Modeling relationships for field strain data under thermal effects using functional data analysis

Abstract In the field of bridge health monitoring, it is ubiquitous to model the relationship for monitoring data. However, in many cases, especially for concrete bridge structures, field response data collected from sensors, such as strains and deflections, present hysteresis phenomena due to the cyclic temperature variation. Such phenomena refer to the time-lag effect of the structure and impede the following correlation analysis because it will weaken the linearity among strains. In conventional methods, correlation analysis will be conducted after eliminating time-lag effect by using averaging method or simple phase shifting. In this paper, correlations between temperature-induced strain responses are investigated after the time-lag effect is accurately quantified by nonlinear phase shifting. In order to capture the features of nonlinear phase variation between responses, a novel approach, named functional data analysis (FDA), is then proposed. Phase component is extracted through warping functions in square-root slope framework (SRSF) under Bayesian inference, in which the warping functions reveal the time delay effect between quasi-static strain data. The deformation pattern of warping function is further studied through functional principal component analysis (FPCA) in tangent space. After the phase difference is eliminated by the warping function, inter-relationship between strain data exhibits highly strong linearity instead of original hysteresis loop. To seek the underlying features of time-lag effect, hundreds of pairs of daily field measurement acquired from different locations on a long-span bridge have been analyzed to disclose statistical regularities. It is found that after the application of warping function, the time-lag effect has been remarkably eliminated and strong linearity of the responses emerges.