Nonparametric Kernel Density Estimation Research Articles

Big data analytics for quality variation over work shifts in manufacturing systems

ABSTRACT In the manufacturing industry, mass production enables manufacturers to produce parts with high precision and lower costs. Multiple shifts operate production processes to maximize efficiency. Several researches have been conducted on the impact of shift work on labor’s health and habits. However, there have been few studies on the influence of shift work on the consistency of product quality. This paper provides a methodology to analyze the impact of different work shifts in a real electronic board manufacturing industry. The study uses big data and analytics to assess product quality from data. Non-parametric kernel density estimation is used to approximate the distribution of good products in each work slot. Then several metrics are used to measure the dissimilarity between the estimated densities. The approach can be leveraged in various problems related to process performance and quality. The obtained results show that there is no significant difference in terms of product quality between work shifts. These prove the consistency of the manufacturing processes and the homogeneity of performance across work shifts in the studied factory. Compared to the literature, the paper presents the first quantitative analysis to compare production process performance and product quality over shift works.

Study on the distribution of average wind speeds at a mountainous bridge site for structural durability design

Conventional wind speed distribution methods (e.g., Rayleigh distribution and Weibull distribution) may not adequately capture complex characteristics of wind fields in mountainous areas. To address this problem, this study proposes a semi-parametric mix method for modeling the distribution of average wind speeds based on the combination of nonparametric Kernel Density Estimation (KDE) and Generalized Pareto Distribution (GPD). In the proposed method, KDE focuses on capturing the distribution in the main part of average wind speeds, while GPD aims at performing the distribution in terms of those in the extreme part. The segment point (i.e., the threshold) between KDE and GPD distributions is determined based on the combination of conditional mean excesses criterion and empirical rule. Meanwhile, the selection of modeling parameters should ensure that the mix distribution model is continuous and differentiable at the identified threshold point. Then, the commonly-used conditional probability model is further introduced to describe the wind direction distribution. Finally, a case study based on the measured 10-min average wind speeds at a mountainous bridge site is employed to demonstrate the effectiveness of the proposed method. The results indicate that: (1) the distribution of omnidirectional average wind speeds in the mountainous bridge site exhibits an obviously single-peak characteristic, while those considering wind directionality present a certain bimodal characteristic; (2) the proposed method can effectively describe wind speed distributions with different statistical characteristics, and the fitting accuracy outperforms the frequently-employed Weibull distribution model.

A novel wind power deterministic and interval prediction framework based on the critic weight method, improved northern goshawk optimization, and kernel density estimation

Wind power prediction holds significant importance for the stable operation of power systems and the enhancement of energy utilization efficiency. Interval prediction, capable of providing more uncertain information, has garnered widespread attention. In this study we have designed a hybrid prediction framework for both deterministic and interval prediction. Initially, the original wind power data undergo cleaning using the quartile method and the fuzzy C-means (FCM) clustering algorithm. This approach not only eliminates scattered outliers but also identifies concentrated outliers more effectively. Subsequently, five distinct single prediction models were employed for point predictions. The critic weight method was applied to yield point forecasting results with higher prediction accuracy. Nonparametric kernel density estimation (KDE) and normal distribution (ND) were incorporated to calculate the prediction interval (PI) under varying confidence levels. Finally, an improved northern goshawk optimization (INGO) algorithm was proposed, integrating three enhancement methods: levy flight, sinusoidal mapping, and a reverse learning strategy. This optimization aims to fine-tune the weight coefficients of the aforementioned two interval prediction methods. The resulting PI overcomes the limitations of a single-interval prediction model. To effectively demonstrate the forecasting performance of the proposed prediction framework, two datasets from a wind turbine in northwest China were selected for simulation verification. In deterministic prediction, the designed hybrid forecast model demonstrates a reduction in root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) by 8.5%, 16.98%, and 11.49%, respectively, compared to other single prediction models. In interval prediction, the prediction interval coverage probability (PICP) is enhanced, while the prediction interval normalized average width (PINAW) is effectively reduced. The designed interval prediction model can reduce the comprehensive evaluation index coverage width-based criterion (CWC) by 10.51%, 9.62%, and 12.95% on average at 95%, 90%, and 80% confidence levels, respectively. Simulation results verified the validity and feasibility of the proposed prediction framework.

Point Cloud Denoising and Feature Preservation: An Adaptive Kernel Approach Based on Local Density and Global Statistics.

Noise removal is a critical stage in the preprocessing of point clouds, exerting a significant impact on subsequent processes such as point cloud classification, segmentation, feature extraction, and 3D reconstruction. The exploration of methods capable of adapting to and effectively handling the noise in point clouds from real-world outdoor scenes remains an open and practically significant issue. Addressing this issue, this study proposes an adaptive kernel approach based on local density and global statistics (AKA-LDGS). This method constructs the overall framework for point cloud denoising using Bayesian estimation theory. It dynamically sets the prior probabilities of real and noise points according to the spatial function relationship, which varies with the distance from the points to the center of the LiDAR. The probability density function (PDF) for real points is constructed using a multivariate Gaussian distribution, while the PDF for noise points is established using a data-driven, non-parametric adaptive kernel density estimation (KDE) approach. Experimental results demonstrate that this method can effectively remove noise from point clouds in real-world outdoor scenes while maintaining the overall structural features of the point cloud.

Robust Bayesian estimation via the [formula omitted]-divergence

In this paper, we introduce a novel framework for robust Bayesian parameter estimation using the K-divergence. The framework incorporates an outlier resilient pseudo-posterior density function, called the K-posterior, which is based on an empirical version of the K-divergence. The latter involves utilizing Parzen’s non-parametric Kernel density estimator to mitigate the influence of outliers. Under the quadratic loss, a new robust analog of the posterior mean estimator (PME), referred here to as the KPME, is obtained. In the paper, we examine the asymptotic behavior of the KPME and investigate its robustness in the presence of outliers. Furthermore, we tackle the task of data-guided selection for the bandwidth parameter of the kernel in order to optimize a performance-oriented objective. Lastly, the KPME is successfully applied to robust Bayesian source localization under intermittent jamming.

Regional disparities, dynamic evolution, and spatial spillover effects of urban-rural carbon emission inequality in China

ObjectiveThis study recalculates the carbon emissions of urban and rural residents in China, analyzing the dynamic evolution trends of urban and rural carbon emissions. It explores the spatial spillover effects centered around the inequality in carbon emissions between urban and rural areas.MethodsThe study calculates the carbon emissions of urban and rural residents in each province based on the IPCC method. Non-parametric kernel density estimation is employed to depict the dynamic evolution characteristics of national, urban, and rural carbon emissions. The Theil Index is used to measure the disparities in urban and rural carbon emissions in major strategic regions, further applying the Theil Index to evaluate the inequality of urban and rural carbon emissions across provinces. This helps identify the driving factors affecting the inequality of urban and rural carbon emissions and their spatio-temporal effects.FindingCarbon emissions from urban and rural residents in China present a divergent development pattern. Urban emissions have increased, with inter-provincial disparities widening; rural emissions tend to stabilize, with slight growth in inter-provincial gaps. The overall inequality of carbon emissions in various regions of China experiences a three-phase journey of rise, decline, and stabilization. Urban inequality first increases then decreases, while rural inequality gradually lessens, showing clear regional and urban-rural differences. Market and government factors significantly impact the inequality of urban and rural carbon emissions. The development of the digital economy aids in reducing inequality and generates significant spatial spillover effects. The relationship between economic development level and carbon emission inequality is U-shaped. Industrial structure optimization can reduce urban-rural inequality, but its spatial spillover effect is not significant. Government intervention has limited effects, while environmental regulations may increase inequality. Opening up to the outside world helps reduce inequality, and the impact of population density is complex.

Analysis of power dispatching decisions with energy storage systems using the optimal probability distribution model of renewable energy

Effectively managing the inherent unpredictability and fluctuation attributes of renewable energy sources within scheduling systems has emerged as a critical matter demanding immediate attention. The incorporation of energy storage technology offers notable advantages by mitigating fluctuations in wind power generation and curtailing peak shaving costs in scheduling systems through economical utilization of energy storage. This study employs the adjustment of energy storage’s reserve capacity function to modify the economic gains and losses arising from fixed spinning reserve. This approach tailors the reserve capacity function by formulating the uncertainty inherent in wind power generation. The paper presents an enhanced selection method for calculating optimal bandwidth within the framework of least squares approximation probability density function scenarios. The fusion of least squares approximation and optimal bandwidth computation permits precise refinement of bandwidth in non-parametric kernel density estimation approaches. Consequently, the study puts forth a comprehensive model for coordinated scheduling and regulation of a multi-scale energy storage power system. Finally, the stability and economy of the proposed method in the scheduling operation process were verified through simulation, and the research results can provide a theoretical basis for future uncertain wind power scheduling.

Electric Vehicle and Photovoltaic Power Scenario Generation under Extreme High-Temperature Weather

In recent years, with the intensification of global warming, extreme weather has become more frequent, intensifying the uncertainty of new energy output and load power, and seriously affecting the safe operation of power systems. Scene generation is an effective method to solve the uncertainty problem of stochastic planning of integrated systems of new energy generation. Therefore, this paper proposes a scenario generation and scenario reduction model of photovoltaic (PV) output and electric vehicle (EV) load power under extreme weather based on the copula function. Firstly, the non-parametric kernel density estimation method is used to fit a large number of sample data. The kernel density estimation expressions of PV and EV powers under extreme weather conditions are obtained and the corresponding goodness of fit tests are carried out. Then, a variety of joint distribution models based on the copula function are established to judge the goodness of fit of each model, and the optimal copula function is selected as the joint probability distribution function by combining the Kendall and Spearman correlation coefficients of each model. Finally, the optimal copula joint probability distribution is used to generate PV and EV power scenarios. The data of extremely hot weather in a certain province were selected for an example analysis. The results show that the output scenario obtained conforms to the correlation under this extreme weather, and has higher accuracy in reflecting the actual PV output and load power in this province under this extreme weather, which can provide a reference for reliability analyses of power systems and power grid planning.

Flood prediction with optimized gated recurrent unit-temporal convolutional network and improved KDE error estimation

<abstract> <p>Flood time series forecasting stands a critical challenge in precise predictive models and reliable error estimation methods. A novel approach utilizing a hybrid deep learning model for both point and interval flood prediction is presented, enhanced by improved kernel density estimation (KDE) for prediction comparison and error simulation. Firstly, an optimized gated recurrent unit-time convolutional network (GRU-TCN) is constructed by tuning the internal structure of the TCN, the activation function, the L2 regularization, and the optimizer. Then, Pearson Correlation is used for feature selection, and the hyperparameters of the improved GRU-TCN are optimized by the subtraction-average-based optimizer (SABO). To further assess the prediction uncertainty, interval predictions are provided via Non-parametric KDE, with an optimized bandwidth setting for accurate error distribution simulation. Experimental comparisons are made on 5-year hydro-meteorological daily data from two stations along the Yangtze River. The proposed model surpasses long short-term memory network (LSTM), TCN, GRU, TCN-LSTM, and GRU-TCN, with a reduction of more than 13% in root mean square error (RMSE) and approximately 15% in mean absolute error (MAE), resulting in better interval estimation and error control. The improved kernel density estimation curves for the errors are closer to the mean value of the confidence intervals, better reflecting the trend of the error distribution. This research enhances the accuracy and reliability of flood predictions and improves the capacity of humans to cope with climate and environmental changes.</p> </abstract>

Research on the spatiotemporal evolution and driving mechanism of coupling coordinating between green transition of urban land use and urban land use efficiency: a case study of the Yangtze River Delta Region in China.

Analyzing the spatiotemporal characteristics and driving mechanisms of the coupling coordination between the Green Transition of Urban Land Use and urban land use efficiency can help explore the future development direction of sustainable land use in cities. This paper constructs a theoretical framework for the coupling coordination between Green Transition of Urban Land Use and urban land use efficiency. We use several models, including the super-efficiency slack-based model, the coupling coordination degree model, the non-parametric kernel density estimation method, exploratory spatial data analysis, and the geographically and temporally weighted regression model to examine the real level of Green Transition of Urban Land Use and urban land use efficiency in the Yangtze River Delta region from 2003 to 2020. Based on this, we investigate the spatiotemporal evolution characteristics and driving mechanisms of the two coupling coordination processes. The study found that (1) from 2003 to 2020, the overall trend of the coupling coordination between Green Transition of Urban Land Use and urban land use efficiency in the Yangtze River Delta region tended to be coordinated and developed, but still at a primary coordination level, with sufficient room for improvement in the future. (2) The coupling coordination level of each city in the Yangtze River Delta region from 2003 to 2020 showed obvious spatial non-equilibrium and correlation characteristics, and overall dynamic polarization effects were exhibited during the study period; the spatial pattern of high-value areas showed a regularity of prioritizing Shanghai and Zhejiang Province, gradually penetrating into Jiangsu Province and Anhui Province. (3) Economic and social factors have a positive influence on the degree of coupling coordination; natural factors and policy factors have a predominantly negative influence on the degree of coupling coordination. Research conclusions include establishing a regional collaborative development mechanism, utilizing the spatial spillover effect of leading cities; emphasizing science, education, and culture, strengthening the introduction of scientific and technological talents, increasing fiscal inputs, raising the level of economic development, and further expanding the driving effect of economic and social factors; and optimizing the layout of urban and rural construction land, developing urban land in an orderly manner, appropriately strengthening environmental regulation, thereby suppressing the negative effects caused by natural and policy factors.

Point and interval forecasting of ultra-short-term carbon price in China

Accurate carbon price prediction is a reference that allows market participants to make decisions. This study adopts a total of 1,857 trading days of data from April 2, 2014, to June 15, 2022, in the Hubei carbon market, one of the first and largest pilot carbon markets in China for carbon price prediction. We propose a new framework based on the GA-VMD-CNN-BiLSTM-Attention hybrid model: a genetic algorithm (GA) is adopted to search the optimal parameter combination of variational mode decomposition (VMD); a convolutional neural network (CNN) is established to discover the relationship between influencing factors and carbon prices; a bidirectional long and short-term memory network (BiLSTM) is applied to extract time series information; and an attention mechanism is used to strengthen the influence of important information on carbon prices. Compared to 11 other models, the GA-VMD-CNN-BiLSTM-Attention model has a higher accuracy and stronger model reliability. In addition to deterministic point prediction, this study uses non-parametric kernel density estimation with the Gaussian kernel function (KDE-Gaussian) for interval forecasting. The forecasting can quantify the uncertainty of carbon prices and serve as a more practical reference for decision-makers. By revealing the particularly challenging issue that underlies carbon price forecasting, our analysis also sheds light on current low-carbon policies in China.

Automated interpretation of comparison scores for firearm toolmarks on cartridge case primers

An automated approach for evaluating the strength of the evidence of firearm toolmark comparison results is presented for a common source scenario. First, comparison scores are derived describing the similarity of marks typically encountered on the primer of fired cartridge cases: aperture shear striations as well as breechface and firing pin impressions. Subsequently, these scores are interpreted using reference distributions of comparison scores obtained for representative known matching (KM) and known non-matching (KNM) ballistic samples in a common source, score-based likelihood ratio (LR) system. We study various alternatives to set up such an LR system and compare them using qualitative and quantitative criteria known from the literature. As an example, results are applied to establish a system suitable for a firearm-ammunition combination often encountered in casework: Glock firearms with Fiocchi nickel primer ammunition. The system outputs an LR and a measure of LR uncertainty. The range of possible LR-values is limited to a minimum and maximum value in areas of the score domain with little reference data. Finally, the feasibility of combining LRs of different mark types into one LR for the entire primer is assessed. For the distribution models considered in this paper, different modeling approaches are optimal for different types of similarity scores. For the chosen firearm-ammunition combination, non-parametric Kernel Density Estimation (KDE) models perform best for similarity scores based on the correlation coefficient, whereas parametric models perform best for the Congruent Matching Cells (CMC) scores, assuming binomial and beta-binomial models for KM and KNM score distributions respectively. Finally, it is demonstrated that individual LRs of different mark types can be combined into one LR, to interpret a set of different marks on the primer as a whole.

Coordinated economic, energy and environment development across China from 2001 to 2020

ABSTRACT With the development of China’s economy, the contradiction between energy, economy and ecological environment is becoming more and more prominent. However, the spatial and temporal evolution of the contradiction system of energy, economy and environment all over China is rarely focused on. This study assesses the provincial coordinated degree of the economy-energy-environment system over the period of 2001–2020 and analyzes their spatial and temporal evolution using principal component analysis (PCA), a coordination degree model, non-parametric Kernel Density Estimation (KDE), and spatial correlation analysis approaches. Results show that provincial coordination degrees from 2001 to 2020 vary between ‘barely balanced’ and ‘superiorly balanced’ with an overall improvement. However, the gap between high and low regional coordination has widen, while middle-level provinces gradually increase and are distributed more evenly. Limited spatial correlation of provincial coordination exists and the clustering level slightly increases over 2001–2020. Additionally, some less-developed regions, which are still staying at the ‘intermediately balanced’ state in 2020, call for attention.

Exploring the Coupling Coordination and Key Factors between Urban–Rural Integrated Development and Land-Use Efficiency in the Yellow River Basin

Exploring the complex dynamic relationship between urban–rural integrated development and land-use efficiency can contribute to most efficient urban–rural land-use and the rational promotion of urban–rural integrated development. This study established an evaluation model of urban–rural integrated development, adopted the super-efficiency SBM model to measure land-use efficiency, and studied the evolution of the spatial–temporal patterns of urban–rural integrated development and land-use efficiency coupling in the Yellow River Basin. We also examined the factors affecting them with the help of the coupling coordination degree model, non-parametric kernel density estimation, and geographic probes. The results indicate the following: (1) Within the study period, the coupled coordination of urban–rural integrated development and land-use efficiency was similar to the spatial distribution characteristics of land-use efficiency, both showing a “high at both ends and low in the middle” trend. (2) The coupled coordination increased over time; however, a lagging land-use efficiency was a crucial impediment to improving the coupling coordination degree. (3) Carbon emissions, urbanization rate, and per capita GDP were key drivers. The results of this study can provide a reference for local governments in the Yellow River Basin and other similar areas to propose paths to optimize the allocation of urban and rural land-use.

An algorithm based on distribution similarity to determine the representative sample size for particle morphology characterization

Selecting the number of representative particles, expressed as representative sample size (RSS), is a crucial step in characterizing morphology of granular materials. Although the widely-used methods such as the method of standard deviation stabilization are straightforward methods to determine an RSS that has a highly similar probability density function (PDF) to its population, they suffer from several drawbacks such as subjectivity in the RSS selection criterion and overestimation of the required RSS. Thus, conflicting findings have been reported from previous studies even for the same material and same morphological descriptor. To tackle this challenge, this study proposes a new RSS determination method that uses relative entropy in combination with progressive consecutive sampling and nonparametric kernel density estimation. The proposed algorithm ensures the similarity of PDFs between an RSS and its population for both normally distributed and highly skewed morphological descriptors. The robustness of the proposed algorithm against a number of potentially influencing factors such as kernel bandwidth is investigated through sensitivity analysis. Applying the algorithm to real micro-computed tomography (μCT) data showed that more than 95% similarity between the PDFs of an RSS and its population can be ensured. Moreover, the RSS returned by the algorithm depends on both the soil tested and the scale of morphological descriptor used in characterizing the morphology (meso vs macro). Results showed that the RSS ranged between 350 and 500 for capturing morphology distributions of two sands that covered a wide range of angularity.

Monthly runoff time series interval prediction based on WOA-VMD-LSTM using non-parametric kernel density estimation

Monthly runoff time series interval prediction based on WOA-VMD-LSTM using non-parametric kernel density estimation

A Comparative Study of Higher Order Kernel Estimation and Kernel Density Derivative Estimation of the Gaussian Kernel Estimator with Data Application

Higher-order kernel estimation and kernel density derivative estimation are techniques for reducing the asymptotic mean integrated squared error in nonparametric kernel density estimation. A reduction in the error criterion is an indication of better performance. The estimation of kernel function relies greatly on bandwidth and the identified reduction methods in the literature are bandwidths reliant for their implementation. This study examines the performance of higher order kernel estimation and kernel density derivatives estimation techniques with reference to the Gaussian kernel estimator owing to its wide applicability in real-life-settings. The explicit expressions for the bandwidth selectors of the two techniques in relation to the Gaussian kernel and the bandwidths were accurately obtained. Empirical results using two data sets obviously revealed that kernel density derivative estimation outperformed the higher order kernel estimation excellently well with the asymptotic mean integrated squared error as the criterion function.

Wind Power Interval Prediction Based on Robust Kernel Density Estimation

Wind power output has a high degree of randomness, so it is difficult to describe it accurately with some typical probability distribution. The extreme values influence the sample’s general non-parametric kernel density estimation method, and the estimated results are relatively conservative. A wind power interval prediction method based on robust kernel density estimation is proposed to improve the compactness and accuracy of interval prediction. In probability estimation, this method will assign a small weight to the extreme sample data to reduce its influence on the probability density estimation accuracy and has better robustness than the general kernel density estimation method. In addition, the bandwidth of robust kernel density estimation is a dynamic parameter, which can be adjusted with the sample data to improve the prediction accuracy and avoid over-conservative prediction.

Parametric Stochastic Modeling of Particle Descriptor Vectors for Studying the Influence of Ultrafine Particle Wettability and Morphology on Flotation-Based Separation Behavior

Practically all particle separation processes depend on more than one particulate property. In the case of the industrially important froth flotation separation, these properties concern wettability, composition, size and shape. Therefore, it is useful to analyze different particle descriptors when studying the influence of particle wettability and morphology on the separation behavior of particle systems. A common tool for classifying particle separation processes are Tromp functions. Recently, multivariate Tromp functions, computed by means of non-parametric kernel density estimation, have emerged which characterize the separation behavior with respect to multidimensional vectors of particle descriptors. In the present paper, an alternative parametric approach based on copulas is proposed in order to compute multivariate Tromp functions and, in this way, to characterize the separation behavior of particle systems. In particular, bivariate Tromp functions for the area-equivalent diameter and aspect ratio of glass particles with different morphologies and surface modification have been computed, based on image characterization by means of mineral liberation analysis (MLA). Comparing the obtained Tromp functions with one another reveals the combined influence of multiple factors, in this case particle wettability, morphology and size, on the separation behavior and introduces an innovative approach for evaluating multidimensional separation. In addition, we extend the parametric copula-based method for the computation of multivariate Tromp functions, in order to characterize separation processes, also in the case when image measurements are not available for all separated fractions.

Using sequential particle methods and non-parametric distributions in bayesian evaluations of abundance and catch at age time series

We describe an approach to analyzing time series for two variables connected through the state model with abundance and catch data sets and cohort and catch equations as an example. First, we create a deterministic model with parameters that maximizes the closeness of given data and data generated by a model. Then, we obtain cohort stochastic models using the difference between initial and modeled data. They are represented as hidden Bayesian models with abundances as states and catches as observations. Using these models, one can evaluate posterior densities and calculate averages, deviations, etc. As a general matter, the recursive equations met by posterior densities have no analytic solutions. We describe several particle methods that may be used for density approximations and following calculations of their statistical quantities. All generated sample densities are smoothed with non-parametric kernel density estimation. The Fishmetica package was extended with functions for generating samples and weights for filtering, predicting and smoothing densities. Numerical simulations were conducted for a test data set. Several extensions of the approach are proposed including an additional option for comparing the basic models with the use of a likelihood function.