Prognostic Methodologies for Repeated Measurement Data of Multiple Unit

This research investigates prognostics modeling methods on repeated measurement data of multiple units in order to improve the prediction accuracy and facilitate effective predictive maintenance. Engineering systems deteriorate in performance over time and are subject to the stresses in operation. Maintenance is carried out to assure satisfactory levels of reliability during the life of systems. Predictive maintenance (PdM) is one of the most effective maintenance policies, where maintenance actions are planned based on the actual system performance. Remaining useful life (RUL) prediction is the keystone of PdM. Prognostics and health management (PHM) is involved in PdM due to its strength in the system's RUL prediction and related health management. Prognostics is the core process of PdM and PHM, that aims to predict the RUL based on the available performance data. Multiple uncertainties, such as input uncertainties and model uncertainties, undermine the prediction performance of prognostics models. To characterize the inherent variability in the degradation process, repeated measurement design is exercised, where repeated measurement data of multiple units is obtained. This type of data is used to detect multiple-source variability and requires advanced modeling techniques due to its complex structures. This research aims to develop adequate prognostics models to quantify multiple-source variability in this type of data and develop robust algorithms for complex data structure with unbalanced/missing data.;Based on the way of modeling the multiple-source variability, four prediction methods are proposed to model the prognostics process based on repeated measurement data of multiple units. General mixed-effect models (GMM), containing fixed and random effects, are widely used to account multiple sources of variability in repeated measures. The combination of fixed and random effects illustrates the variability in a stochastic process. Fixed effects describe the characteristics of the population average over units and the random effects demonstrate the variation of units. Because of the difficulty of GMM dealing with unbalanced data, a joint modeling method (JMM) is proposed where the degradation processes of each unit is interpreted as multivariate normal distributions. The concept of joint modeling is that the mean and covariance are decomposed firstly and then unknown parameters of the mean function and covariance matrix are estimated jointly. In the proposed method, mean, variance, and correlation of measurements are firstly decomposed based on Cholesky decomposition. Trigonometric functions are used to parameterize the correlation matrix. A penalized maximum likelihood estimation is proposed for parameter estimation in JMM. The expensive computation in GMM and JMM due to the high dimension covariance matrix necessitates the dimension reduction techniques. For this purpose, functional principal component analysis (FPCA) is deployed in this research. Functional data refers to data where each observation is modeled as a curve, a surface, or a hypersurface. FPCA applies the concept of functional data analysis in principal component analysis to reduce computation complexity. Finally a general spatio-temporal model is proposed based on the aforementioned methods, where spatial, temporal trends and their dependency will be quantified. Spatial trends can be analogized as the difference between units, while temporal trends illustrate the degradation process.;To reduce the model error, physical understanding is incorporated into the models. Covariate selection for all the proposed methods is done based on physics-based model. With the degradation model, the distribution of time to failure (TTF) can be estimated through simple numerical simulations. This research aims to apply and validate the proposed methods in battery capacity degradation to provide accurate prediction on cycle to failure and elucidate the mechanism of capacity fade.