Zhi-Sheng Ye

Bio: Zhi-Sheng Ye is an academic researcher from National University of Singapore. The author has contributed to research in topics: Computer science & Gamma distribution. The author has an hindex of 32, co-authored 104 publications receiving 3545 citations. Previous affiliations of Zhi-Sheng Ye include City University of Hong Kong & Hong Kong Polytechnic University.

Stochastic modelling and analysis of degradation for highly reliable products

Abstract: Degradation models have become an important analytic tool for complex systems. During the last two decades, a number of degradation models have been developed to capture the degradation dynamics of a system and aid the subsequent decision-makings. This paper is aimed at providing a summary of the state of the arts in the field, and discussing some further research issues from both analytical and practical point of view. In this paper, degradation models are classified into three classes, that is, stochastic process models, general path models, and other models beyond these two classes. A review on the three classes is given with emphasis on the class of stochastic process models. A comprehensive comparison between stochastic process models and general path models is given to expound the pros and cons of these two methods. Applications of degradation models in degradation test planning and burn-in modelling will also be discussed. Copyright © 2014 John Wiley & Sons, Ltd.

The Inverse Gaussian Process as a Degradation Model

Abstract: This article systematically investigates the inverse Gaussian (IG) process as an effective degradation model. The IG process is shown to be a limiting compound Poisson process, which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments. Treated as the first passage process of a Wiener process, the IG process is flexible in incorporating random effects and explanatory variables that account for heterogeneities commonly observed in degradation problems. This flexibility makes the class of IG process models much more attractive compared with the Gamma process, which has been thoroughly investigated in the literature of degradation modeling. The article also discusses statistical inference for three random effects models and model selection. It concludes with a real world example to demonstrate the applicability of the IG process in degradation analysis. Supplementary materials for this article are available online.

Degradation Data Analysis Using Wiener Processes With Measurement Errors

Abstract: Degradation signals that reflect a system's health state are important for diagnostics and health management of complex systems. However, degradation signals are often compounded and contaminated by measurement errors, making data analysis a difficult task. Motivated by the wear problem of magnetic heads used in hard disk drives (HDDs), this paper investigates Wiener processes with measurement errors. We explore the traditional Wiener process with positive drifts compounded with i.i.d. Gaussian noises, and improve its estimation efficiency compared with the existing inference procedure. Furthermore, to capture the possible heterogeneity in a population, we develop a mixed effects model with measurement errors. Statistical inferences of this model are discussed. The mixed effects model subsumes several existing Wiener processes as its limiting cases, and thus it is useful for suggesting an appropriate Wiener process model for a specific dataset. The developed methodologies are then applied to the wear problem of magnetic heads of HDDs, and a light intensity degradation problem of light-emitting diodes.

RUL Prediction of Deteriorating Products Using an Adaptive Wiener Process Model

Abstract: Degradation modeling plays an important role in system health diagnosis and remaining useful life (RUL) prediction. Recently, a class of Wiener process models with adaptive drift was proposed for degradation-based RUL prediction, which has been proven flexible and effective. However, the existing studies use an autoregressive model of order 1 for the adaptive drift, which can result in difficulties in both model estimation and RUL prediction. This paper proposes a new adaptive Wiener process model that utilizes a Brownian motion for the adaptive drift. The new model shares the flexibility of the existing models, but avoids the difficulties in model estimation and RUL prediction. A model estimation procedure based on maximum likelihood estimation is developed, and the RUL prediction based on the proposed model is formulated. The effectiveness of the model in RUL prediction is validated using simulation and through an application to the lithium-ion battery degradation data.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Reliability Engineering and System Safety

Abstract: This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].