Prediction intervals to account for uncertainties in travel time prediction

The accurate prediction of travel times is desirable but frequently prone to error. This is mainly attributable to both the underlying traffic processes and the data that are used to infer travel time. A more meaningful and pragmatic approach is to view travel time prediction as a probabilistic inference and to construct prediction intervals (PIs), which cover the range of probable travel times travelers may encounter. This paper introduces the delta and Bayesian techniques for the construction of PIs. Quantitative measures are developed and applied for a comprehensive assessment of the constructed PIs. These measures simultaneously address two important aspects of PIs: 1) coverage probability and 2) length. The Bayesian and delta methods are used to construct PIs for the neural network (NN) point forecasts of bus and freeway travel time data sets. The obtained results indicate that the delta technique outperforms the Bayesian technique in terms of narrowness of PIs with satisfactory coverage probability. In contrast, PIs constructed using the Bayesian technique are more robust against the NN structure and exhibit excellent coverage probability.

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.

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.

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.

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.

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.

Constructing optimal prediction intervals by using neural networks and bootstrap method

This brief proposes an efficient technique for the construction of optimized prediction intervals (PIs) by using the bootstrap technique. The method employs an innovative PI-based cost function in the training of neural networks (NNs) used for estimation of the target variance in the bootstrap method. An optimization algorithm is developed for minimization of the cost function and adjustment of NN parameters. The performance of the optimized bootstrap method is examined for seven synthetic and real-world case studies. It is shown that application of the proposed method improves the quality of constructed PIs by more than 28% over the existing technique, leading to narrower PIs with a coverage probability greater than the nominal confidence level.

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.