Ensemble Stochastic Configuration Networks for Estimating Prediction Intervals: A Simultaneous Robust Training Algorithm and Its Application

Obtaining accurate point prediction of industrial processes' key variables is challenging due to the outliers and noise that are common in industrial data. Hence the prediction intervals (PIs) have been widely adopted to quantify the uncertainty related to the point prediction. In order to improve the prediction accuracy and quantify the level of uncertainty associated with the point prediction, this article estimates the PIs by using ensemble stochastic configuration networks (SCNs) and bootstrap method. The estimated PIs can guarantee both the modeling stability and computational efficiency. To encourage the cooperation among the base SCNs and improve the robustness of the ensemble SCNs when the training data are contaminated with noise and outliers, a simultaneous robust training method of the ensemble SCNs is developed based on the Bayesian ridge regression and M-estimate. Moreover, the hyperparameters of the assumed distributions over noise and output weights of the ensemble SCNs are estimated by the expectation-maximization (EM) algorithm, which can result in the optimal PIs and better prediction accuracy. Finally, the performance of the proposed approach is evaluated on three benchmark data sets and a real-world data set collected from a refinery. The experimental results demonstrate that the proposed approach exhibits better performance in terms of the quality of PIs, prediction accuracy, and robustness.

Probability Density Forecasting of Wind Speed Based on Quantile Regression and Kernel Density Estimation

Based on quantile regression (QR) and kernel density estimation (KDE), a framework for probability density forecasting of short-term wind speed is proposed in this study. The empirical mode decomposition (EMD) technique is implemented to reduce the noise of raw wind speed series. Both linear QR (LQR) and nonlinear QR (NQR, including quantile regression neural network (QRNN), quantile regression random forest (QRRF), and quantile regression support vector machine (QRSVM)) models are, respectively, utilized to study the de-noised wind speed series. An ensemble of conditional quantiles is obtained and then used for point and interval predictions of wind speed accordingly. After various experiments and comparisons on the real wind speed data at four wind observation stations of China, it is found that the EMD-LQR-KDE and EMD-QRNN-KDE generally have the best performance and robustness in both point and interval predictions. By taking conditional quantiles obtained by the EMD-QRNN-KDE model as the input, probability density functions (PDFs) of wind speed at different times are obtained by the KDE method, whose bandwidth is optimally determined according to the normal reference criterion. It is found that most actual wind speeds lie near the peak of predicted PDF curves, indicating that the probabilistic density prediction by EMD-QRNN-KDE is believable. Compared with the PDF curves of the 90% confidence level, the PDF curves of the 80% confidence level usually have narrower wind speed ranges and higher peak values. The PDF curves also vary with time. At some times, they might be biased, bimodal, or even multi-modal distributions. Based on the EMD-QRNN-KDE model, one can not only obtain the specific PDF curves of future wind speeds, but also understand the dynamic variation of density distributions with time. Compared with the traditional point and interval prediction models, the proposed QR-KDE models could acquire more information about the randomness and uncertainty of the actual wind speed, and thus provide more powerful support for the decision-making work.

A Survey of Computational Intelligence Techniques for Wind Power Uncertainty Quantification in Smart Grids

The high penetration level of renewable energy is thought to be one of the basic characteristics of future smart grids. Wind power, as one of the most increasing renewable energy, has brought a large number of uncertainties into the power systems. These uncertainties would require system operators to change their traditional ways of decision-making. This article provides a comprehensive survey of computational intelligence techniques for wind power uncertainty quantification in smart grids. First, prediction intervals (PIs) are introduced as a means to quantify the uncertainties in wind power forecasts. Various PI evaluation indices, including the latest trends in comprehensive evaluation techniques, are compared. Furthermore, computational intelligence-based PI construction methods are summarized and classified into traditional methods (parametric) and direct PI construction methods (nonparametric). In the second part of this article, methods of incorporating wind power forecast uncertainties into power system decision-making processes are investigated. Three techniques, namely, stochastic models, fuzzy logic models, and robust optimization, and different power system applications using these techniques are reviewed. Finally, future research directions, such as spatiotemporal and hierarchical forecasting, deep learning-based methods, and integration of predictive uncertainty estimates into the decision-making process, are discussed. This survey can benefit the readers by providing a complete technical summary of wind power uncertainty quantification and decision-making in smart grids.

Deterministic and Interval Wind Speed Prediction Method in Offshore Wind Farm Considering the Randomness of Wind

In order to improve the prediction accuracy of wind speed, this paper proposes a hybrid wind speed prediction (WSP) method considering the fluctuation, randomness and nonlinear of wind, which can be applied to short-term deterministic and interval prediction. Variational mode decomposition (VMD) decomposes wind speed time series into nonlinear series Intrinsic mode function 1 (IMF1), stationary time series IMF2 and error sreies (ER). Principal component analysis-Radial basis function (PCA-RBF) model is used to model the nonlinear series IMF1, where PCA is applied to reduce the redundant information. Long short-term memory (LSTM) is used to establish a stationary time series model for IMF2, which can better describe the fluctuation trend of wind speed; mixture Gaussian process regression (MGPR) is used to predict ER to obtain deterministic and interval prediction results simultaneously. Finally, above methods are reconstructed to form VMD-PRBF-LSTM-MGPR which is the abbreviation of hybrid model to obtain the final results of WSP, which can better reflect the volatility of wind speed. Nine comparison models are built to verify the availability of the hybrid model. The mean absolute percentage error (MAE) and mean square error (MSE) of deterministic WSP of the proposed model are only 0.0713 and 0.3158 respectively, which are significantly smaller than the prediction results of comparison models. In addition, confidence intervals (CIs) and prediction interval (PIs) are compared in this paper. The experimental results show that both of them can quantify and represent forecast uncertainty and the PIs is wider than the corresponding CIs.

Deep Learning Method Based on Gated Recurrent Unit and Variational Mode Decomposition for Short-Term Wind Power Interval Prediction

Wind power interval prediction (WPIP) plays an increasingly important role in evaluations of the uncertainty of wind power and becomes necessary for managing and planning power systems. However, the intermittent and fluctuating characteristics of wind power mean that high-quality prediction intervals (PIs) production is a challenging problem. In this article, we propose a novel hybrid model for the WPIP based on the gated recurrent unit (GRU) neural networks and variational mode decomposition (VMD). In the hybrid model, VMD is employed to decompose complex wind power data into simplified modes. Basic GRU prediction models, comprising a GRU input layer, multiple fully connected layers, and a rank-ordered terminal layer, are then trained for each mode to produce PIs, which are combined to obtain final PIs. In addition, an adaptive optimization method based on constructed intervals (CIs) is proposed to build high-quality training labels for supervised learning with the hybrid model. Several numerical experiments were implemented to validate the effectiveness of the proposed method. The results indicate that the proposed method performs better than the traditional interval prediction models with much higher quality PIs, and it requires less training time.

Landslide displacement interval prediction using lower upper bound estimation method with pre-trained random vector functional link network initialization

Interval prediction is an efficient approach to quantifying the uncertainties associated with landslide evolution. In this paper, a novel method, termed lower upper bound estimation (LUBE), of constructing prediction intervals (PIs) based on neural networks (NNs) is applied and extended to landslide displacement prediction. A random vector functional link network (RVFLN) is adopted as the NN used in the improved LUBE. A hybrid evolutionary algorithm, termed PSOGSA, that combines particle swarm optimization (PSO) and gravitational search algorithm (GSA) is utilized to train LUBE. The loss function of LUBE is redesigned by considering the quality of PI centre, which allows for a more comprehensive evaluation of PIs. The population initialization in the training process of LUBE is implemented by transferring the weights of a series of pre-trained RVFLNs. The performance of the improved LUBE method is validated by considering a comprehensive set of cases using seven benchmark datasets. In addition, a hybrid method that integrates ensemble empirical mode decomposition (EEMD) with the improved LUBE is proposed for the special case of landslide displacement prediction. Six real-world reservoir-induced landslides are considered to validate the capability and merit of the proposed hybrid method.

Variational Bayesian Neural Network for Ensemble Flood Forecasting

Disastrous floods are destructive and likely to cause widespread economic losses. An understanding of flood forecasting and its potential forecast uncertainty is essential for water resource managers. Reliable forecasting may provide future streamflow information to assist in an assessment of the benefits of reservoirs and the risk of flood disasters. However, deterministic forecasting models are not able to provide forecast uncertainty information. To quantify the forecast uncertainty, a variational Bayesian neural network (VBNN) model for ensemble flood forecasting is proposed in this study. In VBNN, the posterior distribution is approximated by the variational distribution, which can avoid the heavy computational costs in the traditional Bayesian neural network. To transform the model parameters’ uncertainty into the model output uncertainty, a Monte Carlo sample is applied to give ensemble forecast results. The proposed method is verified by a flood forecasting case study on the upper Yangtze River. A point forecasting model neural network and two probabilistic forecasting models, including hidden Markov Model and Gaussian process regression, are also applied to compare with the proposed model. The experimental results show that the VBNN performs better than other comparable models in terms of both accuracy and reliability. Finally, the result of uncertainty estimation shows that the VBNN can effectively handle heteroscedastic flood streamflow data.

Development and Analysis of Neural Networks Realized in the Presence of Granular Data

In this article, we propose a design and evaluation framework of granular neural networks realized in the presence of information granules. Neural networks realized in this manner are able to process both nonnumerical data, such as information granules as well as numerical data. Information granules are meaningful and semantically sound entities formed by organizing existing knowledge and available experimental data. The directional nature of mapping between the input and output data needs to be considered when building information granules. The development of neural networks advocated in this article is realized as a two-phase process. First, a collection of information granules is formed through granulation of numeric data in the input and output spaces. Second, neural networks are constructed on the basis of information granules rather than original (numeric) data. The proposed method leads to the construction of neural networks in a completely new way. In comparison with traditional (numeric) neural networks, the networks developed in the presence of granular data require shorter learning time. They also produce the results (outputs) that are information granules rather than numeric entities. The quality of granular outputs generated by our neural networks is evaluated in terms of the coverage and specificity criteria that are pertinent to the characterization of the information granules.

Performance Evaluation of Probabilistic Methods Based on Bootstrap and Quantile Regression to Quantify PV Power Point Forecast Uncertainty

This paper presents two probabilistic approaches based on bootstrap method and quantile regression (QR) method to estimate the uncertainty associated with solar photovoltaic (PV) power point forecasts. Solar PV output power forecasts are obtained using a hybrid intelligent model, which is composed of a data filtering technique based on wavelet transform (WT) and a soft computing model (SCM) based on radial basis function neural network (RBFNN) that is optimized by particle swarm optimization (PSO) algorithm. The point forecast capability of the proposed hybrid WT+RBFNN+PSO intelligent model is examined and compared with other hybrid models as well as individual SCM. The performance of the proposed bootstrap method in the form of probabilistic forecasts is compared with the QR method by generating different prediction intervals (PIs). Numerical tests using real data demonstrate that the point forecasts obtained from the proposed hybrid intelligent model can be effectively used to quantify PV power uncertainty. The performance of these two uncertainty quantification methods is assessed through reliability.

A Hybrid Double Forecasting System of Short Term Power Load Based on Swarm Intelligence and Nonlinear Integration Mechanism

Accurate and reliable power load forecasting not only takes an important place in management and steady running of smart grid, but also has environmental benefits and economic dividends. Accurate load point forecasting can provide a guarantee for the daily operation of the power grid, and effective interval forecasting can further quantify the uncertainty of power load on this basis to provide dependable and precise load information. However, most of the previous work focuses on the deterministic point prediction of power load and rarely considers the interval prediction of power load, which makes the prediction of power load not comprehensive. In this study, a new double hybrid load forecasting system including point forecasting module and interval forecasting module is developed, which can make up for the shortcomings of incomplete analysis for the existing research. The point forecasting module adopts a nonlinear integration mechanism based on Back Propagation (BP) network optimized by Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D) to improve the accuracy of point prediction. A fuzzy clustering interval prediction method based on different data feature classification is successfully proposed which provides an effective tool for load uncertainty analysis. The experiment results show that the system not only has a good effect in accurately predicting power load, but also can analyze the uncertainty of the power load, which can be used as an effective technology of power system planning.

Improving Prediction Intervals Using Measured Solar Power with a Multi-Objective Approach

Prediction Intervals are pairs of lower and upper bounds on point forecasts and are useful to take into account the uncertainty on predictions. This article studies the influence of using measured solar power, available at prediction time, on the quality of prediction intervals. While previous studies have suggested that using measured variables can improve point forecasts, not much research has been done on the usefulness of that additional information, so that prediction intervals with less uncertainty can be obtained. With this aim, a multi-objective particle swarm optimization method was used to train neural networks whose outputs are the interval bounds. The inputs to the network used measured solar power in addition to hourly meteorological forecasts. This study was carried out on data from three different locations and for five forecast horizons, from 1 to 5 h. The results were compared with two benchmark methods (quantile regression and quantile regression forests). The Wilcoxon test was used to assess statistical significance. The results show that using measured power reduces the uncertainty associated to the prediction intervals, but mainly for the short forecasting horizons.

Projecting the Most Likely Annual Urban Heat Extremes in the Central United States

Climate studies based on global climate models (GCMs) project a steady increase in annual average temperature and severe heat extremes in central North America during the mid-century and beyond. However, the agreement of observed trends with climate model trends varies substantially across the region. The present study focuses on two different locations: Des Moines, IA and Austin, TX. In Des Moines, annual extreme temperatures have not increased over the past three decades unlike the trend of regionally-downscaled GCM data for the Midwest, likely due to a “warming hole” over the area linked to agricultural factors. This warming hole effect is not evident for Austin over the same time period, where extreme temperatures have been higher than projected by regionally-downscaled climate (RDC) forecasts. In consideration of the deviation of such RDC extreme temperature forecasts from observations, this study statistically analyzes RDC data in conjunction with observational data to define for these two cities a 95% prediction interval of heat extreme values by 2040. The statistical model is constructed using a linear combination of RDC ensemble-member annual extreme temperature forecasts with regression coefficients for individual forecasts estimated by optimizing model results against observations over a 52-year training period.

Solar Power Interval Prediction via Lower and Upper Bound Estimation with a New Model Initialization Approach

This paper proposes a new model initialization approach for solar power prediction interval based on the lower and upper bound estimation (LUBE) structure. The linear regression interval estimation (LRIE) was first used to initialize the prediction interval and the extreme learning machine auto encoder (ELM-AE) is then employed to initialize the input weight matrix of the LUBE. Based on the initialized prediction interval and input weight matrix, the output weight matrix of the LUBE could be obtained, which was close to optimal values. The heuristic algorithm was employed to train the LUBE prediction model due to the invalidation of the traditional training approach. The proposed model initialization approach was compared with the point prediction initialization and random initialization approaches. To validate its performance, four heuristic algorithms, including particle swarm optimization (PSO), simulated annealing (SA), harmony search (HS), and differential evolution (DE), were introduced. Based on the experiment results, the proposed model initialization approach with different heuristic algorithms was better than the point prediction initialization and random initialization approaches. The PSO can obtain the best efficiency and effectiveness of the optimal solution searching in four heuristic algorithms. Besides, the ELM-AE can weaken the over-fitting phenomenon of the training model, which is brought in by the heuristic algorithm, and guarantee the model stable output.

Short-Term Load Interval Prediction Using a Deep Belief Network

In load predication, point-based forecasting methods have been widely applied. However, uncertainties arising in load predication bring significant challenges for such methods. This therefore drives the development of new methods amongst which interval predication is one of the most effective. In this study, a deep belief network-based lower–upper bound estimation (LUBE) approach is proposed, and a genetic algorithm is applied to reinforce the search ability of the LUBE method, instead of simulated an annealing algorithm. The approach is applied to the short-term load prediction on some realistic electricity load data. To demonstrate the effectiveness and efficiency of the proposed method, it is compared with three state-of-the-art methods. Experimental results show that the proposed approach can significantly improve the predication accuracy.

Wind Power Forecasting Using Multi-Objective Evolutionary Algorithms for Wavelet Neural Network-Optimized Prediction Intervals

The intermittency of renewable energy will increase the uncertainty of the power system, so it is necessary to predict the short-term wind power, after which the electrical power system can operate reliably and safely. Unlike the traditional point forecasting, the purpose of this study is to quantify the potential uncertainties of wind power and to construct prediction intervals (PIs) and prediction models using wavelet neural network (WNN). Lower upper bound estimation (LUBE) of the PIs is achieved by minimizing a multi-objective function covering both interval width and coverage probabilities. Considering the influence of the points out of the PIs to shorten the width of PIs without compromising coverage probability, a new, improved, multi-objective artificial bee colony (MOABC) algorithm combining multi-objective evolutionary knowledge, called EKMOABC, is proposed for the optimization of the forecasting model. In this paper, some comparative simulations are carried out and the results show that the proposed model and algorithm can achieve higher quality PIs for wind power forecasting. Taking into account the intermittency of renewable energy, such a type of wind power forecast can actually provide a more reliable reference for dispatching of the power system.

Landslide Displacement Prediction With Uncertainty Based on Neural Networks With Random Hidden Weights

In this paper, we propose a new approach to establish a landslide displacement forecasting model based on artificial neural networks (ANNs) with random hidden weights. To quantify the uncertainty associated with the predictions, a framework for probabilistic forecasting of landslide displacement is developed. The aim of this paper is to construct prediction intervals (PIs) instead of deterministic forecasting. A lower-upper bound estimation (LUBE) method is adopted to construct ANN-based PIs, while a new single hidden layer feedforward ANN with random hidden weights for LUBE is proposed. Unlike the original implementation of LUBE, the input weights and hidden biases of the ANN are randomly chosen, and only the output weights need to be adjusted. Combining particle swarm optimization (PSO) and gravitational search algorithm (GSA), a hybrid evolutionary algorithm, PSOGSA, is utilized to optimize the output weights. Furthermore, a new ANN objective function, which combines a modified combinational coverage width-based criterion with one-norm regularization, is proposed. Two benchmark data sets and two real-world landslide data sets are presented to illustrate the capability and merit of our method. Experimental results reveal that the proposed method can construct high-quality PIs.

Two Machine Learning Approaches for Short-Term Wind Speed Time-Series Prediction

The increasing liberalization of European electricity markets, the growing proportion of intermittent renewable energy being fed into the energy grids, and also new challenges in the patterns of energy consumption (such as electric mobility) require flexible and intelligent power grids capable of providing efficient, reliable, economical, and sustainable energy production and distribution. From the supplier side, particularly, the integration of renewable energy sources (e.g., wind and solar) into the grid imposes an engineering and economic challenge because of the limited ability to control and dispatch these energy sources due to their intermittent characteristics. Time-series prediction of wind speed for wind power production is a particularly important and challenging task, wherein prediction intervals (PIs) are preferable results of the prediction, rather than point estimates, because they provide information on the confidence in the prediction. In this paper, two different machine learning approaches to assess PIs of time-series predictions are considered and compared: 1) multilayer perceptron neural networks trained with a multiobjective genetic algorithm and 2) extreme learning machines combined with the nearest neighbors approach. The proposed approaches are applied for short-term wind speed prediction from a real data set of hourly wind speed measurements for the region of Regina in Saskatchewan, Canada. Both approaches demonstrate good prediction precision and provide complementary advantages with respect to different evaluation criteria.

An Interval-Valued Neural Network Approach for Uncertainty Quantification in Short-Term Wind Speed Prediction

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.