A new fuzzy-based combined prediction interval for wind power forecasting

This paper makes use of the idea of prediction intervals (PIs) to capture the uncertainty associated with wind power generation in power systems. Since the forecasting errors cannot be appropriately modeled using distribution probability functions, here we employ a powerful nonparametric approach called lower upper bound estimation (LUBE) method to construct the PIs. The proposed LUBE method uses a new framework based on a combination of PIs to overcome the performance instability of neural networks (NNs) used in the LUBE method. Also, a new fuzzy-based cost function is proposed with the purpose of having more freedom and flexibility in adjusting NN parameters used for construction of PIs. In comparison with the other cost functions in the literature, this new formulation allows the decision-makers to apply their preferences for satisfying the PI coverage probability and PI normalized average width individually. As the optimization tool, bat algorithm with a new modification is introduced to solve the problem. The feasibility and satisfying performance of the proposed method are examined using datasets taken from different wind farms in Australia.

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 interval-based modelling of polymerization reactor: a new modelling strategy for chemical reactors

Precise and reliable modelling of polymerization reactor is challenging due to its complex reaction mechanism and non-linear nature. Researchers often make several assumptions when deriving theories and developing models for polymerization reactor. Therefore, traditional available models suffer from high prediction error. In contrast, data-driven modelling techniques provide a powerful framework to describe the dynamic behaviour of polymerization reactor. However, the traditional NN prediction performance is significantly dropped in the presence of polymerization process disturbances. Besides, uncertainty effects caused by disturbances present in reactor operation can be properly quantified through construction of prediction intervals (PIs) for model outputs. In this study, we propose and apply a PI-based neural network (PI-NN) model for the free radical polymerization system. This strategy avoids assumptions made in traditional modelling techniques for polymerization reactor system. Lower upper bound estimation (LUBE) method is used to develop PI-NN model for uncertainty quantification. To further improve the quality of model, a new method is proposed for aggregation of upper and lower bounds of PIs obtained from individual PI-NN models. Simulation results reveal that combined PI-NN performance is superior to those individual PI-NN models in terms of PI quality. Besides, constructed PIs are able to properly quantify effects of uncertainties in reactor operation, where these can be later used as part of the control process. © 2014 Taiwan Institute of Chemical Engineers.

A novel fuzzy multi-objective framework to construct optimal prediction intervals for wind power forecast

The forecasting behavior of the high volatile and unpredictable wind power energy has always been a challenging issue in the power engineering area. In this regard, this paper proposes a new multi-objective framework based on fuzzy idea to construct optimal prediction intervals (Pis) to forecast wind power generation more sufficiently. The proposed method makes it possible to satisfy both the PI coverage probability (PICP) and PI normalized average width (PINAW), simultaneously. In order to model the stochastic and nonlinear behavior of the wind power samples, the idea of lower upper bound estimation (LUBE) method is used here. Regarding the optimization tool, an improved version of particle swam optimization (PSO) is proposed. In order to see the feasibility and satisfying performance of the proposed method, the practical data of a wind farm in Australia is used as the case study.

Construction of neural network-based prediction intervals using particle swarm optimization

Prediction intervals (PIs) are excellent tools for quantification of uncertainties associated with point forecasts and predictions. This paper adopts and develops the lower upper bound estimation (LUBE) method for construction of PIs using neural network (NN) models. This method is fast and simple and does not require calculation of heavy matrices, as required by traditional methods. Besides, it makes no assumption about the data distribution. A new width-based index is proposed to quantitatively check how much PIs are informative. Using this measure and the coverage probability of PIs, a multi-objective optimization problem is formulated to train NN models in the LUBE method. The optimization problem is then transformed into a training problem through definition of a PI-based cost function. Particle swarm optimization (PSO) with the mutation operator is used to minimize the cost function. Experiments with synthetic and real-world case studies indicate that the proposed PSO-based LUBE method can construct higher quality PIs in a simpler and faster manner.

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.

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.

Prediction interval-based neural network modelling of polystyrene polymerization reactor - a new perspective of data-based modelling

In this paper, prediction interval (PI)-based modelling techniques are introduced and applied to capture the nonlinear dynamics of a polystyrene batch reactor system. Traditional NN models are developed using experimental datasets with and without disturbances. Simulation results indicate that traditional NNs cannot properly handle disturbances in reactor data and demonstrate a poor forecasting performance, with an average MAPE of 22% in the presence of disturbances. The lower upper bound estimation (LUBE) method is applied for the construction of PIs to quantify uncertainties associated with forecasts. The simulated annealing optimization technique is employed to adjust NN parameters for minimization of an innovative PI-based cost function. The simulation results reveal that the LUBE method generates quality PIs without requiring prohibitive computations. As both calibration and sharpness of PIs are practically and theoretically satisfactory, the constructed PIs can be used as part of the decision-making and control process of polymerization reactors. © 2014 The Institution of Chemical Engineers.

Uncertainty handling using neural network-based prediction intervals for electrical load forecasting

The complexity and level of uncertainty present in operation of power systems have significantly grown due to penetration of renewable resources. These complexities warrant the need for advanced methods for load forecasting and quantifying uncertainties associated with forecasts. The objective of this study is to develop a framework for probabilistic forecasting of electricity load demands. The proposed probabilistic framework allows the analyst to construct PIs (prediction intervals) for uncertainty quantification. A newly introduced method, called LUBE (lower upper bound estimation), is applied and extended to develop PIs using NN (neural network) models. The primary problem for construction of intervals is firstly formulated as a constrained single-objective problem. The sharpness of PIs is treated as the key objective and their calibration is considered as the constraint. PSO (particle swarm optimization) enhanced by the mutation operator is then used to optimally tune NN parameters subject to constraints set on the quality of PIs. Historical load datasets from Singapore, Ottawa (Canada) and Texas (USA) are used to examine performance of the proposed PSO-based LUBE method. According to obtained results, the proposed probabilistic forecasting method generates well-calibrated and informative PIs. Furthermore, comparative results demonstrate that the proposed PI construction method greatly outperforms three widely used benchmark methods. © 2014 Elsevier Ltd.

Improving the quality of prediction intervals through optimal aggregation

Neural networks (NNs) are an effective tool to model nonlinear systems. However, their forecasting performance significantly drops in the presence of process uncertainties and disturbances. NN-based prediction intervals (PIs) offer an alternative solution to appropriately quantify uncertainties and disturbances associated with point forecasts. In this paper, an NN ensemble procedure is proposed to construct quality PIs. A recently developed lower-upper bound estimation method is applied to develop NN-based PIs. Then, constructed PIs from the NN ensemble members are combined using a weighted averaging mechanism. Simulated annealing and a genetic algorithm are used to optimally adjust the weights for the aggregation mechanism. The proposed method is examined for three different case studies. Simulation results reveal that the proposed method improves the average PI quality of individual NNs by 22%, 18%, and 78% for the first, second, and third case studies, respectively. The simulation study also demonstrates that a 3%-4% improvement in the quality of PIs can be achieved using the proposed method compared to the simple averaging aggregation method.

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.

Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.