Multivariate and Multimodal Wind Distribution Model Based on Kernel Density Estimation

This paper presents a new method to accurately characterize and predict the annual variation of wind conditions. Estimation of the distribution of wind conditions is necessary (i) to quantify the available energy (power density) at a site, and (ii) to design optimal wind farm configurations. We develop a smooth multivariate wind distribution model that captures the coupled variation of wind speed, wind direction, and air density. The wind distribution model developed in this paper also avoids the limiting assumption of unimodality of the distribution. This method, which we call the Multivariate and Multimodal Wind distribution (MMWD) model, is an evolution from existing wind distribution modeling techniques. Multivariate kernel density estimation, a standard non-parametric approach to estimate the probability density function of random variables, is adopted for this purpose. The MMWD technique is successfully applied to model (i) the distribution of wind speed (univariate); (ii) the distribution of wind speed and wind direction (bivariate); and (iii) the distribution of wind speed, wind direction, and air density (multivariate). The latter is a novel contribution of this paper, while the former offers opportunities for validation. Ten-year recorded wind data, obtained from the North Dakota Agricultural Weather Network (NDAWN), is used in this paper. We found the coupled distribution to be multimodal. A strong correlation among the wind condition parameters was also observed.

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Short-term wind speed forecasting based on non-parametric kernel density estimation

IEEE PES Innovative Smart Grid Technologies ◽

10.1109/isgt-asia.2012.6303377 ◽

2012 ◽

Cited By ~ 1

Author(s):

Jiegui Zhou ◽

Jia Hongjie ◽

Zhen Tian ◽

Linlin Hu

Keyword(s):

Wind Speed ◽

Density Estimation ◽

Kernel Density Estimation ◽

Kernel Density ◽

Short Term ◽

Wind Speed Forecasting ◽

Non Parametric

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Kernel density estimation model for wind speed probability distribution with applicability to wind energy assessment in China

Renewable and Sustainable Energy Reviews ◽

10.1016/j.rser.2019.109387 ◽

2019 ◽

Vol 115 ◽

pp. 109387 ◽

Cited By ~ 7

Author(s):

Qinkai Han ◽

Sai Ma ◽

Tianyang Wang ◽

Fulei Chu

Keyword(s):

Wind Speed ◽

Probability Distribution ◽

Wind Energy ◽

Density Estimation ◽

Kernel Density Estimation ◽

Kernel Density ◽

Estimation Model ◽

Energy Assessment

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Wind speed forecasting based on Quantile Regression Minimal Gated Memory Network and Kernel Density Estimation

Energy Conversion and Management ◽

10.1016/j.enconman.2019.06.024 ◽

2019 ◽

Vol 196 ◽

pp. 1395-1409 ◽

Cited By ~ 10

Author(s):

Zhendong Zhang ◽

Hui Qin ◽

Yongqi Liu ◽

Liqiang Yao ◽

Xiang Yu ◽

...

Keyword(s):

Wind Speed ◽

Quantile Regression ◽

Density Estimation ◽

Kernel Density Estimation ◽

Kernel Density ◽

Wind Speed Forecasting ◽

Memory Network

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

Energies ◽

10.3390/en13226125 ◽

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.

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Prediction of Cylinder Fatigue Lifetime with Kernel Density Estimation Theory

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.547 ◽

2014 ◽

Vol 644-650 ◽

pp. 547-552 ◽

Cited By ~ 1

Author(s):

Jie Wang ◽

Ping Yang ◽

Qian Li ◽

Jian Bao Wang ◽

Song Yu

Keyword(s):

Density Estimation ◽

Kernel Density Estimation ◽

Estimation Method ◽

Kernel Density ◽

Reliability Function ◽

Adaptive Method ◽

Distribution Model ◽

Mechanical Equipment ◽

Fatigue Lifetime ◽

Gas Leak

As a part of power transfer process, cylinder plays an important role in pneumatic system. Its failure can cause mechanical equipment downtime suddenly and gas leak, so that production and personnel security will be in danger. Cylinder lifetime prediction has been an important topic. In this paper, an adaptive method based on Kernel Density Estimation is put forward for predicting the cylinder lifetime and getting the reliability function of cylinders. Kernel Density Estimation is a nonparametric estimation method of statistics. It can make full use of samples data without assuming distribution model. In the end, a comparison is made on the cylinder experiment between the proposed method and the common used parameter estimation method, Weibull distribution, and the results show that the proposed method has a more satisfactory performance.

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