Parameter Estimation of the Generalized Extreme ValueDistribution for Structural Health Monitoring

摘要

Structural health monitoring can be defined as a statistical pattern recognitionrnproblem which necessitates establishing a decision boundary based on measured data.rnChoosing the decision boundary is often based on the assumption that the distributionrnof measured data is Gaussian in nature. This unwarranted assumption impairs thernperformance of structural health monitoring significantly by increasing false positivernand negative indications of damage. This paper attempts to address the issue of therndecision boundary establishment using extreme value statistics (EVS) so that the tailsrnof a distribution associated with damage can be properly modeled. Encompassingrnthree extreme value distributions (Gumbel, Weibull, and Frechet distributions), therngeneralized extreme value distribution (GEV) is adopted for establishing the decisionrnboundary. A parameter estimation technique based on a nonlinear optimizationrnscheme is developed to automatically estimate the model parameters of the GEV andrnchoose the most appropriate domain of attraction. The validity of the proposedrnmethod is demonstrated in numerical studies using real sample data sets and in therncontext of delamination detection in a composite plate.