Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation

In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.

Diversity Sampling Based Kernel Density Estimation for Background Modeling

A novel diversity-sampling based nonparametric multi-modal background model is proposed. Using the samples having more popular and various intensity values in the training sequence, a nonparametric model is built for background subtraction. According to the related intensifies, different weights are given to the distinct samples in kernel density estimation. This avoids repeated computation using all samples, and makes computation more efficient in the evaluation phase. Experimental results show the validity of the diversity- sampling scheme and robustness of the proposed model in moving objects segmentation. The proposed algorithm can be used in outdoor surveillance systems.

Wind speed model based on kernel density estimation and its application in reliability assessment of generating systems

An accurate probability distribution model of wind speed is critical to the assessment of reliability contribution of wind energy to power systems. Most of current models are built using the parametric density estimation(PDE) methods, which usually assume that the wind speed are subordinate to a certain known distribution(e.g. Weibull distribution and Normal distribution) and estimate the parameters of models with the historical data. This paper presents a kernel density estimation(KDE) method which is a nonparametric way to estimate the probability density function(PDF) of wind speed. The method is a kind of data-driven approach without making any assumption on the form of the underlying wind speed distribution, and capable of uncovering the statistical information hidden in the historical data. The proposed method is compared with three parametric models using wind data from six sites.The results indicate that the KDE outperforms the PDE in terms of accuracy and flexibility in describing the longterm wind speed distributions for all sites. A sensitivity analysis with respect to kernel functions is presented and Gauss kernel function is proved to be the best one. Case studies on a standard IEEE reliability test system(IEEERTS) have verified the applicability and effectiveness of the proposed model in evaluating the reliability performance of wind farms.

Development and application of traffic accident density estimation models using kernel density estimation

Traffic accident frequency has been decreasing in Japan in recent years. Nevertheless, many accidents still occur on residential roads. Area-wide traffic calming measures including Zone 30, which discourages traffic by setting a speed limit of 30 km/h in residential areas, have been implemented. However, no objective implementation method has been established. Development of a model for traffic accident density estimation explained by GIS data can enable the determination of dangerous areas objectively and easily, indicating where area-wide traffic calming can be implemented preferentially. This study examined the relations between traffic accidents and city characteristics, such as population, road factors, and spatial factors. A model was developed to estimate traffic accident density. Kernel density estimation （KDE） techniques were used to assess the relations efficiently. Besides, 16 models were developed by combining accident locations, accident types, and data types. By using them, the applicability of traffic accident density estimation models was examined. Results obtained using Spearman rank correlation show high coefficients between the predicted number and the actual number. The model can indicate the relative accident risk in cities. Results of this study can be used for objective determination of areas where area-wide traffic calming can be implemented preferentially, even if sufficient traffic accident data are not available.

Dm-KDE： dynamical kernel density estimation by sequences of KDE estimators with fixed number of components over data streams

In many data stream mining applications, traditional density estimation methods such as kemel density estimation, reduced set density estimation can not be applied to the density estimation of data streams because of their high computational burden, processing time and intensive memory allocation requirement. In order to reduce the time and space complexity, a novel density estimation method Dm-KDE over data streams based on the proposed algorithm m-KDE which can be used to design a KDE estimator with the fixed number of kernel components for a dataset is proposed. In this method, Dm-KDE sequence entries are created by algorithm m-KDE instead of all kemels obtained from other density estimation methods. In order to further reduce the storage space, Dm-KDE sequence entries can be merged by calculating their KL divergences. Finally, the probability density functions over arbitrary time or entire time can be estimated through the obtained estimation model. In contrast to the state-of-the-art algorithm SOMKE, the distinctive advantage of the proposed algorithm Dm-KDE exists in that it can achieve the same accuracy with much less fixed number of kernel components such that it is suitable for the scenarios where higher on-line computation about the kernel density estimation over data streams is required. We compare Dm-KDE with SOMKE and M-kernel in terms of density estimation accuracy and running time for various stationary datasets. We also apply Dm-KDE to evolving data streams. Experimental results illustrate the effectiveness of the pro- posed method.

Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.

Kernel Density Estimation Based Multiphase Fuzzy Region Competition Method for Texture Image Segmentation

In this paper,we propose a multiphase fuzzy region competition model for texture image segmentation.In the functional,each region is represented by a fuzzy membership function and a probability density function that is estimated by a nonparametric kernel density estimation.The overall algorithm is very efficient as both the fuzzy membership function and the probability density function can be implemented easily.We apply the proposed method to synthetic and natural texture images,and synthetic aperture radar images.Our experimental results have shown that the proposed method is competitive with the other state-of-the-art segmentation methods.

Volumetric magnetic resonance imaging classification for Alzheimer＇s disease based on kernel density estimation of local features

Background The classification of Alzheimer＇s disease （AD） from magnetic resonance imaging （MRI） has been challenged by lack of effective and reliable biomarkers due to inter-subject variability. This article presents a classification method for AD based on kernel density estimation （KDE） of local features. Methods First, a large number of local features were extracted from stable image blobs to represent various anatomical patterns for potential effective biomarkers. Based on distinctive descriptors and locations, the local features were robustly clustered to identify correspondences of the same underlying patterns. Then, the KDE was used to estimate distribution parameters of the correspondences by weighting contributions according to their distances. Thus, biomarkers could be reliably quantified by reducing the effects of further away correspondences which were more likely noises from inter-subject variability. Finally, the Bayes classifier was applied on the distribution parameters for the classification of AD. Results Experiments were performed on different divisions of a publicly available database to investigate the accuracy and the effects of age and AD severity. Our method achieved an equal error classification rate of 0.85 for subject aged 60-80 years exhibiting mild AD and outperformed a recent local feature-based work regardless of both effects. Conclusions We proposed a volumetric brain MRI classification method for neurodegenerative disease based on statistics of local features using KDE. The method may be potentially useful for the computer-aided diagnosis in clinical settings.

Optimization Strategy of Commercial Space in Xianyukou Hutong Based on Kernel Density and Space Syntax

Beijing Xianyukou Hutong(hutong refers to historical and cultural block in Chinese)occupies an important geographical location with unique urban fabric,and after years of renewal and protection,the commercial space of Xianyukou Street and has gained some recognition.This article Xianyukou takes commercial hutong in Beijing as an example,spatial analysis was carried out using methods like GIS kernel density method,space syntax after site investigation and research.Based on the street space problems found,this paper then puts forward strategies to improve and upgrade Xianyukou Street’s commercial space and improve businesses in Xianyukou Street and other similar hutong.

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.

Bandwidth adaption for kernel particle filter

A novel particle filter bandwidth adaption for kernel particle filter （BAKPF） is proposed. Selection of the kernel bandwidth is a critical issue in kernel density estimation （KDE）. The plug-in method is adopted to get the global fixed bandwidth by optimizing the asymptotic mean integrated squared error （AMISE） firstly. Then, particle-driven bandwidth selection is invoked in the KDE. To get a more effective allocation of the particles, the KDE with adap- tive bandwidth in the BAKPF is used to approximate the posterior probability density function （PDF） by moving particles toward the posterior. A closed-form expression of the true distribution is given. The simulation results show that the proposed BAKPF performs better than the standard particle filter （PF）, unscented particle filter （UPF） and the kernel particle filter （KPF） both in efficiency and estimation precision.

Improved Algorithm of Variable Bandwidth Kernel Particle Filter

Aiming at the large cost of calculating variable bandwidth kernel particle filter and the high complexity of its algorithm,a self-adjusting kernel function particle filter is presented. Kernel density estimation is facilitated to iterate and obtain new particle set. And the standard deviation of particle is introduced in the kernel bandwidth. According to the characteristics of particle distribution,the bandwidth is dynamically adjusted,and the particle distribution can thus be more close to the posterior probability density model of the system. Meanwhile,the kernel density is used to estimate the weight of updating particle and the system state. The simulation results show the feasibility and effectiveness of the proposed algorithm.

Improved estimator of the continuous-time kernel estimator

There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases.

2011-2020年我国医学生分布的区域差异及动态演进

目的研究我国医学生分布的集聚水平、空间分布特征和时空演变趋势,为宏观调控医学高等院校区域均衡发展提供依据。方法运用集聚度、空间自相关模型和核密度估计法分析医学生空间分布情况和发展趋势。结果2011—2020年,我国医学生集聚水平在观察末期升至7.478,涨幅15.43%,呈现“东高西低、南高北低”的空间分布格局。各省份间呈空间正相关性,形成稳定的“高高集聚、低低集聚”的空间分布特征。医学生分布的绝对差异在中部地区趋于缓和,在东、西部地区持续扩大,总体呈多极化演化特征。结论我国医学生分布的集聚水平稳步上升且存在不均衡现象,已形成稳定的聚集区域并存在低流动性。建议构建区域医学高等教育协同发展机制,以促进医学院校资源的优质均衡发展。

Active Kriging-Based Adaptive Importance Sampling for Reliability and Sensitivity Analyses of Stator Blade Regulator

The reliability and sensitivity analyses of stator blade regulator usually involve complex characteristics like highnonlinearity,multi-failure regions,and small failure probability,which brings in unacceptable computing efficiency and accuracy of the current analysismethods.In this case,by fitting the implicit limit state function(LSF)with active Kriging(AK)model and reducing candidate sample poolwith adaptive importance sampling(AIS),a novel AK-AIS method is proposed.Herein,theAKmodel andMarkov chainMonte Carlo(MCMC)are first established to identify the most probable failure region(s)(MPFRs),and the adaptive kernel density estimation(AKDE)importance sampling function is constructed to select the candidate samples.With the best samples sequentially attained in the reduced candidate samples and employed to update the Kriging-fitted LSF,the failure probability and sensitivity indices are acquired at a lower cost.The proposed method is verified by twomulti-failure numerical examples,and then applied to the reliability and sensitivity analyses of a typical stator blade regulator.Withmethods comparison,the proposed AK-AIS is proven to hold the computing advantages on accuracy and efficiency in complex reliability and sensitivity analysis problems.

Data-driven source-load robust optimal scheduling of integrated energy production unit including hydrogen energy coupling

A robust low-carbon economic optimal scheduling method that considers source-load uncertainty and hydrogen energy utilization is developed.The proposed method overcomes the challenge of source-load random fluctuations in integrated energy systems(IESs)in the operation scheduling problem of integrated energy production units(IEPUs).First,to solve the problem of inaccurate prediction of renewable energy output,an improved robust kernel density estimation method is proposed to construct a data-driven uncertainty output set of renewable energy sources statistically and build a typical scenario of load uncertainty using stochastic scenario reduction.Subsequently,to resolve the problem of insufficient utilization of hydrogen energy in existing IEPUs,a robust low-carbon economic optimal scheduling model of the source-load interaction of an IES with a hydrogen energy system is established.The system considers the further utilization of energy using hydrogen energy coupling equipment(such as hydrogen storage devices and fuel cells)and the comprehensive demand response of load-side schedulable resources.The simulation results show that the proposed robust stochastic optimization model driven by data can effectively reduce carbon dioxide emissions,improve the source-load interaction of the IES,realize the efficient use of hydrogen energy,and improve system robustness.

Whether the digital economy will successfully encourage the integration of urban and rural development: A case study in China

The digital economy has become an important driver for stimulating economic growth.The digital economy has now widely penetrated the fields of economy and society,providing new opportunities for the develop‐ment of urban-rural integration.Based on panel data for 30 provinces in China from 2011 to 2020,this study constructed an index system for the integration of the digital economy and the development of urban-rural areas and conducted a systematic measurement analysis.Additionally,we used a two-step system of GMM estimation to analyze the impact of the digital economy on the development of urban-rural integra‐tion.The findings demonstrate the significant imbalance paradox of China’s digital economy development,which is shown in a gradient where the eastern region is higher than the center and the central region is higher than the west.Urban-rural integration levels in China fluctuate and display geographical variance,typically displaying high levels in the east and low levels in the west.Urban-rural integration is significantly encouraged by the digital economy,yet it varies in variability between different areas and dimensions.Addi‐tionally,rural human capital moderates the favorable effects of the digital economy on urban-rural integra‐tion.As a result,in order to achieve the integrated development of urban and rural areas,it is imperative to fully exploit the active role of the digital economy,better support the development of rural revitalization,bridge the“digital divide”between urban and rural development,and build a strong foundation for the for‐mation of a digital urban-rural integrated development pattern with urban and rural areas and common con‐struction and sharing.

General limited information diffusion method of small-sample information analysis in insurance

When analyzing and evaluating risks in insurance, people are often confronted with the situation of incomplete information and insufficient data, which is known as a small-sample problem. In this paper, a one-dimensional small-sample problem in insurance was investigated using the kernel density estimation method （KerM） and general limited information diffusion method （GIDM）. In particular, MacCormack technique was applied to get the solutions of GIDM equations and then the optimal diffusion solution was acquired based on the two optimization principles. Finally, the analysis introduced in this paper was verified by treating some examples and satisfying results were obtained.

Spatial Pattern Evolution and Influencing Factors of Cold Storage in China

Cold storage is the vital infrastructure of cold chain logistics. In this study, we analyzed the spatial pattern evolution characteristics, spatial autocorrelation and influencing factors of cold storage in China by using kernel density estimation(KDE), spatial autocorrelation analysis(SAA), and spatial error model(SEM). Results showed that: 1) the spatial distribution of cold storage in China is unbalanced, and has evolved from ‘one core’ to ‘one core and many spots’, that is, ‘one core’ refers to the Bohai Rim region mainly including Beijing, Tianjin, Hebei, Shandong and Liaoning regions, and ‘many spots’ mainly include the high-density areas such as Shanghai, Fuzhou, Guangzhou, Zhengzhou, Hefei, Wuhan, ürümqi. 2) The distribution of cold storage has significant global spatial autocorrelation and local spatial autocorrelation, and the ‘High-High’ cluster area is the most stable, mainly concentrated in the Bohai Rim;the ‘Low-Low’ cluster area is grouped in the southern China. 3) Economic development level, population density, traffic accessibility, temperature and land price, all affect the location choice of cold storage in varying degrees, while the impact of market demand on it is not explicit.