In this paper, a flow variance based structural damage identification method is introduced. It is a practical implementation of phase space warping concept as applied to damage identification. A coupled dynamical system is considered where a slow-time damage process causes drifts in the parameters of fast-time system describing measurable response of a structure. The method is based on the hypothesis that the distribution function of the fast-time trajectory is a function of damage state. In this method, estimated local expectation of trajectory in its phase space is used as a damage tracking feature vector. After the feature vectors are constructed, damage identification is realized by smooth orthogonal decomposition. Data processing time requirements of the flow variance based approach decrease by about 2 orders-of-magnitude compared with the phase space warping based method. A common form of the feature vectors is also discussed.
In this paper a modification to a general-purpose machinery diagnostic/prognostic algorithm that can handle two or more simultaneously occurring failure processes is described. The method is based on a theory that views damage as occurring in a hierarchical dynamical system where slowly evolving, hidden failure processes are causing nonstationarity in a fast, directly observable system. The damage variable tracking is based on statistics calculated using data-based local linear models constructed in the reconstructed phase space of the fast system. These statistics are designed to measure a local change in the fast systems flow caused by the slow-time failure processes. The method is applied to a mathematical model of an experimental electromechanical system consisting of a beam vibrating in a potential field crated by two electromagnets. Two failure modes are introduced through discharging batteries supplying power to these electromagnets. Open circuit terminal voltage of these batteries is a two-dimensional damage variable. Using computer simulations, it is demonstrated both analytically and experimentally that the proposed method can accurately track both damage variables using only a displacement measurements from the vibrating beam. The accurate estimates of remaining time to failure for each battery are given well ahead of actual breakdowns.
A general method for tracking the evolution of hidden damage processes and predicting remaining useful life is presented and applied experimentally to an electromechanical system with a failing supply battery. The fundamental theory for the method is presented. In this theory, damage processes are viewed as occurring in a hierarchical dynamical system consisting of 'fast', directly observable subsystem coupled with a 'slow', hidden subsystem describing damage evolution. In the algorithm, damage tracking is achieved using a two-time-scale modeling strategy based on phase space reconstruction. Using the reconstructed phase space of the reference (undamaged) system, short-time predictive models are constructed. Fast-time data from later stages of damage evolution of a given system are collected and used to estimate the short time reference model prediction error or a tracking metric. The tracking metric is used as an input to a nonlinear recursive filter, the output of which provides an estimate of the current damage state. Estimates of remaining useful life are obtained recursively using the current damage state estimates under the assumption of a particular battery voltage evolution model. In the experimental application, the method is shown to accurately estimate both the battery state and the time to failure throughout the whole experiment.