Early-warning Methods For Long-span Bridges Based On Monitoring Data Correlation Modelling

The safe operation of Long-span bridges has always been a concern in bridge engineering field.In recent years,many long-span bridges were equipped with structural health monitoring systems,to monitor environment or operational loads and structural responses in real-time.It is of great significance to ensure the safe operation of long-span bridges through monitoring data analysis based early-warning.This paper carrys out the study on early-warning methods for long-span bridges based on monitoring data correlation modelling,which includes the early-warning of bridge monitoring data anomaly and the early-warning of bridge structural performance.The research contents are as follows:(1)There exist high correlations between monitoring data at each measuring point of the bridge structure,namely spatial correlation,which can be modeled by principal component analysis(PCA).However,the traditional PCA is not sensitive to the anomaly,the reason is that the difference of anomaly sensitivities of principal directions are not considered.Therefore,this paper proposes a method to quantify the anomaly sensitivity of principal direction.The PCA based Hotelling's T2 statistic is expressed to its generalized form.After that,a sensitive factor is deduced theoretically to quantify the sensitivity,of each principal direction in PCA model,corresponding to the anomaly occurred in a certain measurement variable.According to the difference of the sensitive factor,the principal directions are determined with different weighting coefficients to calculate a weighted statistic,which has enhanced early-warning ability to this measurement variable.Furthermore,Bayesian inference is used to integrate all weighted statistics for the early-warning of the occasional anomaly.In addition,contribution analysis is used to define an isolation index to identify the abnormal measurement variable.(2)The traditional PCA can only be used to establish spatial correlation model.However,when continuous anomaly occurred in bridge monitoring data,the temporal-spatial correlation can be used to improve early-warning ability.Therefore,a novel spatial-temporal correlation modeling method is proposed,which establishes a canonical correlation analysis(CCA)model for the current and past measurement data.Based on that,a canonical correlation generator is defined,and it is divided into two parts,i.e.,the system-related part and the system-unrelated part,by judging whether the corresponding canonical correlation coefficient is eaqual to zero.Furthermore,two statistics are defined to achieve the early-warning of the continuous anomaly.In addition,contribution analysis is used to define isolation indices to identify the abnormal measurement variable.(3)The displacement of bridge expansion joints is mainly influenced by the temperature variations.The key procedure for modelling the relationship between main girder temperature field and expansion joint displacement is the accurate characterization of the main girder temperature field.However,the correlation between temperatures and expansion joint displacements is not considered by the traditional characterization method of main girder temperature field.This leads to the unsatisfactory modeling of the temperature-displacement relationship.Therefore,a new method to characterize the temperature field of main girder is proposed based on CCA.Different from traditional representative temperatures,e.g.,the effective temperature,mean temperature and principal components of temperatures,it can determine a series of optimal combination coefficients,such that the correlation between the linear combination of temperature field measurements and the displacements of expansion joints is maximized.The obtained representative temperature is then defined as canonically correlated temperature,it is used for accurately modeling the temperature-displacement relationship.Furthermore,the model error is used as a performance index,and the reliable early-warning of expansion joint performance is realized through control chart.In addition,a control limit determination method based on kernel density estimation is also developed,which solves the problem that practical monitoring data donnot always obey Gaussian distributions.(4)The strain response can reflect the service performance of the main girder,but it is affected by the time-varying loads.The strain anomaly caused by early performance degradation will be easily covered by the time-varying effects.Therefore,a method to eliminate time-varying effects in main girder strains is proposed,based on that a performance index is deduced.The canonically correlated temperatures are used to establish an accurate temperature-strain relationship model of the main girder,which can eliminate the temperature effect.The PCA is then used to model the main girder strain after eliminating temperature effect.The principal subspace is defined to reconstruct wind and vehicle load effects,whereas the error subspace is defined to compute the reconstruction error.Furthermore,the early-warning model of the main girder performance is described as a hypothesis test problem in the error subspace,a performance index is derived by solving this problem.In addition,kernel density estimation is used to determine the control limit,as well as contribution analysis is used to define an isolation index to identify the abnormal variable.