Hidden Markov Models and their Application for Predicting Failure Events

We show how Markov mixed membership models (MMMM) can be used to predict the degradation of assets. We model the degradation path of individual assets, to predict overall failure rates. Instead of a separate distribution for each hidden state, we use hierarchical mixtures of distributions in the exponential family. In our approach the observation distribution of the states is a finite mixture distribution of a small set of (simpler) distributions shared across all states. Using tied-mixture observation distributions offers several advantages. The mixtures act as a regularization for typically very sparse problems, and they reduce the computational effort for the learning algorithm since there are fewer distributions to be found. Using shared mixtures enables sharing of statistical strength between the Markov states and thus transfer learning. We determine for individual assets the trade-off between the risk of failure and extended operating hours by combining a MMMM with a partially observable Markov decision process (POMDP) to dynamically optimize the policy for when and how to maintain the asset.Comment: Will be published in the proceedings of ICCS 2020; @Booklet{EasyChair:3183, author = {Paul Hofmann and Zaid Tashman}, title = {Hidden Markov Models and their Application for Predicting Failure Events}, howpublished = {EasyChair Preprint no. 3183}, year = {EasyChair, 2020}

Optimal control and optimal sensor activation for Markov decision problems with costly observations

This paper considers partial observation Markov decision processes. Besides the classical control decisions influencing the transition probabilities of the Markov process, we also consider control actions that can activate the sensors to provide more or less accurate information about the system state, explicitly including the cost of activating sensors. We synthesize control laws that minimize a discounted operating cost of the system over an infinite interval of time, where the instantaneous cost function depends on the current state, the control influencing the transition probabilities, and the control actions activating the sensors. A general computationally efficient optimal solution for this problem is not known. Hence we design supoptimal controllers that only use knowledge of the value function for the full state information Markov decision problem. Our solution guarantees that the discounted cost of operating the plant increases only by a bounded amount with respect to the minimal cost for the full state information problem. A new concept of pinned conditional distributions of the state given the observed history of the plant is required in order to implement these control laws online