Multi-aspect renewable energy forecasting

The increasing presence of renewable energy plants has created new challenges such as grid integration, load balancing and energy trading, making it fundamental to provide effective prediction models. Recent approaches in the literature have shown that exploiting spatio-temporal autocorrelation in data coming from multiple plants can lead to better predictions. Although tensor models and techniques are suitable to deal with spatio-temporal data, they have received little attention in the energy domain. In this paper, we propose a new method based on the Tucker tensor decomposition, capable of extracting a new feature space for the learning task. For evaluation purposes, we have investigated the performance of predictive clustering trees with the new feature space, compared to the original feature space, in three renewable energy datasets. The results are favorable for the proposed method, also when compared with state-of-the-art algorithms

Fast higher-order functions for tensor calculus with tensors and subtensors

Tensors analysis has become a popular tool for solving problems in computational neuroscience, pattern recognition and signal processing. Similar to the two-dimensional case, algorithms for multidimensional data consist of basic operations accessing only a subset of tensor data. With multiple offsets and step sizes, basic operations for subtensors require sophisticated implementations even for entrywise operations. In this work, we discuss the design and implementation of optimized higher-order functions that operate entrywise on tensors and subtensors with any non-hierarchical storage format and arbitrary number of dimensions. We propose recursive multi-index algorithms with reduced index computations and additional optimization techniques such as function inlining with partial template specialization. We show that single-index implementations of higher-order functions with subtensors introduce a runtime penalty of an order of magnitude than the recursive and iterative multi-index versions. Including data- and thread-level parallelization, our optimized implementations reach 68% of the maximum throughput of an Intel Core i9-7900X. In comparison with other libraries, the average speedup of our optimized implementations is up to 5x for map-like and more than 9x for reduce-like operations. For symmetric tensors we measured an average speedup of up to 4x

Approaches to Fault Detection for Heating Systems Using CP Tensor Decompositions

Two new signal-based and one model-based fault detection methods using canonical polyadic (CP) tensor decomposition algorithms are presented, and application examples of heating systems are given for all methods. The first signal-based fault detection method uses the factor matrices of a data tensor directly, the second calculates expected values from the decomposed tensor and compares these with measured values to generate the residuals. The third fault detection method is based on multi-linear models represented by parameter tensors with elements computed by subspace parameter identification algorithms and data for different but structured operating regimes. In case of missing data or model parameters in tensor representation, an approximation method based on a special CP tensor decomposition algorithm for incomplete tensors is proposed, called the decompose-and-unfold method. As long as all relevant dynamics has been recorded, this method approximates – also from incomplete data – models for all operating regimes, which can be used for residual generation and fault detection, e.g. by parity equations