Research Of Degradation Modeling And Residual Life Estimation For Deterioriate Products Based On Nonlinear Wiener Process

In recent years, the performance degradation data are widely used by many scholars and engineers to deal with issues of reliability analysis and evaluation for products which are characterized as small sample, long life and highly reliable. Because of this, methods of reliability modeling based on degradation data become a new direction in the field of reliability engineering. In such situations, for the purpose of obtaining reasonable results, a suitable degradation model needs to be adopted to capture the degradation of products over time. Due to the impact from a variety of random factors, such as the random effects from the internal and external environments, the degradation process is often uncertain over time. For this reason, the stochastic process-based models have a wide range of applications in degradation modeling. Among them, due to its good analytical and computational properties, the so called Wiener process is adopted quite widely by many scholars to model the degradation process. However, most existing studies are provided with an assumption that the degradation over time is governed by the Wiener process with a linear drift. In practice, the nonlinear degradation processes exist quite extensively. In such situations, the linear models are difficult to capture the dynamics of the degradation process. As an important measure of ability, the residual life of the target product plays an important role in maintenance decision. With an effective estimate of the residual life of the target product, it is benifit to schedule reasonable maintenance actions so that we can reduce or even avoid the occurrence of failures. For meeting the requirements in engineering practice, this thesis pays more attentions to degradation modeling and residual life estimation based on the nonlinear Wiener process, including issues of parameter estimation of the degradation model, degradation model updating, and the approximation to the PDF(probability density function) of the residual life. In this work, related issues are addressed from one-dimensional situations to multi-dimensional situations subsequently. For clarity, the main achievements are listed as follows:(1) Methods of degradation modeling and residual life estimation of the target product based on the nonlinear Wiener process. A nonlinear Wiener process is presented for meeting the pratical requirements, which can jointly take into account the nonlinearity, the temporal uncertainty, and the product-to-product variability of the degradation. Both the linear degradation process and the nonlinear degradation process can be captured by the proposed degradation model so that it provides great flexibility in degradation modeling. The Wiener process with a linear drift and the Wiener process with a time-scale transformation are special cases of the proposed degradation model. The unknown parameters of the degradation model are estimated based on the population-based degradation information, while the degradation history information up-to-date of the target product is used to update the degradation model. Due to the presence of nonlinearity, exact expressions for PDFs of both the failure time and the residual life are difficult to be derived. For this reason, both of them are approximated in closed-forms under a mild assumption, which lay a solid foundation of maintenance decision. Finally, the validity of the proposed models and methods is demonstrated with an illustration example about fatigue cracks. In addition, the effects of model mis-specification are also addressed in detail.(2) Methods of degradation modeling and residual life estimation of the target product by considering measurement errors. On the basis of the nonlinear Wiener process mentioned above, a degradation model with measurement errors is developed, where the uncertainty of measurement errors is characterized by a normal distribution. As such, the range of the proposed degradation is enlarged. Statistical inference of the proposed degradation model is addressed in detail, and the degradation model is updated though the Kalman filter algorithm. To meet the requirements of practical applications, the PDF of the residual life is approximated in a closed-form. Finally, a simulation study and a numerical example concerning fatigue cracks are used to demonstrate the usefulness of the proposed models and the validity of methods.(3) Methods of degradation modeling and residual life estimation of the target product based on the nonlinear Wiener process with skew-normal random effects. Based on the nonlinear Wiener process, a new degradation model is developed by substituting the normal distribution with the skew-normal distribution to capture the product-to-product variability of the degradation within the population. In general, both the symmetrical and asymmetrical uncertainties can be characterized by the skew-normal distribution. As such, the range of the proposed degradation is enlarged. The unknown parameters of the degradation model are estimated through the EM(expectation-maximization) algorithm, and the degradation model is updated by using the Bayesian method. For convenience, the PDF of the residual life is approximated in a closed-form. Finally, a simulation study is used to demonstrate the validity of the proposed models and methods.(4) Methods of degradation modeling and residual life estimation of the target product based on the bivariate-nonlinear Wiener process. For the case of bivariate degradation, a bivariate-nonlinear Wiener process-based degradation model is presented, in which the Frank Copula function is used to model the dependency, and the nonlinear Wiener process is adopted to capture the degradation of each performance characteristic over time. The unknown parameters of the degradation model are estimated through the Bayesian MCMC(Markov Chain Monte Carlo) algorithm, and the degradation model is updated by using the strong tracking filter algorithm. In addition, the PDF of the residual life is approximated. A numerical example about fatigue cracks is given to demonstrate the usefulness and validity of the proposed models and methods.(5) Methods of degradation modeling and residual life estimation of the target product based on the multivariate-nonlinear Wiener process. For the case of multivariate degradation, a multivariate-nonlinear Wiener process-based model is developed, in which the dependency between performance characteristics is characterized by the covariance matrices. The nonlinearity, the temporal uncertainty, the product-to-product variability of the degradation, and the dependency between performance characteristics are jointly taken into account within the proposed degradation model. The population-based degradation information is used to obtain the estimates of the unknown parameters of the model through the EM algorithm. The degradation model is updated through the strong tracking filter algorithm by using the degradation history information up-to-date of the target product. Moreover, the PDF of the residual life is approximated. To illustrate the usefulness and the validity of the proposed models and methods, a numerical example concerning fatigue cracks is finally presented.