Mathematical Methods in Reliability -uncertainty Quantification

1. Dr Keming Yu (Brunel University) Bayesian quantile regression and applications in energy research In recent years quantile regression has attracted a lot of applications in energy research, for example in electricity price forecasting, electricity demand analysis, energy consumption pattern study, wind power forecasting, gas flow, volatility and so on, but there are many uncertainties in forecasting and modelling as well as analysis in these energy research topics. This talks mainly reviews the methods of Bayesian inference with quantile regression models and applications of quantile regression to energy research. 2. Dr Peter Matthews (Durham University) Data mining operational logs for wind turbine prognosis I discuss some data mining approaches and results from wind farm operational data that show promise in terms of predicting when maintenance will be required. Data mining offers methods for handling the large amounts of data. When coupled with prior domain knowledge, our results show that there are some signals that are given off by the monitoring systems on individual wind turbines that indicate imminent failure. This is very promising, as it provides the tools to increase turbine availability and overall reliability. (Joint work with Bin Di Chen and Jamie Godwin). 3. Prof John Quigley (Strathclyde University) Bayes linear adjustments to improve empirical Bayes inference for correlated event rates Empirical Bayes offers a means of obtaining robust inference by pooling data on processes that have similar, although not identical, rates of occurrence and then adjusting the pooled estimate through Bayes Theorem to adjust the estimate to the experience of each individual process. The accuracy of Empirical Bayes estimates depends on the degree of homogeneity of the processes within the pool. To date, Empirical Bayes inference methods have been developed assuming that rates are statistically independent of one another. While a useful starting assumption, it may not be realistic in practice. We present an approach to estimate the rates of occurrence of events assuming correlations exist between the rates. The approach uses the Method of Moments to find Empirical Bayes estimates of the model parameters. These estimates are adjusted to give individual estimates for each event using Bayes linear methods, a linear fitting procedure which uses a similar subjective basis for inference as a full Bayesian analysis. We compare the accuracy of the estimates obtained with our proposed methods relative to exact inference for a full Bayesian model based on a Homogeneous Poisson Process (HPP) with a multivariate gamma prior distribution. (Joint work with Kevin Wilson, Tim Bedford and Lesley Walls.) 4. Dr Simon Blake and Dr Matthias Troffaes (Durham University) Common-cause failure modelling for power network geometry and maintenance decisions: a case study In power networks, redundancy is one of the main guards against system failure. Often, components, such as transmission lines and transformers, are assumed to fail independently, even if data suggests otherwise. In this talk, we explore a case study at a location in the North of England, consisting of four transformers and three transmission lines. We investigate ways to improve the statistical modelling of system failure, where common-cause failures are explicitly taken into account, and investigate how they affect decisions regarding network maintenance and geometry.