Combined nonparametric prediction intervals for wind power generation

Prediction intervals (PIs) are a promising tool for quantification of uncertainties associated with point forecasts of wind power. However, construction of PIs using parametric methods is questionable, as forecast errors do not follow a standard distribution. This paper proposes a nonparametric method for construction of reliable PIs for neural network (NN) forecasts. A lower upper bound estimation (LUBE) method is adapted for construction of PIs for wind power generation. A new framework is proposed for synthesizing PIs generated using an ensemble of NN models in the LUBE method. This is done to guard against NN performance instability in generating reliable and informative PIs. A validation set is applied for short listing NNs based on the quality of PIs. Then, PIs constructed using filtered NNs are aggregated to obtain combined PIs. Performance of the proposed method is examined using data sets taken from two wind farms in Australia. Simulation results indicate that the quality of combined PIs is significantly superior to the quality of PIs constructed using NN models ranked and filtered by the validation set.

Prediction intervals for short-term wind farm power generation forecasts

Quantification of uncertainties associated with wind power generation forecasts is essential for optimal management of wind farms and their successful integration into power systems. This paper investigates two neural network-based methods for direct and rapid construction of prediction intervals (PIs) for short-term forecasting of power generation in wind farms. The lower upper bound estimation and bootstrap methods are used to quantify uncertainties associated with forecasts. The effectiveness and efficiency of these two general methods for uncertainty quantification is examined using twenty four month data from a wind farm in Australia. PIs with a confidence level of 90% are constructed for four forecasting horizons: five, ten, fifteen, and thirty minutes. Quantitative measures are applied for objective evaluation and unbiased comparison of PI quality. Demonstrated results indicate that reliable PIs can be constructed in a short time without resorting to complicate computational methods or models. Also quantitative comparison reveals that bootstrap PIs are more suitable for short prediction horizon, and lower upper bound estimation PIs are more appropriate for longer forecasting horizons.

Prediction intervals for electricity load forecasting using neural networks

Most of the research in time series is concerned with point forecasting. In this paper we focus on interval forecasting and its application for electricity load prediction. We extend the LUBE method, a neural network-based method for computing prediction intervals. The extended method, called LUBEX, includes an advanced feature selector and an ensemble of neural networks. Its performance is evaluated using Australian electricity load data for one year. The results showed that LUBEX is able to generate high quality prediction intervals, using a very small number of previous lag variables and having acceptable training time requirements. The use of ensemble is shown to be critical for the accuracy of the results.

Short-term load and wind power forecasting using neural network-based prediction intervals

Electrical power systems are evolving from today's centralized bulk systems to more decentralized systems. Penetrations of renewable energies, such as wind and solar power, significantly increase the level of uncertainty in power systems. Accurate load forecasting becomes more complex, yet more important for management of power systems. Traditional methods for generating point forecasts of load demands cannot properly handle uncertainties in system operations. To quantify potential uncertainties associated with forecasts, this paper implements a neural network (NN)-based method for the construction of prediction intervals (PIs). A newly introduced method, called lower upper bound estimation (LUBE), is applied and extended to develop PIs using NN models. A new problem formulation is proposed, which translates the primary multiobjective problem into a constrained single-objective problem. Compared with the cost function, this new formulation is closer to the primary problem and has fewer parameters. Particle swarm optimization (PSO) integrated with the mutation operator is used to solve the problem. Electrical demands from Singapore and New South Wales (Australia), as well as wind power generation from Capital Wind Farm, are used to validate the PSO-based LUBE method. Comparative results show that the proposed method can construct higher quality PIs for load and wind power generation forecasts in a short time.

Linguistic computational model based on 2-tuples and intervals

Herrera and Mart́inez initiated a 2-tuple fuzzy linguistic representation model for computing with words.Moreover, Wang and Hao further developed a new 2-tuple fuzzy linguistic representation model to deal with the linguistic term sets that are not uniformly and symmetrically distributed. This study proposes another linguistic computational model based on 2-tuples and intervals, which we call an interval version of the 2-tuple fuzzy linguistic representation model. The proposed model possesses three steps: 1) interval numerical scale; 2) computation based on interval numbers; and 3) a generalized inverse operation of the interval numerical scale. The first step transforms linguistic terms into interval numbers, based on which the second step is executed with output as an interval number. Finally, this number is then mapped into the interval of the linguistic 2-tuples by the generalized inverse operation. This study also generalizes the numerical scale approach, presented in the Wang and Hao model, to set the interval numerical scale, by considering the context where semantics of linguistic terms are defined by interval type-2 fuzzy sets (IT2 FSs). In order to compare the proposed model with the existing linguistic computational model based on IT2 FSs, we have conducted extensive simulations. The simulations demonstrate that the results obtained by our proposal are consistent with the results of the linguistic computational model based on IT2 FSs (in some sense) in a vast majority of cases.

Construction of neural network-based prediction intervals for short-term electrical load forecasting

Short-term load forecasting (STLF) is of great importance for control and scheduling of electrical power systems. The uncertainty of power systems increases due to the random nature of climate and the penetration of the renewable energies such as wind and solar power. Traditional methods for generating point forecasts of load demands cannot properly handle uncertainties in datasets. To quantify these potential uncertainties associated with forecasts, this paper implements a neural network (NN)-based method for construction of prediction intervals (PIs). A newly proposed method, called lower upper bound estimation (LUBE), is applied to develop PIs using NN models. The primary multi-objective problem is firstly transformed into a constrained single-objective problem. This new problem formulation is closer to the original problem and has fewer parameters than the cost function. Particle swarm optimization (PSO) integrated with the mutation operator is used to solve the problem. Two case studies from Singapore and New South Wales (Australia) historical load datasets are used to validate the PSO-based LUBE method. Demonstrated results show that the proposed method can construct high quality PIs for load forecasting applications.

The addition of a surfactant at regular time intervals in the mechanical alloying process

The impact of regular additions of a surfactant (ethylene bis-stearamide; EBS) at different time intervals was investigated on the powder characteristics of a biomedical Ti-10Nb-3Mo alloy (wt.%). Ball milling was performed for 10 h on the elemental powders in four series of experiments at two rotation speeds (200 and 300 rpm). The addition of 2 wt.% total EBS at different time intervals during ball milling resulted in noticeable changes in particle size and morphology of the powders. The surfactant addition at shorter time intervals led to the formation of finer particles, a more homogenous powder distribution, a higher powder yield, and a lower contamination content in the final materials. Thermal analysis of the powders after ball milling suggested that differing decomposition rates of the surfactant were responsible for the measured powder particle changes and contamination contents. The results also indicated that the addition of surfactant during ball milling at 200 rpm caused a delay in the alloy formation, whereas ball milling at 300 rpm favored the formation of the titanium alloy.Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved.

A penalty-based aggregation operator for non-convex intervals

In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.

Incremental criterion prediction of personality facets over factors: obtaining unbiased estimates and confidence intervals

 Many researchers have argued that higher order models of personality such as the Five Factor Model are insufficient, and that facet-level analysis is required to better understand criteria such as well-being, job performance, and personality disorders. However, common methods in the extant literature used to estimate the incremental prediction of facets over factors have several shortcomings. This paper delineates these shortcomings by evaluating alternative methods using statistical theory, simulation, and an empirical example. We recommend using differences between Olkin-Pratt adjusted r-squared for factor versus facet regression models to estimate the incremental prediction of facets and present a method for obtaining confidence intervals for such estimates using double adjusted-. r-squared bootstrapping. We also provide an R package that implements the proposed methods.