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

A review on machinery diagnostics and prognostics implementing condition-based maintenance

Remaining useful life estimation - A review on the statistical data driven approaches

A survey of maintenance policies of deteriorating systems

In this paper, we present a maintenance model of a two-unit series system with economic dependence. Unit#1 which is considered to be more expensive and more important, is subject to condition monitoring (CM) at equidistant, discrete time epochs and unit#2, which is not subject to CM has a general lifetime distribution. The multivariate observation vectors obtained through condition monitoring carry partial information about the hidden state of unit#1, which can be in a healthy or a warning state while operating. Only the failure state is assumed to be observable for both units. The objective is to find an optimal opportunistic maintenance policy minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the partially observable semi-Markov decision process framework. An effective computational algorithm for finding the optimal policy and the minimum average cost is developed, illustrated by a numerical example. Keywords—Condition-Based Maintenance, Semi-Markov Decision Process, Multivariate Bayesian Control Chart, Partially Observable System, Two-unit System.

Optimal Maintenance Policy for a Partially Observable Two-Unit System

In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock. Keywords—Condition-based maintenance, economic manufacturing quantity, safety stock, stochastic demand.

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Optimal Production and Maintenance Policy for a Partially Observable Production System with Stochastic Demand

Abstract: Fault detection and diagnosis of gear transmission systems have attracted considerable attention in recent years, but there are very few papers dealing with the early detection of shaft cracks. In this paper, an approach to gear shaft fault detection based on the application of the wavelet transform to both the time synchronously averaged (TSA) signal and residual signal is presented. The autocovariance of maximal energy coefficients based on the wavelet transform is first proposed to evaluate the gear shaft fault advancement quantitatively. For a comparison, the advantages and disadvantages of some approaches such as using standard deviation, kurtosis and the application of the Kolmogorov-Smirnov test (K-S test), used as fault indicators with continuous wavelet transform (CWT) and discrete wavelet transform (DWT) for residual signal, are discussed. It is demonstrated using real vibration data that the early faults in gear shafts can be detected and identified successfully using wavelet transforms combined with the approaches mentioned above.

Wavelet Analysis based Gear Shaft Fault Detection

Optimal control policy for a tool-wear process subject to shocks and random failures

In this paper, we consider the problem of modeling and predicting highway accidents in the presence of randomly changing winter driving conditions. Unlike most accident prediction models in the literature, which are typically formulated in a static (e.g. regression models) or discrete time (e.g. time-series models) setting, we propose a continuous- time stochastic model to describe the relation between highway accidents and winter weather dynamics. We believe this to be a more natural way to describe discrete-event highway accidents that occur in continuous-time. In particular, the accident counting process is viewed as a non-homogeneous Poisson process (NHPP) with an intensity function that depends on a (Markovian) weather process. Such a model is known in the stochastic process literature as a Markov- modulated Poisson process (MMPP) and has been successfully applied to queuing and telecommunications problems. One main advantage of such an approach, is its ability to provide explicit closed-form prediction formulae for both weather and accidents over any future time horizon (i.e. short or long-term predictions). To illustrate the effectiveness of the proposed stochastic model, we study a large winter data set provided by Ministry of Transportation of Ontario (MTO) that includes motor vehicle accidents on Highway 401, the busiest highway in North America.

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Viliam Makis

Papers

Optimal Maintenance Policy for a Partially Observable Two-Unit System

Optimal Production and Maintenance Policy for a Partially Observable Production System with Stochastic Demand

Wavelet Analysis based Gear Shaft Fault Detection

Optimal control policy for a tool-wear process subject to shocks and random failures

A Stochastic Model for Highway Accident Predictions with Winter Data