Large-span bridge anti-seismic performance optimization and evaluation system based on digital twinning

Abstract

The invention relates to a large-span bridge anti-seismic performance optimization and evaluation system based on digital twinning, and belongs to the field of computer and bridge engineering. The optimization and evaluation system comprises a data acquisition and pre-processing module, a model updating module and a performance evaluation and optimization module; the optimization and evaluation method comprises the following steps: identifying the modal and frequency of a structure, obtaining the modal shape and natural vibration frequency of a bridge, and establishing a digital twinborn model of an object bridge; and according to the multi-objective optimization design function, carrying out supercomputing driven damping device parameter optimization, outputting an optimal parameter combination, and controlling hierarchical response of the bridge in an earthquake. The artificial waves generated based on the design response spectrum of the bridge can fully consider the dynamic characteristics of the large-span cable-stayed bridge and the seismic oscillation characteristics of the design site; meanwhile, only time history analysis of single seismic oscillation is involved in the anti-seismic optimization design process, the calculation amount of optimization design is greatly reduced, the comprehensive influence of each nonlinear factor on the bridge seismic response is better considered, and the complexity of large-span bridge anti-seismic optimization is remarkably simplified.

Description

Technical Field

[0001] The invention relates to a seismic performance optimization and evaluation system for a long-span bridge based on digital twins, and belongs to the field of computer and bridge engineering. Background Art

[0002] As an important basic transportation facility, the design service life of a long-span cable-stayed bridge is often more than 100 years. During its life cycle, environmental impacts and long-term loads will cause the seismic performance of the bridge to deteriorate. Among them, shock-absorbing devices (such as viscous dampers, tuned mass dampers, etc.) and bearings, as key components affecting the dynamic characteristics of bridge structures, have a significant impact on the seismic response of bridges. During the service of bridges, they need to be regularly inspected, maintained and replaced. However, after the performance of the bridge deteriorates, the calculation model based on the design data cannot accurately reflect its actual service status. Applying it to the maintenance and design of the bridge will result in the replacement components failing 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 usually equipped with advanced monitoring systems to collect measured data of the structure during service to evaluate its immediate service performance. Mapping these measured data to the structural model for performance evaluation often requires model updating technology. Due to the large number of components and complex node connections in long-span cable-stayed bridges, the model updating algorithms for large-span cable-stayed bridges in existing studies have problems such as long calculation time and low accuracy. Summary of the invention

[0004] In view of the above problems, the present invention provides a system for optimizing and evaluating the seismic performance of large-span bridges based on digital twins. The system establishes a digital twin model of the target bridge, simplifies the seismic motion selection process, optimizes the seismic absorption device of large-span bridges under multi-objective control, effectively controls the damage state of different components under earthquakes, and improves the seismic performance of bridges in service.

[0005] The present invention adopts the following technical solutions: a system for optimizing and evaluating the seismic performance of a large-span bridge based on digital twins, the optimization and evaluation system comprising a data acquisition and pre-processing module, a model updating module, and a performance evaluation and optimization module;

[0006] The data acquisition and pre-processing 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 evaluation and optimization module defines the damage classification threshold and target damage level of the target bridge based on the digital twin model;

[0009] Using the optimization and evaluation method of this module, the steps are as follows:

[0010] Step 1: The data acquisition and pre-processing module collects the frequency response data of the long-span bridge under the excitation of the environment and vehicle loads, uses the Kalman filter method to reduce the noise of the frequency response data, and uses the fast Fourier transform to realize the mode and frequency identification of the structure, obtain the modal vibration shape and natural frequency of the bridge, and store them in the cloud;

[0011] Step 2: The model updating module establishes a three-dimensional refined numerical model based on the design data of the target bridge and extracts the bridge modal vibration shape and natural frequency data in the cloud;

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

[0013] Step 3: Performance evaluation and optimization of the performance of the bridge object in the performance optimization module;

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

[0015] Determine the target damage level of the bridge according to its service life;

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

[0017] Artificial earthquake motion is generated according to the design response spectrum of the target bridge, and the nonlinear time history analysis of the digital twin model is carried out to obtain the drift rate of the bridge pier, 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, supercomputer-driven seismic isolation device parameter optimization is carried out to output the optimal parameter combination and control the graded response of the bridge under earthquake.

[0019] The digital twin-based seismic performance optimization and evaluation system for large-span bridges of the present invention comprises the following specific steps: in step 1, the response data of the structure is collected by the structural health monitoring system, and the data is pre-processed to obtain the modal response of the structure.

[0020] S11. Use Kalman filtering method to perform data noise reduction on the modal response data of the structure extracted by the data acquisition system, and reduce the noise and data interference of the data while maintaining the original data characteristics;

[0021] S12. Use the empirical wavelet transform to segment the Fourier spectrum of the structural vibration, identify the modal peak position to obtain the inherent modal function component, and obtain the structural single-degree-of-freedom vibration response signal. 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 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] AM Component

[0031] In the formula, and They are detail coefficient and approximation coefficient respectively, * is convolution;

[0032] S13. Further adopt the random reduction technology to analyze the measured bridge vibration signal, separate the deterministic vibration signal and the stable random signal, and obtain the structural free decay vibration response signal. 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 intercept the amplitude of y(t);

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

[0035] Step 133: Perform superposition and averaging of N time series to obtain the free decay response signal of y(t):

[0036]

[0037] S14. The free decay signal x(t) is processed by Hilbert transform to obtain the amplitude curve and phase curve, and the modal frequency and damping ratio are identified. The steps are as follows:

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

[0039]

[0040] In the formula, A 0j is the amplitude of the signal at time 0, φ j is the jth order undamped circular frequency, ξ j is the j-th order damping ratio, is the j-th order damped original frequency, t is the time;

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

[0042]

[0043] Amplitude function:

[0044]

[0045] Step 143: Phase function θ j (t) Take the derivative to get the j-th order original frequency ω dj , considering that the damping ratio in actual engineering is usually less than 5%, the simplified formula is used to obtain the j-th 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. The sampled structural modal frequency and damping ratio response data are stored in the cloud for subsequent use.

[0050] The large-span bridge seismic performance optimization and evaluation system based on digital twins of the present invention, step 2 is to update the model according to the design data of the target bridge and the monitoring data of the structure to establish a digital twin model of the target bridge,

[0051] The digital twin model develops a particle swarm algorithm suitable for cluster computing based on the computing cluster to implement the iteration process of the model's physical parameters, as follows:

[0052] Step 21: Run dispynode.py on the computing server to create a computing node.

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

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

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

[0056] In the digital twin-based large-span bridge seismic performance optimization and evaluation system of the present invention, OpenSees is selected in step 2 to establish a refined finite element model of the initial state according to the design data of the target bridge;

[0057] The least square error between 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:

[0058]

[0059] 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 corresponding finite element simulation results when the model parameter is x; n represents the number of modes considered by the objective function.

[0060] Since the natural frequency of the structure can only reflect the overall characteristics of the structure, the modal assurance criterion (MAC) is used to match the modal vibration shapes corresponding to the numerical simulation and measured data in the damage identification process, as shown in the following formula:

[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 a larger value indicates a higher modal consistency;

[0063] When a certain measured vibration mode is not matched, a larger number is assigned to Formula 1 as the objective function value to eliminate erroneous recognition results;

[0064] As shown in Formula 2, x in the objective function (x) is the physical parameter of the model that needs to be updated. The physical parameters of the model include the elastic modulus, strength, boundary conditions and geometric dimensions of the material to update the model, and define the upper and lower limits of each parameter. According to the updated physical parameter values ​​of the model, the potential damage position of the structure is mapped on the three-dimensional model using color.

[0065] According to Formula 1, x in the objective function (x) is the physical parameter of the model that needs to be updated. Usually, physical parameters such as the elastic modulus, strength, boundary conditions and geometric dimensions of the material are selected to carry out model updating, and the upper and lower limits of each parameter are defined.

[0066] The model update process is defined in the algorithm, including: the particle size of the particle swarm algorithm (the number of physical parameters), the upper and lower limits of each particle (the upper and lower limits 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 model physical parameter values, colors are used to map the potential damage locations of the structure on the 3D model.

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

[0069] The large-span bridge seismic performance optimization and evaluation system based on digital twins of the present invention defines the optimization objective function of the target bridge according to the service life and target control level of the target bridge, which is expressed as follows:

[0070]

[0071] Among them, x is the optimization parameter; δ1, δ2, δn1, δn2 are the cross-sectional curvatures of the north tower and the south tower and the cross-sectional curvature indexes corresponding to the slight damage state, respectively; φ1, φ y1 ,φ2,φ y2 ,φ3,φ y3 ,φ4,φ y4 are the drift rates of the four piers and the drift rate index corresponding to the slight damage state; Δ pier and Δ towerare the maximum relative displacements of each pier / main tower and main beam (unit: m);

[0072] The Maxwell restoring force model selected for the viscous damper is shown as follows:

[0073]

[0074] Where F(t) is the damping force generated by the viscous damper; C is the damping coefficient; α is the damping index (the value range is generally 0.1 to 2.0); u is the displacement; 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 the time-history analysis design method, it is usually necessary to make the maximum response value of the bridge under three groups of seismic motions or the average response value under seven groups of seismic motions meet the established response control requirements, thereby eliminating the influence of site information and seismic motion uncertainty on the structural response. However, this design process is relatively complicated. On the one hand, whether the selected seismic motion is appropriate has a great influence on the result of the time-history response, and the nonlinear dynamic time-history analysis of multiple seismic motion records is extremely time-consuming. On the other hand, the artificial waves generated based on the design response spectrum of the bridge can fully consider the dynamic characteristics of the large-span cable-stayed bridge and the seismic motion characteristics of the design site. Therefore, the present invention adopts a two-step method to generate artificial waves through the design response spectrum of the bridge, such as Figure 7 and 8 As shown, the seismic performance optimization of the above bridge is carried out as the design ground motion.

[0077] The artificial wave is generated by synthesizing the stationary wave and the intensity envelope curve to obtain the intensity non-stationary wave response spectrum. The steps are as follows:

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

[0079]

[0080] Among them, t1 and t2 are the first and last moments of the stable phase of the earthquake respectively; c is the attenuation factor, which controls the speed of attenuation of the descending phase; t d It indicates the total duration of an earthquake, which refers to the time from the beginning of the earthquake shaking to the time when it drops to about 1 / 10 of the main shaking amplitude;

[0081] Solve using inverse Fourier transform:

[0082]

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

[0084] 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 ),but:

[0085] C k =[4S τ (ω k )·Δω] 1 / 2

[0086] The approximate relationship between the response spectrum and the standard 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, which is 0.5; t d is the duration of the earthquake, which is 20s-30s; T is the period;

[0089] The acceleration response spectrum S of the wave is adopted a (ω k ) and the target response spectrum S T (ω k ) to compare the original power spectrum S τ (ω k ) is corrected to obtain the corrected power spectrum:

[0090]

[0091] 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 the iteration stops.

[0092] The large-span bridge seismic performance optimization and evaluation system based on digital twin described in the present invention optimizes the bridge based on the particle swarm algorithm driven by the supercomputer of dispy. The particle scale of the algorithm is 120, the maximum number of iterations is 50, and a lower threshold of the objective function is set. The Objective Function in the above formula 3 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.

[0093] Beneficial Effects

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

[0095] (2) Subsequent applications based on the digital twin model enable consideration of the immediate service performance of the bridge and ensure the scientific nature and safety of the optimization plan.

[0096] (3) The artificial waves generated based on the design response spectrum of the bridge 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 seismic motion, which greatly reduces the calculation amount of the optimization design and better considers the comprehensive influence of various nonlinear factors on the seismic response of the bridge, significantly simplifying the complexity of the seismic optimization of large-span bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 This is a flow chart of a system for optimizing and evaluating the seismic performance of a large-span bridge based on digital twins according to an embodiment of the present invention;

[0098] Figure 2 The overall flow chart and program software required to establish a digital twin model in the embodiment of the present invention;

[0099] Figure 3 This is the implementation process of the particle swarm algorithm driven by supercomputer developed based on DISPY in the embodiment of the present invention;

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

[0101] Figure 5 A three-dimensional numerical model of the object bridge in an embodiment of the present invention;

[0102] Figure 6 A comparison between the digital twin model response and the measured result of the object bridge in an embodiment of the present invention;

[0103] Figure 7 is a representation of the damage position of the target bridge in an embodiment of the present invention;

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

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

[0106] Fig.10This is the seismic performance optimization process of the target bridge in the embodiment of the present invention. DETAILED DESCRIPTION

[0107] In order to make the purpose and technical solution of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0108] The present invention proposes a simplified method for multi-objective optimization of a large-span bridge shock-absorbing device considering service performance. The overall process is as follows: Figure 1 As shown, the following steps are included:

[0109] S1. Collect the response data of the structure through the structural health monitoring system, and pre-process the data to obtain the modal vibration response of the structure;

[0110] S11. The Kalman filter method is used to perform data noise reduction processing on the modal response data of the structure extracted by the data acquisition system. On the basis of maintaining the original data characteristics, the data noise and data interference 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 the matrix F,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 the true 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. Use the empirical wavelet transform to segment the Fourier spectrum of the structural vibration, identify the modal peak position to obtain the intrinsic mode function (IMF) component, and obtain the structural single degree of freedom vibration response signal. 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 its FM components and AM components

[0134] In the formula, and They are detail coefficient and approximation coefficient respectively, and * is convolution.

[0135] S13. Further adopt the random decrement technique (DRT) to analyze the measured signal, separate the deterministic vibration signal and the stationary random signal, and obtain 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 intercept the amplitude of y(t);

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

[0138] Step 3: Superimpose and average N time series to obtain the free decay response signal of y(t)

[0139] S14. The free decay signal is processed by Hilbert Transform (HT) to obtain the amplitude curve and phase curve to identify the modal frequency and damping ratio. The steps are as follows:

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

[0141] In the formula, A 0j is the amplitude of the signal at time 0, ω j is the jth order undamped circular frequency, ξ j is the j-th order damping ratio, is the j-th order damped original frequency.

[0142] Step 2: Perform Hilbert transformation on the formula in step 1 to obtain the phase function And the amplitude function

[0143] Step 3: For the phase function θ j (t) Take the derivative to get the j-th order original frequency ω dj , considering that the damping ratio in actual engineering is usually less than 5%, the simplified formula is used to obtain the j-th 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 in the cloud for subsequent retrieval.

[0146] S2. Update the model based on the design data of the target bridge and the monitoring data of the structure to establish a digital twin model of the target bridge. The process is as follows: Figure 2 shown.

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

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

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

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

[0151] Step 3: Use the Cluster function submit() to automatically assign the calculation task of each finite element model (particle of the PSO algorithm) to each thread of the computing node and collect the calculation results;

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

[0153] Algorithm 2 Cluster computing assisted particle swarm optimization algorithm

[0154] enter:

[0155] dispy: distributed computing framework

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

[0157] f(x): objective function

[0158] pop: particle size

[0159] dim: Update parameter dimension

[0160] MaxIt: Maximum number of iterations

[0161] limit: objective function threshold

[0162] Output:

[0163] f best :Optimal objective function solution

[0164]

[0165]

[0166]

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

[0168] S24. Define the least square error between the natural frequency response of the finite element model and the measured data as the objective function, as shown in Formula 1

[0169]

[0170] Where x represents the update parameter vector; f i,exp and f i (x) are the finite element simulation results when the i-th natural frequency obtained from the measured data and the corresponding model parameter is x; n represents the number of modes considered by the objective function. Since the natural frequency of the structure can only reflect the overall characteristics of the structure, the modal assurance criterion (MAC) is used to match the modal vibration shape corresponding to the numerical simulation and measured data in the damage identification process, as shown in Formula 2:

[0171]

[0172] 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. The larger the value, the higher the modal consistency. When a measured vibration mode is not matched, a larger number is assigned to Formula 1 as the objective function value to eliminate incorrect identification results.

[0173] S25. According to formula 1 and Figure 2 As shown in the figure, x in the objective function (x) is the physical parameter of the model that needs to be updated. Usually, physical parameters such as elastic modulus, strength, boundary conditions and geometric dimensions of the material are selected to update the model, and the upper and lower limits of each parameter are defined. This example takes a large-span cable-stayed bridge as an example, and selects the elastic model of the structure, the wall thickness of the main beam, and the stiffness of the support as physical parameters.

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

[0175]

[0176]

[0177] S26. The model update process is defined in the algorithm, including: the particle size of the particle swarm algorithm (the number of physical parameters), the upper and lower limits of each particle (the upper and lower limits 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.

[0178]

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

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

[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 the damage classification status of the target bridge.

[0183] S31. Taking the bridge piers, main towers and bearings as damaged components, the graded damage threshold of the structure is determined. The 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 pier based on the digital twin model of the bridge, and carry out the pushover analysis of the piers. Select the drift rate as the engineering requirement parameter, and define the drift rate corresponding to the damage threshold of the pier based on the performance points (crack point, yield point, peak point, and limit point) on the force-displacement curve of the pier;

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

[0186] (3) When classifying the damage state of the branch 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 1 φ<0.432% 0.432%<φ<1.358% 1.358%<φ<4.321% 4.321%<φ<6.728% 6.728%<φ Pier 2 φ<0.060% 0.060%<φ<0.783% 0.783%<φ<4.578% 4.578%<φ<7.108% 7.108%<φ Pier 3 φ<0.542% 0.542%<φ<1.506% 1.506%<φ<5.361% 5.361%<φ<7.892% 7.892%<φ Pier 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 Bridge pier support Δ<0.01 0.01<Δ<0.025 0.025<Δ<0.05 0.05<Δ<0.10 0.10<Δ Main tower support Δ<0.02 0.02<Δ<0.035 0.035<Δ<0.07 0.07<Δ<0.14 0.014<Δ

[0188] S4. According to the service life and target control level of the target bridge, define the optimization objective function of the target bridge, such as formula 3.

[0189] S41. In this example, the drift rate of the bridge pier and the bending moment of the main tower section are taken as the control targets to control the damage of the bridge pier and the main tower without damaging the bearings.

[0190]

[0191] Among them, x is the optimization parameter; δ1, δ2, δn1, δn2 are the cross-sectional curvatures of the north tower and the south tower and the cross-sectional curvature indexes corresponding to the slight damage state, respectively; φ1, φ y1 ,φ2,φ y2 ,φ3,φ y3 ,φ4,φ y4 are the drift rates of the four piers and the drift rate index corresponding to the slight damage state; Δ pier and Δ tower are the maximum relative displacements of each pier / main tower and main beam (unit: m). This 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 bridge components under future earthquakes; (2) to ensure that the relative displacement of the superstructure and the substructure does not exceed the elastic displacement of the bearing to avoid bearing damage or beam falling accidents.

[0192] S42. When encountering an earthquake, the main beam will often produce a large displacement. Therefore, a damper device is usually installed at the connection between the main tower / bridge pier and the main beam to improve the seismic performance of the structure, reduce the displacement of the structure under earthquake, and ensure the safety of the structure under earthquake.

[0193] In this example, a viscous damper is used as an example, and the selected Maxwell restoring force model is shown in Formula 4.

[0194]

[0195] Where F(t) is the damping force generated by the viscous damper; C is the damping coefficient; α is the damping exponent (usually ranging from 0.1 to 2.0); u is the displacement; sgn() is the sign function.

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

[0197] S44. According to existing design specifications, when adopting the design method of time-history analysis, it is usually necessary to make the maximum response value of the bridge under three groups of seismic motions or the average response value under seven groups of seismic motions meet the established response control requirements, so as to eliminate the influence of site information and uncertainty of seismic motions on the structural response. However, this design process is relatively complicated. On the one hand, whether the selected seismic motion is appropriate has a great influence on the result of the time-history response, and the nonlinear dynamic time-history analysis of multiple seismic motion records is extremely time-consuming. On the other hand, the artificial waves generated based on the design response spectrum of the bridge can fully consider the dynamic characteristics of the large-span cable-stayed bridge and the seismic motion characteristics of the design site. Therefore, the present invention adopts a two-step method to generate artificial waves through the design response spectrum of the bridge, such as Figure 7 and 8 As shown in the figure, the seismic performance optimization of the above bridge is carried out as the design ground motion. The method first synthesizes a stationary wave, and then multiplies it by the strength envelope curve to obtain an intensity non-stationary wave. The specific steps are as follows:

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

[0199]

[0200] Among them, t1 and t2 are the first and last moments of the stable phase of the earthquake respectively; c is the attenuation factor, which controls the speed of attenuation of the descending phase; t d It indicates the total duration of an earthquake, which refers to the time from the beginning of the earthquake shaking to the time when the amplitude of the main vibration drops to about 1 / 10.

[0201] Step 2: Solve using inverse Fourier transform

[0202] in, is a random phase angle uniformly distributed in the range [0,2π], and n is the number of separation points in the frequency domain where the response spectrum or power spectrum is calculated. k is the discrete frequency, 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 response spectrum and the standard spectrum

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

[0206] Step 5: Use the wave acceleration response spectrum S a (ω k ) and the target response spectrum S T (ω k ) to compare the original power spectrum S τ (ω k ) is corrected to obtain the corrected power spectrum

[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 the iteration stops.

[0208] S45. After defining the optimization problem, the supercomputer-driven particle swarm algorithm developed based on DISPY invented in step S2 is selected to carry out the optimization of the above-mentioned bridge. The particle scale of the algorithm is 120, the maximum number of iterations is 50, and a lower threshold of the objective function (i.e., Objective Function = 0.1 in Formula 3) is set to ensure that the drift rate of all bridge piers that have been optimized for seismic performance is close to the optimal state as much as possible.

[0209] S46. Based on the above algorithm settings, a computing cluster with 7 computing nodes and 60 working threads is built, and the artificial ground motion generated by S44 is selected to carry out the viscous damper parameter optimization of the above bridge, such as Fig.10 shown.

[0210] S47. According to the design response spectrum, 7 natural earthquake motions are selected to verify the optimization results of seismic performance. The mean response of the optimized model under the 7 natural earthquake motions is calculated and compared with the optimization results. The results show that the method proposed in the present invention has a fast calculation speed, a simpler process and guarantees the optimization results.

[0211]

[0212] In summary, the invention proposes a simplified method for multi-objective optimization of seismic devices for large-span bridges that takes service performance into consideration. The method first maps the monitoring data to the initial model through nonlinear model updating to generate a digital twin model of the target bridge; on this basis, the digital twin model is used to calibrate the current performance level of the structure and the target performance level to be achieved in the future as the seismic response control target of the target bridge; finally, artificial waves are generated based on the design response spectrum of the bridge to carry out cluster computing-assisted seismic performance optimization of large-span cable-stayed bridges, and the responses of different components in the structure under earthquakes are accurately controlled. This method has high computational efficiency and a simpler optimization process.

[0213] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A digital twin-based long-span bridge seismic performance optimization and evaluation system, characterized in that: The optimization and evaluation system includes data acquisition and pre-processing module, model updating module, performance evaluation and optimization module; The data acquisition and pre-processing module is used to analyze and store the response data of the structure; The model update module is used to define the information of each supercomputing node and then build a private computing cluster; The performance optimization evaluation and optimization module defines the damage classification threshold and target damage level of the target bridge based on the digital twin model; Using the optimization and evaluation method of this module, the steps are as follows: Step 1: The data acquisition and pre-processing module collects the frequency response data of the long-span bridge under the excitation of the environment and vehicle loads, uses the Kalman filter method to reduce the noise of the frequency response data, and uses the fast Fourier transform to realize the mode and frequency identification of the structure, obtain the modal vibration shape and natural frequency of the bridge, and store them in the cloud; Step 2: The model update module establishes a three-dimensional refined numerical model based on the design data of the target bridge, extracts the bridge modal vibration shape and natural frequency data 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 the least squares error function based on the frequency modal response in step 1 to carry out nonlinear model update of the target bridge, and establishes a digital twin model of the target bridge; Step 3: The performance optimization evaluation and optimization module evaluates and optimizes the performance of the target bridge; Based on the digital twin model established in step 2, define the engineering requirement parameters of the pier components, support components, and main tower components and calibrate the graded damage performance thresholds; Determine the target damage level of the bridge according to its service life; Establish a multi-objective optimization design function based on the engineering demand parameters of the piers, main towers and bearings; Artificial earthquake motion is generated according to the design response spectrum of the target bridge, and the nonlinear time history analysis of the digital twin model is carried out to obtain the drift rate of the bridge pier, the relative displacement of the superstructure and substructure, and the cross-sectional curvature of the main tower. Based on the multi-objective optimization design function, supercomputer-driven seismic isolation device parameter optimization is carried out to output the optimal parameter combination and control the graded response of the bridge under earthquake.

2. The large-span bridge seismic performance optimization and evaluation system based on digital twin according to claim 1 is characterized in that: In step 1, the response data of the structure is collected through the structural health monitoring system, and the data is pre-processed to obtain the modal vibration response of the structure. The specific steps are as follows: S11. Use Kalman filtering method to perform data noise reduction on the modal response data of the structure extracted by the data acquisition system, and reduce the noise and data interference of the data while maintaining the original data characteristics; S12. Use the empirical wavelet transform to segment the Fourier spectrum of the structural vibration, identify the modal peak position to obtain the inherent modal function component, and obtain the structural single-degree-of-freedom vibration response signal. The operation of the empirical wavelet transform function is as follows: Step 121: Divide the Fourier spectrum into N continuous intervals Λ n L n =[ω n-1 ,oh n ],n=1,2,…,N Step 122: Construct empirical scaling function φ n (ω) Step 123: Construct the empirical wavelet function ψ n (ω) is as follows: Where β(x) = x 4 (35-84x+70x 2 -20x 3 ) Step 124: The bridge vibration signal x(t) collected by the health monitoring system is decomposed into: FM component AM Component In the formula, and They are detail coefficient and approximation coefficient respectively, * is convolution; S13. Further adopt the random reduction technology to analyze the measured bridge vibration signal, separate the deterministic vibration signal and the stable random signal, and obtain the structural free decay vibration response signal. The specific steps are as follows: Step 131: Select a fixed value A from the single-degree-of-freedom vibration response signal y(t) to intercept the amplitude of y(t); Step 132: Let the intersection point of A and the response signal y(t) be t i (i=1,2,…,N), get N segments with t i is the starting point and the time series of length s; Step 133: Perform superposition and averaging of N time series to obtain the free decay response signal of y(t): S14. The free decay signal x(t) is processed by Hilbert transform to obtain the amplitude curve and phase curve, and the modal frequency and damping ratio are identified. The steps are as follows: Step 141: Let x j (t) is a 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, ω j is the jth order undamped circular frequency, ξ j is the j-th order damping ratio, is the j-th order damped original frequency, t is the time; Step 142: Perform Hilbert transformation on the formula in step 1 to obtain the phase function: Amplitude function: Step 143: Phase function θ j (t) Take the derivative to get the j-th order original frequency ω dj , considering that the damping ratio in actual engineering is usually less than 5%, the simplified formula is used to obtain the j-th modal frequency: 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: S15. The sampled structural modal frequency and damping ratio response data are stored in the cloud for subsequent use.

3. The large-span bridge seismic performance optimization and evaluation system based on digital twin according to claim 1 is characterized in that: Step 2: Update the model based on the design data of the target bridge and the monitoring data of the structure to establish a digital twin model of the target bridge. The digital twin model develops a particle swarm algorithm suitable for cluster computing based on the computing cluster to implement the iteration process of the model's physical parameters, as follows: Step 21: Run dispynode.py on the computing server to create a computing node. Step 22. Call the JobCluster class in dispy.py to create a high-performance computing cluster Cluster; Step 23: Use the submit() function of Cluster to automatically assign the calculation task of each finite element model to each thread of the computing node and collect the calculation results; Step 24: Iterate the calculation until the optimal solution reaches the objective function or the number of iterations reaches the maximum number of iterations, and then end the model updating process.

4. The large-span bridge seismic performance optimization and evaluation system based on digital twin according to claim 1 is characterized in that: In step 2, OpenSees is selected to establish a refined finite element model of the initial state according to the design data of the target bridge; The least square error between 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: 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 corresponding finite element simulation results when the model parameter is x; n represents the number of modes considered by the objective function; The modal assurance criterion (MAC) is used to match the modal vibration shapes corresponding to the numerical simulation and measured data, as shown in the following formula: 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 a larger value indicates a higher modal consistency; When a certain measured vibration mode is not matched, a larger number is assigned to Formula 1 as the objective function value to eliminate erroneous recognition results; As shown in Formula 2, x in the objective function (x) is the physical parameter of the model that needs to be updated. The physical parameters of the model include the elastic modulus, strength, boundary conditions and geometric dimensions of the material to update the model, and define the upper and lower limits of each parameter. According to the updated physical parameter values ​​of the model, the potential damage position of the structure is mapped on the three-dimensional model using color.

5. The large-span bridge seismic performance optimization and evaluation system based on digital twin according to claim 1 is characterized in that: According to the service life and target control level of the target bridge, the optimization objective function of the target bridge is defined as follows: Among them, x is the optimization parameter; δ1, δ2, δn1, δn2 are the cross-sectional curvatures of the north tower and the south tower and the cross-sectional curvature indexes corresponding to the slight damage state, respectively; φ1, φ y1 ,φ2,φ y2 ,φ3,φ y3 ,φ4,φ y4 are the drift rates of the four piers and the drift rate index corresponding to the slight damage state; Δ pier and Δ tower are the maximum relative displacements of each pier / main tower and main beam (unit: m); The Maxwell restoring force model selected for the viscous damper is shown as follows: Where F(t) is the damping force generated by the viscous damper; C is the damping coefficient; α is the damping index (the value range is generally 0.1 to 2.0); u is the displacement; sgn() is the sign function; The damping coefficient C and damping exponent α of the viscous damper are selected as optimization parameters. The artificial wave is generated by synthesizing the stationary wave and the intensity envelope curve to obtain the intensity non-stationary wave response spectrum. The specific steps are as follows: The product of the acceleration time history a(t) and the intensity envelope function f(t) of the stationary random process is calculated by the following formula; Among them, t1 and t2 are the first and last moments of the stable phase of the earthquake respectively; c is the attenuation factor, which controls the speed of attenuation of the descending phase; t d It indicates the total duration of an earthquake, which refers to the time from the beginning of the earthquake shaking to the time when it drops to about 1 / 10 of the main shaking amplitude; Solve using inverse Fourier transform: in, is a random phase angle uniformly distributed in the range [0,2π], and n is the number of separation points in the frequency domain where the response spectrum or power spectrum is calculated. k is the discrete frequency, ω k The Fourier amplitude spectrum of the corresponding seismic wave; 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 ),but: C k =[4S τ (oh k )·See] 1 / 2 The approximate relationship between the response spectrum and the standard spectrum is expressed as follows: Where S(T) is the response spectrum value; ξ is the damping ratio; P is the exceedance probability, which is 0.5; t d is the duration of the earthquake, which is 20s-30s; T is the period; The acceleration response spectrum S of the wave is adopted a (ω k ) and the target response spectrum S T (ω k ) to compare the original power spectrum S τ (ω k ) is corrected to obtain the corrected power spectrum: 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 the iteration stops.

6. The long-span bridge seismic performance optimization and evaluation system based on digital twin according to claim 2 or 5, characterized in that: The particle swarm algorithm driven by the dispy supercomputer is used to optimize the bridge. The particle size of the algorithm is 120, the maximum number of iterations is 50, and a lower threshold of the objective function is set. The Objective Function in the above formula 3 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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