scholarly journals Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques

2019 ◽  
Vol 11 (24) ◽  
pp. 6954
Author(s):  
Fuqiang Li ◽  
Shiying Zhang ◽  
Wenxuan Li ◽  
Wei Zhao ◽  
Bingkang Li ◽  
...  
Keyword(s):  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Clustering Algorithm ◽  
Estimation Method ◽  
Kernel Density ◽  
Support Vector ◽  
Average Width ◽  
Power Load ◽  
Density Forecasting

In comparison with traditional point forecasting method, probability density forecasting can reflect the load fluctuation more effectively and provides more information. This paper proposes a hybrid hourly power load forecasting model, which integrates K-means clustering algorithm, Salp Swarm Algorithm (SSA), Least Square Support Vector Machine (LSSVM), and kernel density estimation (KDE) method. Firstly, the loads at 24 times a day are grouped into three categories according to the K-means clustering algorithm, which correspond to the valley period, flat period, and peak period of the load, respectively. Secondly, the load point forecasting value is obtained by LSSVM method optimized by SSA algorithm. Furthermore, the kernel density estimation method is employed to fit the forecasting error of SSA-LSSVM in different time periods, and the probability density function of the error distribution is obtained. The final load probability density forecasting result is obtained by combining the point forecasting value and the error fitting result, and then the upper and lower limits of the confidence interval under the given confidence level are solved. In this paper, the performance of the model is evaluated by two indicators named interval coverage and interval average width. Meanwhile, in comparison with several other models, it can be concluded that the proposed model can effectively improve the forecasting effect.

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

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6125
Author(s):  
Lei Zhang ◽  
Lun Xie ◽  
Qinkai Han ◽  
Zhiliang Wang ◽  
Chen Huang
Keyword(s):  
Wind Speed ◽  
Quantile Regression ◽  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Confidence Level ◽  
Kernel Density ◽  
Conditional Quantiles ◽  
Wind Speeds ◽  
Density Forecasting

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.

scholarly journals Benchmarking the reliability of medium-voltage lines

2017 ◽  
Vol 68 (3) ◽  
pp. 212-215 ◽  
Author(s):  
Michal Kolcun ◽  
Mirosław Kornatka ◽  
Anna Gawlak ◽  
Zsolt Čonka
Keyword(s):  
Density Distribution ◽  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Power Lines ◽  
Probability Density Distribution ◽  
Nonparametric Method ◽  
Medium Voltage

Abstract This paper discusses the problem of reliability of the Polish medium voltage power lines. It presents the benchmarking of power lines and values of SAIDI. The probability density distribution of the medium voltage lines length as well as selected indicators of the MV power lines reliability, being operated by the distribution companies under test, are also introduced. The analysis is based on the actual MV lines and uses the nonparametric method of kernel density estimation.

scholarly journals Effective Dysphonia Detection Using Feature Dimension Reduction and Kernel Density Estimation for Patients with Parkinson’s Disease

2021 ◽  
Author(s):  
Sridhar Krishnan ◽  
Shanshan Yang ◽  
Fang Zheng ◽  
Xin Luo ◽  
Suxian Cai ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Dimension Reduction ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Support Vector ◽  
Linear Discriminant ◽  
Feature Dimension ◽  
Feature Dimension Reduction

Detection of dysphonia is useful for monitoring the progression of phonatory impairment for patients with Parkinson’s disease (PD), and also helps assess the disease severity. This paper describes the statistical pattern analysis methods to study different vocal measurements of sustained phonations. The feature dimension reduction procedure was implemented by using the sequential forward selection (SFS) and kernel principal component analysis (KPCA) methods. Four selected vocal measures were projected by the KPCA onto the bivariate feature space, in which the class-conditional feature densities can be approximated with the nonparametric kernel density estimation technique. In the vocal pattern classification experiments, Fisher’s linear discriminant analysis (FLDA) was applied to perform the linear classification of voice records for healthy control subjects and PD patients, and the maximum a posteriori (MAP) decision rule and support vector machine (SVM) with radial basis function kernels were employed for the nonlinear classification tasks. Based on the KPCA-mapped feature densities, the MAP classifier successfully distinguished 91.8% voice records, with a sensitivity rate of 0.986, a specificity rate of 0.708, and an area value of 0.94 under the receiver operating characteristic (ROC) curve. The diagnostic performance provided by the MAP classifier was superior to those of the FLDA and SVM classifiers. In addition, the classification results indicated that gender is insensitive to dysphonia detection, and the sustained phonations of PD patients with minimal functional disability are more difficult to be correctly identified.

Sign in / Sign up

Export Citation Format

Share Document