IWSHM 2017: Vibration-based damage localization and estimation via the stochastic functional model–based method: An overview

Abstract

The functional model–based method is a unique vibration-based approach to damage localization and magnitude estimation in structures under normal operation, capable of operating on naturally arising random vibration signals without human intervention. It employs an innovative data-based stochastic functional model representing the partial dynamics under various damage scenarios, estimation techniques, and statistical hypothesis testing. Unlike alternative vibration methods employing data-based models but treat the localization and magnitude estimation approximately, as classification problems, it handles them properly as estimation problems. Among its remarkable properties is its ability to operate with a low number of vibration response sensors and low- and limited-frequency bandwidth, characteristics important in many applications. In this article, an overview of the method and its principles are presented, along with three validation case studies.

On the functional model–based method for vibration-based robust damage detection: versions and experimental assessment

“…This essentially corresponds to examining the “consistency” of the current dynamics with the healthy dynamics under all EOCs, as expressed via the VFP-ARX model. This is performed via the following two steps (also see Figure 1): 39…”

“…This essentially corresponds to examining the ''consistency'' of the current dynamics with the healthy dynamics under all EOCs, as expressed via the VFP-ARX model. This is performed via the following two steps (also see Figure 1): 39 Step 1: Estimate the unknown k corresponding to the current EOCs that ''best'' expresses the current signal pair x u ½t, y u ½t. The estimate b k as well as this of the innovations variance b s 2 e ( b k) are obtained as follows:…”

“…FMs, often in the convenient form of functionally pooled autoregressive moving average with exogenous (FP-ARMAX) excitation representations, 44 generalize the corresponding conventional models through the dependence of their parameters on selected operating parameters, referred to as scheduling variables. 39 Accurate representations of the structural (partial) dynamics, as affected by the scheduling variables, may be then obtained. FMs have been developed for the description of linear or non-linear dynamics, [45][46][47] although the class of functionally pooled autoregressive with exogenous (FP-ARX) excitation models 48 are often used due to their structural form and estimation simplicity.…”

“…For overcoming such difficulties, the present authors have, in a series of recent studies 33–36 and within an exclusively data-based (no physics-based models required) statistical time series framework, 37,38 postulated a novel functional model (FM)-based method for robust damage detection under varying and non-measurable EOCs. The method belongs to the broader family of functional model based methods (FMBMs), which was initially introduced by Fassois and colleagues 39–43 in a different context, specifically that of damage precise localization and magnitude estimation under constant EOCs. Yet, it is clearly distinct in its structure and, for the first time, tackling the problem of robust damage detection via the use of FMs.…”

Optimal sensor configuration for structural response prediction by a modified Nelder–Mead simplex method

“…To fulfill this purpose, the concept of structural health monitoring (SHM) was proposed, and there has been great development in the SHM area utilizing dynamic measurements in the last few decades 1 . A large amount of methods has been proposed in this research area and applied to various types of basic structural members, laboratory models, and even real‐life structures, including trusses, 2–4 beams and frames, 5–11 plates and shells, 12–18 periodic structures, 19–23 hydraulic steel structures, 24–26 buildings, 27–33 and bridges 34–40 . However, in addition to the specific methods employed for solving the relevant problems as mentioned above, the success of vibration‐based SHM also highly depends on the quality of collected measurement data, which is ensured by the quantity and detailed layout of employed sensors; at present, the sensor configuration is still designed based on experience in most cases by considering a series of practical constraints.…”