Processing And Modeling Methods For Spatial Monitoring Data Of Loads And Responses Of Long-span Bridges

Structural health monitoring(SHM)has arisen as an important tool for managing,maintaining and even designing civil infrastructure.Long-term online monitoring produces huge amounts of data;data processing,information interpretation and knowledge discovery are becoming new challenges in SHM.The monitoring system of a long-span bridge usually consists of a large number of sensors.Monitoring data collected by such a multi-sensor system contains important information of load distributions;identifying the spatial distribution of loads as well as establishing joint probabilistic models for characterizing corresponding spatial distribution patterns are important subjects in SHM.Additionally,rich spatial interrelationships(e.g.,spatial correlation,spatial mapping,etc.)of structural behaviors and structural responses are hidden in the monitoring data collected by a multi-sensor system;uncovering and modeling spatial interrelationships of monitoring data is not only beneficial to better understand the physical essence of monitoring data,but also has a great potential for practical applications.Therefore,this paper presents approaches for processing and modeling the spatial monitoring data of loads and responses of long-span bridges.Main contents involved in this study are as follows:This paper presents a computer vision-based approach for identifying the spatio-temporal distribution of vehicle loads on long-span bridges by fusing the monitoring data collected by the weight-in-motion(WIM)system.Firstly,background subtraction and image denoising methods are employed to detect moving vehicles in the surveillance video at the WIM,and a sub-image is captured from every detected vehicle;meanwhile,the weight information of the captured vehicle is extracted from the monitoring data of the WIM based on the relationship of pass time.To obtain the spatio-temporal coordinates of the moving load,the subimage recognition and particle filter algorithm are,respectively,employed to identify and track the captured vehicle from a series of videos covering the entire bridge.Finally,monitoring data collected by surveillance cameras and WIM of a real long-span bridge are used to identify the spatio-temporal distribution of vehicle loads on this bridge.This paper presents an approach for modeling the spatial distribution of heavy vehicle loads on long-span bridges.The spatial distribution modeling for heavy vehicle loads is divided into the location modeling and gross weight modeling,and addressed separately.The undirected graphical model is employed to model the location distribution of heavy vehicles on the bridge deck,and a model updating method is also proposed based on the Bayesian theory.The gross weights of heavy vehicles are represented by additional random variables of the undirected graphical model,two distribution models are presented for gross weights in the case of ignoring correlation or considering correlation.Finally,the spatial distribution model of heavy vehicles on a real long-span bridge is established using the spatial distribution samples identified above,and the effectiveness of model is also verified.Taking missing information restoration for probability distributions in SHM as application background,this paper presents the prediction approach for probability distributions of monitoring data by harnessing the correlation of distributions between measurement points.To overcome the limitation of the traditional kernel distribution-to-distribution regression method in extrapolation prediction,a new distribution-to-distribution regression method is proposed for predicting probability distributions of monitoring data based on the warping transformation of distributions.In the proposed method,the warping function is employed to characterize the shape mapping relationship between two probability density functions of monitoring data from different measurement points,thus the original distribution prediction problem is transformed to the warping function prediction problem.Based on the functional kernel regression method,a nonparametric regression model is developed to predict the the warping function(i.e.,the mapping relationship of probability density functions)from the input distribution to the target distribution,then the target distribution can be predicted by performing a warping transformation to the input distribution using the predicted warping function.Distribution prediction tests using strain monitoring data from a real bridge are conducted,corresponding results are comparied with the traditional method.Due to the constraints on probability density functions and warping functions,regression functions in both the traditional kernel distribution-to-distribution regression method and the aforementioned warping-transformation-based method are estimated by the Nadaraya-Watson estimator(a local linear smoothing technique)with relatively low precision.To improve the accuracy,another new distribution-to-distribution regression method is proposed for predicting probability distributions of monitoring data based on theories of log-quantile-density(LQD)transformation and reproducing kernel Hilbert space(RKHS).The LQD transformation is employed to transform probability density functions to ordinary functions(named as representation functions)residing in a Hilbert space,thus the original distribution prediction problem is transformed to the representation function prediction problem.A RKHS-based nonparametric regression model is developed for predicting representation functions,then the target distribution can be predicted by mapping the predicted representation function back to the space of probability density functions using the inverse LQD transformation.Corresponding measures are also taken for,respectively,reducing errors caused by the numerical integration in the inverse LQD transformation and improving the scalability of the regression model.Distribution prediction tests using strain monitoring data from a real bridge are conducted,corresponding results are comparied with the traditional method and the aforementioned warping transformation-based method.This paper presents a refined spatial interrelationship modeling approach for strain monitoring data of bridges.Temperature-induced strains or vehicle-induced local strains are treated as functional data(i.e.,continuous curves),the warping function is employed to characterize the nonlinear phase between curves of strain responses,and the mapping model of strains between measurement points is established based on the phase-amplitude separation method.The stochastic excitation-induced strains are described by random variables,nonparametric copulas are employed to flexibly characterize complex dependence structures and construct joint distributions of stochastic strains between two measurement points.Combined with ordinary functional regression methods and the new proposed distribution-to-distribution regression methods,applications in missing data restoration are further discussed,and the effectiveness is validated through application to field monitoring data.