Novel methods for distributed acoustic sensing data

Wilson, Rebecca and Eckley, Idris and Nunes, Matthew and Park, Timothy Alexander (2019) Novel methods for distributed acoustic sensing data. PhD thesis, Lancaster University.

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Abstract

In this thesis, we propose novel methods for analysing nonstationary, multivariate time series, focusing in particular on the problems of classification and imputation within this context. Many existing methods for time series classification are static, in that they assign the entire series to one class and do not allow for temporal dependence with the signal. In the first part of this thesis, we propose a computationally efficient extension of an existing dynamic classification method to the online setting. Dependence within the series is captured by adopting the multivariate locally stationary wavelet (mvLSW) framework and the signal is classified at each time point into one of a number of known classes. We apply the method to multivariate acoustic sensing data in order to detect anomalous regions and evaluate the results against alternative methods in the literature. The second part of this thesis considers imputation in multivariate locally stationary time series containing missing values. We first introduce a method for estimating the local wavelet spectral matrix that can be used in the presence of missingness. We then propose a novel method for imputing missing values that uses the local auto and cross-covariance functions of a mvLSW process to perform one step-ahead forecasting and backcasting. The performance of this nonstationary imputation approach is then assessed against competitor methods for simulated examples and a case study involving a dataset from a Carbon Capture and Storage facility. The software that implements this imputation scheme is also described, together with examples of the R package functionality.