Nonparametric Kernel Density Estimation Research Articles

Dynamic Evolution and the Mechanism behind the Coupling Coordination Relationship between Industrial Integration and Urban Land-Use Efficiency: A Case Study of the Yangtze River Economic Zone in China

It is of great significance to explore the dynamic coupling relationship between industrial integration and urban land-use efficiency (ULUE) in order to promote high-quality urban development. This paper presents a system for evaluating industrial integration and ULUE which combines the internal theoretical relationships between the two. Based on this system, this paper analyzes the evolution process and the mechanism behind the coupling coordination relationship between industrial integration and ULUE with the help of the coupling coordination model, nonparametric kernel density estimation, and the geographical detector method. The results indicate the following: (1) The coupling coordination relationship between industrial integration and ULUE in the Yangtze River Economic Zone experienced an overall steady increase during the investigation period. However, there were great spatial differences in the coupling coordination relationship among cities. (2) The lag of the industrial integration level was the key area of resistance to the improvement of the coupling coordination level. (3) The interaction between industrial integration and ULUE in the Yangtze River Economic Zone was very significant. In particular, the impact of industrial agglomeration and factor flow on the ULUE and the impact of land on industrial integration in terms of ecological environment were prominent. In addition, the interaction of different detection factors was mainly manifested as a double factor enhancement effect and nonlinear enhancement effect.

Stochastic Optimization Operation of the Integrated Energy System Based on a Novel Scenario Generation Method

The application of integrated energy systems is significant for realizing the comprehensive utilization of various energy sources and improving the utilization rate of renewable energy. At present, the optimal operation of integrated energy systems is a research hotspot. However, shortcomings remain in the stochastic optimization operation and the scenario generation method. This paper proposes a stochastic optimization operation model of an integrated energy microgrid based on an advanced multi-scenario generation method. First, this paper establishes the time-divided probability distribution model of the forecasting error of the uncertain factors, such as photovoltaic (PV) power and load, which provide the basis for generating scenarios. Moreover, the covariance matrix is used to calculate the time correlation of the time-divided probabilistic distributed models, and the parameters of the covariance matrix are optimized. Second, based on multiple typical scenarios, the stochastic optimization operation model of the integrated energy microgrid is established. Finally, the real data is used to verify the proposed method. The results show that the nonparametric kernel density estimation method has the best fitting effect. On this basis, the time correlation and the operation costs are compared with the scenario sets generated by other methods, which proves the advantages of the proposed multi-scenario generation method and stochastic optimization operation model.

Optimized utilization of distributed renewable energies for island microgrid clusters considering solar-wind correlation

Microgrid technology has found applications in various areas including institutional campuses, military bases, and remote islands. This paper proposes an optimization scheme for island microgrid clusters considering solar-wind correlation. Firstly, we propose a method for generating wind and solar scenarios based on non-parametric kernel density estimation and combined Copula function, to obtain a typical daily wind and solar output sequence, with involving the uncertainty and correlation of wind-solar power. Secondly, to reduce the computational pressure of the system and ensure the privacy of each microgrid, we present an improved Alternating Direction Method of Multipliers (ADMM) to speed up the solution process of the established optimization model in a distributed manner. Finally, comparative case studies are used to validate the effectiveness of the proposed schemes.

Multivariate global agricultural drought frequency analysis using kernel density estimation

Drought frequency analysis provides valuable information for drought risk assessment. Nonparametric kernel density estimation (KDE) is applied for agricultural drought frequency analysis at the global scale. Agricultural drought over 1950–2020 is described by the standardized soil moisture index (SSMI), and drought variables (i.e., duration, severity, and peak) are extracted using run theory. The univariate and multivariate joint distributions of drought variables are established by KDE. Given that the averages for drought duration, severity, and peak are 3.10 (months), 1.59, and 0.60, respectively, the spatial distributions of multivariate return periods are mapped to determine regions with higher drought risk. The results showed that: (1) The mean values of drought duration, severity, and peak over different regions were in the ranges of 1.94–5.18 (months), 0.92–2.81, and 0.49–0.72, respectively. (2) Drought severity had higher correlations with drought duration (0.83) and peak (0.91), while the correlation coefficient between drought duration and peak was lower (0.73). (3) KDE can establish reliable joint distributions of drought variables after passing Kolmogorov-Smirnov (KS) and Anderson-Darling (A-D) tests at the 5% significance level with an average root-mean-square error of 0.04. (4) When the univariate return period was equal to 100 years, the multivariate joint return period of the “or” case was generally less than 70 years but that of the “and” case was mainly greater than 200 years. (5) Compared with other regions, West North America, North-East Brazil, Southeastern South America, Central Asia, and the Tibetan Plateau experienced higher drought risks. Accordingly, countermeasures should be established in these regions to alleviate drought impacts.

A new measure for assessment of clustering based on kernel density estimation

A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric univariate kernel density estimation method to the interpoint distances computed between the members of data. Being based on interpoint distances, it is free of the curse of dimensionality and therefore efficiently computable for high-dimensional situations where the number of study variables can be larger than the sample size. The proposed measure is compatible with any clustering algorithm and with every kind of data set where the interpoint distance measure can be defined to have a density function. Our conducted simulation study proves its superiority over widely used cluster validity indices like the average silhouette width and the Dunn index, whereas its applicability is shown with respect to a high-dimensional Biostatistical study of Alon data set and a large Astrostatistical application of time series with light curves of new variable stars.

Examining Body Shape Characteristics on Chinese Urban College Male Students

According to the Chinese National Adolescent Health report, the status of adolescent physical health has been decreasing for 26 years. The associated factors which caused such decline was studied and pointed out by Gao (2018). As many scholars claimed, “Sunshine sports” should be implemented to promote the adolescent physical health development (Yang, 2011). Previous study indicated that the age of 18 has been a transition point to study on adolescent physical health. However, there has been few studies conducted on the differences of Body Shape Characteristics (BSC) among different regions. Therefore, the purpose of this study is to examine the differences of BSC focusing on 19-22 years old Han Urban Male College Students (HUMCS). Quantitative comparison research design was employed in this study. Human Subject Institute Review Board approval was obtained. Data were collected from five Chinese National Physical Health reports (1995, 2000, 2005, 2010, and 2015). Non-parametric Kernel Density estimation and Kruskal-Wallis test were utilized to examine the characteristics of dynamic trends on HUMCS. Analysis of Variance (ANOVA) was employed to reveal the differences on BSC from different regions. The statistical results revealed that there were significant height and weight increase from 2000-2015. HUMCS from East region were significantly higher and heavier than the West region, while no difference revealed between East and Mid region. Specifically, the height growth curve shifted from 171.5cm to 173.1cm and the weight of HUMCS increased first, followed by slightly decreased. In addition, the chest circumference of HUMCS had been maintained consistently at about 86cm from 1995 to 2015, only slight decreased in 2005. Moreover, there was significant chest circumference difference between East and West region in 1999 and 2005, East and Mid region in 1995, and Mid and West region in 2005. The body shape characteristics of 19-22 years old Han Urban Male College Students from West, Mid and East region have been significantly increased, which indicated that the overall life and diet standard and living environment have been improved. However, strategies for overweight and obesity of adolescent in developed region such as East and Mid region should be taken. Low nutrition status in undeveloped region such as West region may need more attention.

Stochastic Planning of Integrated Energy System via Frank-Copula Function and Scenario Reduction

Uncertainty introduces both significant complexity and the high risk of suboptimal investment decisions into power system planning. Considering the multiple uncertainties of wind and solar power output, load demands, and energy prices as well as pollutant emission factors during the planning period, a multi-scenario stochastic programming model of an integrated energy system (IES) is constructed in this paper. Scenarios of wind and solar power output are generated based on non-parametric kernel density estimation and the Frank-Copula function; scenarios of load demands are generated through DeST software, and energy prices and pollutant emission factors are generated corresponding to a uniform distribution. Then the generated scenario results of wind and solar power output and load demands are reduced by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula> -means clustering; the generated scenarios of energy prices and pollutant emission factors are reduced by discrete approximation of continuous distribution based on Gaussian quadrature. An illustrative example with 8 cases is performed to analyze the influences of each uncertain parameter on the optimal configuration and economy of the IES.

Improved assessment of maximum streamflow risk management of hydraulic infrastructures. A case study.

Understanding the risks associated with the likelihood of extreme events and their respective consequences for the stability of hydraulic infrastructures is essential for flood forecasting and engineering design purposes. Accordingly, a hydrological methodology for providing reliable estimates of extreme discharge flows approaching hydraulic infrastructures was developed. It is composed of a preliminary assessment of missing data, quality and reliability for statistically assessing the frequency of flood flows, allied to parametric and non-parametric methods. Model and parameter uncertainties are accounted for by the introduced and proposed modified model averaging (modified MM) approach in the extreme hydrological event's prediction. An assessment of the parametric methods accuracy was performed by using the non-parametric Kernel Density Estimate (KDE) as a benchmark model. For demonstration and validity purposes, this methodology was applied to estimate the design floods approaching the case study ‘new Hintze Ribeiro bridge’, located in the Douro river, one of the three main rivers in Portugal, and having one of Europe's largest river flood flows. Given the obtained results, the modified MM is considered a better estimation method.

Vulnerability of high-speed rail grid-connected system on branch potential energy transfer entropy

With the spurt of the high-speed railway construction, vulnerability analysis of the high-speed rail grid-connected system cannot be underestimated, which is helpful to improve the security of power system by preventive effectively. Therefore, we propose a vulnerability evaluation method for the uncertain high-speed rail grid-connected system combining branch potential energy function and information entropy together. Firstly, we construct a probability model of the high-speed rail loads by the nonparametric kernel density estimation method according to the measured data of traction substation. Secondly, we establish a power system vulnerability evaluation model based on the branch potential energy transfer entropy considering the power system state variables such as voltage magnitudes, voltage phase angles and power flows. Finally, the simulations on the IEEE-39 bus system and an actual power system in China show that the transmission line connecting the two regions is more vulnerable subjected to the influence of the high-speed rail loads, and the grid-connected points of the high-speed rail loads close to the generator help to reduce the output of the balance generator. These provides auxiliary suggestions for the rationalization of grid-connected location of high-speed rail load, and has certain practical application values.

Full waveform inversion based on the non-parametric estimate of the probability distribution of the residuals

SUMMARY In an attempt to overcome the difficulties of the full waveform inversion (FWI), several alternative objective functions have been proposed over the last few years. Many of them are based on the assumption that the residuals (differences between modelled and observed seismic data) follow specific probability distributions when, in fact, the true probability distribution is unknown. This leads FWI to converge to an incorrect probability distribution if the assumed probability distribution is different from the real one and, consequently it may lead the FWI to achieve biased models of the subsurface. In this work, we propose an objective function which does not force the residuals to follow a specific probability distribution. Instead, we propose to use the non-parametric kernel density estimation technique (KDE) (which imposes the least possible assumptions about the residuals) to explore the probability distribution that may be more suitable. As evidenced by the results obtained in a synthetic model and in a typical P-wave velocity model of the Brazilian pre-salt fields, the proposed FWI reveals a greater potential to overcome more adverse situations (such as cycle-skipping) and also a lower sensitivity to noise in the observed data than conventional L2- and L1-norm objective functions and thus making it possible to obtain more accurate models of the subsurface. This greater potential is also illustrated by the smoother and less sinuous shape of the proposed objective function with fewer local minima compared with the conventional objective functions.

Using Kernel Density Estimation to Identify, Rank, and Classify Severe Weather Outbreak Events

A method for ranking severe weather outbreaks of any type using a linear-weighted multivariate scheme has been introduced recently. The results of using this ranking method indicated that the scheme was capable of identifying the most significant severe weather outbreaks. However, the inclusion of days in which numerous reports were widely dispersed across a large region, or in which multiple clusters of reports that were geographically widely separated, was problematic. Though the studies included a variable (the so-called middle-50% parameter) that was effective in identifying these cases, a new way was needed to account for these days in a manner that agrees with subjective perceptions of these events. A candidate scheme introduced here uses nonparametric kernel density estimation to identify clusters of severe weather reports associated with a single severe weather event. Clusters with relatively few reports or sparse coverage within the region associated with the event then can be excluded quite easily. This technique also allows for multiple, regionally-separated clusters of severe reports to be considered in one day. After identifying clusters of severe weather events from 1960-2008, the cases are ranked and classified in a way similar to past research, using multivariate linear-weighting and cluster analysis, respectively. Results suggest that the most significant severe weather outbreaks again are identified appropriately, and the cases could be classified as major tornado, hail-dominant, wind-dominant, and minor mixed-mode events.

Pairwise Exemplar Clustering

Exemplar-based clustering methods have been extensively shown to be effective in many clustering problems. They adaptively determine the number of clusters and hold the appealing advantage of not requiring the estimation of latent parameters, which is otherwise difficult in case of complicated parametric model and high dimensionality of the data. However, modeling arbitrary underlying distribution of the data is still difficult for existing exemplar-based clustering methods. We present Pairwise Exemplar Clustering (PEC) to alleviate this problem by modeling the underlying cluster distributions more accurately with non-parametric kernel density estimation. Interpreting the clusters as classes from a supervised learning perspective, we search for an optimal partition of the data that balances two quantities: 1 the misclassification rate of the data partition for separating the clusters; 2 the sum of within-cluster dissimilarities for controlling the cluster size. The broadly used kernel form of cut turns out to be a special case of our formulation. Moreover, we optimize the corresponding objective function by a new efficient algorithm for message computation in a pairwise MRF. Experimental results on synthetic and real data demonstrate the effectiveness of our method.

Determining the effectiveness of pollution control policies implemented by the Chinese government: Distribution fitting and testing of daily PM2.5 data

Air pollution has become an urgent issue affecting sustainable urban development. The Chinese government has implemented a series of air pollution control policies since 2012. Exploring the effectiveness of pollution control policies is important for future policy-making and improvements in air quality. Mean and variance tests were used for evaluation on the effectiveness of pollution control policies implemented in major cities and estimates of the heterogeneity among cities based on the distribution fitting and testing of daily PM2.5 data from January 2015 to January 2020. The nonparametric kernel density estimation adopted in this paper can effectively describe the data characteristics, and this is very important for air quality monitoring and control. Our findings demonstrate that air pollution prevention and control policies have significantly improved the levels and distribution of urban air quality in China.

Influences of local hydroclimatology and teleconnections on Florida's precipitation and temperature variability

AbstractUnderstanding the influences of local hydroclimatology and two large‐scale oceanic‐atmospheric oscillations (i.e., Atlantic Multidecadal Oscillation (AMO) and El Niño‐Southern Oscillation (ENSO)) on seasonal precipitation (P) and temperature (T) relationships for a tropical region (i.e., Florida) is the focus of this study. The warm and cool phases of AMO and ENSO are initially identified using sea surface temperatures (SSTs). The associations of SSTs and regional minimum, maximum and average surface air temperatures (SATs) with precipitation are then evaluated. The seasonal variations in P‐SATs and P‐SSTs associations considering AMO and ENSO phases for sites in (1) two soil temperature regimes (i.e., thermic and hyperthermic); (2) urban and non‐urban regions; and (3) regions with and without water bodies, are analysed using two monthly datasets. The analyses are carried out using trend tests, two association measures, nonparametric and parametric statistical hypothesis tests and kernel density estimates. Decreasing (increasing) trend in precipitation (SATs) is noted in the recent multi‐decadal period (1985–2019) compared to the previous one (1950–1984) indicating a progression towards warmer and drier climatic conditions across Florida. Spatially and temporally non‐uniform variations in the associations of precipitation with SATs and SSTs are noted. Strong positive (weak negative) P–T associations are noted during the wet (dry) season for both AMO phases and El Niño, while significant (positive) P–T associations are observed across southern Florida during La Niña in the dry season. The seasonal influences are predominant in governing the P–T relationship over the regions with and without water bodies; however, considerable variations between El Niño and La Niña are noted during the dry season. The climate variability influences on P–T correlations for hyperthermic and thermic soil zones are found to be insignificant (significant) during the wet (dry) season. Nonparametric clustering is performed to identify the spatial clusters exhibiting homogeneous P–T relationships considering seasonal and climate variability influences.

Environmental determinants of Anaplasma phagocytophilum infection in cattle using a kernel density function

The study of vector-borne zoonotic diseases often relies on partial data, because of the constraints associated with observing various elements of the transmission cycle: the pathogen, the vector, the host – wild or domestic. Each angle comes with its own practical challenges, leading to data reflecting poorly either on spatial or temporal dynamics, or both. In this study, we investigated the effect of landscape on the presence of bovine ehrlichiosis infection in Walloon cattle. This disease is transmitted to cattle through the bite of a tick infected by the bacterium Anaplasma phagocytophilum. The first case of bovine ehrlichiosis in the southern region of Belgium (Wallonia) was detected in 2005 and the high seroprevalence found in herds suggests that the disease is endemic. The presence of antibodies of A. phagocytophilum in one cow selected in each of 1445 herds in 2010 and 2011 was detected using indirect immunofluorescence. Samples were geolocated at the farm. However, the precise location of infection remains uncertain. To account for the data sparsity, we elaborated a spatial index for the intensity of the presence of seropositive animals, based on a non-parametric kernel density estimation. We examined this index with the landscape surrounding the pastures, using multiple regressions. Landscape factors were selected using a conceptual framework based on the ecological resources needed for the transmission cycle of A. phagocytophilum. Results suggest that our spatial index adequately reflected infection presence in cattle in Wallonia, which was highest in central regions, corresponding to more forested and fragmented landscapes. We noticed that the presence of large hosts, wild or domestic, as well as the composition and configuration of the landscape of the pasture, influenced the capacity of the pasture to support the presence of bovine ehrlichiosis in Walloon herds. This is consistent with the ecology of A. phagocytophilum and current knowledge about risk factors of tick-borne diseases in cattle at the regional scale. The nature of the kernel density index, based on uncertainties over the location of cases positive to A. phagocytophilum, reflected the infectiousness profile at the landscape and not at the pasture level. Results also highlighted that the effects of some environmental variables remain, even when considering the different agro-geographic regions of Wallonia, which present contrasted landscapes and different levels of intensity of A. phagocytophilum infection. The kernel density index is a useful tool to help veterinary practitioner to quickly target areas where A. phagocytophilum infection is likely.

Uncertainty analysis based on non-parametric statistical modelling method for photovoltaic array output and its application in fault diagnosis

Fault diagnosis is crucial for photovoltaic (PV) power generation, but the output uncertainty characteristics of PV arrays caused by different failures and their fluctuations make them facing new challenges. The parameter estimation (PE) method is widely used for uncertainty analysis, but there exist big differences between the PE results and the real output distributions. To solve this problem, this paper proposes a method for acquiring the fault diagnosis threshold based on non-parametric kernel density estimation (NKDE). First, the distribution characteristics of PV arrays output are statistically analysed, it is found that current and power are mainly affected by the solar irradiance, resulting in strong volatility and uncertainty, which makes it hard to get the threshold for fault diagnosis, thus we propose new three status indicators to finish it. Then, the probability models of the three indicators are built based on the kernel density estimation (KDE) method, by assigning the confidence values of the models, the fault diagnosis threshold intervals can be obtained. Verification shows that NKDE method performed better than traditional PE method in fitting the distribution of the PV arrays output, it does not need prior knowledge of the probability density function. And the proposed fault diagnosis method proves it is feasible to apply the uncertainty analysis method to PV array fault diagnosis. The paper provides a new idea for setting the dynamic threshold for PVarray fault diagnosis.

Short-Term Forecasting and Uncertainty Analysis for Wind Power Generation Based on Hybrid Deep Learning and Cloud Model

Due to the fluctuating and intermittent characteristics of wind energy, it leads to uncertainty in forecasting. In order to improve the wind power forecasting (WPF) accuracy, the paper proposes a CNN-BiLSTM model based on the multi-convolution and multi-pooling(MCP) method for the short-term forecasting model of wind power and photovoltaic power generation, and performs multi-scale forecasting and analysis of the output power in a wind farm. The result analysis verified the forecasting accuracy of CNN-BiLSTM model at 4 hours, 24 hours and 72 hours is higher than those of LSTM, BP neural network, BP-PSO hybrid model and wavelet neural network. The uncertainties in WPF caused by different forecasting models at different time scales are qualitatively described by the expectation, entropy, and hyper-entropy of cloud model. The quantification of the uncertainties in WPF are measured by the confidence intervals based on the non-parametric kernel density estimation (NPKDE). The results show that the proposed method can improve the predict accuracy on the uncertainties in WPF at different confidence levels.

Modeling and application of ship density based on ship scale conversion and grid

To explore the regularity of ship density and ensure the safety of maritime traffic, a ship density model based on ship scale conversion and grid is established by considering the impact of ship size on traffic safety. A non-parametric kernel density estimation (KDE) method is used to obtain the probability density function of the ship density by selecting the appropriate kernel function and determining the optimal bandwidth. To process and store Automatic Identification System (AIS) data efficiently, a grid-based storage method of AIS data is proposed in this paper, and the relationship between grid width and sampling interval is established. The experiments result proves that the grid-based AIS data storage method saves 64% of storage space compared with the original AIS data. The ship density model based on ship scale conversion can reflect the impact of ship size on the maritime traffic. The distribution regularity of ship density can be obtained through the probability density curve of ship density and statistical characteristics. The research results show that the proposed method can provide theoretical support for the safety supervision of the maritime authority. It can also be recommended for the evaluation of VTS centers in vessel traffic management.

Research on Optimal Power Flow Calculation Method for Multi-wind Power Distribution Network

The comprehensive consideration of the uncertainty and correlation factors in the power system is of great significance for the comprehensive evaluation of the optimal power flow. For the edge distribution of wind speed in wind fields, the non-parametric kernel density estimation method is adopted in this paper. For the wind speed combined distribution model of multiple wind fields, due to its own characteristics and the complexity of taking the correlation into account, the vine copula function was used in this paper to construct the model. Then, the three-point estimation method is used to generate independent random vectors in the standard normal space, and based on the combined distribution model, Rosenblatt inverse transformation is used to map the random vectors into correlated wind speed vectors. Finally, 2N+1 deterministic optimal power flow calculation is completed according to the interior point method, and the probability statistics information of each state quantity of power system is obtained. Taking the actual wind speed in a certain area as an example, the combined distribution model of multiple wind fields is constructed, and the probabilistic optimal power flow calculation is carried out in the power supply system containing multiple wind fields. The simulation results show that the method presented in this paper gives consideration to the accuracy and efficiency of the calculation.

Circular-linear-linear probabilistic model based on vine copulas: An application to the joint distribution of wind direction, wind speed, and air temperature

Coupling of multiple environmental factors in the engineering sector, in particular, joint distribution modeling based on a high-dimensional environmental dataset containing circular data is very topical. We propose a modeling framework applicable to the 3D joint distribution of circular-linear-linear (C-L-L) dataset consisting of a parametric model based on copulas and a nonparametric kernel density estimation model. In the parametric model, the pair-copula decomposition concept of vine copulas represents the C-L-L dependence structure as a combination of C-L and L-L ones modeled by C-L and L-L copulas, respectively. This allows one to solve the circular variable's cyclicity problem in the trivariate joint distribution and assess C-L and L-L dependencies between paired variables in the C-L-L dataset. A case study is used to establish the joint distribution model based on annual observations of wind direction, wind speed, and air temperature via the structural health monitoring system of the Jiangyin Bridge, China. The modeling framework validity is proved by the case study, which reveals significant differences in the conditional univariate distribution features of wind speed and air temperature, and conditional joint distribution features of two variables under different wind directions. Therefore, in engineering problems sensitive to the wind direction, the latter's effect cannot be neglected.