Structural damage classification using extreme value statistics

The first and most important objective of any damage identification algorithm is to ascertain with confidence if damage is present or not. Many methods have been proposed for damage detection based on ideas of novelty detection founded in pattern recognition and multivariate statistics. The philosophy of novelty detection is simple. Features are first extracted from a baseline system to be monitored, and subsequent data are then compared to see if the new features are outliers, which significantly depart from the rest of population. In damage diagnosis problems, the assumption is that outliers are generated from a damaged condition of the monitored system. This damage classification necessitates the establishment of a decision boundary. Choosing this threshold value is often based on the assumption that the parent distribution of data is Gaussian in nature. While the problem of novelty detection focuses attention on the outlier or extreme values of the data, i.e., those points in the tails of the distribution, the threshold selection using the normality assumption weights the central population of data. Therefore, this normality assumption might impose potentially misleading behavior on damage classification, and is likely to lead the damage diagnosis astray. In this paper, extreme value statistics is integrated with the novelty detection to specifically model the tails of the distribution of interest. Finally, the proposed technique is demonstrated on simulated numerical data and time series data measured from an eight degree-of-freedom spring-mass system.

[1]  Hoon Sohn,et al.  Statistical Damage Classification Under Changing Environmental and Operational Conditions , 2002 .

[2]  Stephen J. Roberts,et al.  Extreme value statistics for novelty detection in biomedical signal processing , 2000 .

[3]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[4]  Terence D. Sanger,et al.  Optimal unsupervised learning in a single-layer linear feedforward neural network , 1989, Neural Networks.

[5]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[6]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[7]  Christopher M. Bishop,et al.  Novelty detection and neural network validation , 1994 .

[8]  Lawrence L. Kupper,et al.  Probability, statistics, and decision for civil engineers , 1970 .

[9]  Keinosuke Fukunaga,et al.  Application of the Karhunen-Loève Expansion to Feature Selection and Ordering , 1970, IEEE Trans. Computers.

[10]  Keith Worden,et al.  DAMAGE DETECTION USING OUTLIER ANALYSIS , 2000 .

[11]  S. Kramer.  Geotechnical Earthquake Engineering , 1996 .

[12]  L. Haan,et al.  Extreme value theory , 2006 .

[13]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[14]  S. Nadarajah,et al.  Extreme Value Distributions: Theory and Applications , 2000 .

[15]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[16]  J. D. T. Oliveira,et al.  The Asymptotic Theory of Extreme Order Statistics , 1979 .

[17]  M. Kramer.  Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[18]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[19]  Charles R. Farrar,et al.  Dynamic characterization and damage detection in the I-40 bridge over the Rio Grande , 1994 .

[20]  Lionel Tarassenko,et al.  Novelty detection for the identification of abnormalities , 2000, Int. J. Syst. Sci..

[21]  S. Roberts.  Novelty detection using extreme value statistics , 1999 .

[22]  Hoon Sohn,et al.  Damage diagnosis using time series analysis of vibration signals , 2001 .

[23]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[24]  Thomas L. Paez,et al.  Random Vibrations: Theory and Practice , 1995 .

[25]  Keinosuke Fukunaga,et al.  Statistical Pattern Recognition , 1993, Handbook of Pattern Recognition and Computer Vision.

[26]  Keith Worden,et al.  Detection of defects in composite plates using Lamb waves and novelty detection , 2000, Int. J. Syst. Sci..

[27]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[28]  R. Reiss,et al.  Statistical Analysis of Extreme Values-with applications to insurance , 1997 .

[29]  Damage Detection , 2003, Science's STKE.

[30]  Keith Worden,et al.  STRUCTURAL FAULT DETECTION USING A NOVELTY MEASURE , 1997 .