Comparison of scale factor estimators for ultrasonic temperature monitoring: Application to structural health monitoring

In Structural Health Monitoring (SHM) of materials, estimating the effects of environmental and operational conditions such as temperature is important. Indeed, temperature changes induce modifications of the mechanical properties of the material and therefore cause a dilation of the acoustic signals characterized by a scale factor. This paper described four scale factor estimators able to monitor changes in temperature: The short-time cross-correlation (STXC) method, the stretching method (STRE), the Minimum Variance Based Estimator method (MVBE) and the Scale Transform Based Estimator method (STBE). The first two methods have already been assessed in the literature while the latter two have been specifically developed for this study. First, closed-form for the Cramer-Rao bound on the estimates of the scale factor, from a simplified deterministic signal, are derived and simplified expressions are given. Then, a statistical evaluation of the quality of estimates is conducted through Monte-Carlo simulations using synthetic signals, based on a model taking into account the influence of temperature. A raw estimate of the computational complexity of signal processing methods also completes this evaluation phase. Finally, the experimental validation of estimation methods is conducted on an aluminum plate subjected to temperatures variations in a controlled thermal environment. The temperature estimates are then faced with an analytical model describing the material behavior.