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

A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes

Optimal replacement of a tool subject to random failure

A new competing risk model is proposed to calculate the Conditional Mean Residual Life (CMRL) and Conditional Reliability Function (CRF) of a system subject to two dependent failure modes, namely, degradation failure and catastrophic failure. The degradation process can be represented by a three-state continuous-time stochastic process having a healthy state, a warning state, and a failure state. The system is subject to condition monitoring at regular sampling times that provides partial information about the system is working state and only the failure state is observable. To model the dependency between two failure modes, it is assumed that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follow Marshal–Olkin bivariate exponential distributions. The Expectation–Maximization algorithm is developed to estimate the model's parameters and the explicit formulas for the CRF and CMRL are derived in terms of the posterior probability that the system is in...

Reliability estimation of a system subject to condition monitoring with two dependent failure modes

Due to the non‐stationarity of vibration signals resulting from either varying operating conditions or natural deterioration of machinery, both the frequency components and their magnitudes vary with time. However, little research has been done on the parameter estimation of time‐varying multivariate time series models based on adaptive filtering theory for condition‐based maintenance purposes. This paper proposes a state‐space model of non‐stationary multivariate vibration signals for the online estimation of the state of rotating machinery using a modified extended Kalman filtering algorithm and spectral analysis in the time‐frequency domain. Adaptability and spectral resolution capability of the model have been tested by using simulated vibration signal with abrupt changes and time‐varying spectral content. The implementation of this model to detect machinery deterioration under varying operating conditions for condition‐based maintenance purposes has been conducted by using real gearbox vibration monitoring signals. Experimental results demonstrate that the proposed model is able to quickly detect the actual state of the rotating machinery even under highly non‐stationary conditions with abrupt changes and yield accurate spectral information for an early warning of incipient fault in rotating machinery diagnosis. This is achieved through combination with a change detection statistic in bi‐spectral domain.

Adaptive model for vibration monitoring of rotating machinery subject to random deterioration

In this paper, we propose a new model for availability maximization under partial observations for maintenance applications. Compared with the widely studied cost minimization models, few structural results are known about the form of the optimal control policy for availability maximization models. We consider a failing system with unobservable operational states. Only the failure state is observable. System deterioration is driven by an unobservable, continuous-time homogeneous Markov process. Multivariate condition monitoring data which is stochastically related to the unobservable state of the system is collected at equidistant sampling epochs and is used to update the posterior state distribution for decision making. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The objective is to determine the form of the optimal control policy that maximizes the long-run expected average availability per unit time. We formulate the problem as an optimal stopping problem with partial information. Under standard assumptions, we prove that a control limit policy is optimal. A computational algorithm is developed, illustrated by numerical results.

Viliam Makis

Papers

A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes

Optimal replacement of a tool subject to random failure

Reliability estimation of a system subject to condition monitoring with two dependent failure modes

Adaptive model for vibration monitoring of rotating machinery subject to random deterioration

Availability maximization under partial observations