Interval Width Research Articles

Forecasting Hourly Global Horizontal Solar Irradiance in South Africa Using Machine Learning Models

Solar irradiance forecasting is essential in renewable energy grids amongst others for back-up programming, operational planning, and short-term power purchases. This study focuses on forecasting hourly solar irradiance using data obtained from the Southern African Universities Radiometric Network at the University of Pretoria radiometric station. The study compares the predictive performance of long short-term memory (LSTM) networks, support vector regression and feed forward neural networks (FFNN) models for forecasting short-term solar irradiance. While all the models outperform principal component regression model, a benchmark model in this study, the FFNN yields the lowest mean absolute error and root mean square error on the testing set. Empirical results show that the FFNN model produces the most accurate forecasts based on mean absolute error and root mean square error. Forecast combination of machine learning models' forecasts is done using convex combination and quantile regression averaging (QRA). The predictive performance we found is statistically significant on the Diebold Mariano and Giacomini-White tests. Based on all the forecast accuracy measures used in this study including the statistical tests, QRA is found to be the best forecast combination method. QRA was also the best forecasting model compared with the stand-alone machine learning models. The median method for combining interval limits gives the best results on prediction interval widths analysis. This is the first application of LSTM on South African and African solar irradiance data to the best of our knowledge. This study has shown that providing adequate and detailed evaluation metrics, including statistical tests in forecasting gives more insight into the developed forecasting models.

Interval Overvoltage Risk Based PV Hosting Capacity Evaluation Considering PV and Load Uncertainties

The increasing penetration of photovoltaic (PV) systems presents significant impacts on distribution network (DN) operations. To this end, an accurate evaluation of PV hosting capacity (PVHC) can help utilities to carry out PV capacity planning and configuration more effectively, ensuring the efficiency, economy, and reliability of DNs. First, the definition of interval overvoltage probability (IOP) is introduced and the IOP based PVHC evaluation method is presented. Next, this method is improved considering PV and load uncertainties, where the interval arithmetic (IA) and affine arithmetic (AA) are both applied to deal with uncertainties. In addition, the overvoltage severity is taken into account on the basis of IOP, and the concept of interval overvoltage risk (IOR) is proposed. A practical 55-bus rural feeder in China is used to illustrate the advantages of the proposed method compared with the conventional method, and also to verify the value in decision-making of PV planning for utilities. Moreover, the sensitivity of interval valued PVHC against the number of Monte Carlo simulation (MCS) and width of PV installation capacity interval (PICI) is analyzed. And the impacts of on-load tap changer (OLTC) tap positions and static var compensator (SVC) configurations are also explored. Finally, the proposed method is tested on the NYSEG 292-bus system to validate its adaptability on a larger and unbalanced system.

Risk Assessment of Power Generated from a Wind Turbine in Different Climate Cities in Indonesia.

In this paper, a risk analysis based on Monte Carlo Simulation has been used to examine the power generated from a wind turbine. There are five cities are selected based on the wind speed to be examined the power density generated from the wind turbine. The cities are Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak. Among the five cities, Kupang has the highest wind speed, while Pontianak has the lowest wind speed. In this study, the wind speed is assumed to be an unspecified parameter or a random variable. The Monte Carlo Simulation is run by using a software @RISK. The results show that the mean of power density generated from the wind turbine is found 171.23, 113.97, 71.28, 28.67, and 12.49 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively. The width of the confidence interval with the level of probability 90% is 110.30, 75.00, 69.10, 19.64, and 7.34 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively. The upper bound of the confidence intervals are 230.1, 154.7, 113.3, 39.27, and 16.30 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively, while the lower bounds are 119.8, 79.7, 44.2, and 19.63 W/m2 for Kupang, Tanjung Pinang, Krinci, Kotabaru, and Pontianak respectively. The probability of the power density will exceed the upper bound or will below the lower bound is 5%.

A new numerical technique for interval analysis of convection-diffusion heat transfer problems using LSE and optimization algorithm

This article devotes to the uncertain analysis of steady-state convection-diffusion heat transfer problems with interval input parameters in material properties, thermal source and boundary conditions. The optimization strategy is adopted to ensure a reliable bounds estimation when scales of interval width is larger, and a Galerkin system is derived to construct a Legendre Series Expansion (LSE) to surrogate FE solutions of deterministic problems, so as to reduce the computational expense in the optimization based bounds estimation with sufficient accuracy. A LSE-GS (global search), and a LSE-CM (combinatorial method) are presented to solve uncertain steady-state convection-diffusion heat transfer problems with multiple interval variables, and are extended to the fuzzy analysis. Various numerical examples are provided to verify the performance of the proposed method, and evidence the accuracy and effectiveness of the proposed methods for interval prediction of steady-state convection-diffusion heat transfer problems.

Influence of varying the Ethylene-Vinyl Acetate layer thicknesses on the performance of a polycrystalline silicon solar cell integrated with a microchannel heat sink

Modifying the polycrystalline silicon solar cell by reducing the thermal resistance of the ethylene–vinyl acetate (EVA) layer is essential to enhance the thermal management process. This modification will improve the heat dissipation process from the silicon wafer especially at a higher solar concentration ratio (CR) and in return enhance the solar cell performance and output power. Thus, a modified design of a solar cell integrated with a microchannel heat sink is developed. In this new design, variations of the Ethylene-Vinyl Acetate (EVA) upper- and lower-layer thickness along with the interval width between the two consecutive silicon layers are investigated. To determine the effect of varying the design parameters on the cell temperature at various solar concentration ratios and coolant mass rates, a three-dimensional comprehensive model for the solar cell integrated with a heat sink is developed. The model is simulated and validated with numerical results and measurements. Results indicate that reducing the EVA lower layer thickness has a remarkable effect on the solar cell temperature. At a solar concentration ratio of 20, varying the EVA lower layer thickness from 1.0 mm to 0.2 mm results in decreasing the maximum cell temperature from 102.3 °C to 69.3 °C. With further increase of the concentration ratio up to 30, the maximum cell temperature reduces from 138.3 °C to 87.4 °C. It is found that at a coolant rate of 2000 gm/min, and a concentration ratio of 20, maximum temperature in the modified and conventional solar cell with a lower EVA thickness of 0.2 mm and 0.5 mm, reaches 69.3 °C and 81.5 °C, respectively. Furthermore, the conventional cell efficiency is about 8.90%, while the modified one achieves 9.6%. At a CR = 30, the maximum temperature of the modified cell is 87.4 °C, while it is beyond the permissible temperature for the conventional cell. However, the solar cell temperature was not affected by varying the EVA upper layer and the interval width between the silicon layers. The finding of the current results provides another direction for researchers to utilize a higher concentration ratio with polycrystalline silicon solar cells.

Neural network-based construction of online prediction intervals

With the emergence of online learning systems which generate ever-growing amounts of data, quantifying the uncertainty in predictions regarding the system’s operation is becoming increasingly more important. Prediction intervals offer a powerful tool for assessing prediction uncertainty in artificial neural network applications; nevertheless, little work has been conducted on constructing prediction intervals for online learning applications. In this work, we propose a hybrid approach which employs artificial neural networks to directly estimate prediction intervals for both batch and online approximation scenarios. The aim of the approach is to provide high-quality prediction intervals, combining high coverage probability for future observations with small and thus informative interval widths. Compared with three popular methods for offline construction of prediction intervals, the proposed approach demonstrates a strong capacity for reliably representing prediction uncertainty in real-world regression applications. The approach is extended to adaptive approximation, whereby four online learning schemes are proposed to iteratively update prediction intervals based on recent measurements, requiring a reduced computational cost compared to offline approximation. The four online prediction intervals methods are compared over two synthetic and one real-world regression datasets, whereby data arrive in a sequential manner. Our results suggest the potential of an online learning scheme relying on a human-like memory mechanism, to construct high-quality online prediction intervals, capable of adapting to dynamic changes in data patterns. The proposed method is associated with low computational cost—an attractive feature for online learning applications requiring real-time performance.

Prediction Interval Adjustment for Load-Forecasting using Machine Learning

Electricity load-forecasting is an essential tool for effective power grid operation and energy markets. However, the lack of accuracy on the estimation of the electricity demand may cause an excessive or insufficient supply which can produce instabilities in the power grid or cause load cuts. Hence, probabilistic load-forecasting methods have become more relevant since these allow an understanding of not only load-point forecasts but also the uncertainty associated with it. In this paper, we develop a probabilistic load-forecasting method based on Association Rules and Artificial Neural Networks for Short-Term Load Forecasting (2 h ahead). First, neural networks are used to estimate point-load forecasts and the variance between these and observations. Then, using the latter, a simple prediction interval is calculated. Next, association rules are employed to adjust the prediction intervals by exploiting the confidence and support of the association rules. The main idea is to increase certainty regarding predictions, thus reducing prediction interval width in accordance to the rules found. Results show that the presented methodology provides a closer prediction interval without sacrificing accuracy. Prediction interval quality and effectiveness is measured using Prediction Interval Coverage Probability (PICP) and the Dawid–Sebastiani Score (DSS). PICP and DSS per horizon shows that the Adjusted and Normal prediction intervals are similar. Also, probabilistic and point-forecast Means Absolute Error (MAE) and Root Mean Squared Error (RMSE) metrics are used. Probabilistic MAE indicates that Adjusted prediction intervals fail by less than 2.5 MW along the horizons, which is not significant if we compare it to the 1.3 MW of the Normal prediction interval failure. Also, probabilistic RMSE shows that the probabilistic error tends to be larger than MAE along the horizons, but the maximum difference between Adjusted and Normal probabilistic RMSE is less than 6 MW, which is also not significant.

A comparison of some modified confidence intervals based on robust scale estimators for process capability index

This paper aims to compare the performances of modified confidence intervals based on robust scale estimators with classical confidence interval for process capability index (Cp) when the process has a non-normal distribution. The estimated coverage probability and the average width of the confidence intervals were obtained by a Monte-Carlo simulation under different scenarios. Simulation results showed that the modified confidence intervals performed well in terms of coverage probability and average width for all cases. Two real-life numerical examples from industry are analyzed to illustrate the performance and the implementation of the classical and modified confidence intervals for the process capability index (Cp) which also supported the results of the simulation study to some extent.

Noise Reduction with Fuzzy Inference Based on Generalized Mean and Singleton Input–Output Rules: Toward Fuzzy Rule Learning in a Unified Inference Platform

A method is proposed for reducing noise in learning data based on fuzzy inference methods called α-GEMII (α-level-set and generalized-mean-based inference with the proof of two-sided symmetry of consequences) and α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is particularly effective for reducing noise in randomly sampled data given by singleton input–output pairs for fuzzy rule optimization. In the proposed method, α-GEMII and α-GEMINAS are performed with singleton input–output rules and facts defined by fuzzy sets (non-singletons). The rules are initially set by directly using the input–output pairs of the learning data. They are arranged with the facts and consequences deduced by α-GEMII and α-GEMINAS. This process reduces noise to some extent and transforms the randomly sampled data into regularly sampled data for iteratively reducing noise at a later stage. The width of the regular sampling interval can be determined with tolerance so as to satisfy application-specific requirements. Then, the singleton input–output rules are updated with consequences obtained in iteratively performing α-GEMINAS for noise reduction. The noise reduction in each iteration is a deterministic process, and thus the proposed method is expected to improve the noise robustness in fuzzy rule optimization, relying less on trial-and-error-based progress. Simulation results demonstrate that noise is properly reduced in each iteration and the deviation in the learning data is suppressed considerably.

Landcover classification of satellite images based on an adaptive interval fuzzy c-means algorithm coupled with spatial information

ABSTRACTLandcover classifications have large uncertainty related to the heterogeneity of similar objects and complex spatial correlations in satellite images, making it difficult to obtain ideal classification results using traditional classification methods. Therefore, to address the uncertainty in landcover classifications based on remotely sensed information, we propose a novel fuzzy c-means algorithm, which integrates adaptive interval-valued modelling and spatial information. It dynamically adjusts the interval width according to the fuzzy degree of the target membership without pre-setting any parameters, controls the fuzziness of the target, and mines the inherent distribution of the data. Furthermore, reliability-based spatial correlation modelling is used to describe the spatial relationship of the target and to improve both robustness and accuracy of the algorithm. Experimental data consisting of SPOT5 (10-m spatial resolution) or Thematic Mapper (30-m spatial resolution) satellite data for three case study areas in China are used to test this algorithm. Compared with other state-of-the-art fuzzy classification methods, our algorithm markedly improved the ground-object separability. Moreover, it balanced improvement of pixel separability and suppression of heterogeneity of intra-class objects, producing more compact landcover areas and clearer boundaries between classes.

Large-Scale Assessment of a Smartwatch to Identify Atrial Fibrillation

BackgroundOptical sensors on wearable devices can detect irregular pulses. The ability of a smartwatch application (app) to identify atrial fibrillation during typical use is unknown.MethodsParticipants without atrial fibrillation (as reported by the participants themselves) used a smartphone (Apple iPhone) app to consent to monitoring. If a smartwatch-based irregular pulse notification algorithm identified possible atrial fibrillation, a telemedicine visit was initiated and an electrocardiography (ECG) patch was mailed to the participant, to be worn for up to 7 days. Surveys were administered 90 days after notification of the irregular pulse and at the end of the study. The main objectives were to estimate the proportion of notified participants with atrial fibrillation shown on an ECG patch and the positive predictive value of irregular pulse intervals with a targeted confidence interval width of 0.10.ResultsWe recruited 419,297 participants over 8 months. Over a median of 117 days of monitoring, 2161 participants (0.52%) received notifications of irregular pulse. Among the 450 participants who returned ECG patches containing data that could be analyzed — which had been applied, on average, 13 days after notification — atrial fibrillation was present in 34% (97.5% confidence interval [CI], 29 to 39) overall and in 35% (97.5% CI, 27 to 43) of participants 65 years of age or older. Among participants who were notified of an irregular pulse, the positive predictive value was 0.84 (95% CI, 0.76 to 0.92) for observing atrial fibrillation on the ECG simultaneously with a subsequent irregular pulse notification and 0.71 (97.5% CI, 0.69 to 0.74) for observing atrial fibrillation on the ECG simultaneously with a subsequent irregular tachogram. Of 1376 notified participants who returned a 90-day survey, 57% contacted health care providers outside the study. There were no reports of serious app-related adverse events.ConclusionsThe probability of receiving an irregular pulse notification was low. Among participants who received notification of an irregular pulse, 34% had atrial fibrillation on subsequent ECG patch readings and 84% of notifications were concordant with atrial fibrillation. This siteless (no on-site visits were required for the participants), pragmatic study design provides a foundation for large-scale pragmatic studies in which outcomes or adherence can be reliably assessed with user-owned devices. (Funded by Apple; Apple Heart Study ClinicalTrials.gov number, NCT03335800.)

Correlations between multiplicities and transverse momenta in nucleus-nucleus collisions from model with cluster of fused color strings

The long-range rapidity correlations between the multiplicities (n-n) and the transverse momentum and the multiplicity (pT-n) of charged particles are analyzed in the framework of the simple string inspired model with two types of sources. The sources of the first type correspond to the initial strings formed in a hadronic collision. The sources of the second type imitate the appearance of the emitters of a new kind resulting from interaction (fusion) of the initial strings. The model enabled to describe effectively the influence of the string fusion effects on the strength both the n-n and the pT-n correlations. Modification of the model to the analogue of the “core-corona” mechanism allows to take into account event selection criteria based on centrality and perform a comparison with existing experimental data on correlation measurements in nucleus-nucleus collisions at LHC energies. It is shown that string fusion effects in the model with the core-corona mechanism lead to the change of a sign of the pT-n correlation coefficient with a decrease of a centrality interval width.

Interval estimation of proportion ratios for stratified bilateral correlated binary data.

Confidence interval (CI) methods for the ratio of two proportions in the presence of correlated bilateral binary data are constructed for comparative clinical trials with stratified design. Simulations are conducted to evaluate the performance of the presented CIs with respect to mean coverage probability (MCP), mean interval width (MIW), and the ratio of mesial non-coverage probability to the distal non-coverage probability (RMNCP). Based on the empirical results, we suggest the use of the proposed CI method based on the complete score statistics (CS) for general applications. An example from a rheumatology study is used to demonstrate the proposed methodologies.

THERMAL ANALYSIS OF FOOD PRODUCTS USING DIFFERENTIAL SCANNING CALORIMETRY (DSC)

Intensity of changes during the freezing storage of frozen foods, depends on several factors. Changes of foods during freezing and thawing can be rapidly determined by scanning calorimetry (DSC). The aim of this study was to test the influence of scanning rate on the thermal properties of previously heat-treated food products (boiled apple), using the differential scanning calorimetry method. By increasing the scanning rate, significant changes (p0.05) Tcon from -14,20 °C (rate 5 °C/min) to -15.57 °C (rate 15 °C/min) and Tcend (from -17.53 °C to -22.90 °C) were determined, and ΔTc increased from 3.33 °C to 7.33 °C. At the same time, the width of the melting temperature interval (ΔTm) increased from 7.80 °C to 12.87 °C. The glass transition temperature (Tgmid) ranged from -7.15 °C (rate 5 °C/min) to -6.60 °C (rate 15 °C/min). Based on the obtained results, it was found that the scanning rate during the DSC determination statistically significantly (p0.05) influenced the measured values of the thermal properties of the tested heat-treated apple samples.

Comparison between two generalized process capability indices for Burr XII distribution using bootstrap confidence intervals

Process capability index is an effective indicator for gauging the capability of a process potential and performance. It is used to quantify the relation between the actual performance of the process and the preset specifications of the product. In this article, we utilize bootstrap re-sampling simulation method to construct bootstrap confidence intervals, namely, standard bootstrap, percentile bootstrap, Student’s t bootstrap (STB) and bias-corrected percentile bootstrap to study the difference between two generalized process capability indices $$C_{\text {pTk1}}$$ and $$C_{\text {pTk2}}$$ ($$\delta =C_{\text {pTk1}}-C_{\text {pTk2}}$$) and to select the better of the two processes or manufacturer’s (or supplier’s) through simulation when the underlying distribution is Burr XII distribution. The model parameters are estimated by maximum likelihood method. The proposed four bootstrap confidence intervals can be effectively employed to determine which one of the two processes or manufacturers (or suppliers) has a better process capability. Monte Carlo simulations are performed to compare the performances of the proposed bootstrap confidence intervals for $$\delta $$ in terms of their estimated average widths, coverage probabilities and relative coverages. Simulation results showed that the estimated average width and relative coverages of the STB confidence interval perform better than their counterparts. Finally, real data are presented to illustrate the bootstrap confidence intervals of the difference between two process capability indices.

Complexities in power analysis: Quantifying uncertainties with a Bayesian-classical hybrid approach.

Power analysis serves as the gold standard for evaluating study feasibility and justifying sample size. However, mainstream power analysis is often oversimplified, poorly reflecting complex reality during data analysis. This article highlights the complexities inherent in power analysis, especially when uncertainties present in data analysis are realistically taken into account. We introduce a Bayesian-classical hybrid approach to power analysis, which formally incorporates three sources of uncertainty into power estimates: (a) epistemic uncertainty regarding the unknown values of the effect size of interest, (b) sampling variability, and (c) uncertainty due to model approximation (i.e., models fit data imperfectly; Box, 1979; MacCallum, 2003). To illustrate the nature of estimated power from the Bayesian-classical hybrid method, we juxtapose its power estimates with those obtained from traditional (i.e., classical or frequentist) and Bayesian approaches. We employ an example in lexical processing (e.g., Yap & Seow, 2014) to illustrate underlying concepts and provide accompanying R and Rcpp code for computing power via the Bayesian-classical hybrid method. In general, power estimates become more realistic and much more varied after uncertainties are incorporated into their computation. As such, sample sizes should be determined by assurance (i.e., the mean of the power distribution) and the extent of variability in power estimates (e.g., interval width between 20th and 80th percentiles of the power distribution). We discuss advantages and challenges of incorporating the three stated sources of uncertainty into power analysis and, more broadly, research design. Finally, we conclude with future research directions. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Optical Method of Detection of Oil Contamination on Water Surface in UV Spectral Range

Efficiency analysis of optical (photo and radiometric) method of oil contamination detection based on differences between reflective characteristics of clean and oil-contaminated water surfaces was conducted with sounding wave selection in UV, visible, near-infrared and medium-infrared regions of the spectrum. It is shown that, in terms of eye safety, width of thickness interval of detected oil films and atmospheric attenuation, the most promising type of sounding for monitoring of oil contamination is UV sounding at a wavelength of 0.355 µm, which allowing to detect oil films with thickness of at least 2 µm reliably with probability of correct detection exceeding 0.9 and probability of false alarms of 0.002 with relative measurement noise not exceeding 5 %.

Confidence interval-based sample size determination formulas and some mathematical properties for hierarchical data.

The use of hierarchical data (also called multilevel data or clustered data) is common in behavioural and psychological research when data of lower-level units (e.g., students, clients, repeated measures) are nested within clusters or higher-level units (e.g., classes, hospitals, individuals). Over the past 25years we have seen great advances in methods for computing the sample sizes needed to obtain the desired statistical properties for such data in experimental evaluations. The present research provides closed-form and iterative formulas for sample size determination that can be used to ensure the desired width of confidence intervals for hierarchical data. Formulas are provided for a four-level hierarchical linear model that assumes slope variances and inclusion of covariates under both balanced and unbalanced designs. In addition, we address several mathematical properties relating to sample size determination for hierarchical data via the standard errors of experimental effect estimates. These include the relative impact of several indices (e.g., random intercept or slope variance at each level) on standard errors, asymptotic standard errors, minimum required values at the highest level, and generalized expressions of standard errors for designs with any-level randomization under any number of levels. In particular, information on the minimum required values will help researchers to minimize the risk of conducting experiments that are statistically unlikely to show the presence of an experimental effect.

Percentile-based grain size distribution analysis tools (GSDtools) – estimating confidence limits and hypothesis tests for comparing two samples

Abstract. Most studies of gravel bed rivers present at least one bed surface grain size distribution, but there is almost never any information provided about the uncertainty in the percentile estimates. We present a simple method for estimating the grain size confidence intervals about sample percentiles derived from standard Wolman or pebble count samples of bed surface texture. The width of a grain size confidence interval depends on the confidence level selected by the user (e.g., 95 %), the number of stones sampled to generate the cumulative frequency distribution, and the shape of the frequency distribution itself. For a 95 % confidence level, the computed confidence interval would include the true grain size parameter in 95 out of 100 trials, on average. The method presented here uses binomial theory to calculate a percentile confidence interval for each percentile of interest, then maps that confidence interval onto the cumulative frequency distribution of the sample in order to calculate the more useful grain size confidence interval. The validity of this approach is confirmed by comparing the predictions using binomial theory with estimates of the grain size confidence interval based on repeated sampling from a known population. We also developed a two-sample test of the equality of a given grain size percentile (e.g., D50), which can be used to compare different sites, sampling methods, or operators. The test can be applied with either individual or binned grain size data. These analyses are implemented in the freely available GSDtools package, written in the R language. A solution using the normal approximation to the binomial distribution is implemented in a spreadsheet that accompanies this paper. Applying our approach to various samples of grain size distributions in the field, we find that the standard sample size of 100 observations is typically associated with uncertainty estimates ranging from about ±15 % to ±30 %, which may be unacceptably large for many applications. In comparison, a sample of 500 stones produces uncertainty estimates ranging from about ±9 % to ±18 %. In order to help workers develop appropriate sampling approaches that produce the desired level of precision, we present simple equations that approximate the proportional uncertainty associated with the 50th and 84th percentiles of the distribution as a function of sample size and sorting coefficient; the true uncertainty in any sample depends on the shape of the sample distribution and can only be accurately estimated once the sample has been collected.

An Inter Type-2 FCR Algorithm Based T–S Fuzzy Model for Short-Term Wind Power Interval Prediction

Due to the intermittent and random nature of wind energy, wind power interval prediction (WPIP) is important to weaken the uncertainty and support the planning and scheduling of the power system. To improve the quality of WPIP, a novel fuzzy interval prediction model (FIPM) based on the lower upper bound estimation method is proposed in this paper. In the frame of the FIPM, a novel inter type-2 (IT-2) fuzzy model is designed to construct the lower and upper bounds of the prediction interval (PI), in which an IT-2 fuzzy c-regression algorithm is used to partition the data space and identify the fuzzy model. The gravitational search algorithm is employed to optimize the FIPM by minimizing coverage width-based criterion to reach a tradeoff between the interval width and coverage probability. In order to verify the effectiveness of the proposed method, existing interval prediction approaches are adopted in comparative experiments with 17 datasets extracted from five wind fields. The experimental results show that the proposed IT-2 FIPM achieves significant performance with huge promotion in the quality of the PI compared to the traditional forecasting models.