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 …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

The Theory of Stochastic Processes. By D. R. Cox and H. D. Miller. Pp. x, 398. 70s. (Methuen)

Applications of machine learning to machine fault diagnosis: A review and roadmap

Bearing remaining useful life (RUL) prediction plays a crucial role in guaranteeing safe operation of machinery and reducing maintenance loss. In this paper, we present a new deep feature learning method for RUL estimation approach through time frequency representation (TFR) and multiscale convolutional neural network (MSCNN). TFR can reveal nonstationary property of a bearing degradation signal effectively. After acquiring time-series degradation signals, we get TFRs, which contain plenty of useful information using wavelet transform. Owing to high dimensionality, the size of these TFRs is reduced by bilinear interpolation, which are further regarded as inputs for deep learning models. Here, we introduce an MSCNN model structure, which keeps the global and local information synchronously compared to a traditional convolutional neural network (CNN). The salient features, which contribute for RUL estimation, can be learned automatically by MSCNN. The effectiveness of the presented method is validated by the experiment data. Compared to traditional data-driven and different CNN-based feature extraction methods, the proposed method shows enhanced performance in the prediction accuracy.

Estimation of Bearing Remaining Useful Life Based on Multiscale Convolutional Neural Network

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.

The Inverse Gaussian Process as a Degradation Model

Prognostics and health management (PHM) is a framework that offers comprehensive yet individualized solutions for managing system health. In recent years, PHM has emerged as an essential approach for achieving competitive advantages in the global market by improving reliability, maintainability, safety, and affordability. Concepts and components in PHM have been developed separately in many areas such as mechanical engineering, electrical engineering, and statistical science, under varied names. In this paper, we provide a concise review of mainstream methods in major aspects of the PHM framework, including the updated research from both statistical science and engineering, with a focus on data-driven approaches. Real world examples have been provided to illustrate the implementation of PHM in practice.

/pdf/prognostics-and-health-management-a-review-on-data-driven-sq6v3j030k.pdf

Nan Chen

Papers

Estimation of Bearing Remaining Useful Life Based on Multiscale Convolutional Neural Network

The Inverse Gaussian Process as a Degradation Model

Prognostics and Health Management: A Review on Data Driven Approaches

A new class of Wiener process models for degradation analysis

Condition-based maintenance using the inverse Gaussian degradation model