Analysis of composite plate dynamics using spatial maps of frequency-domain features described by Gaussian processes

Abstract This paper develops a novel framework for analysing dynamics of vibrating structures using spatial maps of frequency-domain features, represented with Gaussian processes. A signal model is used to transform dynamic features of vibration from the time- to frequency domain. Frequency-domain characteristics of vibrations are then represented continuously over space at separate harmonics using Gaussian process regression to form a spatial map. To demonstrate the utility of this method, we provide an example using data from single frequency excitation of a composite plate, in both healthy and damaged conditions. The results show that different structural conditions of composite plates can be described and analysed in the frequency-domain, motivating the development of future structural health monitoring schemes based on the signal model/Gaussian process framework presented here.

[1]  Visakan Kadirkamanathan,et al.  Multiple Gaussian process models for direct time series forecasting , 2011 .

[2]  Anand Kumar,et al.  Vibration suppression and damage detection in smart composite laminate using high precision finite element , 2011, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[3]  Visakan Kadirkamanathan,et al.  Spatio-temporal dynamic modelling of smart structures using a robust expectation?maximization algorithm , 2011 .

[4]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[5]  Wei Chu,et al.  Gaussian Processes for Ordinal Regression , 2005, J. Mach. Learn. Res..

[6]  Jouni Hartikainen,et al.  Kalman filtering and smoothing solutions to temporal Gaussian process regression models , 2010, 2010 IEEE International Workshop on Machine Learning for Signal Processing.

[7]  Visakan Kadirkamanathan,et al.  A Canonical Space-Time State Space Model: State and Parameter Estimation , 2007, IEEE Transactions on Signal Processing.

[8]  Grant P. Steven,et al.  VIBRATION-BASED MODEL-DEPENDENT DAMAGE (DELAMINATION) IDENTIFICATION AND HEALTH MONITORING FOR COMPOSITE STRUCTURES — A REVIEW , 2000 .

[9]  C. R. Farrar,et al.  A STATISTICAL PATTERN RECOGNITION PARADIGM FOR VIBRATION-BASED STRUCTURAL HEALTH MONITORING , 2000 .

[10]  Hoon Sohn,et al.  VIBRATION-BASED DAMAGE DETECTION USING STATISTICAL PROCESS CONTROL , 2001 .

[11]  Keith Worden,et al.  An introduction to structural health monitoring , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Ranjan Ganguli,et al.  Structural damage detection in a helicopter rotor blade using radial basis function neural networks , 2003 .

[13]  David A. Nix,et al.  Vibration–based structural damage identification , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Visakan Kadirkamanathan,et al.  Monitoring of Aircraft Engines , 2009 .

[15]  Javier Ramírez,et al.  A new Kullback-Leibler VAD for speech recognition in noise , 2004, IEEE Signal Processing Letters.

[16]  K. Craig,et al.  Damage detection in composite structures using piezoelectric materials (and neural net) , 1994 .

[17]  James Hensman,et al.  Locating acoustic emission sources in complex structures using Gaussian processes , 2008 .

[18]  L. H. Yam,et al.  Vibration-based damage detection for composite structures using wavelet transform and neural network identification , 2003 .

[19]  Rune Brincker,et al.  Vibration Based Inspection of Civil Engineering Structures , 1993 .

[20]  S. Masri,et al.  Application of Neural Networks for Detection of Changes in Nonlinear Systems , 2000 .

[21]  Simo Särkkä,et al.  Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression , 2011, ICANN.

[22]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[23]  A. Gelfand,et al.  Gaussian predictive process models for large spatial data sets , 2008, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[24]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.