A seismic design method for suspension bridges based on BPNN and DBO algorithms

Abstract

The present invention relates to the technical field of suspension bridge seismic optimization design, and specifically to a suspension bridge seismic design method based on BPNN and DBO algorithm. The method comprises the following steps: S1, determining the invariant value and design variables of the suspension bridge in seismic design, and constructing a function between the structural cost and the design variable x; S2, determining the state variables of the structure verification according to the industry specifications and structural characteristics, and integrating them into the function in the form of a penalty function to form an augmented function; S3, determining the initial linearity of the suspension bridge according to the segmented catenary equation, solving the modeling parameters of the suspension bridge through the spatial catenary lock unit equation, and solving the structural response after establishing a finite element model according to the modeling parameters; S4, repeating S3, performing multiple sampling, taking the response under static action corresponding to different design variables X, and the matrix A under earthquake action, forming a training sample of BPNN, and storing the current BPNN model when the response output by BPNN reaches the error threshold of the finite element result.

Description

Technical Field

[0001] The invention relates to the technical field of suspension bridge seismic optimization design, and in particular to a suspension bridge seismic design method based on BPNN and DBO algorithms. Background Art

[0002] The space cable self-anchored suspension bridge is a special bridge structure, whose main cables and suspenders are inclined in the transverse direction of the bridge, and the entire structural system presents a spatial three-dimensional structure. This structural system can increase the lateral stiffness and dynamic stability without changing the vertical bearing capacity. Therefore, in the selection of bridge sites in rivers and straits with high wind speeds and frequent earthquakes, the space cable self-anchored suspension bridge has a certain competitiveness.

[0003] When conducting seismic design of suspension bridges, a reasonable seismic resistance system is often preliminarily determined based on the site selection and site information. Then a seismic analysis is conducted to verify whether the strength and stiffness of the structure under seismic action meet the requirements of the specifications, and the structural parameters and geometric configuration are adjusted based on the verification results.

[0004] However, the existing methods have the following problems:

[0005] 1. The design method of "trial calculation-verification-parameter adjustment" not only wastes a lot of computing costs, but also makes it difficult to find the optimal configuration design solution that meets the specification requirements.

[0006] 2. The structure of the spatial cable-shaped self-anchored suspension bridge is relatively complex. When analyzing it, it is necessary to first find the shape and then establish a finite element model for analysis and settlement. The optimization process is very cumbersome. Summary of the invention

[0007] The technical problem solved by the present invention is to provide a suspension bridge seismic design method based on BPNN and DBO algorithms.

[0008] The basic scheme provided by the present invention comprises the following steps: A suspension bridge seismic design method based on BPNN and DBO algorithm comprises the following steps:

[0009] S1. Determine the invariant values ​​and design variables of the suspension bridge in seismic design and construct the structural cost Function between and design variable x:

[0010]

[0011] Where f(x) represents the material cost function of a suspension bridge consisting of n components; for component i, Ci represents the cost per unit volume of the material, Li represents the length of the component, and Ai represents the area of ​​the component;

[0012] S2. Determine the state variables of the structure verification according to industry standards and structural characteristics, and integrate them into the function in the form of penalty functions. , forming an augmented function ;

[0013] S3. Determine the initial linearity of the suspension bridge according to the segmented catenary equation, solve the modeling parameters of the suspension bridge through the spatial catenary lock unit equation, and establish a finite element model according to the modeling parameters and solve it to obtain the structural response;

[0014] S31, obtain the static load by solving the response of the key points of the record;

[0015] S32. Introduce the ETDM method and convert the time history analysis into a simple row matrix multiplication form to calculate the seismic load:

[0016]

[0017] The element A is only related to the system matrix related, are coefficient matrices related only to the structural system arrive is the earthquake acceleration from the start time to the end time T, and at least two earthquake loads are introduced into the finite element model to obtain the structural response of the structure at each moment;

[0018] S4, repeat S3, perform multiple sampling, take the response under static force corresponding to different design variables X, and the matrix A under earthquake action, form BPNN training samples, train the BPNN model through the training samples, and when the response output by BPNN reaches the error threshold of the finite element result, store the current BPNN model;

[0019] S5. Select the optimization algorithm DBO, build the seismic design optimization model of the suspension bridge, call the form-finding program and BPNN model to complete the solution of F(x) until the maximum number of iterations is reached or the error accuracy is met, and output the material cost and design variables at this time.

[0020] Furthermore, in S3, the seismic response of the structure is calculated by introducing the ETDM method.

[0021] Furthermore, in S4, the BPNN model is used to obtain the state variables, and the static response and dynamic response of the structure can be output by inputting the design variables.

[0022] The principles and advantages of the present invention are:

[0023] 1. The ETDM and BPNN models are introduced, and the cumbersome finite element analysis is replaced by the function mapping relationship of BPNN. When the design variables are input, the static response and seismic response of the key points of the structure can be directly obtained, which improves the calculation efficiency.

[0024] 2. The DBO algorithm is introduced to replace the empirical calculation process, making the optimization design process more efficient and concise. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow chart of an embodiment of a suspension bridge seismic design method based on BPNN and DBO algorithms of the present invention;

[0026] Figure 2 A schematic diagram of the force on a single cable of a spatial cable in an embodiment of a suspension bridge seismic design method based on BPNN and DBO algorithms of the present invention;

[0027] Figure 3 It is a schematic diagram of design variables of a spatial cable self-anchored suspension bridge according to an embodiment of a suspension bridge seismic design method based on BPNN and DBO algorithms of the present invention. DETAILED DESCRIPTION

[0028] The following is further described in detail through specific implementation methods:

[0029] The embodiment is basically as shown in the attached Figure 1 As shown:

[0030] A suspension bridge seismic design method based on BPNN and DBO algorithm includes the following steps:

[0031] S1. Determine the invariant values ​​and design variables of the suspension bridge in seismic design and construct the structural cost is a function of the design variable x.

[0032] The structural characteristics of a self-anchored suspension bridge mainly depend on several key parameters, such as the spatial layout shape of the bridge structure, the material properties and cross-sectional parameters of key load-bearing components, and boundary conditions. Before the preliminary design is carried out, the bridge deck width, main span, and clear height under the bridge are usually determined according to navigation requirements and traffic needs. In order to improve the feasibility of optimization, this application considers that the hanger spacing, tower height, side span span, and material properties of each material are unchanged. In summary, when optimizing, the design variables considered in this application are as follows: stiffening beam: section width, section height, top and bottom plate thickness, web thickness; main tower: section width, section height, top and bottom plate thickness, web thickness; crossbeam: section width, section height, top and bottom plate thickness, web thickness; cable: main cable area, sling area; spatial layout: vertical rise span ratio, transverse rise span ratio. The goal of the optimization design is to minimize the material cost while ensuring the safety of the structural force and the applicability of the function. Therefore, the objective function should be the total cost of the material, as shown in the following formula:

[0033]

[0034] Where f(x) represents the material cost function of a suspension bridge consisting of n components; for component i, Ci represents the cost per unit volume of the material, Li represents the length of the component, and Ai represents the area of ​​the component;

[0035] S2. Determine the state variables of the structure verification according to industry standards and structural characteristics, and integrate them into the function in the form of penalty functions. , forming an augmented function ;

[0036] Specifically, the structural state variables can be divided into state variables under static force and state variables under seismic load. According to the requirements of the specification, the strength requirements and use requirements for suspension bridges under the most unfavorable conditions of dead load + live load are as follows:

[0037] Strength requirements: The allowable stress of the main cable and sling is 500MPa, the allowable stress of the stiffening beam is 120MPa, and the allowable stress of the main tower and beam is 150MPa.

[0038] Usage requirements: The allowable vertical deflection of the beam should be less than Lm / 500, and the maximum horizontal displacement of the tower should be less than 1 / 800 of the tower height.

[0039] The requirements for suspension bridges under earthquakes are as follows: Under E1 design earthquakes, only the strength of the structure needs to be verified; under E2 rare earthquakes, the strength and stiffness of the structure need to be checked at the same time. According to the requirements of the specification, the ultimate bearing capacity state should be verified under accidental earthquakes. The ultimate bearing capacity state in the short-term state should not exceed 0.8fk, which is 220MPa. The vertical displacement limit of the stiffening beam is l / 250, and the lateral displacement limit is l / 150.

[0040] S3. Determine the initial linearity of the suspension bridge according to the segmented catenary equation. The spatial catenary lock unit equation is as follows:

[0041]

[0042] The modeling parameters of the suspension bridge are solved by the equation. The finite element model is established according to the modeling parameters and then solved. The single cable force diagram of the spatial cable is shown in Figure 2 As shown. Assume that the stress-free cable length of the i-th cable segment is Si, the elastic modulus of the cable is E, and the cross-sectional area is A; the vertical downward load concentration along the cable length is q; the coordinate system is set to the horizontal right as the positive direction of the x-axis, the vertical outward as the positive direction of the y-axis, and the vertical downward as the positive direction of the z-axis; the x-axis coordinate difference, y-axis coordinate difference, and z-axis coordinate difference between the terminal and the starting end of the i-th single cable are li, yi, and hi respectively; the x-direction force, y-direction force, and z-direction force at the head end of the cable are Hxi, Hyi, and Vi respectively.

[0043] It can be seen from the above formula that if the two horizontal forces Hxi and Hyi are determined, then the spatial direction of the plumb plane where the cable segment is located is also determined. In the calculation of the completed bridge, if the tension Hx1, Hy1, and V1 of the main cable at the first end are given, then the linear shape and internal force value of the first section of the main cable can be solved and then recursively deduced to the last section of the main cable. At this time, if the horizontal coordinate, vertical coordinate, and mid-span sag value of the end point do not meet the given allowable error, the tension value at the first end is updated and iterated until the linear shape converges to the allowable error range. At this time, the linear shape and internal force values ​​of each section of the main cable are the exact solution.

[0044] S31, obtain the static load by solving the response of the key points of the record;

[0045] S32. Introduce the ETDM method and convert the time history analysis into a simple row matrix multiplication form to calculate the seismic load:

[0046]

[0047] The element A is only related to the system matrix related, arrive is the seismic acceleration from the start time to the end time T, and at least two seismic loads are introduced into the finite element model to obtain the structural response of the structure at a moment; if the matrix A is obtained, then under any given seismic motion, the response time history of the structure can be calculated by the above formula. Here, two finite element analyses are performed using two unit pulse seismic motions to obtain the matrix A. In this embodiment, the two impact seismic motions are shown in the following formula:

[0048]

[0049] S4, repeat S3, perform multiple sampling, take the response under static force corresponding to different design variables X, and the matrix A under seismic action, form BPNN training samples, and train the BPNN model through the training samples. When the response output by BPNN reaches the error threshold of the finite element result, store the current BPNN model. The input-output of this BPNN corresponds to the design variable-structural response of the structure.

[0050] S5. Select the optimization algorithm DBO, build the seismic design optimization model of the suspension bridge, call the form-finding program and BPNN model to complete the solution of F(x), until the maximum number of iterations is reached or the error accuracy is met, and output the material cost and design variables at this time. The design variables at this time are a set of values ​​that meet the specification requirements and have the lowest material cost.

[0051] In S3, the seismic response of the structure is calculated by introducing the ETDM method.

[0052] In S4, the BPNN model is used to obtain the state variables, and the static response and dynamic response of the structure can be output by inputting the design variables.

[0053] The principles and advantages of the present invention are:

[0054] 1. The ETDM and BPNN models are introduced, and the cumbersome finite element analysis is replaced by the function mapping relationship of BPNN. When the design variables are input, the static response and seismic response of the key points of the structure can be directly obtained, which improves the calculation efficiency.

[0055] 2. The DBO algorithm is introduced to replace the empirical calculation process, making the optimization design process more efficient and concise.

[0056] The present invention is described below by taking a spatial cable-shaped self-anchored suspension bridge with a main span of 300 m as an example.

[0057] Determined Figure 3 The design variables shown in the figure are used to construct the augmented objective function as shown below:

[0058]

[0059] Write a form-finding program, establish a finite element model to analyze and obtain the training samples required for the BPNN model, and complete the training of the BPNN model.

[0060] For the four load conditions of dead load + live load, the comparison of the results predicted by the finite element method and the BPNN model is shown in the following table:

[0061] Table 1

[0062]

[0063] Table 2

[0064]

[0065] Table 3

[0066]

[0067] Table 4

[0068]

[0069] It can be seen from the data in the table that under the four load conditions, the errors between the finite element analysis results and the BPNN prediction results are concentrated around 5%, and it is believed that the model has a certain degree of accuracy.

[0070] For the verification of earthquake response, after comparative analysis, the maximum error in the maximum stress time history at the tower bottom was 13.86 s, and the stress error was 8.16%. The maximum error in the maximum stress time history at the tower-beam junction was 15.12 s, and the stress error was 5.32%. To further reduce the error, a large number of training samples need to be increased, and the acquisition of samples requires a lot of time cost. Therefore, the model is considered to have a certain degree of accuracy after training so far.

[0071] Set the maximum number of iterations T of the DBO algorithm to 100 and the population size D to 30 (according to the classification of dung beetle individuals in the DBO algorithm, the population size must be a multiple of 30). Output a set of optimal solutions and target cost fitness values ​​through iterative calculation of the optimization model.

[0072] Table 5

[0073]

[0074] As shown in Table 5, the change range of each design variable and material cost of the optimization results without changing any parameters for three times does not exceed 2%, and the volatility is small, indicating that the algorithm can converge stably. The selection of the optimal value can be averaged by multiple independent optimization operations, and the entire optimization process only takes 2.1 hours.

[0075] It can be seen that the design variable values ​​obtained by adopting the present invention are scientific and reasonable, and provide a more efficient and quick method for the preliminary seismic design of the future spatial cable-shaped self-anchored suspension bridge.

[0076] The above are only embodiments of the present invention. Common knowledge such as the known specific structures and characteristics in the scheme is not described in detail here. Ordinary technicians in the relevant field know all the common technical knowledge in the technical field to which the invention belongs before the application date or priority date, can obtain all the existing technologies in the field, and have the ability to apply conventional experimental means before that date. Ordinary technicians in the relevant field can improve and implement this scheme in combination with their own abilities under the enlightenment given by this application. Some typical known structures or known methods should not become obstacles for ordinary technicians in the relevant field to implement this application. It should be pointed out that for those skilled in the art, without departing from the structure of the present invention, several deformations and improvements can be made, which should also be regarded as the scope of protection of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A seismic design method for suspension bridges based on BPNN and DBO algorithms, characterized by: The following steps are involved: S1. Determine the invariant values ​​and design variables of the suspension bridge in seismic design and construct the structural cost Function between and design variable x: Where f(x) represents the material cost function of a suspension bridge consisting of n components; for component i, Ci represents the cost per unit volume of the material, Li represents the length of the component, and Ai represents the area of ​​the component; S2. Determine the state variables of the structure verification according to industry standards and structural characteristics, and integrate them into the function in the form of penalty functions. , forming an augmented function ; S3. Determine the initial linearity of the suspension bridge according to the segmented catenary equation, solve the modeling parameters of the suspension bridge through the spatial catenary lock unit equation, and establish a finite element model according to the modeling parameters and solve it to obtain the structural response; S4, repeat S3, perform multiple sampling, take the response under static force corresponding to different design variables X, and the matrix A under earthquake action, form BPNN training samples, train the BPNN model through the training samples, and when the response output by BPNN reaches the error threshold of the finite element result, store the current BPNN model; S5. Select the optimization algorithm DBO, build the seismic design optimization model of the suspension bridge, call the form-finding program and the BPNN model to complete the solution of F(x), until the maximum number of iterations is reached or the error accuracy is met, and output the material cost and design variables at this time; S31, obtain the static load by solving the response of the key points of the record; S32. Introduce the ETDM method and convert the time history analysis into a simple row matrix multiplication form to calculate the seismic load: The element A is only related to the system matrix related, are coefficient matrices related only to the structural system arrive is the seismic acceleration from the start time to the end time T, and at least two seismic loads are introduced into the finite element model to obtain the structural response of the structure at each moment.

2. The seismic design method for suspension bridge based on BPNN and DBO algorithm according to claim 1, characterized in that: In S3, the seismic response of the structure is calculated by introducing the ETDM method.

3. The seismic design method for suspension bridge based on BPNN and DBO algorithm according to claim 2, characterized in that: In S4, the BPNN model is used to obtain the state variables, and the static response and dynamic response of the structure can be output by inputting the design variables.

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