Prognostic modelling options for remaining useful life estimation by industry

Over recent years a significant amount of research has been undertaken to develop prognostic models that can be used to predict the remaining useful life of engineering assets. Implementations by industry have only had limited success. By design, models are subject to specific assumptions and approximations, some of which are mathematical, while others relate to practical implementation issues such as the amount of data required to validate and verify a proposed model. Therefore, appropriate model selection for successful practical implementation requires not only a mathematical understanding of each model type, but also an appreciation of how a particular business intends to utilise a model and its outputs. This paper discusses business issues that need to be considered when selecting an appropriate modelling approach for trial. It also presents classification tables and process flow diagrams to assist industry and research personnel select appropriate prognostic models for predicting the remaining useful life of engineering assets within their specific business environment. The paper then explores the strengths and weaknesses of the main prognostics model classes to establish what makes them better suited to certain applications than to others and summarises how each have been applied to engineering prognostics. Consequently, this paper should provide a starting point for young researchers first considering options for remaining useful life prediction. The models described in this paper are Knowledge-based (expert and fuzzy), Life expectancy (stochastic and statistical), Artificial Neural Networks, and Physical models.

On the empirical eigenvalue distribution of slotted amplify-and-forward relaying protocol model

In this paper we consider the case of large cooperative communication systems where terminals use the protocol known as slotted amplify-and-forward protocol to aid the source in its transmission. Using the perturbation expansion methods of resolvents and large deviation techniques we obtain an expression for the Stieltjes transform of the asymptotic eigenvalue distribution of a sample covariance random matrix of the type HH† where H is the channel matrix of the transmission model for the transmission protocol we consider. We prove that the resulting expression is similar to the Stieltjes transform in its quadratic equation form for the Marcenko-Pastur distribution.