the central column in the first group of struts, as well as the coordinates of the outward extension points. The coordinates of the intersection point of the first set of struts and the central column are obtained by differentiating the coordinates with respect to the height, the angle, and the distance between the connection points of the two struts and the central column. The coordinates of the extended end nodes of the first set of struts are also obtained by differentiating the coordinates with respect to the height, the angle, and the distance between the connection points of the two struts and the central column.

10. An optimization system for a branched cable-supported prestressed column structural system, characterized in that, Includes a computing device, which is configured as follows: Using the height of the connection between the strut and the central column in the branched cable-supported prestressed column and the angle between the strut and the central column as optimization variables, and taking the maximum linear buckling load of the structure as the optimization objective, an optimization equation for the branched cable-supported prestressed column is constructed. The neighborhood stochastic gradient method is used to iteratively solve the optimization equation of the branched cable-supported prestressed column. In each iteration step, a disturbance point is randomly selected in the neighborhood of the iteration point, and the gradient at the disturbance point is calculated. The perturbation point gradient calculated by the neighborhood stochastic gradient method is used as the search direction, and the iteration point is used as the base point to perform a line search until the line search satisfies the constraint conditions. Update the optimization variables and judge the convergence of the optimization. If the convergence condition is not met, enter a new iteration step and update the iteration point. Repeat the neighborhood stochastic gradient method for the new iteration step until the optimization meets the convergence condition.

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