A bridge suspender damage identification method based on bayesian optimization and additional mass

Abstract

The application discloses a bridge suspender damage identification method based on Bayesian optimization and an additional mass method, and the method comprises the following steps: first, an additional mass is added to different parts of a bridge suspender to obtain the measured frequency of the bridge suspender under the additional mass. A stiffness-frequency-cable force equation is established based on the structural mechanics theory to obtain the theoretical frequency value of the bridge suspender under the action of the additional mass at different parts. The error between the theoretical solution and the measured value is taken as an objective function, the influence of different boundary conditions and environmental errors is considered, and the damage conditions of the suspender stiffness and the cable force are calculated based on the Bayesian optimization method. The application can quickly and accurately identify the damage conditions of the suspender and can be used for safety state evaluation of the suspender of a long-span bridge.

Description

Technical Field

[0001] This invention relates to the field of safety assessment of bridge suspenders, and more specifically, to a method for identifying bridge suspender damage based on Bayesian optimization and added mass. Background Technology

[0002] Bridge suspenders are a crucial component of long-span suspension bridges, cable-stayed bridges, and arch bridges. In terms of load transmission, the load on the bridge deck is transferred to the towers and then to the foundation via the suspenders. Therefore, changes in the physical parameters of the bridge suspenders will alter the overall stress state of the bridge. The lightweight, high flexibility, and low damping characteristics of bridge suspenders make them susceptible to damage. Specifically, under cyclic and random loads such as wind, vehicles, pedestrians, and other types of loads, bridge suspenders inevitably suffer cumulative damage over time, including material degradation, corrosion, overload, and fatigue. Currently, damage identification of bridge suspenders primarily relies on manual inspection methods, such as manual handheld flaw detectors. This method consumes significant manpower and resources, and when damage is at the top of the suspender, the flaw detector struggles to accurately identify the damage condition. Therefore, how to conveniently, quickly, and accurately identify the damage status of bridge suspenders during construction and operation is an urgent problem to be solved. Summary of the Invention

[0003] In view of the shortcomings of existing methods for identifying bridge hanger damage, the purpose of this invention is to establish a convenient, fast, and accurate method for identifying bridge hanger damage.

[0004] To achieve the above objectives, the present invention provides a bridge hanger damage identification method based on Bayesian optimization and added mass, comprising the following steps: Divide the bridge hanger into n parts, meaning there are n+1 nodes on the bridge hanger; Different masses are added to m nodes (m≤n+1) of the bridge hanger, and the measured frequency values ​​of the bridge hanger under the added masses are obtained; Based on structural mechanics theory, a stiffness-frequency-cable force equation was established to obtain the theoretical frequency value of the bridge hanger without damage under different nodes and different added masses. The measured frequency values ​​of the bridge suspenders under added mass were obtained using accelerometers. The error between the theoretical frequency value and the measured frequency value is used as the objective function. This objective function is a function of the stiffness of the boom and the damage of the cable force. The objective function is minimized based on the Bayesian optimization method to obtain the damage of the boom stiffness and the cable force.

[0005] In the above technical solution, further, the bridge suspenders are equally divided into n units according to their lengths. Generally, n should not be too small, as it is not conducive to globally identifying the damage of the bridge suspenders. It can be set to a number greater than 5. Different masses are added at m nodes of the bridge suspenders (m < n + 1), and the measured frequency values of the bridge suspenders under the added masses are obtained through accelerometers.

[0006] Based on the theory of structural mechanics, establish the free vibration equation of the suspender:

[0007] where U is the vibration displacement, is the vibration acceleration;

[0008]

[0009]

[0010]

[0011] where M is the global mass matrix, that is, M = {M1, M2,..., M m}; K is the global stiffness matrix, that is, K = {K1, K2,..., K n}; K G is the geometric stiffness matrix generated by unit tension; is the mass matrix of the m-th node, , are the stiffness matrix and geometric stiffness matrix of the n-th unit respectively; the global matrix can be assembled from the unit matrices, θ n is the stiffness damage of the n-th bridge suspender, and its value is between 0 and 1; is the density of the suspender material, A is the cross-sectional area of the suspender, l is the unit length after the suspender is divided, E is the elastic modulus of the suspender, and I is the moment of inertia of the suspender material.

[0012] Establish the stiffness-frequency-cable force equation to obtain the theoretical frequency values of the bridge suspenders under the action of different additional masses:

[0013]

[0014] where, is the determinant; the cable tension T; f m is the measured frequency value of the m-th additional mass method, with a total of m additional mass methods; α is the cable force damage of the bridge suspender, and its value is between 0 and 1; M*1 – M* m are the global mass matrices corresponding to different additional mass methods. For example, the first additional mass method is to add a mass of m1 at the 1st node. Then: Where m1 is the mass attached to node 1.

[0015] In the method of adding mass, additional mass can be added at different locations on the suspender structure; that is, mass can be placed at one location, or mass can be placed at two or more locations.

[0016] After adding mass to different parts of the bridge suspender, the measured frequency value of the bridge suspender under the added mass is obtained by using an accelerometer.

[0017] Measured values ​​include theoretical calculation values Sum of error terms :

[0018]

[0019] The error between the measured value and the theoretical value is used as the objective function:

[0020]

[0021] Solve according to the principle of minimizing error:

[0022]

[0023] Where ξ is the damage parameter value, which includes stiffness damage and cable force damage, i.e., ξ={θ1, θ2, …,θ n , α}; These are sample values ​​containing unknown parameters.

[0024] Considering the uncertainty of parameters, the objective function is updated by sampling based on the Bayesian optimization method:

[0025] First, t-1 samples are randomly extracted from the objective function.

[0026] The optimal damage parameter value is obtained by selecting the probability enhancement function in the Bayesian optimization algorithm.

[0027]

[0028] Updated sample:

[0029]

[0030] Repeat steps (2)-(3) until the number of iterations stops or the damage parameter value is no longer updated. The beneficial effects of this invention are: This invention obtains the measured frequency of bridge suspenders under added mass using an added mass method, and derives the theoretical frequency values ​​of bridge suspenders under added mass at different locations based on structural mechanics theory. Using the error between the theoretical solution and the measured values ​​as the objective function, a Bayesian optimization method is used to determine the damage status of suspender stiffness and cable forces. This method can quickly and accurately identify suspender damage and can be used for safety status assessment of suspenders in long-span bridges. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the added mass method test process.

[0032] Figure 2 This is a damage assessment process based on Bayesian optimization.

[0033] Figure 3 Iterative Process for Unknown Parameters - Case Study 2

[0034] Figure 4 Case Study 2: Iterative Process of Objective Function under Different Boundary Conditions Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and examples.

[0036] Divide the bridge suspenders into i equal parts.

[0037] Based on structural mechanics theory, the equation for the free vibration of the suspension rod is established:

[0038]

[0039]

[0040]

[0041]

[0042] Where M is the global mass matrix; K is the global stiffness matrix; K G It is the geometric stiffness matrix generated by unit tension; Let m be the mass matrix of the m-th node. , These are the stiffness matrix and geometric stiffness matrix of the nth element, respectively; the element matrices can be assembled into a global matrix, θ. n The value of the nth bridge hanger stiffness damage is between 0 and 1. A is the density of the boom material, l is the cross-sectional area of ​​the boom, E is the unit length of the boom after division, and I is the elastic modulus of the boom and the moment of inertia of the boom material.

[0043] By establishing the stiffness-frequency-cable force equation, the theoretical frequency values ​​of the bridge suspenders under the action of additional mass at different locations are obtained:

[0044]

[0045] in, For determinant; boom tension T; f m M*1 represents the measured frequency of the m-th type of added mass method, and there are a total of m types of added mass methods; α represents the cable stress damage of the bridge hanger, with a value between 0 and 1; M*1 – M* m This represents the global mass matrix corresponding to different mass addition methods. For example, the first mass addition method adds mass m1 to node 1. Then: Where m1 is the mass attached to node 1.

[0046] In the method of adding mass, additional mass can be added at different locations on the suspender structure; that is, mass can be placed at one location, or mass can be placed at two or more locations.

[0047] After adding mass to different parts of the bridge suspender, the measured frequency values ​​of the bridge suspender under the added mass are obtained.

[0048] The measured values ​​include theoretical calculations and error terms:

[0049]

[0050] The error between the measured value and the theoretical value is used as the objective function:

[0051]

[0052] Solve according to the principle of minimizing error:

[0053]

[0054] Where ξ is the damage parameter value, which includes stiffness damage and cable force damage, i.e., ξ={θ1, θ2, …,θ n , α}; These are sample values ​​containing unknown parameters.

[0055] Considering the uncertainty of parameters, the objective function is updated by sampling based on the Bayesian optimization method:

[0056] First, t-1 samples are randomly extracted from the objective function.

[0057] The optimal damage parameter value is obtained by selecting the probability enhancement function in the Bayesian optimization algorithm.

[0058]

[0059] Updated sample:

[0060]

[0061] Repeat steps (2)-(3) until the number of iterations stops or the damage parameter value is no longer updated.

[0062] Case 1: Assume the bridge hanger is divided into 10, 20, 30, and 50 equal parts; the additional mass at node 2 is 20 kg; the additional mass at node 3 is 40 kg; the hanger stiffness damage parameter is... The length of the boom is 4m, the cross-sectional diameter is 0.077m, and the elastic modulus is 1.9×10⁻⁶. 8 kPa, material density is 7850 kN / m³ 3 The initial tension inside the boom is 1700kN.

[0063] Table 1 shows the influence of the number of bridge hanger unit divisions on stiffness and damage parameters.

[0064]

[0065] Case 2: The bridge suspender is divided into 10 equal parts; the boundary conditions of the suspender are fixed at both ends, hinged at both ends, and fixed at one end with one section hinged; the stiffness and cable force damage parameters of the suspender are as follows: Other parameters are as in Case 1.

[0066] Table 2 shows the influence of different bridge hanger boundary conditions on stiffness damage and cable force damage parameters.

[0067]

[0068] Figure 3 Iterative process for unknown parameters

[0069] Figure 4 Iterative process of objective function under different boundary conditions

[0070] Case 3: The bridge suspender is divided into 10 equal parts; the boundary condition of the suspender is that both ends are fixed; the stiffness and cable force damage parameters of the suspender are as follows: Other parameters are as in Case 1. The performance of Bayesian Optimization (BO), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Natural Least Squares (NLS) in damage identification is compared and discussed, considering the presence of 1% and 2% monitoring errors.

[0071]

[0072] in, These are measured values ​​(excluding noise). is the measured value (including noise); R is a random variable that follows a normal distribution; std is the noise level.

[0073] Table 3 compares the damage identification results of each method when the ambient noise level is 1%.

[0074]

[0075] Table 4 compares the computational efficiency of each method when the environmental noise level is 1%.

[0076]

[0077] Table 5 compares the damage identification results of each method when the ambient noise level is 2%.

[0078]

[0079] Table 6 compares the computational efficiency of each method when the environmental noise level is 2%.

[0080]

[0081] From Tables 3 to 6, it can be concluded that the rod damage identification method based on the Bayesian optimization algorithm has the characteristics of high accuracy and fast computational efficiency.

[0082] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying bridge hanger damage based on Bayesian optimization and added mass, characterized in that, Includes the following steps: Divide the bridge hanger into n parts, that is, there are n+1 nodes on the bridge hanger; Different masses are added to m nodes of the bridge suspender, and the measured frequency values ​​of the bridge suspender under the added masses are obtained, wherein m≤n+1; Based on structural mechanics theory, a stiffness-frequency-cable force equation was established to obtain the theoretical frequency value of the bridge hanger without damage under different nodes and different added masses. The measured frequency values ​​of the bridge suspenders under added mass were obtained using accelerometers. The error between the theoretical and measured frequency values ​​is used as the objective function, which is a function of the gantry stiffness and cable stress damage. The objective function is minimized using the Bayesian optimization method to obtain the gantry stiffness and cable stress damage. Among them, a stiffness-frequency-cable force equation was established based on structural mechanics theory to obtain the frequency values ​​of bridge hangers under the action of additional mass at different locations: Where M is the global quality matrix, i.e., M = {M1, M2, ..., M} m K is the global stiffness matrix, which consists of n element stiffness matrices, i.e., K = [K1, K2, ... K]. n ];K G It is the geometric stiffness matrix generated by unit tension; For determinant; T is the tension in the boom cable; f m Let θ be the measured frequency value of the m-th mass addition method, and there are a total of m mass addition methods; n Let α represent the stiffness damage of the nth bridge hanger, with a value between 0 and 1; let α represent the cable force damage of the bridge hanger, with a value between 0 and 1; let E represent the elastic modulus of the hanger material; let I represent the moment of inertia of the hanger material; and let l represent the length of the bridge hanger element, with a value of L / n, where L is the total length of the bridge hanger. It can be seen that there are n+1 unknown parameters, while the system of equations is less than n+1, which falls within the scope of hyperparameter solving. Based on the principle of minimizing error, an objective function is established regarding the damage condition ξ: Where ξ is the damage parameter value, which includes stiffness damage and cable force damage, i.e., ξ={θ1, θ2, …,θ n , α}; It is the theoretical frequency value of the i-th additional mass method containing unknown parameters. Let be the measured frequency value of the i-th mass addition method, and there are a total of m mass addition methods.

2. The bridge hanger damage identification method based on Bayesian optimization and added mass according to claim 1, characterized in that, The bridge suspender is divided into n equal units according to its length. Different masses are added at m nodes of the bridge suspender. The measured frequency values ​​of the bridge suspender under the added masses are obtained by using an accelerometer.

3. The bridge hanger damage identification method based on Bayesian optimization and added mass according to claim 1, characterized in that, Solving for hyperparameters of the objective function using Bayesian optimization methods: (1) First, t-1 samples are randomly extracted from the objective function. (2) Select the probability enhancement function in the Bayesian optimization algorithm to obtain the current optimal damage parameter value: (3) Update the sample: Repeat steps (2)-(3) until the number of iterations stops or the damage parameter value is no longer updated.

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