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result(s) for
"polynomial regression"
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Enhancing Medium-Term Load Forecasting Accuracy in Post-Pandemic Tropical Regions: A Comparative Analysis of Polynomial Regression, Split Polynomial Regression, and LSTM Networks
2025
This research focuses on medium-term load forecasting in a tropical region post-pandemic. This study presents one of the first attempts to analyze medium-term forecasting using half-hourly resolution in the Java-Bali power system post-COVID-19 period. The dataset comprises load measurements recorded every 30 min (48 data points per day) from 2014 to 2022. Three distinct methods, namely polynomial regression, split polynomial regression, and Long Short-Term Memory (LSTM) networks, were employed and compared to predict the electricity load demand. The analysis found that LSTM outperformed the other methods, exhibiting the lowest error rates with Mean Absolute Percentage Error (MAPE) at 3.86% and Root Mean Squared Error (RMSE) at 1247.93. Additionally, a consistent observation emerged, showing that all methods performed better in predicting load demand during nighttime hours (6 p.m. to 6 a.m.). The hypothesis is that data stability during nighttime, with fewer significant fluctuations, contributed to the improved prediction accuracy. These findings provide valuable insights for improving load forecasting in the post-pandemic tropical region and offer opportunities for enhancing power grid efficiency and reliability.
Journal Article
Model selection for long-term load forecasting under uncertainty
by
Jaipuria, Sanjita
,
Dadabada, Pradeep Kumar
,
Thangjam, Aditya
in
Accuracy
,
Forecasting
,
Mean square errors
2024
Purpose
The purpose of this study is to propose a systematic model selection procedure for long-term load forecasting (LTLF) for ex-ante and ex-post cases considering uncertainty in exogenous predictors.
Design/methodology/approach
The different variants of regression models, namely, Polynomial Regression (PR), Generalised Additive Model (GAM), Quantile Polynomial Regression (QPR) and Quantile Spline Regression (QSR), incorporating uncertainty in exogenous predictors like population, Real Gross State Product (RGSP) and Real Per Capita Income (RPCI), temperature and indicators of breakpoints and calendar effects, are considered for LTLF. Initially, the Backward Feature Elimination procedure is used to identify the optimal set of predictors for LTLF. Then, the consistency in model accuracies is evaluated using point and probabilistic forecast error metrics for ex-ante and ex-post cases.
Findings
From this study, it is found PR model outperformed in ex-ante condition, while QPR model outperformed in ex-post condition. Further, QPR model performed consistently across validation and testing periods. Overall, QPR model excelled in capturing uncertainty in exogenous predictors, thereby reducing over-forecast error and risk of overinvestment.
Research limitations/implications
These findings can help utilities to align model selection strategies with their risk tolerance.
Originality/value
To propose the systematic model selection procedure in this study, the consistent performance of PR, GAM, QPR and QSR models are evaluated using point forecast accuracy metrics Mean Absolute Percentage Error, Root Mean Squared Error and probabilistic forecast accuracy metric Pinball Score for ex-ante and ex-post cases considering uncertainty in the considered exogenous predictors such as RGSP, RPCI, population and temperature.
Journal Article
Analysis of parametric and non-parametric regression techniques to model the wind turbine power curve
2019
Wind turbine power curve provides technical specification of the wind turbine in the form of nominal wind power readings. This information may used to monitor the performance of the power system, estimate the power produced by the turbine, optimize the operational cost, and improve the reliability of the power system. However, this information is not sufficient to accomplish these tasks. To accomplish these tasks, the accurate modeling of the wind power curve is required. In this article, various curve fitting techniques, namely polynomial regression, locally weighted polynomial regression, spline regression, piecewise polynomial regression, and smoothing spline, have been applied to model the power curve of wind turbine. All these techniques have been used to model the power curve on National Renewable Energy Laboratory (NREL) 2012 dataset with site-id 124693.
Journal Article
Spatiotemporal Analysis on the Teleconnection of ENSO and IOD to the Stream Flow Regimes in Java, Indonesia
2022
While many studies on the relationship between climate modes and rainfall in Indonesia already exist, studies targeting climate modes’ relationship to streamflow remain rare. This study applied multiple regression (MR) models with polynomial functions to show the teleconnection from the two prominent climate modes—El Niño–Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD)—to streamflow regimes in eight rivers in Java, Indonesia. Our MR models using data from 1970 to 2018 successfully show that the September–November (SON) season provides the best predictability of the streamflow regimes. It is also found that the predictability in 1970–1989 was better than that in 1999–2018. This suggests that the relationships between the climate modes and streamflow in Java were changed over periods, which is suspected due to the river basin development. Hence, we found no clear spatial distribution patterns of the predictability, suggesting that the effect of ENSO and IOD are similar for the eight rivers. Additionally, the predictability of the high flow index has been found higher than the low flow index. Having elucidated the flow regimes’ predictability by spatiotemporal analysis, this study gives new insight into the teleconnection of ENSO and IOD to the Indonesian streamflow.
Journal Article
Determination of semi-empirical models for mean wave overtopping using an evolutionary polynomial paradigm
by
Laucelli, Daniele
,
Altomare, Corrado
,
Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
in
Beach slope
,
Boundary conditions
,
Data analysis
2020
The present work employs the so-called Evolutionary Polynomial Regression (EPR) algorithm to build up a formula for the assessment of mean wave overtopping discharge for smooth sea dikes and vertical walls. EPR is a data-mining tool that combines and integrates numerical regression and genetic programming. This technique is here employed to dig into the relationship between the mean discharge and main hydraulic and structural parameters that characterize the problem under study. The parameters are chosen based on the existing and most used semi-empirical formulas for wave overtopping assessment. Besides the structural freeboard or local wave height, the unified models highlight the importance of local water depth and wave period in combination with foreshore slope and dike slope on the overtopping phenomena, which are combined in a unique parameter that is defined either as equivalent or imaginary slope. The obtained models aim to represent a trade-off between accuracy and parsimony. The final formula is simple but can be employed for a preliminary assessment of overtopping rates, covering the full range of dike slopes, from mild to vertical walls, and of water depths from the shoreline to deep water, including structures with emergent toes.
Journal Article
Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs
by
Gelman, Andrew
,
Imbens, Guido
in
Causal identification
,
Policy analysis
,
Polynomial regression
2019
It is common in regression discontinuity analysis to control for third, fourth, or higher-degree polynomials of the forcing variable. There appears to be a perception that such methods are theoretically justified, even though they can lead to evidently nonsensical results. We argue that controlling for global high-order polynomials in regression discontinuity analysis is a flawed approach with three major problems: it leads to noisy estimates, sensitivity to the degree of the polynomial, and poor coverage of confidence intervals. We recommend researchers instead use estimators based on local linear or quadratic polynomials or other smooth functions.
Journal Article
Estimation of Dissolved Oxygen Levels using Landsat 8 Images: Application to Kuwait Territorial Waters
by
Al-Attar, Ikram
,
Almutawa, Jaafar
in
Dissolved oxygen
,
Kernal Gaussian regression
,
multiple linear regression
2024
Al-Attar, I. and Almutawa, J., 2024. Estimation of dissolved oxygen levels using Landsat 8 images: Application to Kuwait Territorial waters. In: Phillips, M.R.; Al-Naemi, S., and Duarte, C.M. (eds.), Coastlines under Global Change: Proceedings from the International Coastal Symposium (ICS) 2024 (Doha, Qatar). Journal of Coastal Research, Special Issue No. 113, pp. 514-518. Charlotte (North Carolina), ISSN 0749-0208. Dissolved Oxygen (DO) concentration is a crucial water quality parameter used in pollution assessments and water environments. Advancements in satellite technology have made remote sensing techniques essential for estimating DO concentration, making it a vital tool for monitoring water quality. This study used 15 water measurement stations in situ combined with Landsat-8 Operational Land Imager (OLI) data and geographic information system (GIS) to derive the dissolved oxygen of territorial water in Kuwait for sustainable management. The image acquisition dates were selected to be cloud-free from 2015 to 2018. Reflectance values of OLI band ratios (B2/B6, B5/B6) were compared with in situ measurements of water samples using three models: multiple linear regression, Kernal Gaussian regression, and polynomial regression. The images underwent radiometric and atmospheric corrections before creating the models. The proposed algorithms' efficiency was assessed using bias, mean square, and root-mean-square error values. The dissolved oxygen multiple linear regression models had reached a coefficient of determination (R2) of 0.867. The Gaussian Kernel regression reached a coefficient of determination (R2) of 0.9786. The polynomial had reached a coefficient of determination (R2) 0.986, demonstrating the viability of applying Landsat 8 images to characterize dissolved oxygen in Kuwait Bay. Remote sensing was used to quantify dissolved oxygen by transforming satellite images into Dissolved oxygen maps using retrieved models for Kuwait Bay. The study's findings suggest that Landsat-8 when combined with GIS, can effectively retrieve the dissolved oxygen.
Journal Article
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
2018
Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the mean-squared error (MSE)-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too \"large.\" Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available. Supplementary materials for this article are available online.
Journal Article
Methods for Scalar-on-Function Regression
by
Ogden, R. Todd
,
Goldsmith, Jeff
,
Shang, Han Lin
in
Data analysis
,
Data points
,
Functional additive model
2017
Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images and so on are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorising the basic model types as linear, non-linear and non-parametric. We discuss publicly available software packages and illustrate some of the procedures by application to a functional magnetic resonance imaging data set.
Journal Article
Smartphone-Based Indoor Localization with Bluetooth Low Energy Beacons
2016
Indoor wireless localization using Bluetooth Low Energy (BLE) beacons has attracted considerable attention after the release of the BLE protocol. In this paper, we propose an algorithm that uses the combination of channel-separate polynomial regression model (PRM), channel-separate fingerprinting (FP), outlier detection and extended Kalman filtering (EKF) for smartphone-based indoor localization with BLE beacons. The proposed algorithm uses FP and PRM to estimate the target’s location and the distances between the target and BLE beacons respectively. We compare the performance of distance estimation that uses separate PRM for three advertisement channels (i.e., the separate strategy) with that use an aggregate PRM generated through the combination of information from all channels (i.e., the aggregate strategy). The performance of FP-based location estimation results of the separate strategy and the aggregate strategy are also compared. It was found that the separate strategy can provide higher accuracy; thus, it is preferred to adopt PRM and FP for each BLE advertisement channel separately. Furthermore, to enhance the robustness of the algorithm, a two-level outlier detection mechanism is designed. Distance and location estimates obtained from PRM and FP are passed to the first outlier detection to generate improved distance estimates for the EKF. After the EKF process, the second outlier detection algorithm based on statistical testing is further performed to remove the outliers. The proposed algorithm was evaluated by various field experiments. Results show that the proposed algorithm achieved the accuracy of <2.56 m at 90% of the time with dense deployment of BLE beacons (1 beacon per 9 m), which performs 35.82% better than <3.99 m from the Propagation Model (PM) + EKF algorithm and 15.77% more accurate than <3.04 m from the FP + EKF algorithm. With sparse deployment (1 beacon per 18 m), the proposed algorithm achieves the accuracies of <3.88 m at 90% of the time, which performs 49.58% more accurate than <8.00 m from the PM + EKF algorithm and 21.41% better than <4.94 m from the FP + EKF algorithm. Therefore, the proposed algorithm is especially useful to improve the localization accuracy in environments with sparse beacon deployment.
Journal Article