Modeling of fatigue crack propagation process: Generalized linear mixed model approach
Abstract
In this dissertation, we develop a generalized linear mixed model for analyzing fatigue crack propagation data and provide a method for estimating the parameters of this model. Experimental data on fatigue crack propagation show considerable random scatter. We model the crack growth process by means of generalized linear mixed model. Both heterogeneity of specimens and correlation between observations taken from the same specimen are accounted for by random effects included in the model. The model fits experimental data very well. Based on the results from this generalized linear mixed model, we also give an estimate of increase in crack size caused by a single stress cycle starting from any arbitrary crack size. Finally, model validation issues as well as linkage between computer simulated data and physical data are discussed. The generalized linear mixed model (GLMM) used here for the fatigue crack propagation process allows responses that are both non-normal and correlated. Since for a typical GLMM the likelihood function involves high dimensional and complicated integrals, the likelihood based inference requires numerical analysis method. We demonstrate that the maximum likelihood estimators for model parameters in GLMMs can be obtained through an iterative algorithm called the ECM algorithm. Comparison with other estimation methods such as Wolfinger and O'Connell's pseudo-likelihood (PL) method and Breslow and Clayton's penalized quasi-likelihood (PQL) method are discussed both numerically and theoretically.
Degree
Ph.D.
Advisors
McCabe, Purdue University.
Subject Area
Statistics|Mechanical engineering
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