Bridge finite element model updating method based on random vehicle-induced response monitoring

Abstract

A bridge finite element model correction method based on random vehicle-induced response monitoring, the steps are as follows: obtaining random vehicle-induced response from finite element; extracting random vehicle-induced response from actual monitoring response data; finite element model correction based on random vehicle-induced response. The method takes the random vehicle flow load with known probability characteristics as the known static load, and can well realize the finite element model correction based on static response monitoring data by reducing the error of the actual response probability characteristics and the finite element predicted response probability characteristics, avoiding the inconvenience and cost brought by the bridge load test. The loading mode of the random vehicle flow affecting the surface loading based on the finite element can improve the efficiency of the bridge finite element model correction based on the random vehicle flow and the statistical characteristics of the static response monitoring data. The application can be applied to any bridge capable of obtaining long-term random vehicle flow and response monitoring data, and has high universality.

Description

Technical Field

[0001] This invention belongs to the field of bridge structural health monitoring, specifically involving a method for correcting a bridge finite element model based on random vehicle-induced response monitoring. Background Technology

[0002] Long-span bridges, as a crucial component of transportation systems, are exposed to diverse environments and loads during operation. Extreme load conditions, material degradation, and vehicle overloading can all lead to structural damage, impacting bridge operational safety. The finite element model (FEM) is a powerful numerical analysis tool for predicting the static and dynamic performance of bridges and assessing their condition. However, the initial FEM model established based on design documents often fails to accurately describe the physical structure due to simplifications and errors during the modeling process, as well as uncertainties in structural parameters. To effectively evaluate bridge performance and safety, FEM model correction is necessary. This involves adjusting structural design parameters to reduce the discrepancy between FEM predictions and experimental measurements.

[0003] Currently, existing methods mainly include model correction based on static response and model correction based on dynamic response. Static testing and data processing are less complex, and static measurements generally offer higher accuracy than dynamic measurements. Therefore, finite element model correction techniques based on static characteristics are more reliable and practical for evaluating the mechanical state of long-span bridges. For example, patents with publication numbers CN107844669A and CN106706239A obtain static responses through load tests to correct the finite element model. However, static-based model correction requires known static loads and corresponding static responses, which may lead to long-term traffic disruptions. For long-span bridges, bridge closure load tests are too costly, and frequent testing may be unaffordable for owners. Furthermore, in recent years, public expectations for transportation projects have increased, and it is now generally believed that collecting data from infrastructure systems minimizes disruption to daily use.

[0004] To address this, the present invention proposes a bridge finite element model correction method based on random vehicle response monitoring. Based on the statistical characteristics of long-term monitoring of random traffic flow and static response, the random traffic load with certain statistical characteristics is used as a known static load. The model is corrected by reducing the error between the statistical characteristics of the predicted response and the actual response, thus avoiding the significant cost of traffic disruption during bridge closure load tests. Summary of the Invention

[0005] The purpose of this invention is to provide a method for correcting the finite element model of a bridge based on random vehicle-induced response monitoring.

[0006] The technical solution of the present invention:

[0007] A method for correcting a bridge finite element model based on random vehicle-induced response monitoring, comprising the following steps:

[0008] Step 1. Obtain the random vehicle-induced response from the finite element method.

[0009] (1.1) Obtain random traffic loading information based on WIM monitoring data from the dynamic weighing system.

[0010] Based on the vehicle weight, speed, lane, and arrival time of the WIM random traffic flow, the probabilistic statistical characteristics of vehicle weight, speed, and spacing of the random traffic flow are obtained. Monte Carlo sampling is used to simulate the actual random traffic flow. The loading information of the random traffic flow includes the longitudinal driving position, lateral driving position, and load size of the vehicles. The longitudinal driving position of the vehicles is determined by the speed and spacing of the random traffic flow, the lateral driving position is determined by the lane information of the random traffic flow, and the load size is determined by the vehicle weight of the random traffic flow.

[0011] (1.2) Finite element influence surface extraction and random vehicle-induced response acquisition

[0012] Finite element model correction requires repeated iterative loading. During the correction process, unit force is iteratively applied in the finite element model to extract the finite element influence surface. Random traffic flow is then applied to the finite element influence surface to obtain the finite element predicted quasi-static random vehicle-induced response. The loading time step of the random traffic flow is consistent with the sampling frequency of the actual response monitoring data.

[0013] Step 2. Extract random vehicle-induced responses from actual monitoring response data.

[0014] The load responses actually monitored by the Structural Health Monitoring (SHM) system include vehicle-induced responses and static load responses caused by temperature effects. Therefore, it is necessary to process the actual monitored static load response data to extract the quasi-static vehicle-induced response. The steps are as follows:

[0015] (2.1) Perform preliminary cleaning on the original load response data to remove outliers; use the moving window method to calculate the load response corresponding to the maximum probability density of the load response every 10 minutes as the static load response caused by temperature effects, etc. during that period.

[0016] (2.2) Subtract the time-varying trend term of the static load response extracted in step (2.1) from the actual monitored load response to obtain the random vehicle-induced response;

[0017] (2.3) Noise and dynamic effects are removed by low-pass filtering to obtain the actual monitored quasi-static random vehicle-induced response;

[0018] Step 3. Finite element model correction based on stochastic vehicle-induced response

[0019] (3.1) Establishing a modified finite element objective function based on the characteristics of random vehicle-induced response

[0020] Steps 1 and 2 yield the finite element-predicted quasi-static random vehicle-induced response and the actual monitored quasi-static random vehicle-induced response, respectively. The probability distribution conforming to the long-term random vehicle-induced response is well fitted by a Gaussian mixture model. The fitting parameters for the random vehicle-induced response include the number of Gaussian distributions, their weights, mean, and standard deviation. The expression for the probability model of the random vehicle-induced response synthesized from M Gaussian distributions is as follows:

[0021]

[0022] In the formula, x represents long-term random vehicle-induced response data. Let w represent the probability density function of the i-th Gaussian distribution of the random vehicle-induced response. i μ represents the weight of the i-th Gaussian distribution of the random vehicle-induced response. i and σ i Let represent the mean and standard deviation of the i-th Gaussian distribution corresponding to the random vehicle-induced response, respectively;

[0023] The objective function F, based on the probabilistic characteristics of random vehicle-induced responses, is expressed as the error between the measured response and the predicted response probability model parameters at each measurement point, as follows:

[0024]

[0025] Where J represents the total number of actual monitored load response measurement points. and These represent the weights of the i-th Gaussian distribution in the probability model of the random vehicle-induced response at the j-th measuring point, based on the actual monitoring and finite element prediction methods. and Let be the mean of the i-th Gaussian distribution of the random vehicle-induced response probability model of the actual monitoring and finite element prediction at the j-th measuring point, respectively. and These are the standard deviations of the i-th Gaussian distributions in the actual monitoring and finite element prediction probabilistic models of the random vehicle-induced response at the j-th measuring point, respectively.

[0026] (3.2) Implementation of Model Correction Based on Stochastic Vehicle Response

[0027] By using engineering experience and sensitivity analysis methods, model correction parameters with higher sensitivity that may have finite element modeling errors are selected; based on the objective function established in step (3.1), the selected model parameters are updated by optimization algorithm so that the objective function based on the probability characteristics of random vehicle response reaches the minimum value, thereby realizing the correction of the finite element model.

[0028] The beneficial effects of this invention are:

[0029] 1. This invention uses random traffic loads with known probability characteristics as known static loads. By reducing the error between the actual response probability characteristics and the finite element predicted response probability characteristics, it can effectively achieve finite element model correction based on static response monitoring data, avoiding the inconvenience and cost of bridge closure load tests.

[0030] 2. The loading method of loading random traffic flow based on the influence surface extracted by finite element method of the present invention can effectively solve the problem that loading a random traffic flow for a long period of time in finite element method can take a lot of time, resulting in excessive optimization time and low efficiency. It improves the efficiency of bridge finite element model correction based on the statistical characteristics of random traffic flow and static response monitoring data.

[0031] 3. The method of taking the maximum response probability through the sliding response interval of the present invention can effectively eliminate the influence of environmental factors such as temperature effect in the monitoring response, obtain a more accurate static vehicle-induced response, and improve the accuracy of the bridge finite element model correction method based on random vehicle-induced response monitoring.

[0032] 4. The bridge finite element model correction method based on random vehicle response monitoring data of the present invention can be applied to any bridge that can obtain long-term random traffic flow and response monitoring data, and has high universality. Attached Figure Description

[0033] Figure 1 This is a flowchart of the present invention;

[0034] Figure 2 The actual vehicle-induced response and the original finite element predicted vehicle-induced response obtained by implementing the method of the present invention;

[0035] Figure 3 The results of sensitivity analysis are for the method of this invention;

[0036] Figure 4 Comparison of finite element model correction results implemented using the method of this invention;

[0037] Figure 5 The influence lines extracted by the modified finite element method of the present invention are compared with the identification results of the load test. Detailed Implementation

[0038] The invention will now be described in further detail with reference to the accompanying drawings and a numerical example.

[0039] A method for correcting a bridge finite element model based on random vehicle-induced response monitoring, comprising the following steps:

[0040] Step 1. Use influence surface loading to obtain finite element vehicle-induced response from long-term random traffic flow.

[0041] (1.1) Obtain the random traffic flow loading information matrix based on the monitoring data of the dynamic weighing system (WIM).

[0042] Loading random traffic flow in the finite element method requires only vehicle position and load information. Based on long-term WIM random traffic flow monitoring data on vehicle weight, speed, lane, and arrival time, the probabilistic statistical characteristics of vehicle weight, speed, and spacing can be obtained to simulate actual random traffic flow. The vehicle information matrix L of the random traffic flow includes the vehicle lateral movement position matrix L... X Vehicle longitudinal position matrix L Y Vehicle load size matrix L P The lateral driving position is determined by vehicle speed and arrival time, the longitudinal driving position is determined by lane information, and the load is represented by vehicle weight. The matrix representation is as follows:

[0043]

[0044]

[0045]

[0046] Where T represents T equally spaced moments within a certain time period, and N max Let K be the maximum number of vehicles running on the bridge at a certain moment, and K be the total number of vehicles crossing the bridge during this period.

[0047] (1.2) Finite element influence surface extraction and loading process

[0048] Finite element model (FEM) corrections require repeated loading iterations, while long-term random traffic flow loads involve numerous steps. Loading a prolonged period of random traffic flow into the FEM model is time-consuming, leading to excessively long optimization times and low efficiency. Therefore, during the optimization process, iteratively loading unit forces into the FEM model, extracting the FEM influence surface, and then loading random traffic flow onto this surface can significantly improve the loading and optimization speed.

[0049] The response equation for the random traffic flow loaded on the influence surface is:

[0050] R=LΦ

[0051] Where R is the response vector, L is the vehicle information matrix L={L X ,L Y ,L P}, where Φ is the influence surface vector.

[0052] Step 2. Vehicle-induced response extracted from monitoring response data

[0053] Loading random traffic flow into the finite element method yields a quasi-static vehicle-induced response. However, the actual load response monitored by the structural health monitoring (SHM) system includes both vehicle-induced response and static load response caused by environmental factors such as temperature effects. Therefore, it is necessary to process the monitored response data to extract the quasi-static vehicle-induced response. The steps are as follows:

[0054] (2.1) Perform preliminary cleaning on the original response monitoring data to remove outliers; use the moving window method to calculate the response corresponding to the maximum probability density of the response every 10 minutes as the static load response caused by environmental factors such as temperature effect during that period.

[0055] (2.2) Subtract the time-varying trend term of the static load response extracted in step (2.1) from the actual monitored load response to obtain the vehicle-induced response;

[0056] (2.3) Noise and dynamic effects are removed by low-pass filtering to obtain the quasi-static vehicle response.

[0057] Step 3. Establish an objective function based on the vehicle-induced response probability characteristics.

[0058] Gaussian mixture models have the advantage of fitting arbitrary probability distributions well, and are therefore used to establish probabilistic models for long-term static response monitoring data, describing the statistical characteristics of the response. A Gaussian mixture model is synthesized by combining M Gaussian distributions, and its expression is as follows:

[0059]

[0060] In the formula, Let w represent the probability density function of the i-th Gaussian distribution. i μ represents the weight of the i-th Gaussian distribution. i and Let represent the mean and variance of the response data corresponding to the i-th Gaussian distribution, respectively.

[0061] The expression for the objective function F based on the response probability characteristics is as follows:

[0062]

[0063] Where J represents the total number of actual monitoring load response measurement points used in the model correction. and , where are the i-th Gaussian distribution weights of the monitored response and the finite element predicted response at the j-th measuring point, respectively; and These are the mean values ​​of the i-th Gaussian distributions of the monitored response and the finite element predicted response at the j-th measuring point, respectively. and Let be the variances of the i-th Gaussian distributions of the monitored response and the finite element predicted response at the j-th measurement point, respectively.

[0064] Step 4. Finite element model correction based on optimization algorithm

[0065] (4.1) Selection of correction parameters for finite element model

[0066] The model correction parameters are selected using a combination of empirical and average sensitivity methods. The relative local sensitivity of the i-th model parameter at the j-th sample point is defined as follows:

[0067]

[0068] Where, x j Let be the structural parameters of the j-th sample point; Δ is a small perturbation, which can be set to 0.1%.

[0069] The average sensitivity of the i-th parameter is defined as:

[0070]

[0071] Where, n s The total number of sample points selected in the i-th parameter.

[0072] (4.2) Implementation of Finite Element Model Correction Based on Optimization Algorithm

[0073] Based on the objective function established in step 3, and using the measured and finite element model prediction data obtained in steps 1 and 2, the selected model parameters are corrected through an optimization algorithm to minimize the objective function based on response probability characteristics, thereby achieving finite element model correction. An optimization algorithm combining particle swarm optimization (PSO) and pattern search is used. First, a global search is performed using PSO to obtain an approximate optimal solution for the optimization parameters. Then, using the results obtained from PSO as initial values, pattern search is used for further local optimization, which can improve search efficiency and increase the probability of finding the global optimum.

[0074] In this specific numerical example, actual monitoring data of a long-span suspension bridge is used to correct the finite element model based on static response monitoring data, and the correction results are compared with the influence line identification results from load tests. Deflection monitoring data for 6 consecutive days at 1 / 4, 1 / 2, and 3 / 4 of the main girder are selected, with a sampling frequency of 1Hz.

[0075] First, the quasi-static vehicle-induced response is extracted from the measured response data. Following the process described in step 2, the response corresponding to the maximum response probability density is calculated in 10-minute windows as the static load response caused by environmental factors such as temperature effects during that period. Then, the extracted time-varying trend term of the static load response is subtracted from the measured response to obtain the vehicle-induced response. The time history of the measured quasi-static vehicle-induced response at 1 / 4 of the main beam is shown below. Figure 2 As shown.

[0076] Secondly, by loading random traffic flow with the same statistical characteristics as reality into the finite element method (FEM), and by extracting the influence surface in the FEM, the loading efficiency is greatly improved; loading 6 days of random traffic flow only takes 1 second. The finite element method predicts the vehicle-induced response time history as follows: Figure 2 As shown, the predicted response has the same trend as the actual response, both reflecting the change in vehicle-induced response with the density of traffic flow.

[0077] Next, the correction parameters for the finite element model are selected. Using the method described in step (3.2), sensitivity analysis is performed on eight parameters: the elastic modulus of the main cable, the elastic modulus of the main tower, the elastic modulus of the main beam, the density of the main beam, the initial strain of the main cable, the initial strain of the suspender, the translational spring stiffness, and the rotational spring stiffness. The analysis results are as follows: Figure 3 As shown. The main cable elastic modulus, main beam density, translational spring stiffness, and rotational spring stiffness are highly sensitive parameters, and these four parameters are used as correction parameters.

[0078] Finally, the finite element model based on stochastic vehicle-induced response is corrected. In this implementation, the corrected model results are as follows: Figure 4 As shown, the corrected finite element response probability model basically matches the probability model of the monitored response. Deflection influence lines are extracted from the corrected finite element model, and compared with the influence lines identified in the load test. Figure 5 As shown, the correction result is basically consistent with the identification result, which verifies the effectiveness of the bridge finite element model correction method based on random vehicle response monitoring of the present invention.

Claims

1. A method for correcting a bridge finite element model based on random vehicle-induced response monitoring, characterized by the following steps: Step 1. Obtain the random vehicle-induced response from the finite element method. (1.1) Obtain random vehicle loading information based on monitoring data from the WIM dynamic weighing system. Based on the vehicle weight, speed, lane, and arrival time of the WIM random traffic flow, the probabilistic statistical characteristics of vehicle weight, speed, and spacing of the random traffic flow are obtained. Monte Carlo sampling is used to simulate the actual random traffic flow. The loading information of the random traffic flow includes the longitudinal driving position, lateral driving position, and load size of the vehicles. The longitudinal driving position of the vehicles is determined by the speed and spacing of the random traffic flow, the lateral driving position is determined by the lane information of the random traffic flow, and the load size is determined by the vehicle weight of the random traffic flow. (1.2) Finite element influence surface extraction and random vehicle-induced response acquisition Finite element model correction requires repeated iterative loading. During the correction process, unit force is iteratively applied in the finite element model to extract the finite element influence surface. Random traffic flow is then applied to the finite element influence surface to obtain the finite element predicted quasi-static random vehicle-induced response. The loading time step of the random traffic flow is consistent with the sampling frequency of the actual response monitoring data. Step 2. Extract random vehicle-induced responses from actual monitoring response data. The load responses actually monitored by the Structural Health Monitoring (SHM) system include vehicle-induced responses and static load responses caused by temperature effects. Therefore, it is necessary to process the actual monitored static load response data to extract the quasi-static vehicle-induced response. The steps are as follows: (2.1) Perform preliminary cleaning on the original load response data to remove outliers; use the moving window method to calculate the load response corresponding to the maximum probability density of the load response every 10 minutes as the static load response caused by the temperature effect during that period. (2.2) Subtract the static load response time-varying trend term extracted in step (2.1) from the actual monitored load response to obtain the random vehicle-induced response; (2.3) Noise and dynamic effects are removed by low-pass filtering to obtain the actual monitored quasi-static random vehicle-induced response; Step 3. Finite element model correction based on stochastic vehicle-induced response (3.1) Establishing a modified finite element objective function based on the characteristics of random vehicle-induced response Steps 1 and 2 yield the finite element-predicted quasi-static random vehicle-induced response and the actual monitored quasi-static random vehicle-induced response, respectively. The probability distribution conforming to the long-term random vehicle-induced response is well fitted by a Gaussian mixture model. The fitting parameters for the random vehicle-induced response include the number of Gaussian distributions, their weights, mean, and standard deviation. The expression for the probability model of the random vehicle-induced response synthesized from M Gaussian distributions is as follows: In the formula, x represents long-term random vehicle-induced response data. Let w represent the probability density function of the i-th Gaussian distribution of the random vehicle-induced response. i μ represents the weight of the i-th Gaussian distribution of the random vehicle-induced response. i and σ i Let represent the mean and standard deviation of the i-th Gaussian distribution corresponding to the random vehicle-induced response, respectively; The objective function F, based on the probabilistic characteristics of random vehicle-induced responses, is expressed as the error between the measured response and the predicted response probability model parameters at each measurement point, as follows: in, J represents the total number of actual monitoring load response measurement points. and These represent the weights of the i-th Gaussian distribution in the probability model of the random vehicle-induced response at the j-th measuring point, based on the actual monitoring and finite element prediction methods. and Let be the mean of the i-th Gaussian distribution of the random vehicle-induced response probability model of the actual monitoring and finite element prediction at the j-th measuring point, respectively. and These are the standard deviations of the i-th Gaussian distributions in the actual monitoring and finite element prediction probabilistic models of the random vehicle-induced response at the j-th measuring point, respectively. (3.2) Implementation of Model Correction Based on Stochastic Vehicle Response By using engineering experience and sensitivity analysis methods, model correction parameters with higher sensitivity that may have finite element modeling errors are selected; based on the objective function established in step (3.1), the selected model parameters are updated by optimization algorithm so that the objective function based on the probability characteristics of random vehicle response reaches the minimum value, thereby realizing the correction of the finite element model.

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