Bayesian prediction of bridge extreme stresses based on DLTM and monitoring coupled data

Abstract

For predicting dynamic coupled extreme stresses of bridges with monitoring coupled data, this article considers monitoring extreme stress data as a time series, and takes into account its coupling generated by the fusion of non-stationarity and randomness. First, the local polynomial theory is introduced, and the local polynomial order of monitoring coupled extreme stress data is estimated with time-series analysis method. Second, based on time-series analysis results, dynamic linear trend models (DLTM) and the corresponding Bayesian probability recursive processes are given to predict dynamic coupled extreme stresses. Finally, through the illustration of monitoring coupled extreme stress data from an actual bridge, the proposed method, which is compared with the traditional Bayesian dynamic linear models, is proved to be more effective for predicting dynamic coupled extreme stresses of bridges.

Incorporation of Structural Health Monitoring Coupled Data in Dynamic Extreme Stress Prediction of Steel Bridges Using Dynamic Coupled Linear Models

“…It is supposed that there is a general dynamic coupled time series set D t with (n − 1)-order local trends, which includes the data at and before time t. e state set, also taken as a coupled time series approximately obtained with cubical smoothing algorithm with five-point approximation [1,2,17] through resampling D t , is denoted with D θ t , where θ t is the state at time t, D θ t includes all the state data at and before time t, and the i th difference data set of D θ t is D θ t,i . In general, for the general coupled time series set D t with (n − 1)-order local trends, difference can be carried out until the time series after difference is stationary, and the number (n − 1) of difference is the order of local trends.…”

“…According to the research studies in [1,[34][35][36], model monitoring is achieved through Bayesian factors under the normal assumption. e main idea is firstly to build an alternative model and then to combine an existing probability model for constructing the formula of Bayesian factors.…”

“…, y t−N+1 . In this paper, according to the engineering experience, the adopted monitoring criterion [1,[34][35][36] is as follows: if k � 3 and B (t) < 0.15, then the corresponding monitoring data is abnormal, which needs to be removed; otherwise, the monitoring data is normal.…”

“…During long-term service periods, many steel bridges are subjected to many random dynamic loads like vehicle load, temperature load, and wind load; even these loads occur simultaneously. erefore, the accumulated extreme stress data by structural health monitoring (SHM) system commonly has the characteristic of coupling including randomness, dynamicity, and tendency [1]; furthermore, based on the monitoring coupled extreme stress data which is considered as Markov chains, dynamic coupled extreme stress prediction for steel bridges is particularly important as bridges age, which could reflect bridge safety and help to guide the important decisions regarding the structural preventive maintenance.…”

A dynamic harmonic regression approach for bridge structural health monitoring

“…Oscillating functions describing the diurnal and seasonal trends can be included as additional regression components in modelling including sinusoidal functions 37–39 and Fourier series of sine / cosine terms. 29,40,41 Autoregressive moving average (ARMA) class of models are well known in SHM 11,42 and have been used to model stress 26 and strain data. 11 An AR component can also be included within a Bayesian dynamic linear model (BDLM) framework.…”