커널 밀도 추정 기법을 이용한 풍력발전량에 대한 확률론적 모델

Accurate forecast results of medium and long-term wind power quantity can provide an important basis for power distribution plans, energy storage allocation plans and medium and long-term power generation plans after wind power integration. However, there are still some problems such as low forecast accuracy and a low degree of integration for wind power physical processes. In this study, the Multi-step Informer network is proposed to add meteorological parameters to wind power generation forecast and make network interpretable. The Multi-step Informer network uses Informer to obtain the initial training model according to the historical data of wind power generation, introduces the Informer model of wind speed and air pressure training involved in the dynamic pressure model, and compares the historical data of wind power generation to obtain model modification, so as to further improve the forecast accuracy of Multi-step Informer network. The backpropagation process of the pre-trained Informer should be truncated to avoid being influenced by the pre-trained Informer during training of the Multi-step Informer network, which also guarantees the interpretability of the running results of the network. The Multi-step Informer network has the advantage of error correction of wind power generation, which improves the forecast accuracy. From the calculation results of the root mean square error, Multi-step Informer network improves forecast accuracy by 29% compared to Informer network.

China is a broad territory country. There are significant differences in the terrain, climate, and other environmental factors between different provinces, which affect wind power generation. In order to better analyze the situation of wind power generation in Chinese provinces, this paper uses the functional clustering analysis to classify the monthly data of wind power generation in 30 Chinese provinces from March 2013 to October 2019. The empirical results of this paper show that the wind energy generation in Chinese provinces can be divided into three categories, and the results are consistent with the actual situation. In this paper, functional clustering analysis is used to analyze monthly data, compared with the traditional clustering analysis to analyze annual data which are obtained by accumulated monthly data. Higher-dimensional data can be used for analysis to reduce information loss. Moreover, data can be viewed as functions, and more information can be mined by analyzing derivative functions, and so on. The analysis of wind energy generation has certain guiding significance for the development and utilization of renewable energy.

Kernel density estimation is an important data smoothing technique. It has been applied most successfully for univariate data whilst for multivariate data its development and implementation have been relatively limited. The performance of kernel density estimators depends crucially on the bandwidth selection. Bandwidth selection in the univariate case involves selecting a scalar parameter which controls the amount of smoothing. In the multivariate case, the bandwidth matrix controls both the degree and direction of smoothing so its selection is more difficult. So far most of the research effort has been expended on automatic, data-driven selectors for univariate data. There is, on the other hand, a relative paucity of multivariate counterparts. Most of these multivariate bandwidth selectors are focused on the restricted case of diagonal matrices. In this thesis practical algorithms are constructed, with supporting theoretical justifications, for unconstrained bandwidth matrices. The two main classes of univariate bandwidth selectors are plug-in and cross validation. These unidimensional selectors are generalised to the multidimensional case. The univariate framework for theoretically analysing kernel density estimators is extended to a general multivariate version. This framework has at its core the quantification of the relative rates of convergence which provide a guide to the asymptotic behaviour of bandwidth selectors. Simulation studies and real data analysis are employed to illustrate their finite sample behaviour. It is found that unconstrained selectors possess good asymptotic and finite sample properties in a wide range of situations. Buoyed by this success, two extensions are embarked upon. The first is variable bandwidth selection, generalising the above case where the bandwidth is fixed throughout the sample space. The variation of the bandwidths is controlled by the local properties of the data. The novel contribution is to use non-parametric clustering to summarise these local properties, along with unconstrained bandwidth matrices. The second is in kernel discriminant analysis where unconstrained bandwidth matrices are shown to produce more accurate discrimination.

This paper proposes a wind power probabilistic model (WPPM) using the reflection method and multi-kernel function kernel density estimation (KDE). With the increasing penetration of renewable energy sources (RESs) into power systems, several probabilistic approaches have been introduced to assess the impact of RESs on the power system. A probabilistic approach requires a wind power scenario (WPS), and the WPS is generated from the WPPM. Previously, WPPM was generated using a parametric density estimation, and it had limitations in reflecting the characteristics of wind power data (WPD) due to a boundary bias problem. The paper proposes a WPPM generated using the KDE, which is a non-parametric method. Additionally, the paper proposes a reflection method correcting for the boundary bias problem caused by the double-bounded characteristic of the WPD and the multi-kernel function KDE minimizing the effect of tied values. Six bandwidth selectors are used to calculate the bandwidth for the KDE, and one is selected by analyzing the correlation between the normalized WPD and the calculated bandwidth. The results were validated by generating WPPMs with WPDs in six regions of the Republic of Korea, and it was confirmed that the accuracy and goodness-of-fit are improved when the proposed method is used.

Kernel density estimation is a widely used statistical tool and bandwidth selection is critically important. The Sheather and Jones’ (SJ) selector [A reliable data-based bandwidth selection method for kernel density estimation, J. R. Stat. Soc. Ser. B 53 (1991), pp. 683–690] remains the best available data-driven bandwidth selector. It can, however, perform poorly if the true density deviates too much in shape from normal. This paper first develops an alternative selector by following ideas in Park and Marron [On the use of pilot estimators in bandwidth selection, Nonparametr. Stat. 1 (1992), pp. 231–240] to reduce the impact of the normal reference density. The selector can bring drastic improvement to less smooth densities that the SJ selector has difficulty with, but may be slightly worse off otherwise. We then propose to combine the alternative selector and SJ selector by using the smaller of the two bandwidths, which has the effect of automatically picking the better one for a particular density. In our extensive simulation, study using the 15 benchmark densities in Marron and Wand [Exact mean integrated squared error, Ann. Statist. 20 (1992), pp. 712–736], the combined selector significantly improves the SJ selector for 5 difficult densities and retains the superior performance of the SJ selector for the other 10. A ready-to-use R function is provided.

Kernel density estimation (KDE) is a widely used method in geography to study concentration of point pattern data. Geographical networks are 1.5 dimensional spaces with specific characteristics, analyzing events occurring on networks (accidents on roads, leakages of pipes, species along rivers, etc.). In the last decade, they required the extension of spatial KDE. Several versions of Network KDE (NKDE) have been proposed, each with their particular advantages and disadvantages, and are now used on a regular basis. However, scant attention has been given to the temporal extension of NKDE (TNKDE). In practice, when the studied events happen at specific time points and are constrained on a network, the methodologies used by geographers tend to overlook either the network or the temporal dimension. Here we propose a TNKDE based on the recent development of NKDE and the product of kernels. We also adapt classical methods of KDE (Diggle's correction, Abramson's adaptive bandwidth and bandwidth selection by leave‐one‐out maximum likelihood). We also illustrate the method with Montreal road crashes involving a pedestrian between 2016 and 2019.

K-nearest neighbors and a kernel density estimator for GEFCom2014 probabilistic wind power forecasting

Wind power serves as a clean and sustainable form of energy. However, its generation is fraught with variability and uncertainty, owing to the stochastic and dynamic characteristics of wind. Accurate forecasting of wind power is indispensable for the efficient planning, operation, and grid integration of wind energy systems. In this paper, we introduce a novel forecasting method termed Temporal Collaborative Attention (TCOAT). This data-driven approach is designed to capture both temporal and spatial dependencies in wind power generation data, as well as discern long-term and short-term patterns. Utilizing attention mechanisms, TCOAT dynamically adjusts the weights of each input variable and time step based on their contextual relevance for forecasting. Furthermore, the method employs collaborative attention units to assimilate directional and global information from the input data. It also explicitly models the interactions and correlations among different variables or time steps through the use of self-attention and cross-attention mechanisms. To integrate long-term and short-term information effectively, TCOAT incorporates a temporal fusion layer that employs concatenation and mapping operations, along with hierarchical feature extraction and aggregation. We validate the efficacy of TCOAT through extensive experiments on a real-world wind power generation dataset from Greece and compare its performance against twenty-two state-of-the-art methods. Experimental results demonstrate that TCOAT outperforms existing methods in terms of both accuracy and robustness in wind power forecasting. Moreover, we conduct a generality study on an additional real-world dataset from a different climate condition and wind power characteristics. The results show that TCOAT can achieve comparable or better performance than the state-of-the-art methods, confirming the generalization ability of TCOAT.

Context Despite the diversity of available home range estimators, no single method performs equally well in all circumstances. It is therefore important to understand how different estimators perform for data collected under diverse conditions. Kernel density estimation is a popular approach for home range estimation. While many studies have evaluated different kernel bandwidth selectors, few studies have compared different formulations of the bandwidth matrix using wildlife telemetry data. Additionally, few studies have compared the performance of kernel bandwidth selectors using VHF radio-telemetry data from small-bodied taxa. Aims In this study, we used eight different combinations of bandwidth selectors and matrices to evaluate their ability to meet several criteria that could be potentially used to select a home range estimator. Methods We used handheld VHF telemetry data from two species of snake displaying non-migratory and migratory movement patterns. We used subsampling to estimate each estimator’s sensitivity to sampling duration and fix rate and compared home range size, the number of disjunct volume contours and the proportion of telemetry fixes not included in those contours among estimators. Key Results We found marked differences among bandwidth selectors with regards to our criteria but comparatively little difference among bandwidth matrices for a given bandwidth selector. Least-squares cross-validation bandwidths exhibited near-universal convergence failure whereas likelihood cross-validation bandwidths showed high sensitivity to sampling duration and fix rate. The reference, plug-in and smoothed cross-validation bandwidths were more robust to variation in sampling intensity, with the former consistently producing the largest estimates of home range size. Conclusions Our study illustrates the performance of multiple kernel bandwidth estimators for estimating home ranges with datasets typical of many small-bodied taxa. The reference and plug-in bandwidths with an unconstrained bandwidth matrix generally had the best performance. However, our study concurs with earlier studies indicating that no single home range estimator performs equally well in all circumstances. Implications Although we did not find strong differences between bandwidth matrices, we encourage the use of unconstrained matrices because of their greater flexibility in smoothing data not parallel to the coordinate axes. We also encourage researchers to select an estimator suited to their study objectives and the life history of their study organism.

Abstract: Home‐range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home‐range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home‐range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space‐use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home‐range estimation: 1) KDE with reference bandwidths, 2) KDE with least‐squares cross‐validation, 3) KDE with plug‐in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home‐range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home‐range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home‐range estimation.

In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.

Runoff prediction is crucial for water resource allocation and hydropower planning. To address low accuracy and uncertainty in runoff forecasting, this study proposes a framework integrating the Information Acquisition Optimizer (IAO), Variational Mode Decomposition (VMD), Convolutional Neural Network-Support Vector Machine (CNN-SVM), and Kernel Density Estimation (KDE) for interval prediction. An IAO-based optimized VMD (IVMD) is employed to decompose non-stationary runoff series and enhance feature extraction, with the resulting components used as inputs to the CNN-SVM model for point prediction. To quantify predictive uncertainty, KDE is applied to model the prediction error distribution, where a B-spline-based least squares cross-validation bandwidth selection method (LSCV-B) is adopted. By combining B-spline basis functions with data-driven cross-validation, LSCV-B overcomes the limited local adaptability of conventional AMISE-based bandwidth selection, enabling more accurate error density estimation and narrower prediction intervals with reliable coverage. Experiments in the Yangtze River Basin show that the IVMD-CNN-SVM framework reduces RMSE and MAPE by approximately 40–50% on the testing dataset compared with VMD-based counterparts, while producing highly reliable and compact 90% interval predictions.

An integrated development environment based situational awareness for operational reliability evaluation in wind energy systems incorporating uncertainties

An ensemble-based approach for short-term load forecasting for buildings with high proportion of renewable energy sources

The anomalous pixel detection efficiency of algorithms on UAV images is represented by the two criteria: anomalous pixel detection effect (which uses the area under ROC curve for evaluation) and calculation time. A highly effective researcher-recommended technique for anomaly detection on UAV images is to apply Neyman-Pearson lemma by calculating Kernel Density Estimation (KDE) for background data and making decision therefrom. In this method, the selection of kernel function and bandwidth plays the determinant role in anomaly detection efficiency. However, there has not been any research that mentions this issue to date. Hereby, in this study, we evaluate anomaly detection efficiency on UAV images through a number of common kernel functions typically cited in researches on KDE, and follow up with making recommendations for appropriate uses of kernel functions. Experiments and evaluations are carried out on the sample data set photographed on varied terrain types and objects of interest.