Unbiased cross-validation kernel density estimation for wind and PV probabilistic modelling

Wahbah, Maisam; Mohandes, Baraa; EL-Fouly, Tarek H. M.; Moursi, Mohamed Shawky El

doi:10.1016/j.enconman.2022.115811

Cited by 51 publications

(6 citation statements)

References 48 publications

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“…Similar to QR, KDE is a non-parametric method that enables the direct calculation of the probability density for predicting PV power values without making distributional assumptions. In this study, we employed the cosine kernel function as the KDE technique [ 35 ]. The formula for KDE computation is presented as follows:

where

is the bandwidth, and

.…”

Section: Methodsmentioning

confidence: 99%

Photovoltaic Power Prediction Based on Hybrid Deep Learning Networks and Meteorological Data

Guo,

Xu,

Wang

et al. 2024

Sensors

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Conventional point prediction methods encounter challenges in accurately capturing the inherent uncertainty associated with photovoltaic power due to its stochastic and volatile nature. To address this challenge, we developed a robust prediction model called QRKDDN (quantile regression and kernel density estimation deep learning network) by leveraging historical meteorological data in conjunction with photovoltaic power data. Our aim is to enhance the accuracy of deterministic predictions, interval predictions, and probabilistic predictions by incorporating quantile regression (QR) and kernel density estimation (KDE) techniques. The proposed method utilizes the Pearson correlation coefficient for selecting relevant meteorological factors, employs a Gaussian Mixture Model (GMM) for clustering similar days, and constructs a deep learning prediction model based on a convolutional neural network (CNN) combined with a bidirectional gated recurrent unit (BiGRU) and attention mechanism. The experimental results obtained using the dataset from the Australian DKASC Research Centre unequivocally demonstrate the exceptional performance of QRKDDN in deterministic, interval, and probabilistic predictions for photovoltaic (PV) power generation. The effectiveness of QRKDDN was further validated through ablation experiments and comparisons with classical machine learning models.

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where

is the bandwidth, and

.…”

Section: Methodsmentioning

confidence: 99%

Photovoltaic Power Prediction Based on Hybrid Deep Learning Networks and Meteorological Data

Guo,

Xu,

Wang

et al. 2024

Sensors

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“…To analyze the distribution of environmental sensor data, we utilized the non-parametric density estimation method known as Kernel Density Estimation (KDE). Among the various kernel functions available, we specifically employed the commonly used Gaussian kernel density estimation [50,51] in this study. The Gaussian function and the Gaussian kernel density estimation are shown in Equations ( 11) and ( 12), respectively:…”

Section: Kernel Density Estimation Analysismentioning

confidence: 99%

Prediction of Sensor Data in a Greenhouse for Cultivation of Paprika Plants Using a Stacking Ensemble for Smart Farms

Han,

Mutahira,

Jang

2023

Applied Sciences

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Ensuring food security has become of paramount importance due to the rising global population. In particular, the agriculture sector in South Korea faces several challenges such as an aging farming population and a decline in the labor force. These issues have led to the recognition of smart farms as a potential solution. In South Korea, the smart farm is divided into three generations. The first generation primarily concentrates on monitoring and controlling precise cultivation environments by leveraging information and communication technologies (ICT). This is aimed at enhancing convenience for farmers. Moving on to the second generation, it takes advantage of big data and artificial intelligence (AI) to achieve improved productivity. This is achieved through precise cultivation management and automated control of various farming processes. The most advanced level is the 3rd generation, which represents an intelligent robotic farm. In this stage, the entire farming process is autonomously managed without the need for human intervention. This is made possible through energy management systems and the use of robots for various farm operations. However, in the current Korean context, the adoption of smart farms is primarily limited to the first generation, resulting in the limited utilization of advanced technologies such as AI, big data, and cloud computing. Therefore, this research aims to develop the second generation of smart farms within the first generation smart farm environment. To accomplish this, data was collected from nine sensors spanning the period between 20 June to 30 September. Following that, we conducted kernel density estimation analysis, data analysis, and correlation heatmap analysis based on the collected data. Subsequently, we utilized LSTM, BI-LSTM, and GRU as base models to construct a stacking ensemble model. To assess the performance of the proposed model based on the analyzed results, we utilized LSTM, BI-LSTM, and GRU as the existing models. As a result, the stacking ensemble model outperformed LSTM, BI-LSTM, and GRU in all performance metrics for predicting one of the sensor data variables, air temperature. However, this study collected nine sensor data over a relatively short period of three months. Therefore, there is a limitation in terms of considering the long-term data collection and analysis that accounts for the unique seasonal characteristics of Korea. Additionally, the challenge of including various environmental factors influencing crops beyond the nine sensors and conducting experiments in diverse cultivation environments with different crops for model generalization remains. In the future, we plan to address these limitations by extending the data collection period, acquiring diverse additional sensor data, and conducting further research that considers various environmental variables.

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“…When selecting the bandwidth for kernel density estimation, it is crucial to consider the trade-off between smoothness and capturing local features [23]. As a popular objective function for bandwidth selection, cross-validation [24] can help determine the optimal bandwidth for kernel density estimation by minimizing bias and variance simultaneously. However, if the data contains outliers, caution will be advised when using cross-validation methods to select the bandwidth for kernel density estimation.…”

Section: Introductionmentioning

confidence: 99%

A two-stage optimized robust kernel density estimation for Bayesian classification with outliers

Wei,

Peng,

et al. 2024

Preprint

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A Bayesian classifier based on kernel density estimation (KDE) is an effective routine for continuous data classification. However, the presence of outliers and inappropriate selection of bandwidth may cause inaccurate and distorted estimations of the density function. This paper presents an improved Bayesian classification approach by employing an optimized robust kernel density estimation (ORKDE). The impact of outliers can be down-weighted by a two-stage optimization in the conditional probability density calculation. In the first stage, an improved hybrid rice optimization (HRO) algorithm is proposed for selecting the bandwidth of a Gaussian KDE using a mixed cross-validation function. It incorporates Levy flight and elite reverse learning strategy to enhance the global optimization searching capability. In the second stage, a soft-redescending Welsch function is applied as the loss function to reduce the weights of outliers using the M-estimation in the kernel space. The relative efficiency index is used to derive the tuning parameter of the influence function. A kernelized iteratively re-weighted least-squares procedure employs both the tuning parameter and the quantile rule for effectively calculating the optimal weights of samples. With the proposed ORKDE method, the Naive Bayesian classifier enhances the generalization in the classification with outliers. The effectiveness of our method is demonstrated by the experiments using synthetic and real-world datasets.

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Unbiased cross-validation kernel density estimation for wind and PV probabilistic modelling

Cited by 51 publications

References 48 publications

Photovoltaic Power Prediction Based on Hybrid Deep Learning Networks and Meteorological Data

Photovoltaic Power Prediction Based on Hybrid Deep Learning Networks and Meteorological Data

Prediction of Sensor Data in a Greenhouse for Cultivation of Paprika Plants Using a Stacking Ensemble for Smart Farms

A two-stage optimized robust kernel density estimation for Bayesian classification with outliers

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