TY - JOUR

T1 - Detecting mode-shape discontinuities without differentiation

T2 - examining a Gaussian process approach

AU - Hensman, James

AU - Surace, Cecilia

AU - Gherlone, Marco

PY - 2011

Y1 - 2011

N2 - Detecting damage by inspection of mode-shape curvature is an enticing approach which is hindered by the requirement to differentiate the inferred mode-shape. Inaccuracies in the inferred mode-shapes are compounded by the numerical differentiation process; since these small inaccuracies are caused by noise in the data, the method is untenable for most real situations. This publication proposes a new method for detecting discontinuities in the smoothness of the function, without directly calculating the curvature i.e. without differentiation. We present this methodology and examine its performance on a finite element simulation of a cracked beam under random excitation. In order to demonstrate the advantages of the approach, increasing amounts of noise are added to the simulation data, and the benefits of the method with respect to simple curvature calculation is demonstrated. The method is based upon Gaussian Process Regression, a technique usually used for pattern recognition and closely related to neural network approaches. We develop a unique covariance function, which allows for a non-smooth point. Simple optimisation of this point (by complete enumeration) is effective in detecting the damage location. We discuss extensions of the technique (to e.g. multiple damage locations) as well as pointing out some potential pitfalls.

AB - Detecting damage by inspection of mode-shape curvature is an enticing approach which is hindered by the requirement to differentiate the inferred mode-shape. Inaccuracies in the inferred mode-shapes are compounded by the numerical differentiation process; since these small inaccuracies are caused by noise in the data, the method is untenable for most real situations. This publication proposes a new method for detecting discontinuities in the smoothness of the function, without directly calculating the curvature i.e. without differentiation. We present this methodology and examine its performance on a finite element simulation of a cracked beam under random excitation. In order to demonstrate the advantages of the approach, increasing amounts of noise are added to the simulation data, and the benefits of the method with respect to simple curvature calculation is demonstrated. The method is based upon Gaussian Process Regression, a technique usually used for pattern recognition and closely related to neural network approaches. We develop a unique covariance function, which allows for a non-smooth point. Simple optimisation of this point (by complete enumeration) is effective in detecting the damage location. We discuss extensions of the technique (to e.g. multiple damage locations) as well as pointing out some potential pitfalls.

U2 - 10.1088/1742-6596/305/1/012001

DO - 10.1088/1742-6596/305/1/012001

M3 - Journal article

AN - SCOPUS:80052075938

VL - 305

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012001

ER -