A method for calculating cable force of a special-shaped cable-stayed bridge

Abstract

This invention discloses a method for calculating the cable forces of an irregularly shaped cable-stayed bridge upon completion, belonging to the field of bridge engineering. The method involves establishing a finite element model of the irregularly shaped cable-stayed bridge based on engineering drawings; obtaining the influence matrix of the cable forces on the main girder and main tower; establishing an objective function based on the influence matrix, with the goal of minimizing the overall strain energy of the irregularly shaped cable-stayed bridge, and determining the constraints; establishing a cable force optimization model for the irregularly shaped cable-stayed bridge; calculating the initial cable forces of each stay cable in the irregularly shaped cable-stayed bridge using the cable force optimization model; and calculating the final cable forces based on the initial cable forces of each stay cable. This invention, based on the particle swarm optimization algorithm, realizes the calculation of the final cable forces of an irregularly shaped cable-stayed bridge with a novel cable arrangement, enabling rapid and accurate acquisition of the reasonable completed bridge state of the irregularly shaped cable-stayed bridge.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically a method for calculating the cable force of an irregularly shaped cable-stayed bridge. Background Technology

[0002] Cable-stayed bridges consist of a main girder, cables, and towers. By adjusting the tension of the cables, a cable-stayed bridge can achieve a reasonable bridge state with "flat girder and straight tower" and uniform cable tension, making full use of the tensile strength of the cables and effectively reducing the bending moment and displacement of the main girder. With social development, bridges are increasingly focusing on aesthetics while meeting functional requirements, leading to the emergence of various more aesthetically pleasing irregular-shaped cable-stayed bridges. In addition to main towers of various shapes, a new type of cable arrangement has emerged, in which cables are arranged in a crisscross pattern between multiple main towers in irregular-shaped cable-stayed bridges. Compared with traditional cable-stayed bridges, the structural and mechanical systems of the new cable arrangement irregular-shaped cable-stayed bridges are more complex. To ensure the structural stability of the cable-stayed bridge, cable tension optimization is crucial.

[0003] Traditional cable force optimization methods, such as zero displacement, rigid support continuous beam method, and minimum bending moment energy method, have limitations when determining the cable force of a non-standard cable-stayed bridge with novel cable arrangement, resulting in cumbersome optimization process or low reliability of optimization results. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for calculating the cable force of an irregularly shaped cable-stayed bridge, which can easily and accurately obtain the initial cable force of the irregularly shaped cable-stayed bridge with a novel cable arrangement and calculate the final cable force.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for calculating the cable forces of an irregularly shaped cable-stayed bridge upon completion includes the following steps:

[0007] Step 1: Establish a finite element model of the irregular cable-stayed bridge based on the engineering drawings;

[0008] Step 2: Obtain the influence matrix of cable forces on the main beam and main tower;

[0009] Step 3: With the goal of minimizing the overall strain energy of the irregular cable-stayed bridge, establish the objective function based on the influence matrix and determine the constraints.

[0010] Step 4: Establish a cable force optimization model for the irregular cable-stayed bridge;

[0011] Step 5: Calculate the initial cable force of each cable in the irregular cable-stayed bridge using the cable force optimization model, and calculate the final cable force of the bridge based on the initial cable force of each cable.

[0012] Furthermore, the influence matrix includes: the influence matrix of the stay cable on the bending moment of the main beam, the influence matrix of the stay cable on the axial pressure of the main tower, the bending moment of each element of the main beam when only a dead load is applied, the axial pressure of each element of the main tower when only a dead load is applied, the stiffness of the main beam, and the stiffness of the main tower.

[0013] Furthermore, the formula for the objective function is as follows:

[0014]

[0015] In the formula, M is the bending moment of the main beam; E is the elastic modulus of the main beam and the main tower; I is the bending moment of inertia of the main beam; N is the axial force of the main tower; A is the cross-sectional area of ​​the main tower; and U is the strain energy of the cable-stayed bridge. The goal is to find the minimum strain energy of the cable-stayed bridge.

[0016] For the discrete finite element model of an irregular cable-stayed bridge, it can be written in matrix form:

[0017] U = {M L} T [B1]{M L}{M R} T [B1]{M R}{N L} T [B2]{N L}+{N R} T [B2]{N R}

[0018] {M L}=[C L ]{S}+{M L0}

[0019] {M R}=[C R ]{S}+{M R0}

[0020] {N L}=[C Ln ]{S}+{N L0}

[0021] {N R}=[C Rn ]{S}+{M R0}

[0022]

[0023]

[0024] In the formula, [B1] and [B2] are the stiffness coefficient matrices of the main beam and the main tower, respectively, and {M L {、{M R} are the matrices of the bending moments on the left and right sides of the beam element, respectively. L}、{N R} represents the matrix of axial forces acting on the left and right sides of each unit of the main tower; T represents the transpose matrix; C L C R M represents the influence matrices of the applied cable force S on the bending moments on the left and right sides of the main beam element, respectively. L0 M R0 This represents the bending moment matrix on the left and right sides of each element of the main beam before the application of the adjustment vector cable force S; C Ln C Rn N represents the influence matrix of the applied cable force S on the axial forces on the left and right sides of the main tower unit, respectively. L0 N R0 This represents the matrix of axial forces acting on the left and right sides of the main tower element before the application of the adjustment vector cable force S; This represents the stiffness coefficient of the i-th main beam element. L represents the stiffness coefficient of the i-th main tower element, n represents the number of main beam elements or main tower elements, and L represents the stiffness coefficient of the i-th main tower element. i E represents the length of the i-th main beam element or the i-th main tower element. i Let I be the elastic modulus of the i-th main beam element or the i-th main tower element. i Let A be the bending moment of inertia of the i-th main beam element. i Let be the cross-sectional area of ​​the i-th main tower unit.

[0025] Furthermore, the constraints include the range of maximum bending moment, maximum displacement, maximum axial force, and cable force for the main beam and main tower.

[0026] Furthermore, step 4 includes:

[0027] 4.1) Taking the number of cable-stayed bridge groups n as the dimension and the population size N, an n×N unknown matrix is ​​formed. The position matrix of the particles is defined as X. i =(x i1 ,x i2 ,x i3 ,……,x in The velocity matrix is ​​V. i =(v i1 ,v i2 ,v i3 ,……,v in ), where x in v represents the initial cable force of the nth group of stay cables corresponding to particle i. in This represents the nth dimension velocity value of particle i;

[0028] 4.2) Initialize the learning factor, maximum search speed, minimum search speed, inertia factor, and total number of iterations of the particle swarm; initialize the n×N position matrix X and velocity matrix V.

[0029] 4.3) Using the objective function described in step 3 as the fitness function in the particle swarm optimization algorithm, the optimal fitness function is calculated iteratively. When the algorithm converges, the optimal particle is output to obtain the optimal initial cable force of n groups of stay cables in the irregular cable-stayed bridge.

[0030] Furthermore, the inertia factor is a linearly decreasing inertia factor, as shown in the following formula:

[0031]

[0032] Where w is the inertia factor, w min and w max Let G be the minimum and maximum values ​​of the inertia factor, G be the total number of iterations, and k be the current iteration step.

[0033] Furthermore, during iterative calculations, the optimal value of an individual particle in the particle swarm at the k-th iteration is denoted as... The population optimum in particle swarm optimization is denoted as Then, in the (k+1)th iteration, the particle's position and velocity are updated using the following formula:

[0034]

[0035]

[0036] In the formula, r1 and r2 are random numbers between [0,1], and c1 and c2 are learning factors; This represents the cable force of the j-th group of stay cables corresponding to particle i at the k-th iteration; This represents the velocity of particle i in the j-th dimension during the k-th iteration; Let the j-th dimension be the optimal value of an individual in the particle swarm at the k-th iteration. Let represent the j-th dimension of the swarm optimum in the particle swarm at the k-th iteration.

[0037] Furthermore, the formula for calculating the final cable force of the bridge based on the initial cable force of each stay cable is as follows:

[0038] {S1, S2……S n}=X·C S +G S

[0039] Where n is the number of stay cables. C is the initial cable force of the stay cable. SG is the influence matrix of the applied vector cable force on the completed bridge cable force. S The cable force of the irregular cable-stayed bridge when only a constant load is applied.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] This invention combines the particle swarm optimization algorithm in intelligent optimization algorithms, takes the minimum strain energy of the bridge as the objective, obtains the constraints based on the actual engineering conditions, and establishes a bridge cable force optimization model for a novel cable-stayed bridge with irregular cable arrangement. It can quickly and accurately obtain the initial cable force of the novel cable-stayed bridge with irregular cable arrangement and calculate the final cable force. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the method for calculating the cable force of an irregularly shaped cable-stayed bridge proposed in this invention;

[0043] Figure 2 This is a general layout diagram of a novel cable-stayed bridge with irregular cable arrangement, as shown in an embodiment of the present invention.

[0044] Figure 3 This is a comparison diagram of the bending moments of the irregular cable-stayed bridge before and after optimization, as well as the completed bridge state in the design drawings, as shown in the embodiments of the present invention.

[0045] Figure 4 This is a comparison diagram of the cable forces of the irregular cable-stayed bridge before and after optimization, as well as the completed bridge cable forces in the design drawings, as shown in the embodiments of the present invention. Detailed Implementation

[0046] The present invention will become clearer from the following detailed description with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0047] like Figure 1 As shown, the method for calculating the cable force of an irregularly shaped cable-stayed bridge proposed in this invention includes the following steps:

[0048] Step (1): Obtain the material parameters, cross-sectional parameters, boundary conditions, and load conditions of the new type of cable-stayed bridge to be calculated based on the engineering drawings, and establish the finite element model of the new type of cable-stayed bridge.

[0049] In this embodiment, the irregular cable-stayed bridge refers to the irregular cable-stayed bridge with a new type of cable arrangement. Compared with the traditional cable-stayed bridge, the irregular cable-stayed bridge with a new type of cable arrangement has more complex structure due to the addition of cross-arranged cable stays between the multiple main towers.

[0050] Step (2): Obtain the influence matrix of the cable force on the main beam and the main tower;

[0051] Step (3): Establish the objective function based on the influence matrix, and determine the constraints based on the finite element calculation results and the actual engineering situation;

[0052] Constraints can be boundary values ​​for bending moment and displacement of the main girder of an irregularly shaped cable-stayed bridge, boundary values ​​for bending moment and displacement of the main tower, and the range of maximum and minimum cable forces representing cable force uniformity. When specific objectives are given in the engineering design, they are directly adopted; when specific constraints cannot be determined in actual engineering practice, they are estimated in conjunction with finite element analysis of the structure. 80% of the maximum bending moment before cable adjustment is taken as the constraint on the main girder bending moment, and 110-120% of the maximum axial compression under design conditions is taken as the constraint on the maximum axial compression.

[0053] Step (4): Establish a cable force optimization model for irregular cable-stayed bridges;

[0054] Step (5): Calculate the initial cable force of each cable in the irregular cable-stayed bridge using the cable force optimization model, and calculate the final cable force based on the initial cable force of each cable.

[0055] In one specific embodiment of the present invention, the influence matrix is ​​a matrix formed by arranging the changes in all elements of the controlled vector when all elements of the influence vector undergo a unit change. In the cable force optimization problem of a cable-stayed bridge, the influence matrix describes the changes in the structural internal forces, displacements, and cable forces of the bridge when a unit tension force is applied to the cable stays.

[0056] In a specific embodiment of the present invention, the objective function of step (2) is the strain energy of the cable-stayed bridge, expressed as:

[0057]

[0058] In the formula, M is the bending moment of the main beam; E is the elastic modulus of the main beam and the main tower; I is the bending moment of inertia of the main beam and the main tower; N is the axial force of the main beam and the main tower; A is the cross-sectional area of ​​the main beam and the main tower; and U is the strain energy of the cable-stayed bridge. The goal is to find the minimum strain energy of the cable-stayed bridge.

[0059] For the discrete finite element model of an irregular cable-stayed bridge, it can be written in matrix form:

[0060] U = {M L} T [B1]{M L}+{M R} T [B1]{M R}+{N L} T [B2]{N L}+{N R} T [B2]{N R}

[0061] In the formula, [B1] and [B2] are the stiffness coefficient matrices of the main beam and the main tower, respectively.

[0062]

[0063]

[0064] In the formula [M L}、{M R} are the matrices of the bending moments on the left and right sides of the beam element, respectively. L}、{N R The matrix representing the axial forces acting on the left and right sides of each element of the main tower is as follows:

[0065] {M L}=[C ; ]{S}+{M L0}

[0066] {M R}=[C R ]{S}+{M R0}

[0067] {N L}=[C Ln ]{S}+{N L0}

[0068] {N R}=[C Rn ]{S}+{M R0}

[0069] In the formula, C L C R M represents the influence matrix of the adjustment vector, i.e., the cable force S of the stay cable, on the bending moment on the left and right sides of the main beam element, respectively. L0 M R0 This represents the bending moment matrix on the left and right sides of each element of the main beam before the application of the adjustment vector cable force S. Ln C Rn N represents the influence matrix of the applied cable force S on the axial forces on the left and right sides of the main tower unit, respectively. L0 N R0 This represents the matrix of axial forces acting on the left and right sides of the main tower element before the application of the control vector cable force S.

[0070] In a specific embodiment of the present invention, the cable force optimization model in step (4) is established based on the particle swarm optimization algorithm, and the specific method is as follows:

[0071] (4.1) Taking the number of cable-stayed bridge groups n as the dimension and the population size N, an n×N unknown matrix is ​​formed. The position matrix of the particles is defined as X. i =(x i1 ,x i2 ,x i3 ,……,x in The velocity matrix is ​​V. i =(v i1 ,v i2 ,v i3 ,……,v in ), where x in v represents the initial cable force of the nth group of stay cables corresponding to particle i. in This represents the velocity value of particle i in the nth dimension.

[0072] (4.2) Initialize the learning factor, maximum optimization speed, minimum optimization speed, inertia factor, total number of iterations and other parameters of the particle swarm, and initialize the n×N position matrix X and velocity matrix V.

[0073] In this embodiment, the learning factor, inertia factor, and total number of iterations are selected based on actual engineering conditions. The learning factor is typically selected between 1 and 2, and the inertia factor adopts a linearly decreasing inertia factor, expressed as:

[0074]

[0075] Where w is the inertia factor, w min and w max The minimum and maximum values ​​of the inertia factor are usually taken as w. min =0.4, w max =0.9; G is the total number of iterations, usually above 10000; k is the current iteration step, i.e. the number of iterations already completed; the total number of iterations G is usually above 10000.

[0076] Maximum and minimum optimization speeds V max V min Selected based on actual engineering conditions, maximum initial cable force X max and minimum initial tension X min According to formula V max =aX max V min =aX min Choose a constant where a is between 0.1 and 0.2.

[0077] The initial velocity matrix is ​​randomly generated, and the value of each initial tension force for each particle ranges from 0 to V. max Between; the value of each set of tension forces for each particle in the initial position matrix is ​​randomly generated within a limited range of initial values.

[0078] (4.3) Use the objective function described in step (3) as the fitness function in the particle swarm algorithm to determine the constraints such as the maximum bending moment, maximum displacement, maximum axial force, and cable force range of the main beam and main tower.

[0079] In a specific embodiment of the present invention, during the cable force optimization calculation in step (5), the optimal value is calculated iteratively based on the particle swarm optimization algorithm. During the iteration process, the optimal value of each individual in the particle swarm at the k-th iteration is denoted as... The population optimum in particle swarm optimization is denoted as Then, in the (k+1)th iteration, the particle's position and velocity are updated using the following formula:

[0080]

[0081]

[0082] In the formula, =1,2,3……m represents the i-th particle; j=1,2,3……N represents the dimension of the particle; k is the iteration step; r1, r2 are random numbers between [0,1], and c1, c2 are learning factors; This represents the cable force of the j-th group of stay cables corresponding to particle i at the k-th iteration; This represents the velocity of particle i in the j-th dimension during the k-th iteration; Let the j-th dimension be the optimal value of an individual in the particle swarm at the k-th iteration. Let represent the j-th dimension of the swarm optimum in the particle swarm at the k-th iteration.

[0083] Once the algorithm converges, it outputs the optimal particle, which represents the optimal initial cable force for the n sets of stay cables in the irregular cable-stayed bridge. After obtaining the optimal initial cable force, the final cable force of the completed bridge can be obtained using the following formula or by directly substituting it into the finite element model:

[0084] Based on the principle of influence matrix, define Given the initial cable force of the stay cable, the corresponding completed cable forces are {S1, S2, ..., S...} 21}=X·C S +G S Where n is the number of stay cables, C S G is the influence matrix of the applied vector cable force on the completed bridge cable force. S The cable force of the irregular cable-stayed bridge when only a constant load is applied.

[0085] The following specific embodiments illustrate the implementation effects of the method of the present invention.

[0086] like Figure 2The diagram shows the overall layout of a novel cable-stayed bridge with an irregular cable arrangement. This bridge uses V-shaped double-arch main towers. In addition to the cable stays connecting the main girder and the main towers, additional cable stays are added between the two inclined arches, employing a novel cross-arrangement cable arrangement. The bridge span is (45+55+25)m, the road width is 20m, the standard cross-section width of the steel box girder is 22.5m, the center beam height is 1.8m, and there are a total of 20 segments. Each side of the bridge has 14 pairs of cable stays, and the main towers are connected by 7 sets of cables, totaling 21 pairs and 42 cable stays. The cable spacing along the side spans is 4 meters, and the cable spacing along the main span is 5 meters.

[0087] according to Figure 1 The process shown is used to determine a reasonable bridge completion status. The specific steps are as follows:

[0088] (1) Obtain parameters such as cross section, material, and load from the engineering drawings and use finite element software for modeling; only consider dead load, including the self-weight of the bridge body, the main beam diaphragm and the second-stage dead load of the bridge deck, and take 68.2KN / m for the second-stage dead load of the bridge deck.

[0089] (2) Considering that the main beam is mainly subjected to bending and the main tower is a double circular arch, the main tower is also subjected to compression while being subjected to bending. Neglecting shear deformation, the objective function of the discrete element is established based on the total strain energy of the bending strain of the main beam and the tensile and compressive strain of the main tower:

[0090]

[0091] Among them, M Li M Ri N represents the bending moments at the left and right ends of the i-th main beam element, respectively. Li N Ri L represents the axial forces acting on the left and right ends of the i-th main tower unit, respectively. i E represents the length of the i-th main beam element or the i-th main tower element. i Let I be the elastic modulus of the i-th main beam element or the i-th main tower element. i Let A be the bending moment of inertia of the i-th main beam element. i Let be the cross-sectional area of ​​the i-th main tower unit.

[0092] Introducing the influence matrix, the objective function of the finite element model of the irregular cable-stayed bridge can be written in matrix form:

[0093] U = {M L} T [B1]{M L}{M R} T [B1]{M R}{N L} T [B2]{N L}+{NR} T [B2]{N R}

[0094] In the formula, [B1] and [B2] are the coefficient matrices of the main beam and the main tower, respectively, and are expressed as follows:

[0095]

[0096]

[0097] In the formula And {M L}、{M R} are the matrices of the bending moments on the left and right sides of the beam element, respectively, [N L}、[N R} represents the matrix of axial forces acting on the left and right sides of each unit of the main tower; they are...

[0098] {M L}=[C L ]{S}+{M L0}

[0099] {M R}=[C R ]{S}+{M R0}

[0100] {N L}=[C Ln ]{S}+{N L0}

[0101] {N R}=[C Rn ]{S}+{M R0}

[0102] In the formula C L C R M represents the influence matrix of the adjustment vector, i.e., the cable force S of the stay cable, on the bending moment on the left and right sides of the main beam element, respectively. L0 M R0 C represents the left and right moment matrices of each element of the main beam before the application of the adjustment vector cable force S. Ln C Rn N represents the influence matrix of the applied cable force S on the axial forces on the left and right sides of the main tower unit, respectively. L0 N R0 These represent the matrices of the axial forces acting on the left and right sides of the main tower element before the application of the adjustment vector cable force S.

[0103] (3) Export the influence matrix of the stay cable on the bending moment of the main beam, the influence matrix of the stay cable on the axial pressure of the main tower, the bending moment of each element of the main beam when only a dead load is applied, the axial pressure of each element of the main tower when only a dead load is applied, the stiffness of the main beam and the stiffness of the main tower from the finite element software.

[0104] (4) Determining Constraints: Based on the actual conditions of the bridge, the maximum negative bending moment of the main girder without cable adjustment is -36000 KN·m, and the maximum positive bending moment is 26000 KN·m. In the designed bridge state given in the drawings, the maximum negative bending moment of the main girder is -25800 KN·m, the maximum positive bending moment is 15800 KN·m, and the maximum axial pressure on the main tower is 2310 KN. Taking 80% of the maximum bending moment without cable adjustment as the constraint condition for the bending moment of the main girder, and 110-120% of the maximum axial pressure in the design state as the constraint condition for the maximum axial pressure, that is, the maximum negative bending moment of the main girder does not exceed -30000 KN·m, the maximum positive bending moment does not exceed 20000 KN·m, and the maximum axial pressure on the main tower does not exceed 2600 KN.

[0105] To ensure the uniformity of the initial cable force in the search results, the maximum and minimum cable forces are specified to differ by no more than 250 kN, i.e., R = 2.5(X). max -X min <2.5).

[0106] (5) Establishing a cable force optimization model for an irregular cable-stayed bridge based on particle swarm optimization: taking the initial cable forces of 21 sets of cables as unknowns, and defining the position matrix of the particles as X. i =(x i1 ,x i2 ,x i3 ,……,x in The velocity matrix is ​​V. i =(v i1 ,v i2 ,v i3 ,……,v in ), where x in v represents the initial cable force of the nth group of stay cables corresponding to particle i. in Let i represent the nth dimension velocity value of particle i, where i = 1, 2, 3... 21.

[0107] The particle swarm parameters are determined: population size N is 21, learning factors c1 = c2 = 2, and maximum velocity V. max =2m / s, the maximum initial cable force is specified as 600KN, and the minimum initial cable force is specified as 100KN. The value of the inertia factor w is... Take w min =0.4, w max =0.9, G is the total number of iterations, taken as 10000.

[0108] The initial cable force matrix X, the initial value of each cable is randomly generated between 100KN and 200KN, i.e., 1 < i <2, i = 1, 2, 3……21.

[0109] The initial velocity matrix V, with each particle's initial value being 0V. max Randomly generated.

[0110] (6) Calculate the initial cable force of each cable in the irregular cable-stayed bridge by using the cable force optimization model, substitute the initial cable force of each cable into the finite model, calculate the cable force of the completed bridge, and obtain the reasonable completed bridge state.

[0111] The calculated bending moment of the main girder in the completed bridge state is compared with that in the unadjusted state and the designed completed bridge state on the drawings, such as... Figure 3 Among all bridge configurations, the particle swarm optimization algorithm yielded the most uniform main girder bending moment. The calculated main girder bending moments in the completed bridge configurations were then compared with the cable forces in the unadjusted configuration and the design cable forces in the drawings. Figure 4 The calculated overall cable force of the completed bridge is the largest, making greater use of the stay cables within permissible limits, and the cable force of each group of cables is relatively uniform. A comparison of the completed bridge bending moment and cable force shows that the method of this invention can optimize the cable force of irregularly shaped cable-stayed bridges, thus optimizing the completed bridge condition. Compared with the design values ​​given in the design drawings, it meets engineering requirements and may even be superior. Furthermore, the calculation from the start of the cable force optimization model to obtaining the result takes less than 30 seconds, making it very fast and convenient.

[0112] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the cable force of an irregularly shaped cable-stayed bridge upon completion, characterized in that, Includes the following steps: Step 1: Establish a finite element model of the irregular cable-stayed bridge based on the engineering drawings; Step 2: Obtain the influence matrix of cable forces on the main beam and main tower; Step 3: With the goal of minimizing the overall strain energy of the irregular cable-stayed bridge, establish the objective function based on the influence matrix and determine the constraints. Step 4: Establish a cable force optimization model for the irregular cable-stayed bridge, including: 4.1) Taking the number of cable-stayed bridge groups n as the dimension, and taking the population size N, we form n The unknown matrix of N, and the position matrix of the particle are defined as follows. The velocity matrix is ,in, This represents the initial cable force of the nth group of stay cables corresponding to particle i. This represents the nth dimension velocity value of particle i; 4.2) Initialize the particle swarm optimization's learning factor, maximum search speed, minimum search speed, inertia factor, and total number of iterations, and initialize n. The position matrix X and velocity matrix V of N; the inertia factor is a linearly decreasing inertia factor, as shown in the following formula: ； in, Inertia factor Let G be the minimum and maximum values ​​of the inertia factor, G be the total number of iterations, and k be the current iteration step. 4.3) Using the objective function described in step 3 as the fitness function in the particle swarm optimization algorithm, the optimal fitness function is calculated iteratively; during the iterative calculation, the optimal value of an individual in the particle swarm at the k-th iteration is denoted as... The population optimum in the particle swarm is denoted as Then, in the (k+1)th iteration, the position and velocity of the particle are updated using the following formula: ； ； In the formula, A random number between [0,1] For learning factors; This represents the cable force of the j-th group of stay cables corresponding to particle i at the k-th iteration; This represents the velocity of particle i in the j-th dimension during the k-th iteration; Let the j-th dimension be the optimal value of an individual in the particle swarm at the k-th iteration. Let j represent the j-th dimension of the swarm optimization value in the particle swarm at the k-th iteration. Once the algorithm converges, the optimal particle is output, yielding the optimal initial cable force for n sets of stay cables in the irregular cable-stayed bridge. Step 5: Calculate the initial cable force of each cable in the irregular cable-stayed bridge using the cable force optimization model, and calculate the final cable force of the bridge based on the initial cable force of each cable.

2. The method for calculating the cable force of an irregularly shaped cable-stayed bridge according to claim 1, characterized in that, The influence matrix includes: the influence matrix of the stay cables on the bending moment of the main beam, the influence matrix of the stay cables on the axial pressure of the main tower, the bending moment of each element of the main beam when only a dead load is applied, the axial pressure of each element of the main tower when only a dead load is applied, the stiffness of the main beam, and the stiffness of the main tower.

3. The method for calculating the cable force of an irregularly shaped cable-stayed bridge according to claim 1 or 2, characterized in that, The formula for the objective function is as follows: ； In the formula, M is the bending moment of the main beam; E is the elastic modulus of the main beam and the main tower; I is the bending moment of inertia of the main beam and the main tower; N is the axial force of the main tower; A is the cross-sectional area of ​​the main tower; and U is the strain energy of the cable-stayed bridge. The goal is to find the minimum strain energy of the cable-stayed bridge. For the discrete finite element model of an irregular cable-stayed bridge, it can be written in matrix form: ； ； ； ； ； ； ； In the formula, , These are the stiffness coefficient matrices for the main beam and the main tower, respectively. These are the matrices representing the bending moments acting on the left and right sides of the beam element, respectively. The matrix representing the axial forces acting on the left and right sides of each unit of the main tower; T represents the transpose matrix; These represent the influence matrices of the applied cable force S on the bending moments on the left and right sides of the main beam element, respectively. This represents the bending moment matrix of each element of the main beam before the application of the adjustment vector cable force S; These represent the influence matrices of the applied cable force S on the axial forces on the left and right sides of the main tower element, respectively. This represents the matrix of axial forces acting on the left and right sides of the main tower element before the application of the adjustment vector cable force S; This represents the stiffness coefficient of the i-th main beam element. represents the stiffness coefficient of the i-th main tower element, and n represents the number of main beam elements or main tower elements. Let be the length of the i-th main beam element or the i-th main tower element. Let be the elastic modulus of the i-th main beam element or the i-th main tower element. Let be the bending moment of inertia of the i-th main beam element. Let be the cross-sectional area of ​​the i-th main tower unit.

4. The method for calculating the cable force of an irregularly shaped cable-stayed bridge according to claim 1, characterized in that, The constraints include the maximum bending moment, maximum displacement, maximum axial force, and cable force range of the main beam and main tower.

5. The method for calculating the cable force of an irregularly shaped cable-stayed bridge according to claim 1, characterized in that, The formula for calculating the total cable force of the bridge based on the initial cable force of each cable is as follows: ； Where n is the number of stay cables. The initial cable force of the stay cable. This is the influence matrix of the applied vector cable force on the completed bridge cable force. The cable force of the irregular cable-stayed bridge when only a constant load is applied.

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