A nonlinear dynamical systems framework for structural diagnosis and prognosis

Adams, Douglas E.; Nataraju, Madhura

doi:10.1016/s0020-7225(02)00112-x

Cited by 72 publications

(33 citation statements)

References 11 publications

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“…Specifically, they represent the normal forms of bifurcation phenomenon exhibited by the nonlinear systems. Similar models were presented in [1]. Bifurcation is a phenomenon exhibited by nonlinear systems related to the change in the number or stability of the equilibrium points and represents a qualitative change in the system dynamics for a small change in the system parameters.…”

Section: Damage Modelsmentioning

confidence: 95%

“…Two approaches are of most interest to this paper. The first is the development of a preliminary nonlinear dynamical systems approach for damage detection as presented by Adams and Nataraju [1]. In this work a framework for damage related dynamics and features are developed to exploit them for extraction of features for damage detection and a mechanism for quantification of the damage states.…”

Section: Introductionmentioning

confidence: 99%

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Smart damage prediction: a distance-to-bifurcation-based approach

Shukla

Frederick

2004

SPIE Proceedings

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Damage detection and prediction is essential for structural health monitoring. Vibration based methods have been used in health monitoring. In this work damage is proposed to be a nonlinear dynamical phenomenon and can be analyzed by utilizing the bifurcation theory. A methodology for predicting failure is proposed which utilizes the concepts of distance to stability boundary as estimated by bifurcation analysis. The proposed methodology is illustrated by developing bifurcation boundary for a two degree of freedom nonlinear mass-spring-damper system. Two damage models are investigated to illustrate the utility the proposed methodology in capturing and estimating the evolution of damage phenomenon.

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Section: Damage Modelsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Smart damage prediction: a distance-to-bifurcation-based approach

Shukla

Frederick

2004

SPIE Proceedings

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“…More precisely, we assume that the behavior of the technological process can be described by the following system ( [1], [3], [22]):…”

Section: Introductionmentioning

confidence: 99%

“…However, only the structure of the subsystem (1b) is supposed to be known a priori. Generally, the dynamics for the damage state is supposed to be polynomial (see for instance [1], [6] and [3]). Hence, from the inputs and outputs of fast dynamic behavior subsystem, the main objective is to identify parameters of slow dynamic behavior subsystem model.…”

Section: Introductionmentioning

confidence: 99%

Observer design applied to prognosis of system

Gucik‐Derigny

Outbib

Ouladsine³

2011

2011 IEEE Conference on Prognostics and Health Management

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This paper is dedicated to model-based prognosis to predict remaining useful life of a system. This methodology is applied on multiple time scale systems made up of a slow and a fast dynamic behaviors subsystems, defining damage state and state of system behaviors respectively. Prediction of remaining useful life implies to have a slow dynamic behavior subsystem model. Slow dynamic subsystem behavior is supposed to be unknown, only the structure is assumed to be known a priori. For that, in the fast dynamic behavior subsystem, unmeasured state are estimated based on the design of unknown input observers. Slow dynamic behavior state in the fast dynamic behavior subsystem is led back to an unknown input. High gain observer is used to obtain accurate state and unknown input estimates. Slow dynamic behavior model parameters are then identified with the previous estimates. Prediction of remaining useful life is finally achieved based on relative accuracy of the observer estimates. Pertinence of the proposed methodology is illustrated based on simulation results to an electromechanical oscillator.Index Terms-Prognosis, predictive diagnosis, unknown input observer, electromechanical system.

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“…Thus, the appearance of nonlinear phenomenon in a nominally linear systems can be used as an indication of damage. Douglas et al [1] propose a damage identification approach based on model deduction near bifurcations. This method uses an assumption that an undamaged system is linear, and nonlinearity is only introduced by damage.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Damage Identification Based on Phase Space Warping: An Experimental Study

Chelidze

Liu

2006

Nonlinear Dyn

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A multidimensional damage identification scheme developed in previous work is modified and investigated experimentally. An experimental apparatus consists of a driven two-well magneto-elastic oscillator, where a cantilever beam vibrates in a magnetic potential field perturbed by two electromagnets. These electromagnets are activated by a computer controlled power supply and their terminal voltages are considered a two-dimensional damage variable. The effect of total change in the supply voltage of the electromagnets is approximately 4% shift in the experimentally measured natural frequencies of small oscillations in each well of the potential. Experimental runs are started in a nominally chaotic regime. The battery voltages are altered on specific trajectories in the damage (voltage) phase space. Damage identification is accomplished based on the elastic vibration data collected using laser vibrometers and a accelerometer. The phase space warping based damage tracking feature vectors are estimated using a new phase space partitioning scheme. The damage identification is achieved by applying smooth orthogonal decomposition to the obtained statistics. The effect of the data record size on the quality of reconstructed damage trajectory is investigated in a series of experiments. It is also demonstrated that the new partitioning scheme considerably improves signal-to-noise ration of the identified damage states.

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A nonlinear dynamical systems framework for structural diagnosis and prognosis

Cited by 72 publications

References 11 publications

Smart damage prediction: a distance-to-bifurcation-based approach

Smart damage prediction: a distance-to-bifurcation-based approach

Observer design applied to prognosis of system

Multidimensional Damage Identification Based on Phase Space Warping: An Experimental Study

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