Integrated design method and equipment for cable hoisting and buckling based on Grey Wolf optimization algorithm

Abstract

The present invention relates to the technical field of construction calculation for cable-stayed buckle-hang arch bridges, and particularly to a cable hoisting and buckle-hanging integrated design method and equipment based on a Grey Wolf optimization algorithm. The method comprises the following steps: establishing a finite element model, extracting displacement changes of each control point under a unit buckle force to form a control point displacement influence matrix, performing random sampling through a BBD design experiment, and establishing a response surface model between the buckle force and the control point displacement; setting minimization of the control point displacement error in the response surface model as an objective function, optimizing and solving the objective function through an improved TCGWO algorithm, and obtaining an optimal solution combination of the buckle force; inputting the optimal solution combination of the buckle force into the finite element model for calculation to obtain actual displacements of the control points, comparing the actual displacements of the control points with displacements predicted by the response surface model, and verifying whether the accuracy of the response surface model reaches a preset value. If not, re-performing random sampling; and if so, outputting the optimal solution combination of the buckle force.

Description

Technical Field

[0001] The present invention relates to the field of arch bridge cable hoisting construction calculation technology, and in particular to a cable hoisting buckle-hanging integrated design method and equipment based on a Grey Wolf optimization algorithm. Background Art

[0002] Steel tube concrete arch bridges have been vigorously developed in recent years due to their advantages such as high strength, good span, and beautiful appearance. At present, existing arch bridges are usually constructed using cable hoisting and inclined buckle hanging methods. As the span of the arch bridge continues to increase, the number of hoisting segments also increases accordingly, making the precise docking of each segment more difficult. This leads to insufficient construction accuracy of the arch bridge, affecting the stability and safety of the overall structure. In addition, with the increase in hoisting segments, the safety risks during construction also increase accordingly, especially in high-altitude operations and heavy object lifting. Based on this, to address the above problems, we designed an integrated design method and equipment for cable hoisting and buckling based on the Gray Wolf optimization algorithm. Summary of the Invention

[0003] The purpose of the present invention is to provide an integrated cable hoisting and buckling design method and equipment based on the Grey Wolf optimization algorithm. The method optimizes the construction process of the arch bridge by establishing an integrated finite element model of the arch-cable system for construction simulation, and combines the response surface method with the improved Grey Wolf optimization algorithm (TCGWO). This not only ensures the stability and safety of the arch bridge structure and extends the service life of the structure; it also reduces safety risks during the construction process, ensures the safety of construction workers, and reduces construction complexity.

[0004] The embodiments of the present invention are achieved through the following technical solutions:

[0005] An integrated design method for cable hoisting and buckling based on the Grey Wolf optimization algorithm includes the following steps:

[0006] An integrated finite element model of the arch-cable system was established to extract the displacement changes of each control point of the arch bridge under the action of unit cable force to form a control point displacement influence matrix. A response surface model between cable force and control point displacement was established through random sampling through BBD design experiments.

[0007] The objective function is set as minimization of the control point displacement error in the response surface model, and the objective function is optimized and solved using the improved TCGWO algorithm to obtain the optimal solution combination of the cable force.

[0008] The optimal solution combination of the cable force is input into the integrated finite element model of the arch-cable system for calculation to obtain the actual displacement of the control point. The actual displacement of the control point is compared with the displacement predicted by the response surface model to verify whether the accuracy of the response surface model reaches the preset value. If not, random sampling is re-performed through the BBD design test; if so, the optimal solution combination of the cable force is output.

[0009] Optionally, the integrated finite element model of the arch-cable system is specifically constructed by inputting design parameters of the arch bridge and constructing a finite element mesh through the Midas / Civil module to form the integrated finite element model of the arch-cable system.

[0010] Optionally, the process of forming the control point displacement influence matrix is:

[0011] Initialize the control points in the integrated finite element model of the arch-cable system,

[0012] A unit force is applied to the cables in the integrated finite element model of the arch-cable system, and the displacement change of each control point under the action of the unit cable force is solved. It should be noted that during the application of the unit force, the other cable forces remain unchanged. At the same time, the corresponding cable force of the back cable is solved with the minimization of the horizontal displacement error of the tower as the objective function.

[0013]

[0014] in, is the displacement of the i-th control point when a unit force is applied to the j-th cable, is the displacement of the ith control point when the jth cable force is 0, is the displacement change of the i-th arch rib control point under the unit force of the j-th cable;

[0015]

[0016] in, is the displacement generated by applying x times the unit force to the j-th back cable when the i-th control point applies a unit force to the j-th cable, is the displacement of the i-th control point when the j-th back cable tension is 0;

[0017] Calculate all the obtained The control point displacement influence matrix is formed by extracting the control point displacement influence matrix with n rows and m columns. The above steps are repeated for each cable in the integrated finite element model of the arch-cable system to obtain the control point displacement influence matrix.

[0018] Optionally, the specific establishment process of the response surface model is as follows:

[0019] Random sampling was performed through BBD design experiment to obtain the test samples;

[0020] The test sample is used as input, and the arch-cable system integrated finite element model is used for calculation to obtain the corresponding control point displacement value as output, and the corresponding control point displacement value is represented as the response value;

[0021] A quadratic polynomial is used as the functional form of the response surface model, and the input and output are brought into the least square method for calculation to complete the construction of the responsiveness model. The established responsiveness model characterizes the mapping relationship between the cable force and the control point displacement.

[0022] Optionally, minimizing the displacement error of the control points in the response surface model is set as the objective function, and the specific calculation formula of the objective function is:

[0023]

[0024] in, is the cable force adjustment vector of each cable of the arch bridge, , is the displacement value of the i-th control point after adjustment, is the target displacement of the control point.

[0025] Optionally, the objective function is optimized and solved by the improved TCGWO algorithm to obtain the optimal solution combination of the cable force, and the specific process is as follows:

[0026] S1: Initialize the parameters of the improved TCGWO algorithm;

[0027] S2: Generate the initial population through the Tent chaos map and solve the objective function value of each individual in the initial population;

[0028] S3: Based on the objective function value of each individual in the initial population, iteratively update the position information of α wolf, β wolf and δ wolf, and update the control parameters according to the number of iterations;

[0029] S4: Update the position of each individual according to the updated control parameters and the position information of α wolf, β wolf and δ wolf, and recalculate the updated individual objective function value according to the updated individual position;

[0030] S5: Determine whether the maximum number of iterations has been reached. If not, repeat steps S2-S4. If so, output the individual position of the α wolf, where the individual position of the α wolf represents the optimal solution combination of the cable force.

[0031] Optionally, the comparison of the actual displacement of the control point with the displacement predicted by the response surface model is specifically:

[0032] The optimal solution combination of the cable force obtained in S5 is input into the integrated finite element model of the arch-cable system, and the actual displacement of the control point is calculated by the integrated finite element model of the arch-cable system;

[0033] Calculate the error between the actual displacement of the control point and the displacement predicted by the response surface model, and determine whether the error is lower than the set value. If not, re-random sampling is performed through the BBD design experiment and the steps are re-executed; if so, the optimal solution combination of the cable force is output.

[0034] An electronic device, comprising:

[0035] memory for storing computer programs;

[0036] The processor is used to implement the steps of the cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm when executing the computer program.

[0037] The technical solutions of the embodiments of the present invention have at least the following advantages and beneficial effects:

[0038] The embodiment of the present invention optimizes the construction process of the arch bridge by establishing an integrated finite element model of the arch-cable system for construction simulation and combining the response surface methodology with the improved TCGWO algorithm. This not only ensures the stability and safety of the arch bridge structure and extends the service life of the structure; it also reduces safety risks during the construction process, ensures the safety of construction workers, and reduces construction complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic diagram of a flow chart of an integrated design method for cable hoisting, buckling and hanging based on the Grey Wolf optimization algorithm provided by an embodiment of the present invention;

[0040] Figure 2 A schematic diagram of the TCGWO algorithm optimization process provided by an embodiment of the present invention;

[0041] Figure 3 A schematic diagram of a calculation example provided for an embodiment of the present invention, which illustrates the arch structure, cable stays, back cable stays, and tower;

[0042] Figure 4 An integrated finite element model of the arch-cable system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0044] like Figure 1 As shown, the present invention provides one embodiment: a cable hoisting buckle and hanging integrated design method based on the Gray Wolf optimization algorithm, the method comprising the following steps:

[0045] An integrated finite element model of the arch-cable system was established to extract the displacement changes of each control point of the arch bridge and cable system tower under the action of unit cable force and corresponding back cable force to form a control point displacement influence matrix. A response surface model was established between the cable force and back cable force and the control point displacement by random sampling through BBD design experiments.

[0046] The objective function is set as minimization of the control point displacement error in the response surface model, and the objective function is optimized and solved by the improved TCGWO algorithm to obtain the optimal solution combination of the buckle back cable force.

[0047] The optimal solution combination of the back-cable force is input into the integrated finite element model of the arch-cable system for calculation to obtain the actual displacement of the control point. The actual displacement of the control point is compared with the displacement predicted by the response surface model to verify whether the accuracy of the response surface model reaches the preset value. If not, random sampling is re-performed through the BBD design test; if so, the optimal solution combination of the back-cable force is output.

[0048] In this embodiment, the influence matrix method has been widely used in the cable adjustment process of cable-stayed bridges. The influence matrix mainly involves the concepts of the adjusted vector, the adjusting vector, the influencing vector, and the influence matrix. Specifically, the integrated finite element model of the arch-cable system is constructed by inputting the design parameters of the arch bridge and constructing a finite element mesh using the Midas / Civil module.

[0049] In this embodiment, the process of forming the control point displacement influence matrix is as follows:

[0050] Initialize the control points in the integrated finite element model of the arch-cable system,

[0051] A unit force is applied to the cables in the integrated finite element model of the arch-cable system, and the displacement change of each control point under the action of the unit cable force is solved. It should be noted that during the application of the unit force, the other cable forces remain unchanged. At the same time, the corresponding cable force of the back cable is solved with the minimization of the horizontal displacement error of the tower as the objective function.

[0052]

[0053] in, is the displacement of the i-th control point when a unit force is applied to the j-th cable, is the displacement of the ith control point when the jth cable force is 0, is the displacement change of the i-th arch rib control point under the unit force of the j-th cable;

[0054]

[0055] in, is the displacement generated by applying x times the unit force to the j-th back cable when the i-th control point applies a unit force to the j-th cable, is the displacement of the i-th control point when the j-th back cable tension is 0;

[0056] Calculate all the obtained The control point displacement influence matrix is formed by extracting the control point displacement influence matrix with n rows and m columns. The above steps are repeated for each cable in the integrated finite element model of the arch-cable system to obtain the control point displacement influence matrix.

[0057] In this embodiment, the specific establishment process of the response surface model is as follows:

[0058] Random sampling was performed through BBD design experiment to obtain the test samples;

[0059] The test sample is used as input, and the arch-cable system integrated finite element model is used for calculation to obtain the corresponding control point displacement value as output, and the corresponding control point displacement value is represented as the response value;

[0060] A quadratic polynomial is used as the functional form of the response surface model, and the input and output are brought into the least square method for calculation to complete the construction of the responsiveness model. The established responsiveness model characterizes the mapping relationship between the cable force and the control point displacement.

[0061] In practice, in the calculation of arch bridge cable forces, the mathematical model of the optimization problem generally consists of design variables, objective functions, and constraints. Design variables: Design variables refer to the unknown quantities that need to be solved in the problem, usually expressed as an n-dimensional vector. In the calculation of arch bridge cable forces, the design variables are usually the adjustment amounts of the cable forces, which are used to adjust the initial cable forces to meet the design requirements. Objective function: The objective function is a function of the target pursued expressed by the design variables. In the calculation of cable forces, the objective function can be the minimization of the sum of the squares of the differences between the displacement of the control points and the target displacement after the cables are connected and released. By minimizing the objective function, the line shape after the cables are connected and released can be made as close to the target line shape as possible. Constraints: Constraints are the restrictions that the design variables must meet when solving the extreme values of the objective function. In the calculation of cable forces, the constraints may include the following aspects: the adjusted cable force value must be non-negative, the adjusted cable force value cannot exceed the allowable value of the cable, etc.

[0062] Design variables: ;

[0063] State variables: ;

[0064] Objective function: ;

[0065] Constraints: ;

[0066] in, is the vector composed of all cable force adjustments, is the vector consisting of the difference between the line shape after the rope is loosened and the target line shape in the previous calculation. is the displacement influence matrix of the control points during construction, is the cable force adjustment of No. i cable, is the tension value of the i-th cable before adjustment, L is the number of steel strands that make up the cable, is the cable force when a single steel strand yields, is the safety factor of the cable, is the displacement value of the i-th control point after adjustment, 、 are the lower and upper limits of the allowable displacement after cable adjustment, is the target displacement of the control point.

[0067] In summary, the optimization problem of calculating arch bridge cable tension can be expressed as a mathematical model that seeks the optimal solution for the design variable (cable tension adjustment value) while minimizing the objective function (the sum of the squares of the differences between the control point displacements and the target displacement after cable closure and cable release) while satisfying the constraints (non-negative cable tension and allowable cable tension value). The calculation process involves using the influence matrix, using the cable tension adjustment value as the design variable, and continuously approaching the target displacement.

[0068] like Figure 1 、 Figure 2 、 Figure 3 and Figure 4 As shown, based on the above, the calculation steps of this embodiment are as follows:

[0069] (1) A three-dimensional finite element model of the bridge considering the construction stage is established based on the structural design parameters. The linear data {S} of the arch frame falling under the action of deadweight is used as the control parameter, and the displacement influence matrix [M] and related structural parameters in the construction stage are extracted.

[0070] (2) When using the influence matrix method for calculation, the deviation caused by tangent assembly cannot be considered. The structural parameters of the bridge should be corrected by the influence matrix using the offset vector [K1] and the vertical displacement vector [K2] to obtain the corrected influence matrix [M'];

[0071] (3) Determine the iterative calculation accuracy p, the value of p is ≤ L / 3000 (L is the calculated span of the arch bridge) , What happens is an n-dimensional vector (n is the number of control points);

[0072] (4) The initial tension force of each segment is solved by the simplified moment balance formula: The initial value of the iteration to be calculated Substituting into the model, the cable tension force is obtained as The bridge is in its completed state at this time. At this time, the vertical displacement of each control point after the closure and cable release is , calculate the difference between the displacement of each control point and the target displacement in the current state : , the vector composed of the displacement allowable values of all control points is obtained as: When calculating, the corresponding elements in the vectors on both sides of the inequality must meet the following conditions:

[0073] (5) Substitute the relevant parameters into the cable force calculation program written in MATLAB, where x 0 is the initial value of the design variable, that is, the initial value of x in each calculation, which can be taken as 0. At this time, ΔT is an n-dimensional zero column vector, and A is the coefficient matrix of the linear inequality constraint, which is expressed as A x ≤b, according to the above formula, the coefficient matrix A is composed of the modified displacement influence matrix { M '} and {− M '}, b consists of {b1} and {b2}, lb 、 ub is the cable force adjustment during calculation x In order to ensure that the adjusted cable force value is non-negative and does not exceed the limit, lb={− T 0}, ub The elements in are the allowable cable force and { T 0}, the objective function is:

[0074]

[0075] (6) The cable force calculation program written in MATLAB can be used to obtain the cable force adjustment value ΔT1 under the dual control of cable force and displacement. The cable force value after the first adjustment becomes T1: .

[0076] (7) Substitute T1 as the second round of cable tension into the model to calculate the displacement S1 of each control point after the cable is closed and released in the T1 state. ,like Any element in satisfies , the calculation converges, otherwise continue to calculate the vector composed of the allowable values of the control point displacement during the second adjustment: Repeat steps (5) and (6) to calculate the cable tension adjustment at this time. T 2, then the cable tension value after the second adjustment becomes T 2: .Will T 2 is substituted into the model as the tension of the third wheel cable, and the result is T Displacement of each control point after the cable is closed in state 2 S 2. Calculation , if any element in ΔS1 satisfies , the calculation converges, otherwise repeat the above steps until the nth calculation ΔS n Any element in satisfies , the cable force corresponding to the structure is T n This is the desired cable tension.

[0077] like Figure 2 As shown, in this embodiment, the objective function is optimized and solved by the improved TCGWO algorithm to obtain the optimal solution combination of the cable force. The specific process is as follows:

[0078] S1: Initialize the parameters of the improved TCGWO algorithm;

[0079] S2: Generate the initial population through the Tent chaos map and solve the objective function value of each individual in the initial population;

[0080] S3: Based on the objective function value of each individual in the initial population, iteratively update the position information of α wolf, β wolf and δ wolf, and update the control parameters according to the number of iterations;

[0081] S4: Update the position of each individual according to the updated control parameters and the position information of α wolf, β wolf and δ wolf, and recalculate the updated individual objective function value according to the updated individual position;

[0082] S5: Determine whether the maximum number of iterations has been reached. If not, repeat steps S2-S4. If so, output the individual position of the α wolf, where the individual position of the α wolf represents the optimal solution combination of the cable force.

[0083] An electronic device, comprising:

[0084] memory for storing computer programs;

[0085] The processor is used to implement the steps of the cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm when executing the computer program.

[0086] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. The cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm is characterized by: The steps of the method include: An integrated finite element model of the arch-cable system was established to extract the displacement changes of each control point of the arch rib of the arch bridge under the action of unit cable force, as well as the displacement changes of each control point of the cable system tower under the action of unit cable force and back cable force. This was used to form a control point displacement influence matrix. Random sampling was performed through BBD design experiments to establish a response surface model between cable force and control point displacement. The objective function is to minimize the displacement error of the control points in the response surface model and to make the displacement of the tower control points approach 0. The improved TCGWO algorithm is used to optimize and solve the objective functions respectively, and the optimal solution combination of the cable force and the back cable force is obtained. The optimal solution combination of the cable force is input into the integrated finite element model of the arch-cable system for calculation to obtain the actual displacement of the control point. The actual displacement of the control point is compared with the displacement predicted by the response surface model to verify whether the accuracy of the response surface model reaches the preset value. If not, random sampling is re-performed through the BBD design test; if so, the optimal solution combination of the cable force is output; The formation process of the control point displacement influence matrix is: Initialize the control points in the integrated finite element model of the arch-cable system, A unit force is applied to the cables in the integrated finite element model of the arch-cable system to calculate the displacement change of each control point under the unit cable force. During the application of the unit force, the remaining cable forces remain unchanged. At the same time, the corresponding cable force of the back cable is calculated using the minimization of the horizontal displacement error of the tower as the objective function. in, is the displacement of the i-th control point when a unit force is applied to the j-th cable, is the displacement of the ith control point when the jth cable force is 0, is the displacement change of the i-th arch rib control point under the unit force of the j-th cable; in, is the displacement generated by applying x times the unit force to the j-th back cable when the i-th control point applies a unit force to the j-th cable, is the displacement of the i-th control point when the j-th back cable tension is 0; Calculate all the obtained Extract and form a control point displacement influence sub-matrix with n rows and m columns. Repeat the above steps for each cable in the integrated finite element model of the arch-cable system to obtain the control point displacement influence matrix. The value of approaches 0 to solve the back buckle.

2. The cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm according to claim 1 is characterized in that: The integrated finite element model of the arch-cable system is specifically constructed by inputting relevant design parameters of the arch bridge and the cable system according to their layout, and constructing a finite element mesh to form the integrated finite element model of the arch-cable system.

3. The cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm according to claim 2 is characterized in that: The specific establishment process of the response surface model is as follows: Random sampling was performed through BBD design experiment to obtain the test samples; The test sample is used as input, and the arch-cable system integrated finite element model is used for calculation to obtain the corresponding control point displacement value as output, and the corresponding control point displacement value is represented as the response value; A quadratic polynomial is used as the functional form of the response surface model, and the input and output are brought into the least square method for calculation to complete the construction of the responsiveness model. The established responsiveness model characterizes the mapping relationship between the cable force and the control point displacement.

4. The cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm according to claim 3 is characterized in that: The objective function is to minimize the displacement error of the control points in the response surface model. The specific calculation formula of the objective function is: in, is the cable force adjustment vector of each cable of the arch bridge, , is the displacement value of the i-th control point after adjustment, is the target displacement of the control point.

5. The cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm according to claim 4 is characterized in that: The objective function is optimized and solved by the improved TCGWO algorithm to obtain the optimal solution combination of the cable force. The specific process is as follows: S1: Initialize the parameters of the improved TCGWO algorithm; S2: Generate the initial population through the Tent chaos map and solve the objective function value of each individual in the initial population; S3: Based on the objective function value of each individual in the initial population, iteratively update the position information of α wolf, β wolf and δ wolf, and update the control parameters according to the number of iterations; S4: Update the position of each individual according to the updated control parameters and the position information of α wolf, β wolf and δ wolf, and recalculate the updated individual objective function value according to the updated individual position; S5: Determine whether the maximum number of iterations has been reached. If not, repeat steps S2-S4. If so, output the individual position of the α wolf, where the individual position of the α wolf represents the optimal solution combination of the cable force.

6. The cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm according to claim 5 is characterized in that: The comparison of the actual displacement of the control point and the displacement predicted by the response surface model is specifically as follows: The optimal solution combination of the cable force obtained in S5 is input into the integrated finite element model of the arch-cable system, and the actual displacement of the control point is calculated by the integrated finite element model of the arch-cable system; Calculate the error between the actual displacement of the control point and the displacement predicted by the response surface model, and determine whether the error is lower than the set value. If not, re-random sampling is performed through the BBD design experiment and the steps are re-executed; if so, the optimal solution combination of the cable force is output.

7. An electronic device, characterized in that: include: memory for storing computer programs; A processor is used to implement the steps of the cable hoisting buckle and hanging integrated design method based on the Grey Wolf optimization algorithm as described in any one of claims 1 to 6 when executing the computer program.

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