A Dynamical Systems Approach to Failure Prognosis

2004 ◽  
Vol 126 (1) ◽  
pp. 2-8 ◽  
Author(s):  
David Chelidze ◽  
Joseph P. Cusumano
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Damage Evolution ◽  
Systems Approach ◽  
Remaining Useful Life ◽  
Electromechanical System ◽  
Time To Failure ◽  
Damage Tracking ◽  
Failure Prognosis ◽  
Short Time

In this paper, a previously published damage tracking method is extended to provide failure prognosis, and applied experimentally to an electromechanical system with a failing supply battery. The method is based on a dynamical systems approach to the problem of damage evolution. In this approach, damage processes are viewed as occurring in a hierarchical dynamical system consisting of a “fast,” directly observable subsystem coupled to a “slow,” hidden subsystem describing damage evolution. 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 a tracking function by calculating the short time reference model prediction error. In this paper, the tracking metric based on these estimates is used as an input to a nonlinear recursive filter, the output of which provides continuous refined estimates of the current damage (or, equivalently, health) state. Estimates of remaining useful life (or, equivalently, time to failure) are obtained recursively using the current damage state estimates under the assumption of a particular damage evolution model. The method is experimentally demonstrated using an electromechanical system, in which mechanical vibrations of a cantilever beam are dynamically coupled to electrical oscillations in an electromagnet circuit. Discharge of a battery powering the electromagnet (the “damage” process in this case) is tracked using strain gauge measurements from the beam. The method is shown to accurately estimate both the battery state and the time to failure throughout virtually the entire experiment.

Phase space warping: nonlinear time-series analysis for slowly drifting systems

2006 ◽  
Vol 364 (1846) ◽  
pp. 2495-2513 ◽  
Author(s):  
D Chelidze ◽  
J.P Cusumano
Keyword(s):  
Phase Space ◽  
Damage Evolution ◽  
Systems Approach ◽  
Reference Model ◽  
Recursive Estimation ◽  
Time To Failure ◽  
Damage State ◽  
Beam Experiment ◽  
Vector Tracking ◽  
Phase Space Warping

A new general dynamical systems approach to data analysis is presented that allows one to track slowly evolving variables responsible for non-stationarity in a fast subsystem. The method is based on the idea of phase space warping , which refers to the small distortions in the fast subsystem's phase space that results from the slow drift, and uses short-time reference model prediction error as its primary measurement of this phenomenon. The basic theory is presented and the issues associated with its implementation in a practical algorithm are discussed. A vector-tracking version of the procedure, based on smooth orthogonal decomposition analysis, is applied to the study of a nonlinear vibrating beam experiment in which a crack propagates to complete fracture. Our method shows that the damage evolution is governed by a scalar process, and we are able to give real-time estimates of the current damage state and identify the governing damage evolution model. Using a final recursive estimation step based on this model, the time to failure is continuously and accurately predicted well in advance of actual failure.

Failure Prognosis Using Nonlinear Short-Time Prediction and Multi-Time Scale Recursive Estimation

2001 ◽  
Author(s):  
David Chelidze ◽  
Joseph P. Cusumano ◽  
Anindya Chatterjee
Keyword(s):  
Phase Space ◽  
Time Scale ◽  
Remaining Useful Life ◽  
Fast Time ◽  
Time Data ◽  
Fast Subsystem ◽  
Damage State ◽  
Useful Life ◽  
Short Time ◽  
Slow Subsystem

Abstract In this paper we describe a new, general purpose machinery diagnostic/prognostic algorithm for tracking and predicting evolving damage using only available “macroscopic” observable quantities. The damage is viewed as occurring in a hierarchical dynamical system consisting of a directly observable, “fast” subsystem coupled with a hidden, “slow” subsystem describing damage evolution. This method provides damage diagnostics and failure prognostics requiring only the measurements from the fast subsystem and a model of the slow subsystem. Damage tracking is accomplished by a two-time-scale modeling strategy based on phase space reconstruction using the measured fast-time data. Short-time predictive models are constructed using the reconstructed phase space of the reference (undamaged) fast subsystem. Later, fast-time data for the damaged system is collected and used to estimate the short-time reference model prediction error, or a tracking function. An average value of the tracking function over a given data record is used as a tracking metric, or measure of the current damage state. Recursive, nonlinear filtering is used to estimate the actual damage state based on the tracking metric input. Estimates of remaining useful life are obtained recursively using a linear Kalman filter. This method is applied to an experimental nonlinear oscillator containing a beam with a crack which propagates to complete failure. We demonstrate the ability to track the evolving damage state of the beam using only strain time series data. We also give accurate predictions of remaining useful life, in real time, beginning well in advance of the final complete fracture at the end of experiment.

Dynamical Systems Approach to Material Damage Diagnosis

2003 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Dynamical Systems ◽  
Fatigue Damage ◽  
Time Scale ◽  
Damage Accumulation ◽  
Damage Identification ◽  
Systems Approach ◽  
Material Damage ◽  
Accumulation Process ◽  
Damage Tracking ◽  
Early Damage

In this paper, a dynamical systems approach to material damage identification is presented. This methodology does not depend on knowledge of the particular damage physics of material fatigue. Instead, it provides experimental means to determine what are practically observable and observed facts of damage accumulation, thus making it possible to develop or experimentally verify appropriate damage evolution laws. The procedure implicitly uses the fact that the system undergoing fatigue damage accumulation possesses time scale separation, where damage accumulation occurs on a much slower time scale than the observable dynamics of a system. Damage tracking is achieved using a two-time-scale modeling strategy based on phase space reconstruction. Fast-time oscillation data is collected and used to estimate a damage tracking function by calculating the short time reference model prediction error. Tracking metrics based on these estimates are used as feature vectors. Damage identification is achieved either by applying proper orthogonal decomposition or optimal tracking methods to these vectors. The method is experimentally validated using an elasto-magnetic system, in which a harmonically forced cantilever beam in a nonlinear magnetic field accumulates fatigue damage. The damage tracking results were virtually identical for both identification schemes. In both cases tracking data showed power-law type monotonic trends. These results were in good agreement with the Paris fatigue crack growth model during the time-period of macroscopic crack growth. In addition, the tracking provides much needed insight into the incipient or early damage accumulation process, where only one scalar damage variable is needed to describe the incipient or early damage accumulation process.

Sign in / Sign up

Export Citation Format

Share Document