Statistical Methods for Multivariate Functional Data Clustering, Recurrent Event Prediction, and Accelerated Degradation Data Analysis

Jin, Zhongnan

Statistical Methods for Multivariate Functional Data Clustering, Recurrent Event Prediction, and Accelerated Degradation Data Analysis

dc.contributor.author	Jin, Zhongnan	en
dc.contributor.committeechair	Hong, Yili	en
dc.contributor.committeemember	Kim, Inyoung	en
dc.contributor.committeemember	Wu, Xiaowei	en
dc.contributor.committeemember	Sands, Laura P.	en
dc.contributor.committeemember	Deng, Xinwei	en
dc.contributor.department	Statistics	en
dc.date.accessioned	2021-03-06T07:00:29Z	en
dc.date.available	2021-03-06T07:00:29Z	en
dc.date.issued	2019-09-12	en
dc.description.abstract	In this dissertation, we introduce three projects in machine learning and reliability applications after the general introductions in Chapter 1. The first project concentrates on the multivariate sensory data, the second project is related to the bivariate recurrent process, and the third project introduces thermal index (TI) estimation in accelerated destructive degradation test (ADDT) data, in which an R package is developed. All three projects are related to and can be used to solve certain reliability problems. Specifically, in Chapter 2, we introduce a clustering method for multivariate functional data. In order to cluster the customized events extracted from multivariate functional data, we apply the functional principal component analysis (FPCA), and use a model based clustering method on a transformed matrix. A penalty term is imposed on the likelihood so that variable selection is performed automatically. In Chapter 3, we propose a covariate-adjusted model to predict next event in a bivariate recurrent event system. Inspired by geyser eruptions in Yellowstone National Park, we consider two event types and model their event gap time relationship. External systematic conditions are taken account into the model with covariates. The proposed covariate adjusted recurrent process (CARP) model is applied to the Yellowstone National Park geyser data. In Chapter 4, we compare estimation methods for TI. In ADDT, TI is an important index indicating the reliability of materials, when the accelerating variable is temperature. Three methods are introduced in TI estimations, which are least-squares method, parametric model and semi-parametric model. An R package is implemented for all three methods. Applications of R functions are introduced in Chapter 5 with publicly available ADDT datasets. Chapter 6 includes conclusions and areas for future works.	en
dc.description.abstractgeneral	This dissertation focuses on three projects that are all related to machine learning and reliability. Specifically, in the first project, we propose a clustering method designated for events extracted from multivariate sensory data. When the customized event is corresponding to reliability issues, such as aging procedures, clustering results can help us learn different event characteristics by examining events belonging to the same group. Applications include diving behavior segmentation based on vehicle sensory data, where multiple sensors are measuring vehicle conditions simultaneously and events are defined as vehicle stoppages. In our project, we also proposed to conduct sensor selection by three different penalizations including individual, variable and group. Our method can be applied for multi-dimensional sensory data clustering, when optimal sensor design is also an objective. The second project introduces a covariate-adjusted model accommodated to a bivariate recurrent event process system. In such systems, events can occur repeatedly and event occurrences for each type can affect each other with certain dependence. Events in the system can be mechanical failures which is related to reliability, while next event time and type predictions are usually of interest. Precise predictions on the next event time and type can essentially prevent serious safety and economy consequences following the upcoming event. We propose two CARP models with marginal behaviors as well as the dependence structure characterized in the bivariate system. We innovate to incorporate external information to the model so that model results are enhanced. The proposed model is evaluated in simulation studies, while geyser data from Yellowstone National Park is applied. In the third project, we comprehensively discuss three estimation methods for thermal index. They are the least-square method, parametric model and semi-parametric model. When temperature is the accelerating variable, thermal index indicates the temperature at which our materials can hold up to a certain time. In reality, estimating the thermal index precisely can prolong lifetime of certain product by choosing the right usage temperature. Methods evaluations are conducted by simulation study, while applications are applied to public available datasets.	en
dc.description.degree	Doctor of Philosophy	en
dc.format.medium	ETD	en
dc.identifier.other	vt_gsexam:22101	en
dc.identifier.uri	http://hdl.handle.net/10919/102628	en
dc.publisher	Virginia Tech	en
dc.rights	In Copyright	en
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/	en
dc.subject	accelerated destructive degradation test	en
dc.subject	clustering	en
dc.subject	functional principal component analysis	en
dc.subject	geyser eruption	en
dc.subject	multivariate analysis	en
dc.subject	recurrent process	en
dc.subject	sensory data	en
dc.subject	thermal index	en
dc.subject	variable selection.	en
dc.title	Statistical Methods for Multivariate Functional Data Clustering, Recurrent Event Prediction, and Accelerated Degradation Data Analysis	en
dc.type	Dissertation	en
thesis.degree.discipline	Statistics	en
thesis.degree.grantor	Virginia Polytechnic Institute and State University	en
thesis.degree.level	doctoral	en
thesis.degree.name	Doctor of Philosophy	en