A seismic performance optimization and evaluation system for long-span bridges based on digital twins

Abstract

This invention relates to a seismic performance optimization and evaluation system for long-span bridges based on digital twins, belonging to the fields of computer science and bridge engineering. The optimization and evaluation system includes a data acquisition and preprocessing module, a model update module, and a performance evaluation and optimization module. The optimization and evaluation method includes identifying the structural modes and frequencies to obtain the bridge's mode shapes and natural frequencies, and establishing a digital twin model of the target bridge. Based on a multi-objective optimization design function, supercomputing-driven optimization of vibration reduction device parameters is performed, outputting the optimal parameter combination to control the bridge's graded response under earthquakes. The artificial wave generated based on the bridge's design response spectrum can fully consider the dynamic characteristics of long-span cable-stayed bridges and the seismic motion characteristics of the design site. Simultaneously, the seismic optimization design process only involves the time history analysis of a single ground motion, significantly reducing the computational load of the optimization design and better considering the comprehensive influence of various nonlinear factors on the bridge's seismic response, thus significantly simplifying the complexity of seismic optimization for long-span bridges.

Description

Technical Field

[0001] This invention relates to a system for optimizing and evaluating the seismic performance of long-span bridges based on digital twins, belonging to the fields of computer science and bridge engineering. Background Technology

[0002] Long-span cable-stayed bridges, as crucial basic transportation infrastructure, are often designed for a service life exceeding 100 years. During their lifespan, environmental impacts and long-term loads lead to a degradation of their seismic performance. Among these components, damping devices (such as viscous dampers and tuned mass dampers) and bearings are key components affecting the dynamic characteristics of the bridge structure, significantly influencing its seismic response. During the bridge's service life, they require regular inspection, maintenance, and replacement. However, once bridge performance degrades, calculation models based on design data cannot accurately reflect its actual service condition. Applying these models to bridge maintenance and design can result in replacement components that fail to meet the actual seismic requirements of the bridge.

[0003] With the development of structural health monitoring technology, important infrastructure such as long-span cable-stayed bridges are typically equipped with advanced monitoring systems to collect measured data during service to assess their immediate performance. Mapping this measured data to a structural model for performance evaluation often relies on model update techniques. However, due to the large number of components and complex node connections in long-span cable-stayed bridges, existing model update algorithms suffer from problems such as long computation time and low accuracy. Summary of the Invention

[0004] This invention addresses the aforementioned problems by providing a digital twin-based seismic performance optimization and evaluation system for long-span bridges. This system simplifies the selection process for seismic motion by establishing a digital twin model of the target bridge, optimizes the vibration reduction devices of long-span bridges under multi-objective control, effectively controls the damage state of different components under earthquakes, and improves the seismic performance of in-service bridges.

[0005] The present invention adopts the following technical solution: a seismic performance optimization and evaluation system for long-span bridges based on digital twins, the optimization and evaluation system including a data acquisition and preprocessing module, a model update module, and a performance evaluation and optimization module;

[0006] The data acquisition and preprocessing module is used to analyze and store the response data of the structure;

[0007] The model update module is used to define the information of each supercomputing node and then build a private computing cluster.

[0008] The performance optimization assessment and optimization module defines the damage grading threshold and target damage level of the target bridge based on the digital twin model.

[0009] The optimization and evaluation methods using this module follow these steps:

[0010] Step 1: The data acquisition and preprocessing module collects frequency response data of the long-span bridge under environmental and vehicle load excitation. After noise reduction of the frequency response data using Kalman filtering, Fast Fourier Transform is used to identify the modes and frequencies of the structure, obtain the mode shapes and natural frequencies of the bridge, and store them in the cloud.

[0011] Step 2: The model update module establishes a three-dimensional refined numerical model based on the design data of the object bridge and extracts the bridge mode shape and natural frequency data from the cloud.

[0012] Define the upper and lower limits and parameter types of the physical parameters that need to be updated in the bridge. Based on the frequency modal response in step 1, establish the least squares error function to carry out the nonlinear model update of the object bridge and establish a digital twin model of the object bridge.

[0013] Step 3: Performance Optimization and Evaluation, and Performance Evaluation and Optimization of the Bridge Module Object;

[0014] Based on the digital twin model established in step 2, define the engineering requirement parameters and calibrate the graded damage performance thresholds for pier components, bearing components, and main tower components.

[0015] The target damage level of the bridge is determined based on its service life.

[0016] Establish a multi-objective optimization design function based on the engineering requirements parameters of the bridge piers, main towers, and supports;

[0017] Artificial ground motion was generated based on the design response spectrum of the bridge. Nonlinear time history analysis of the digital twin model was then performed to obtain the pier drift rate, the relative displacement of the superstructure and substructure, and the cross-sectional curvature of the main tower.

[0018] Based on the multi-objective optimization design function, supercomputing-driven optimization of vibration reduction device parameters is carried out, and the optimal parameter combination is output to control the graded response of the bridge under earthquake.

[0019] The seismic performance optimization and evaluation system for long-span bridges based on digital twins described in this invention includes the following steps in step 1: collecting structural response data through a structural health monitoring system, and preprocessing the data to obtain the modal response of the structure.

[0020] S11. The Kalman filter method is used to perform noise reduction processing on the modal response data of the extracted structure of the data acquisition system, so as to reduce the noise and interference of the data while maintaining the original data characteristics.

[0021] S12. The Fourier spectrum of the structural vibration is segmented using empirical wavelet transform to identify the modal peak positions and obtain the intrinsic modal function components, thus obtaining the single-degree-of-freedom vibration response signal of the structure. The operation of the empirical wavelet transform function is as follows:

[0022] Step 121: Divide the Fourier spectrum into N continuous intervals Λ n

[0023] Λ n =[ω n-1 ,ω n ], n=1,2,…,N

[0024] Step 122: Construct the empirical scaling function φ n (ω)

[0025]

[0026] Step 123: Construct the empirical wavelet function ψ n (ω) is as follows:

[0027]

[0028] Where β(x)=x 4 (35-84x+70x 2 -20x 3 )

[0029] Step 124: The bridge vibration signal x(t) collected by the health monitoring system is decomposed into: frequency modulation component

[0030] Amplitude Modulation Components

[0031] In the formula, and These are the detail coefficients and approximation coefficients, respectively, and * represents convolution;

[0032] S13. Further analysis of the measured bridge vibration signal using random reduction techniques is conducted. After separating the deterministic vibration signal and the stationary random signal, the structural free decay vibration response signal is obtained. The specific steps are as follows:

[0033] Step 131: Select a fixed value A from the single-degree-of-freedom vibration response signal y(t) of the linear system to truncate the amplitude of y(t);

[0034] Step 132: Let t be the intersection point between A and the response signal y(t). i (i = 1, 2, ..., N), obtain N segments starting from t i A time series starting from [starting point] and of length s;

[0035] Step 133: By stacking and averaging the N time series segments, the free decay response signal of y(t) can be obtained:

[0036]

[0037] S14. The Hilbert transform is used to process the free decaying signal x(t) to obtain the amplitude curve and phase curve, thereby identifying the modal frequency and damping ratio. The steps are as follows:

[0038] Step 141: Let x j (t) represents a free decay response signal obtained by the RDT method in S13:

[0039]

[0040] In the formula, A 0j Let φ be the amplitude of the signal at time 0. j Let ξ be the j-th order undamped circular frequency. j For the j-th order damping ratio, Let be the j-th order damped primary frequency, and t be time;

[0041] Step 142: Perform a Hilbert transform on the formula in Step 1 to obtain the phase function:

[0042]

[0043] Amplitude function:

[0044]

[0045] Step 143: For the phase function θ j Differentiating (t) yields the j-th order original frequency ω. dj Considering that the damping ratio in practical engineering is usually less than 5%, the simplified formula yields the j-th order modal frequency:

[0046]

[0047] Step 144: Construct an exponential decay curve for the amplitude function A j (t) is fitted to obtain the value of b, and then the j-th order damping ratio is obtained:

[0048]

[0049] S15. Store the sampled structural modal frequencies and damping ratio response data to the cloud for later retrieval.

[0050] The seismic performance optimization and evaluation system for long-span bridges based on digital twins described in this invention, in step 2, involves updating the model and establishing a digital twin model of the target bridge based on its design data and structural monitoring data.

[0051] This digital twin model utilizes a particle swarm optimization algorithm suitable for cluster computing to implement the iterative process of the model's physical parameters, as detailed below:

[0052] Step 21: Run dispynode.py on the compute server to create compute nodes;

[0053] Step 22: Call the JobCluster class in dispy.py to create a high-performance computing cluster (Cluster);

[0054] Step 23: Automatically assign the calculation task of each finite element model to each thread of the computing node and collect the calculation results using the submit() function of Cluster;

[0055] Step 24: Iterate until the optimal solution reaches the objective function or the number of iterations reaches the maximum number of iterations, then end the model update process.

[0056] In the seismic performance optimization and evaluation system for long-span bridges based on digital twins described in this invention, OpenSees is selected in step 2 to establish a refined finite element model of the initial state based on the design data of the target bridge.

[0057] The objective function is defined as the least squares error between the natural frequency response of the finite element model and the measured data, as shown in the following equation:

[0058]

[0059] In the formula, x represents the updated parameter vector; f i,exp and f i (x) represents the finite element simulation results of the i-th natural frequency obtained from the measured data and the corresponding model parameter x; n represents the number of modes considered by the objective function.

[0060] Since the natural frequency of a structure can only reflect its overall characteristics, the modal assurance criterion (MAC) is used to match the mode shapes corresponding to numerical simulations and measured data during damage identification, as shown in the following equation:

[0061]

[0062] In the formula, {φ exp} and {φ FE} are the bridge vibration mode vectors obtained based on numerical simulation and measured data, respectively; MAC is a scalar with a value between 0 and 1, and the larger the value, the higher the modal consistency.

[0063] If a measured vibration mode is not matched, a large number is assigned to Formula 1 as the objective function value to exclude erroneous identification results;

[0064] As shown in Formula 2, x in the objective function Objective Function(x) represents the physical parameters of the model that need to be updated. The physical parameters of the model include the elastic modulus, strength, boundary conditions, and geometric dimensions of the material. The model is updated by updating the physical parameters and defining the upper and lower limits of each parameter. Based on the updated physical parameter values, the potential damage locations of the structure are mapped on the three-dimensional model using color.

[0065] As shown in Formula 1, x in the objective function Objective Function(x) represents the physical parameters of the model that need to be updated. Typically, physical parameters such as the elastic modulus, strength, boundary conditions, and geometric dimensions of the material are selected to carry out model updates, while upper and lower limits for each parameter are defined.

[0066] The algorithm defines the model update process, including: the particle size (number of physical parameters) of the particle swarm optimization algorithm, the upper and lower bounds of each particle (upper and lower bounds of the physical parameters), the maximum number of iterations of the objective function, the threshold of the objective function, and the IPv4 address of the computing node.

[0067] Based on the updated physical parameter values ​​of the model, color is used to map the potential damage locations of the structure on the 3D model.

[0068] The comparison between the structural response of the final digital twin model and the measured data shows that the seismic performance optimization and evaluation system for long-span bridges based on digital twins proposed in this invention is effective, reliable and efficient. The calculation speed of the algorithm in this invention can be improved by nearly N times (the total number of threads in the computing cluster) compared with the single-threaded calculation used by other technologies.

[0069] The seismic performance optimization and evaluation system for long-span bridges based on digital twins described in this invention defines an optimization objective function for the bridge based on its service life and target control level, as follows:

[0070]

[0071] Where x is the optimization parameter; δ1, δ2, δn1, δn2 are the cross-sectional curvature of the North Tower and the South Tower, respectively, and the cross-sectional curvature indices corresponding to the minor damage state; φ1, φ y1 ,φ2,φ y2 ,φ3,φ y3 ,φ4,φ y4 These are the drift rates of the four bridge piers and the drift rate indices corresponding to the minor damage state, respectively; Δ pier and Δ towerThese represent the maximum relative displacements (in meters) between each pier / main tower and the main beam.

[0072] The Maxwell restoring force model selected for the viscous damper is shown in the following equation:

[0073]

[0074] In the formula, F(t) is the damping force generated by the viscous damper; C is the damping coefficient; α is the damping exponent (generally ranging from 0.1 to 2.0); u is the displacement; and sgn() is the sign function.

[0075] The damping coefficient C and damping exponent α of the viscous damper are selected as optimization parameters.

[0076] According to existing design specifications, when using time-history analysis in design, the maximum response of a bridge under three sets of ground motions or the average response under seven sets of ground motions must meet predetermined response control requirements to eliminate the influence of uncertainties in site information and ground motion on the structural response. However, this design process is relatively complex. On the one hand, the suitability of the selected ground motions greatly affects the time-history response results, and the nonlinear dynamic time-history analysis of multiple ground motion records is extremely time-consuming. On the other hand, artificial waves generated based on the bridge's design response spectrum can fully consider the dynamic characteristics of long-span cable-stayed bridges and the ground motion characteristics of the design site. Therefore, this invention employs a two-step method to generate artificial waves from the bridge's design response spectrum, such as... Figure 7 and 8 As shown, the seismic performance of the aforementioned bridges was optimized based on the design ground motion.

[0077] Artificial waves are generated by synthesizing stationary waves and intensity envelope curves to obtain the response spectrum of non-stationary intensity waves. The steps are as follows:

[0078] The product of the acceleration time history a(t) and the intensity envelope function f(t) of a stationary random process is calculated using the following formula;

[0079]

[0080] Where t1 and t2 are the beginning and end times of the stable phase of the earthquake, respectively; c is the attenuation factor, which controls the rate of attenuation during the descent phase; t d The total duration of an earthquake refers to the time from the onset of the main shock to the point where the amplitude drops to about 1 / 10 of the main shock amplitude.

[0081] Solve using inverse Fourier transform:

[0082]

[0083] in, C represents a random phase angle uniformly distributed within the range [0, 2π], and n is the number of separation points in the frequency domain where the calculated response spectrum or power spectrum is located. k For discrete frequencies, ω k The Fourier amplitude spectrum of the corresponding seismic wave;

[0084] The discrete frequency C is calculated based on the relationship between the power spectrum and the response spectrum. k Let the power spectrum of a(t) be S. τ (ω k ),but:

[0085] C k =[4S τ (ω k )·Δω] 1 / 2

[0086] The approximate relationship between the reaction spectrum and the gauge spectrum is expressed as follows:

[0087]

[0088] Where S(T) is the response spectrum value; ξ is the damping ratio; P is the exceedance probability, taken as 0.5; t d The duration of the earthquake is taken as 20-30 seconds; T is the period.

[0089] Using the acceleration response spectrum of the wave S a (ω k ) and target reaction spectrum S T (ω k Compare the original power spectrum S with the original power spectrum S. τ (ω k The corrected power spectrum is obtained by performing a correction.

[0090]

[0091] The artificial seismic wave is resynthesized using the same set of random phase angles. The iteration is repeated until the response spectrum of the artificial seismic wave is close to the target spectrum, at which point the iteration stops.

[0092] The seismic performance optimization and evaluation system for long-span bridges based on digital twins described in this invention optimizes the bridge using a supercomputing-driven particle swarm optimization algorithm based on Dispy. The algorithm has a particle size of 120, a maximum number of iterations of 50, and a low threshold for the objective function (Objective Function = 0.1 in Formula 3 above). A computing cluster with 7 computing nodes and 60 working threads is built, and the viscous damper parameters of the bridge are optimized using generated artificial waves.

[0093] Beneficial effects

[0094] (1) The method proposed in this invention establishes a high-precision digital twin model of a long-span bridge based on a refined finite element model and with the assistance of supercomputing. The calculation accuracy of the digital twin model is controlled within 1% of the measured data. At the same time, it can improve the efficiency of establishing a digital twin model of a complex structure by about 51 times in a 60-thread computing environment.

[0095] (2) Subsequent applications based on the digital twin model have enabled consideration of the bridge’s immediate service performance, ensuring the scientific nature and safety of the optimization scheme.

[0096] (3) Based on the design response spectrum of the bridge, the artificial wave can fully consider the dynamic characteristics of the long-span cable-stayed bridge and the seismic motion characteristics of the design site. At the same time, the seismic optimization design process only involves the time history analysis of a single ground motion, which greatly reduces the amount of calculation for optimization design and better considers the comprehensive influence of various nonlinear factors on the seismic response of the bridge, significantly simplifying the complexity of seismic optimization of long-span bridges. Attached Figure Description

[0097] Figure 1 This is a flowchart of a digital twin-based seismic performance optimization and evaluation system for long-span bridges, according to an embodiment of the present invention.

[0098] Figure 2 This is a flowchart illustrating the overall process of establishing a digital twin model and the software programs required in this embodiment of the invention.

[0099] Figure 3 This is the implementation flow of the supercomputing-driven particle swarm algorithm based on Dispy in this embodiment of the invention;

[0100] Figure 4 This is the implementation process of the computing cluster client in this embodiment of the invention;

[0101] Figure 5 This is a three-dimensional numerical model of the object bridge in this embodiment of the invention;

[0102] Figure 6 This is a comparison between the digital twin model response of the object bridge and the measured results in an embodiment of the present invention;

[0103] Figure 7 This represents the location of damage to the bridge in this embodiment of the invention.

[0104] Figure 8 This is an example of an intensity function in an embodiment of the present invention;

[0105] Figure 9 The artificial wave response spectrum and acceleration time history generated in the embodiments of the present invention;

[0106] Figure 10This describes the process of optimizing the seismic performance of the bridge in this embodiment of the invention. Detailed Implementation

[0107] To make the objectives and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0108] This invention proposes a simplified method for multi-objective optimization of vibration damping devices for long-span bridges, considering service performance. The overall process is as follows: Figure 1 As shown, it includes the following steps:

[0109] S1. Collect structural response data through a structural health monitoring system, and preprocess the data to obtain the modal response of the structure;

[0110] S11. The Kalman filter method is used to perform noise reduction processing on the modal response data of the extracted structure from the data acquisition system. While maintaining the original data characteristics, the noise and interference of the data are reduced. The implementation steps of the Kalman filter method are as follows:

[0111] Input: x est ,P est ,z,Q,R

[0112] Output: x updated ,P updated

[0113] Step 1: Initialize matrices F and M

[0114] Step 2: Predict the state vector and covariance

[0115] x prd =Fx est

[0116] P prd =FP prd FT+Q

[0117] Step 3: Error Estimation

[0118] S = HP prd HT+R

[0119] Step 4: Calculate the Kalman gain coefficient

[0120] K gain =P prd H T S -1

[0121] Step 5: Correction based on truth value

[0122] x updated =x prd +K gain (z-Hx prd )

[0123] P updated =P prd -K gain HP prd

[0124] Step 6: Return x updated ,P updated

[0125] S12. The Fourier spectrum of the structural vibration is segmented using empirical wavelet transform to identify the modal peak positions and obtain the Intrinsic Mode Function (IMF) components, thus obtaining the single-degree-of-freedom vibration response signal of the structure. The operation of the empirical wavelet transform function is as follows:

[0126] Step 1: Divide the Fourier spectrum into N continuous intervals Λ n

[0127] Λ n =[ω n-1 ,ω n ], n=1,2,…,N

[0128] Step 2: Construct the empirical scaling function φ n (ω)

[0129]

[0130] Step 3: Construct the empirical wavelet function ψ n (ω)

[0131]

[0132] Where β(x)=x 4 (35-84x+70x 2 -20x 3 )

[0133] Step 4: Decompose the signal x(t) into frequency-modulated components and amplitude modulation components

[0134] In the formula, and These are the detail coefficients and approximation coefficients, respectively, and * represents convolution.

[0135] S13. Further analysis of the measured signal using the Random Decrement Technique (DRT) is conducted to separate the deterministic vibration signal and the stationary random signal, thereby obtaining the structural free decay vibration response signal. The specific steps are as follows:

[0136] Step 1: Select a fixed value A from the single-degree-of-freedom vibration response signal y(t) of the linear system to truncate the amplitude of y(t);

[0137] Step 2: Let t be the intersection point between A and the response signal y(t). i (i = 1, 2, ..., N), obtain N segments starting from t i A time series starting from [starting point] and of length s;

[0138] Step 3: By stacking and averaging the N time series segments, the free decay response signal of y(t) can be obtained.

[0139] S14. The Hilbert Transform (HT) is used to process the free decay signal to obtain the amplitude curve and phase curve, thereby identifying the modal frequency and damping ratio. The steps are as follows:

[0140] Step 1: Let x j (t) represents a free decay response signal obtained by the RDT method in S13.

[0141] In the formula, A 0j Let ω be the amplitude of the signal at time 0. j Let ξ be the j-th order undamped circular frequency. j For the j-th order damping ratio, Let be the damped primary frequency of order j.

[0142] Step 2: Perform a Hilbert transform on the formula in Step 1 to obtain the phase function. and amplitude function

[0143] Step 3: Adjust the phase function θ j Differentiating (t) yields the j-th order original frequency ω. dj Considering that the damping ratio in actual engineering is usually less than 5%, the simplified formula yields the j-th order modal frequency.

[0144] Step 4: Construct an exponential decay curve for the amplitude function A j (t) is fitted to obtain the value of b, and then the j-th order damping ratio is obtained.

[0145] S15. Store the sampled structural modal frequency and damping ratio response data to the cloud for later retrieval.

[0146] S2. Based on the design data and structural monitoring data of the target bridge, update the model and establish a digital twin model of the target bridge. The process is as follows: Figure 2 As shown.

[0147] S21. In order to improve the efficiency of model updates, a local private computing cluster is built based on the supercomputing nodes called by dispy. The computing client sends computing tasks to each computing node and collects computing results through the IPv4 address of each computing node.

[0148] S22. A particle swarm optimization algorithm suitable for cluster computing was developed based on a computing cluster to implement the iterative process of the model's physical parameters, such as... Figure 3 and Figure 4 As shown, the details are as follows:

[0149] Step 1: Run dispynode.py on each compute server to create a compute node;

[0150] Step 2: Call the JobCluster class in dispy.py to create a high-performance computing cluster (Cluster);

[0151] Step 3: Automatically assign the computational tasks (particles of the PSO algorithm) of each finite element model to each thread of the computing node and collect the computational results using the submit() function of Cluster;

[0152] Step 4: Iterate until the optimal solution reaches the objective function or the number of iterations reaches the maximum number of iterations, then end the model update process;

[0153] Algorithm 2: Cluster Computation-Assisted Particle Swarm Optimization Algorithm

[0154] enter:

[0155] dispy: Distributed computing framework

[0156] node: The IPv4 address of each compute node

[0157] f(x): Objective function

[0158] pop: Particle size

[0159] dim: Update parameter dimension

[0160] MaxIt: Maximum number of iterations

[0161] limit: Threshold of the objective function

[0162] Output:

[0163] f best Solution to the optimal objective function

[0164]

[0165]

[0166]

[0167] S23. Select OpenSees and build a refined finite element model of the initial state of the bridge based on its design data. The model in this example is as follows: Figure 4 As shown.

[0168] S24. The least squares error between the natural frequency response of the finite element model and the measured data is defined as the objective function, as shown in Equation 1.

[0169]

[0170] In the formula, x represents the updated parameter vector; f i,exp and f i (x) represents the ith natural frequency obtained from measured data and the corresponding finite element simulation result with model parameter x, respectively; n represents the number of modes considered in the objective function. Since the natural frequency of a structure can only reflect its overall characteristics, the modal confidence criterion (MAC) is used to match the mode shapes corresponding to the numerical simulation and measured data during damage identification, as shown in Equation 2:

[0171]

[0172] In the formula, {φ exp} and {φ FE} represents the bridge mode shape vectors obtained based on numerical simulation and measured data, respectively; MAC is a scalar with a value between 0 and 1, where a larger value indicates higher modal consistency. When a measured mode shape is not matched, a larger number is assigned to Formula 1 as the objective function value to exclude erroneous identification results.

[0173] S25. According to formula 1 in step S24 and Figure 2 As shown, in the objective function (x), x represents the physical parameters of the model that need to be updated. Typically, physical parameters such as the material's elastic modulus, strength, boundary conditions, and geometric dimensions are selected for model updates, while upper and lower limits are defined for each parameter. This example uses a long-span cable-stayed bridge as an example, selecting the structure's elastic model, main girder wall thickness, and support stiffness as physical parameters.

[0174] The details are shown in the table below:

[0175]

[0176]

[0177] S26. Define the model update process in the algorithm, including: the particle size (number of physical parameters) of the particle swarm optimization algorithm, the upper and lower bounds of each particle (upper and lower bounds of physical parameters), the maximum number of iterations of the objective function, the threshold of the objective function, and the IPv4 address of the computing node.

[0178]

[0179] S27. Based on the updated physical parameter values ​​of the model, use color to map the potential damage locations of the structure on the 3D model, such as... Figure 7 As shown.

[0180] S28. The comparison between the structural response of the final digital twin model and the measured data shows that the seismic performance optimization and evaluation system for long-span bridges based on digital twins proposed in this invention is effective, reliable and efficient. The calculation speed of the algorithm in this invention can be improved by nearly N (the total number of threads in the computing cluster) times compared with the single-threaded calculation used by other technologies. For example, in this example, the speed is improved by about 51 times in a 60-thread computing environment.

[0181]

[0182] S3. Based on the digital twin model established in step S2, it is necessary to determine the damage threshold of key components in the structure and determine the damage classification status of the object bridge.

[0183] S31. Determine the graded damage threshold of the structure using piers, main towers, and supports as damaged components. A specific example process is as follows:

[0184] (1) When classifying the damage state of the bridge piers, first calculate the load of the superstructure on each bridge pier based on the digital twin model of the bridge, and carry out the overthrow analysis of the bridge piers. Select the drift rate as the engineering requirement parameter, and define the drift rate corresponding to the damage threshold of the bridge pier based on each performance point (cracking point, yield point, peak point and limit point) on the force-displacement curve of the bridge pier.

[0185] (2) When classifying the damage state of the main tower, nonlinear analysis is performed on the main tower, and the unit section curvature envelope diagrams of the main tower and the pier at different heights are extracted to determine the vulnerable locations of the main tower and the pier. The bending moment curvature of the vulnerable section is selected as the engineering requirement parameter, and the damage threshold of the main tower is defined.

[0186] (3) When classifying the damage state of the support, the relative displacement between the upper structure and the lower structure is selected as the engineering requirement parameter, and the graded damage performance of the support is determined according to the selected support type and the spatial position relationship of the main beam.

[0187] intact minor damage Moderate damage Severe damage Complete destruction Pier No. 1 φ<0.432% 0.432%<φ<1.358% 1.358%<φ<4.321% 4.321%<φ<6.728% 6.728%<φ Pier No. 2 φ<0.060% 0.060%<φ<0.783% 0.783%<φ<4.578% 4.578%<φ<7.108% 7.108%<φ Pier No. 3 φ<0.542% 0.542%<φ<1.506% 1.506%<φ<5.361% 5.361%<φ<7.892% 7.892%<φ Pier No. 4 φ<0.556% 0.556%<φ<1.543% 1.543%<φ<5.309% 5.309%<φ<8.025% 8.025%<φ South Tower ε<1.00% 1.00%<ε<1.33% 1.33%<ε<4.57% 4.57%<ε<12.8% 12.8%<ε North Tower ε<1.20% 1.20%<ε<1.73% 1.93%<ε<7.57% 7.57%<ε<17.8% 17.8%<ε Pier Support Δ<0.01 0.01<Δ<0.025 0.025<Δ<0.05 0.05<Δ<0.10 0.10<Δ Support at the main tower Δ<0.02 0.02<Δ<0.035 0.035<Δ<0.07 0.07<Δ<0.14 0.014<Δ

[0188] S4. Based on the service life of the bridge and the target control level, define the optimization objective function of the bridge, as shown in Formula 3.

[0189] S41. In this example, the control targets are the drift rate of the piers and the bending moment of the main tower section, and the damage to the piers and main tower is controlled under the premise of ensuring that the supports are not damaged.

[0190]

[0191] Where x is the optimization parameter; δ1, δ2, δn1, δn2 are the cross-sectional curvature of the North Tower and the South Tower, respectively, and the cross-sectional curvature indices corresponding to the minor damage state; φ1, φ y1 ,φ2,φ y2 ,φ3,φ y3 ,φ4,φ y4 These are the drift rates of the four bridge piers and the drift rate indices corresponding to the minor damage state, respectively; Δ pier and Δ tower These represent the maximum relative displacements (in meters) between each pier / tower and the main beam. The objective function aims to achieve two control objectives: (1) to minimize the drift rate of each pier and ensure the normal use of the structure by controlling the damage state of the bridge components under future earthquakes; and (2) to ensure that the relative displacement between the superstructure and the substructure does not exceed the elastic displacement of the supports, thereby avoiding support failure or beam collapse.

[0192] S42. During an earthquake, the main girder often undergoes significant displacement. Therefore, damping devices are typically installed at the connection between the main tower / pier and the main girder to improve the structure's seismic performance, reduce displacement during earthquakes, and ensure the structure's safety under seismic loads.

[0193] This example uses a viscous damper, and the selected Maxwell restoring force model is shown in Equation 4.

[0194]

[0195] In the formula, F(t) is the damping force generated by the viscous damper; C is the damping coefficient; α is the damping exponent (the value range is generally from 0.1 to 2.0); u is the displacement; and sgn() is the sign function.

[0196] S43. When optimizing the parameters of a damper, it is necessary to select appropriate parameters and define the parameter range. In this example, the damping coefficient C and damping exponent α of the viscous damper are selected as optimization parameters, i.e., x in Formula 4.

[0197] S44. According to existing design specifications, when using time-history analysis in a design process, the maximum response value of a bridge under three sets of ground motions or the average response value under seven sets of ground motions must meet predetermined response control requirements to eliminate the influence of uncertainties in site information and ground motion on the structural response. However, this design process is relatively complex. On the one hand, the suitability of the selected ground motion has a significant impact on the time-history response results, and the nonlinear dynamic time-history analysis of multiple ground motion records is extremely time-consuming. On the other hand, artificial waves generated based on the bridge's design response spectrum can fully consider the dynamic characteristics of long-span cable-stayed bridges and the ground motion characteristics of the design site. Therefore, this invention employs a two-step method to generate artificial waves from the bridge's design response spectrum, such as... Figure 7 and 8 As shown, the seismic performance optimization of the aforementioned bridge is carried out using the design ground motion as the basis. This method first synthesizes a stationary wave, then multiplies it by the intensity envelope curve to obtain a non-stationary intensity wave. The specific steps are as follows:

[0198] Step 1: Calculate the product of the acceleration time history a(t) and the intensity envelope function f(t) of the stationary random process, as shown in Formula 5.

[0199]

[0200] Where t1 and t2 are the beginning and end times of the stable phase of the earthquake, respectively; c is the attenuation factor, which controls the rate of attenuation during the descent phase; t d The total duration of an earthquake refers to the time from the onset of the seismic motion to the point where the amplitude of the main shock decreases to about 1 / 10 of the amplitude of the main shock.

[0201] Step 2: Solve using inverse Fourier transform

[0202] in, C represents a random phase angle uniformly distributed within the range [0, 2π], and n is the number of separation points in the frequency domain where the calculated response spectrum or power spectrum is located. k For discrete frequencies, ω k The Fourier amplitude spectrum of the corresponding seismic wave;

[0203] Step 3: Calculate the discrete frequency C based on the relationship between the power spectrum and the response spectrum. k Let the power spectrum of a(t) be S. τ (ω k ), then C k =[4S τ (ω k )·Δω]1 / 2 ;

[0204] Step 4: Based on the approximate relationship between the reaction spectrum and the standard spectrum

[0205] Where S(T) is the response spectrum value; ξ is the damping ratio; P is the exceedance probability, taken as 0.5; t d The duration of the earthquake is taken as 20-30 seconds; T is the period.

[0206] Step 5: Use the wave acceleration response spectrum S a (ω k ) and target reaction spectrum S T (ω k Compare the original power spectrum S with the original power spectrum S. τ (ω k The corrected power spectrum is obtained by performing corrections.

[0207] Step 6: Continue to use the same set of random phase angles to resynthesize artificial seismic waves, and iterate repeatedly until the response spectrum of the artificial seismic waves is close to the target spectrum, then stop the iteration.

[0208] S45. After defining the optimization problem, the supercomputing-driven particle swarm optimization algorithm based on Dispy, invented in step S2, is selected to optimize the bridge. The particle size of the algorithm is 120, the maximum number of iterations is 50, and a low threshold for the objective function (i.e., Objective Function = 0.1 in Formula 3) is set to ensure that the drift rate of all bridge piers after seismic performance optimization is close to the optimal state.

[0209] S46. Based on the above algorithm settings, a computing cluster with 7 computing nodes and 60 working threads is built. The artificial seismic motion generated in S44 is used to optimize the viscous damper parameters of the bridge. Figure 10 As shown.

[0210] S47. Based on the design response spectrum, seven natural ground motions were selected to verify the seismic performance optimization results. The mean response of the optimized model under the seven natural ground motions was calculated and compared with the optimization results. The results show that the method proposed in this invention has a fast calculation speed, a simpler process, and guarantees the optimization results.

[0211]

[0212] In summary, this invention proposes a simplified method for multi-objective optimization of seismic damping devices for long-span bridges, considering service performance. This method first maps monitoring data to an initial model through nonlinear model updates, generating a digital twin model of the target bridge. Based on this, the digital twin model calibrates the current performance level and the target performance level to be achieved in the future, serving as the seismic response control targets for the target bridge. Finally, artificial waves are generated based on the bridge's design response spectrum to conduct cluster computation-assisted seismic performance optimization of the long-span cable-stayed bridge, precisely controlling the response of different components under earthquakes. This method boasts high computational efficiency and a simpler optimization process.

[0213] 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 variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A digital twin-based large-span bridge seismic performance optimization and evaluation system, characterized in that, The optimization and evaluation system comprises a data acquisition and preprocessing module, a model updating module, and a performance evaluation and optimization module. The data acquisition and preprocessing module is used for analyzing and storing response data of the structure; The model updating module is used for defining information of each supercomputing node and then building a private computing cluster; The performance evaluation and optimization module defines damage classification thresholds and target damage levels of the object bridge according to the digital twin model; The optimization and evaluation method of the module comprises the following steps: Step 1: The data acquisition and preprocessing module collects the frequency response data of the long-span bridge under the excitation of environmental and vehicle loads, and uses the Kalman filter method to process the frequency response data, and then uses the fast Fourier transform to identify the modal and frequency of the structure, so as to obtain the modal shape and natural frequency of the bridge and store them in the cloud. Step 2: The model updating module establishes a three-dimensional refined numerical model according to the design data of the object bridge, extracts the modal shape and natural frequency data of the bridge in the cloud, defines the upper and lower limits and parameter types of the physical parameters that need to be updated in the bridge, establishes a least squares error function according to the frequency modal response in step 1 to carry out nonlinear model updating of the object bridge, and establishes a digital twin model of the object bridge. Step 3: The performance evaluation and optimization module evaluates and optimizes the performance of the object bridge. According to the digital twin model established in step 2, the engineering requirement parameters and the calibrated damage performance threshold values of the pier component, the support component and the main tower component are defined. According to the service life of the bridge, the target damage level of the bridge is determined. According to the engineering requirement parameters of the pier, the main tower and the support, a multi-objective optimization design function is established. According to the design response spectrum of the object bridge, artificial ground motion is generated, and the nonlinear time history analysis of the digital twin model is carried out to obtain the drift ratio of the pier, the relative displacement of the upper structure and the lower structure, and the cross-sectional curvature of the main tower. According to the multi-objective optimization design function, the supercomputer-driven damping device parameter optimization is carried out, and the optimal parameter combination is output to control the classification response of the bridge under the earthquake. （3） wherein x is an optimization parameter; δ1, δ2, δn1, δn2 are the cross-sectional curvature and the cross-sectional curvature index corresponding to the slight damage state of the north tower and the south tower, respectively; φ1, φ y1 , φ y2 2, φ y3 3, φ y4 4 are the drift rate and the drift rate index corresponding to the slight damage state of the four piers, respectively; Δ pier and Δ tower are the maximum relative displacement of each pier / tower and the main beam, unit: m; According to the service life and target control level of the object bridge, the optimization objective function of the object bridge is defined as follows: （4） The Maxwell restoring force model of the viscous damper is as follows: Wherein F(t) is the damping force generated by the viscous damper; C is the damping coefficient; alpha is the damping index, the value range is 0.1 to 2.0; u is the displacement; sgn() is the sign function; The damping coefficient C and the damping index alpha of the viscous damper are selected as the optimization parameters; The acceleration time history of the stationary random process is calculated by the formula and the intensity envelope function is the product of ； （5）； wherein, and are the first and last time of the earthquake stationary section, respectively; is the decay factor, which controls the speed of the decay section; represents the total duration of the earthquake, which refers to the duration from the start of the ground motion to the decay to 1 / 10 of the main shock amplitude. The specific steps are as follows: ； wherein, is random phase angles uniformly distributed in the range [0, 2π], n is the number of separation points in the frequency domain of the calculated response spectrum of the power spectrum, is the discrete frequency, corresponds to the Fourier amplitude spectrum of the seismic wave; Calculating discrete frequencies from the relation between power spectrum and response spectrum , let the power spectrum of be: ； Inverse Fourier transform is used to solve: ； wherein, is a response spectrum value; is a damping ratio; is an exceedance probability, taken as 0.5; is an earthquake duration, taken as 20s-30s; is a period; Using wave acceleration response spectrum With the target reaction spectrum Compare the original power spectra. The corrected power spectrum is obtained by performing corrections: ； According to the approximate relationship between the response spectrum and the standard spectrum, the expression is as follows:

2. The digital-twin-based long-span bridge seismic performance optimization and evaluation system according to claim 1, characterized in that, The same set of random phase angles is used to synthesize artificial seismic waves, and the iteration is repeated until the response spectrum of the artificial seismic wave is close to the target spectrum, and then the iteration stops. In step 1, the response data of the structure is collected by the structural health monitoring system, and the modal shape response of the structure is obtained by preprocessing the data, and the specific steps are as follows: S11. The modal response data of the data acquisition system is extracted and denoised by using Kalman filtering method, which reduces the noise and data interference of the data while keeping the original data characteristics; S12. The Fourier spectrum of the structural vibration is segmented by using empirical wavelet transform to identify the modal peak position and obtain the inherent modal function component, and the single degree of freedom vibration response signal of the structure is obtained. The operation of the empirical wavelet transform function is as follows: Step 121 : dividing the Fourier spectrum into N consecutive intervals : ； Step 122: Constructing the empirical scale function : ； Step 123: Constructing the empirical wavelet function As follows: ； wherein ; Step 124: Bridge vibration signal collected by health monitoring system Breaks down into: Frequency modulated component ; amplitude modulation component ; wherein and are the detail and approximation coefficients, respectively, is a convolution; S13. Further adopt random decrement technique to analyze the measured bridge vibration signal, separate the deterministic vibration signal and stationary random signal, and obtain the structure free decay vibration response signal, the specific steps are as follows: Step 131: Select a fixed value A for the amplitude of y(t) in the single degree of freedom vibration response signal y(t); Step 132: Let the intersection of A and the response signal y(t) be t i , i = 1, 2, …, N, obtain N time sequences with a length of s starting from t i ; Step 133: Superimposed average of N time series, that is, the free decay response signal of y(t) is obtained: ； S14、 Adopting Hilbert transform to free decay signal The amplitude curve and the phase curve are obtained by processing, and the modal frequency and the damping ratio are identified, and the steps are as follows: Step 141: Let x j (t) is a certain free decay response signal obtained by the RDT method in S13: ； In the formula, A 0j is the amplitude of the signal at time 0, is the jth order undamped circular frequency, is the jth order damping ratio, is the jth order damped natural frequency, and t is time. Step 142: Hilbert transform of the formula in step 1 is carried out to obtain the phase function: ； Amplitude function: ； Step 143: Derive the phase function The jth order natural frequency is obtained by derivation Considering that the damping ratio is usually less than 5% in actual engineering, the jth order modal frequency is obtained by simplifying the formula: ； Step 144: Constructing the exponential decay curve versus amplitude function A j (t) is fitted to obtain the value of b, and then the jth damping ratio is obtained: ； S15. Store the structure modal frequency and damping ratio response data obtained by sampling in the cloud for subsequent calling.

3. The digital-twin-based long-span bridge seismic performance optimization and evaluation system according to claim 1, characterized in that, Step 2: According to the design data and monitoring data of the object bridge, the model is updated to establish the digital twin model of the object bridge, The digital twin model is based on the particle swarm algorithm developed by the computing cluster to realize the iteration process of the model physical parameters, which is as follows: Step 21: Run dispynode.py on the calculation server to create a calculation node; Step 22: Create a high-performance computing cluster Cluster by calling the JobCluster class in dispy.py; Step 23: Automatically distribute each finite element model calculation task to each thread of the calculation node through the submit() function of Cluster and collect the calculation results; Step 24: Iterative calculation until the optimal solution reaches the target function or the number of iterations reaches the maximum number of iterations, and the model updating process is ended.

4. The digital-twin-based long-span bridge seismic performance optimization and evaluation system according to claim 1, characterized in that, In step 2, OpenSees is selected, and the initial state of the refined finite element model is established according to the design data of the object bridge; The least square error of the natural frequency response of the finite element model and the measured data is defined as the objective function, as shown in the following formula: （1） where x represents the update parameter vector; f i, exp and f i (x) are the i-th natural frequency obtained from the measured data and the finite element simulation result when the corresponding model parameter is x, respectively; n represents the number of modes considered by the objective function. The modal shape corresponding to the numerical simulation and the measured data is matched by using the modal confidence criterion, as shown in the following formula: （2） where {φ exp} and {φ FE} are the bridge mode shape vectors obtained based on numerical simulation and measured data, respectively; MAC is a scalar whose value is between 0 and 1, and the larger the value is, the higher the mode consistency is. When a measured mode shape is not matched, a larger number is assigned to formula 1 as the objective function value to exclude incorrect identification results; According to formula 1, x of the objective function Objective function(x) is the model physical parameter that needs to be updated, which includes the material modulus of elasticity, strength, boundary condition and geometric size. The model is updated, and the upper and lower limits of each parameter are defined. According to the updated model physical parameter value, the color is mapped on the three-dimensional model to map the potential damage location of the structure.

5. The digital-twin-based long-span bridge seismic performance optimization and evaluation system according to claim 4, characterized in that, The bridge is optimized by the particle swarm algorithm driven by the supercomputer based on dispy. The particle size of the algorithm is 120, the maximum number of iterations is 50, a lower threshold of the objective function is set, and the objective function in the above formula 1 is 0.

1. A computing cluster with 7 computing nodes and 60 working threads is built, and the viscous damper parameters of the bridge are optimized by generating artificial waves.

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