We consider the task of performing prediction with neural networks (NNs) on the basis of uncertain input data expressed in the form of intervals. We aim at quantifying the uncertainty in the prediction arising from both the input data and the prediction model. A multilayer perceptron NN is trained to map interval-valued input data onto interval outputs, representing the prediction intervals (PIs) of the real target values. The NN training is performed by nondominated sorting genetic algorithm-II, so that the PIs are optimized both in terms of accuracy (coverage probability) and dimension (width). Demonstration of the proposed method is given in two case studies: 1) a synthetic case study, in which the data have been generated with a 5-min time frequency from an autoregressive moving average model with either Gaussian or Chi-squared innovation distribution and 2) a real case study, in which experimental data consist of wind speed measurements with a time step of 1 h. Comparisons are given with a crisp (single-valued) approach. The results show that the crisp approach is less reliable than the interval-valued input approach in terms of capturing the variability in input.

In this paper, a novel Dynamic-Weighted Probabilistic Support Vector Regression-based Ensemble (DW-PSVR-ensemble) approach is proposed for prognostics of time series data monitored on components of complex power systems. The novelty of the proposed approach consists in i) the introduction of a signal reconstruction and grouping technique suited for time series data, ii) the use of a modified Radial Basis Function (RBF) kernel for multiple time series data sets, iii) a dynamic calculation of sub-models weights for the ensemble, and iv) an aggregation method for uncertainty estimation. The dynamic weighting is introduced in the calculation of the sub-models' weights for each input vector, based on Fuzzy Similarity Analysis (FSA). We consider a real case study involving 20 failure scenarios of a component of the Reactor Coolant Pump (RCP) of a typical nuclear Pressurized Water Reactor (PWR). Prediction results are given with the associated uncertainty quantification, under the assumption of a Gaussian distribution for the predicted value.