Learning from time series:Supervised Aggregative Feature Extraction

Many modeling problems require to estimate a scalar output from one or more time series. Such problems are usually tackled by extracting a fixed number of features from the time series (like their statistical moments), with a consequent loss in information that leads to suboptimal predictive models. Moreover, feature extraction techniques usually make assumptions that are not met by real world settings (e.g. uniformly sampled time series of constant length), and fail to deliver a thorough methodology to deal with noisy data. In this paper a methodology based on functional learning is proposed to overcome the aforementioned problems; the proposed Supervised Aggregative Feature Extraction (SAFE) approach allows to derive continuous, smooth estimates of time series data (yielding aggregate local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The SAFE paradigm enjoys several properties like closed form solution, incorporation of first and second order derivative information into the regressor matrix, interpretability of the generated functional predictor and the possibility to exploit Reproducing Kernel Hilbert Spaces setting to yield nonlinear predictive models. Simulation studies are provided to highlight the strengths of the new methodology w.r.t. standard unsupervised feature selection approaches. © 2012 IEEE.

An ultra-short-term wind power prediction method using “offline classification and optimization, online model matching” based on time series features

The applicability of ultra-short-term wind power prediction (USTWPP) models is reviewed. The USTWPP method proposed extracts featrues from historical data of wind power time series (WPTS), and classifies every short WPTS into one of several different subsets well defined by stationary patterns. All the WPTS that cannot match any one of the stationary patterns are sorted into the subset of nonstationary pattern. Every above WPTS subset needs a USTWPP model specially optimized for it offline. For on-line application, the pattern of the last short WPTS is recognized, then the corresponding prediction model is called for USTWPP. The validity of the proposed method is verified by simulations.

Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.

Analysis of groundwater-level response to rainfall and recharge estimates in fractured hard rock aquifers, NW Ireland

Despite fractured hard rock aquifers underlying over 65% of Ireland, knowledge of key processes controlling groundwater recharge in these bedrock systems is inadequately constrained. In this study, we examined 19 groundwater-level hydrographs from two Irish hillslope sites underlain by hard rock aquifers. Water-level time-series in clustered monitoring wells completed at the subsoil, soil/bedrock interface, shallow and deep bedrocks were continuously monitored hourly over two hydrological years. Correlation methods were applied to investigate groundwater-level response to rainfall, as well as its seasonal variations. The results reveal that the direct groundwater recharge to the shallow and deep bedrocks on hillslope is very limited. Water-level variations within these geological units are likely dominated by slow flow rock matrix storage. The rapid responses to rainfall (⩽2 h) with little seasonal variations were observed to the monitoring wells installed at the subsoil and soil/bedrock interface, as well as those in the shallow or deep bedrocks at the base of the hillslope. This suggests that the direct recharge takes place within these units. An automated time-series procedure using the water-table fluctuation method was developed to estimate groundwater recharge from the water-level and rainfall data. Results show the annual recharge rates of 42–197 mm/yr in the subsoil and soil/bedrock interface, which represent 4–19% of the annual rainfall. Statistical analysis of the relationship between the rainfall intensity and water-table rise reveal that the low rainfall intensity group (⩽1 mm/h) has greater impact on the groundwater recharge rate than other groups (>1 mm/h). This study shows that the combination of the time-series analysis and the water-table fluctuation method could be an useful approach to investigate groundwater recharge in fractured hard rock aquifers in Ireland.