Showing papers by "Viliam Makis published in 2012"

Maximum Likelihood Estimation for a Hidden Semi-Markov Model with Multivariate Observations

Abstract: In this paper, a parameter estimation procedure for a condition-based maintenance model under partial observations is presented. The deterioration process of the partially observable system is modeled as a continuous-time homogeneous semi-Markov process. The system can be in a healthy or unhealthy operational state, or in a failure state, and the sojourn time in the operational state follows a phase-type distribution. Only the failure state is observable, whereas operational states are unobservable. Vector observations that are stochastically related to the system state are collected at equidistant sampling times. The objective is to determine maximum likelihood estimates of the model parameters using the Expectation–Maximization (EM) algorithm. We derive explicit formulae for both the pseudo likelihood function and the parameter updates in each iteration of the EM algorithm. A numerical example is developed to illustrate the efficiency of the estimation procedure. Copyright © 2012 John Wiley & Sons, Ltd.

Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

Abstract: We model a partially observable deteriorating system subject to random failure. The state process follows an unobservable continuous time homogeneous Markov chain. At equidistant sampling times vector-valued observations having multivariate normal distribution with state-dependent mean and covariance matrix are obtained at a positive cost. At each sampling epoch a decision is made either to run the system until the next sampling epoch or to carry out full preventive maintenance, which is assumed to be less costly than corrective maintenance carried out upon system failure. The objective is to determine the optimal control policy that minimizes the long-run expected average cost per unit time. We show that the optimal preventive maintenance region is a convex subset of Euclidean space. We also analyze the practical three-state version of this problem in detail and show that in this case the optimal policy is a control limit policy. An efficient computational algorithm is developed for the three-state probl...

A Bayesian model and numerical algorithm for CBM availability maximization

Abstract: In this paper, we consider an availability maximization problem for a partially observable system subject to random failure. System deterioration is described by a hidden, continuous-time homogeneous Markov process. While the system is operational, multivariate observations that are stochastically related to the system state are sampled through condition monitoring at discrete time points. The objective is to design an optimal multivariate Bayesian control chart that maximizes the long-run expected average availability per unit time. We have developed an efficient computational algorithm in the semi-Markov decision process (SMDP) framework and showed that the availability maximization problem is equivalent to solving a parameterized system of linear equations. A numerical example is presented to illustrate the effectiveness of our approach, and a comparison with the traditional age-based replacement policy is also provided.

Wavelet Analysis based Gear Shaft Fault Detection

Abstract: 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.