  Modern-day civil, mechanical, and aeronautical structures are transitioning
towards a continuous, online, and automated maintenance paradigm in order to
ensure increased safety and reliability. The field of structural health
monitoring (SHM) is playing a key role in this respect and active sensing
acousto-ultrasound guided-wave based SHM techniques have shown great promise
due to their potential sensitivity to small changes in the structure. However,
the methods' robustness and diagnosis capability become limited in the presence
of environmental and operational variability such as changing temperature. In
order to circumvent this difficulty, in this paper, a novel stochastic time
series-based framework was adopted to model guided wave propagation under
varying temperatures. Different stochastic time-varying time series models,
such as Recursive Maximum Likelihood Time-varying Auto-Regressive (RML-TAR) and
Recursive Maximum Likelihood Time-varying Auto-Regressive with Exogenous
Excitation (RML-TARX) models are put forward to model and capture the
underlying dynamics of guided wave propagation under varying temperatures. The
steps and facets of the identification procedure are presented and clearly
explained. Then the identified models are used to perform one-step-ahead
prediction as well as "simulation" of the guided wave signals. In order to gain
insight from a physics perspective, high-fidelity finite element (FE) models
were also established to model the effect of temperature variation on guided
wave propagation. Finally, surrogate models are formulated through the use of
stochastic time-dependent RML-TARX models and compared with the FE models under
varying temperatures.
