Kernel Density Estimation Model Research Articles

A short-term load forecasting method based on QRLSTM considering multiple factors analysis

Abstract Complex characteristics of power loads terribly affect the safety of the power grid. Thus, accurate short-term load forecasting is regarded as a solution to mitigate the effect of load complications. In this regard, this work is putting forward a Long Short-Term Memory Network Quantile Regression (LSTMQR) for power load, obtaining the probability density function (PDF). Firstly, the quantile of future power load was obtained using the LSTMQR model. The conditional quantile obtained by the LSTMQR model is used as the input of the Kernel Density Estimation model (KDE) to predict the future probability density distribution of short-term power load at different prediction times. Furthermore, an assessment method is proposed to quantify the effect of different factors on power load to improve prediction accuracy. Finally, a numerical simulation based on actual data in China is established to validate the effectiveness of the proposed forecasting algorithm, indicating the proposed forecasting algorithm can effectively evaluate the relationship between different factors and power load, and probability density prediction can accurately quantify the uncertainty of load information. The proposed algorithm results in a reduction of 37.6% in forecast error compared to the traditional forecasting algorithm.

Assessing wind energy exploitation potential in several regions of Viet Nam using Kernel density estimation model

This article analyzes and assesses the potential for wind energy exploitation in six regions of Vietnam. The wind speed data are used to construct wind speed probability distributions (WSPDs) based on kernel density estimation (KDE). The KDE distribution, with six bandwidth selection methods, is implemented to generate probability density functions (PDFs) for each region's data to describe wind speed characteristics. The statistical tests Cramér-Von Mises (CvM), Anderson-Darling (A-D), and Kolmogorov-Smirnov (K-S) are applied to evaluate the PDFs' goodness-of-fit performance. The analysis results present the KDE distribution using the least-squares cross-validation (LSCV), and the Scott bandwidth selection method has outstanding fitting performance. Based on these PDF distributions, the wind turbine (WT) power curve is used to estimate and predict the amount of electricity that can be produced. This study also proposes a reliable method for wind power output planning based on wind speed that can be universally applied.

Analysis of Regional Differences and Convergence of Equalization Level of Marine Public Services in China’s Coastal Areas

The equalization of marine public services is an effective way to achieve harmonious coexistence of the sea. In this paper, a variable fuzzy recognition model is used to measure the equalization level of marine public services in 11 provinces and cities in China’s coastal areas from 2006 to 2019. The Dagum Gini coefficient, kernel density estimation model, and convergence model are used to study their regional differences, distribution dynamics, and convergence characteristics. The results show that the equalization level of marine public services in China’s coastal areas increased year by year from 2006 to 2019. In terms of spatial distribution, the equalization level of marine public services in coastal areas presents an unbalanced distribution pattern. The overall regional differences in the equalization level of marine public services in China’s coastal areas have narrowed, and the inter-regional differences are the main reasons for the overall differences. The absolute difference in the equalization level of marine public services in China’s coastal areas shows an expanding trend. The equalization level of marine public services in China’s coastal areas has α convergence and β convergence.

Spatio-temporal coordinated development pattern evolution and driving factors of regional population and green economy: Evidence from Shandong Province in China.

The study of spatio-temporal evolution characteristics and factors affecting the coordinated development of population and green economy (CD_PGE) in Shandong province, China, has significant decision-making implications for promoting high-quality and sustainable regional development. Based on 2001 to 2020 panel data for each city and economic zone in Shandong province, this paper constructs an evaluation model for the CD_PGE systems. Using growth elasticity models, geographic concentration models, kernel density estimation models, spatial autocorrelation, analysis of population and regional green economy development in Shandong Province from the perspective of spatial agglomeration coupling, spatial and temporal coupling coordination patterns, and evolutionary characteristics. In addition, we use the fixed effect models and panel quantile models to empirically test the effects of coordinated demographic and green economy development. The results show that: (1) In terms of demo-graphic and economic development characteristics, Shandong's demographic and green economy development trends are good, but there are still many challenges. (2) According to the time series evolution and spatial distribution characteristics, the degree of CD_PGE in Shandong Province is on the rise, and the level of spatial distribution is distinct. (3) From the spatio-temporal dynamical grid evolution of the degree of CD_PGE, the CD_PGE is characterized by significant spatial clustering, but with large regional differences. (4) From an impact factor perspective, both market mechanisms and government intervention have a significant impact on the degree of CD_PGE, but the direction and extent of the impact vary.

Stable training of probabilistic models using the leave-one-out maximum log-likelihood objective

Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation mechanism as a probability distribution to assess the data quality and generate more data, if needed. Kernel density estimation (KDE) based models are popular choices for this task, but they fail to adapt to data regions with varying densities. In this paper, an adaptive KDE model is employed to circumvent this, where each kernel in the model has an individual bandwidth. The leave-one-out maximum log-likelihood (LOO-MLL) criterion is proposed to prevent the singular solutions that the regular MLL criterion gives rise to, and it is proven that LOO-MLL prevents these. Relying on this guaranteed robustness, the model is extended by adjustable weights for the kernels. In addition, a modified expectation–maximization algorithm is employed to accelerate the optimization speed reliably. The performance of the proposed method and models are exhibited on two power systems datasets using different statistical tests and by comparison with Gaussian mixture models. Results show that the proposed models have promising performance, in addition to their singularity prevention guarantees.

Uncovering the spatiotemporal patterns of traffic-related CO2 emission and carbon neutrality based on car-hailing trajectory data

Traffic-related carbon dioxide (CO2) emissions constitute a significant portion of greenhouse gas emissions in urban areas, necessitating a comprehensive understanding of their spatiotemporal patterns and their implications for carbon neutrality. While previous studies have focused on exploring CO2 emission patterns, they often overlook the current carbon neutrality associated with these emissions. This study addresses this gap by investigating spatiotemporal patterns and carbon neutrality using car-hailing trajectory data from Xi'an, China. Initially, a link-based CO2 emission model is formulated by considering various driving conditions. Subsequently, the spatiotemporal patterns of traffic-related CO2 emissions are examined by kernel density estimation (KDE) and Getis-Ord models. Finally, carbon neutrality is assessed using the coupling coordination degree (CCD) model, which explores the relationship between traffic-related CO2 emissions and urban vegetation coverage. Empirical experiments found that hotspots of traffic-related CO2 emissions are concentrated at main roads or intersections, while coldspots are dispersed on residential roads. The findings highlight the significant influence of land use type, public services, and road levels on CO2 emission patterns, as well as the critical role of vegetation coverage in improving carbon neutrality levels. Based on these findings, several strategies are recommended to foster low-carbon city development, including expanding public transport services, integrating subway stations along main roads, optimizing traffic lights, increasing urban green spaces, and diversifying commercial facilities in traffic-related areas. These strategies emphasize the importance of incorporating carbon neutrality into urban planning and policy-making to achieve sustainable urban development.

A hybrid residual correction method with auxiliary particle filter and conditional kernel density estimation for remaining useful life prediction

Predicting the remaining useful life (RUL) is crucial for prognosis and health management and provides an essential foundation for maintenance decisions. This study constructed a hybrid RUL prediction method based on residual correction to enhance prediction accuracy, minimize uncertainty, and mitigate errors caused by local fluctuations in the degeneration state within complex environments. This approach combined an auxiliary particle filter (APF), complementary ensemble empirical mode decomposition (CEEMD), and conditional kernel density estimation (CKDE). First, a Wiener degradation model was established, and the APF was used to acquire the initial state estimate of the equipment and residual difference between actual observations. Second, CEEMD was used to reconstruct the residual sequence and reduce interference. Subsequently, the nonparametric CKDE predicted the residual to correct the filter estimation. The corrected degeneration state value elucidated the local details of the system degradation process, and the point prediction of the RUL at the current time was obtained. The probability density distribution of the remaining life was estimated by substituting the modified degeneration state values into the kernel density estimation (KDE) model. Finally, the method was tested using an aircraft engine dataset. The results demonstrated the efficacy of the proposed method and its superiority over alternative approaches.

Coupling efficiency and spatial dynamic evolution of urban water–energy–food in China–A case of evidence from 94 cities

Quantifying and interpreting the water–energy–food (WEF) nexus is critical to achieve the sustainable development of urban resources. The mismatch between urban water, energy and food allocations is a prominent problem that is particularly acute in the Yellow River Basin (YRB) of China. In this study, models for the WEF coupling degree and coupling efficiency were constructed. The WEF coupling efficiencies of the 94 cities in the YRB from 2011 to 2020 were quantified using a data envelopment analysis (DEA) model. On this basis, the spatial distribution characteristics and evolutionary trends of different urban WEF coupling efficiencies were analysed and explored using an exploratory spatial data analysis (ESDA) model and a parametric kernel density estimation model. The results show that the energy subsystem constrain the development of the WEF nexus, and the food subsystem, in turn, regulates the development of the WEF nexus. In some years, the phenomenon of ‘resource curse’ occurred, in which the WEF coupling degree increased while the coupling efficiency decreased. Overall, the values of the urban WEF coupling efficiency were low, ranging from 0.5300 to 0.6300, which is not effective. Spatial clustering was detected in the urban WEF coupling efficiency. The clustering types were ‘high–high’ clustering areas in less developed regions and ‘low–low’ clustering areas in developed regions. The two clusters and the median contiguous group had different evolutionary trends. Both efficiency and polarisation increased in the high-clustering group, efficiency improved in the low-clustering group, and a new efficiency pole was formed in the median contiguous group. Among the three grouped cities, we discuss the potential of policies such as cross-city cooperation, intra-city multi-sectoral cooperation and cultivating new central growth cities to improve the WEF coupling efficiency in the YRB.

Enhancing Broiler Weight Estimation through Gaussian Kernel Density Estimation Modeling

The management of individual weights in broiler farming is not only crucial for increasing farm income but also directly linked to the revenue growth of integrated broiler companies, necessitating prompt resolution. This paper proposes a model to estimate daily average broiler weights using time and weight data collected through scales. In the proposed model, a method of self-adjusting weights in the bandwidth calculation formula is employed, and the daily average weight representative value is estimated using KDE. The focus of this study is to contribute to the individual weight management of broilers by intensively researching daily fluctuations in average broiler weight. To address this, weight and time data are collected and preprocessed through scales. The Gaussian kernel density estimation model proposed in this paper aims to estimate the representative value of the daily average weight of a single broiler using statistical estimation methods, allowing for self-adjustment of bandwidth values. When applied to the dataset collected through scales, the proposed Gaussian kernel density estimation model with self-adjustable bandwidth values confirmed that the estimated daily weight did not deviate beyond the error range of ±50 g compared with the actual measured values. The next step of this study is to systematically understand the impact of the broiler environment on weight for sustainable management strategies for broiler demand, derive optimal rearing conditions for each farm by combining location and weight data, and develop a model for predicting daily average weight values. The ultimate goal is to develop an artificial intelligence model suitable for weight management systems by utilizing the estimated daily average weight of a single broiler even in the presence of error data collected from multiple weight measurements, enabling more efficient automatic measurement of broiler weight and supporting both farms and broiler demand.

Distribution dynamics and quantile dynamic convergence of the digital economy: Prefecture-level evidence in China

The digital-substantive fusion is the realistic need to crack the problem of “out of the real to the virtual” in the real economy. Based on the panel data of 288 prefecture-level cities in China from 2011 to 2019, we use kernel density estimation and quantile convergence model to explore the distribution dynamics and convergence trend of the digital economy across the country and in the eastern, central, and western regions. In doing so, we unearth several key findings. First, the development of the digital economy in Chinese cities is on the rise, but absolute differences among cities still exist. Second, the overall development of the digital economy exhibits a dynamic q-σ convergence trend, but the development of the digital economy in the central region from the 0.75 to 0.95 quantiles shows a divergence trend. Third, our analysis reveals quantile heterogeneity and regional heterogeneity in the dynamic absolute q-β convergence of digital economy development. The tendency to converge is stronger in the extreme quantile regions than in other regions, while the convergence speed of central and western regions is higher than that of eastern regions. Finally, the dynamic conditional q-β convergence trend of digital economy development across the country and in the eastern, central, and western regions is stronger than the dynamic absolute q-β convergence, with the trend of convergence weakening only in the eastern high quantile regions. These findings provide empirical evidence for promoting regional coordinated high-quality development of digital economy, as well as theoretical references for vigorously promoting the construction of a modernized industrial system and accelerating the development of new-quality productive forces.

Interpretable Machine Learning for Finding Intermediate-mass Black Holes

Definitive evidence that globular clusters (GCs) host intermediate-mass black holes (IMBHs) is elusive. Machine-learning (ML) models trained on GC simulations can in principle predict IMBH host candidates based on observable features. This approach has two limitations: first, an accurate ML model is expected to be a black box due to complexity; second, despite our efforts to simulate GCs realistically, the simulation physics or initial conditions may fail to reflect reality fully. Therefore our training data may be biased, leading to a failure in generalization to observational data. Both the first issue—explainability/interpretability—and the second—out of distribution generalization and fairness—are active areas of research in ML. Here we employ techniques from these fields to address them: we use the anchors method to explain an Extreme Gradient Boosting (XGBoost) classifier; we also independently train a natively interpretable model using Certifiably Optimal RulE ListS (CORELS). The resulting model has a clear physical meaning, but loses some performance with respect to XGBoost. We evaluate potential candidates in real data based not only on classifier predictions but also on their similarity to the training data, measured by the likelihood of a kernel density estimation model. This measures the realism of our simulated data and mitigates the risk that our models may produce biased predictions by working in extrapolation. We apply our classifiers to real GCs, obtaining a predicted classification, a measure of the confidence of the prediction, an out-of-distribution flag, a local rule explaining the prediction of XGBoost, and a global rule from CORELS.

Method for analysing of wind power wave nature based on kernel density estimation

It is beneficial for improving the accuracy of wind power output prediction by analysing and mastering the inherent laws of the fluctuation characteristics of wind power output, guiding the power grid dispatching department to reasonably arrange power generation plans, and improving the economic efficiency of system operation. In order to characterize the probability density distribution of wind power output fluctuation, two adaptive bandwidth kernel density estimation models are established by correcting the fixed bandwidth obtained from the empirical method and unbiased cross-validation method respectively, and then the two models are combined and optimized, and ultimately, the probability density distribution model of wind power output fluctuation based on Hybrid Adaptive Kernel Density Estimation (HAKDE) is established. A variety of probability density distribution models are used to fit the wind power output fluctuations at different spatial and temporal scales in a province in North China, and the example results show that the hybrid adaptive kernel density estimation model has the best fitting effect, thus verifying the effectiveness of the hybrid adaptive kernel density estimation model.

Research on Coupling Coordination of China’s Urban Resilience and Tourism Economy—Taking Yangtze River Delta City Cluster as an Example

Urban resilience provides the foundation and guarantee for the tourism economy, and the development of the tourism industry provides new opportunities and impetus for urban resilience. The coordinated development of urban resilience (UR) and the tourism economy (TE) contributes to the high-quality development of the regional economy. This study takes 27 cities in the Yangtze River Delta (YRD) urban agglomeration as an example. Various analytical techniques, including the entropy method, coupling coordination degree model (CCDM), kernel density estimation, Theil index, and obstacle degree model, are employed to investigate the spatiotemporal evolution patterns and influencing factors that affect the coupling coordination degree (CCD) between UR and TE. The findings indicate that: (1) The urban resilience and tourism economy exhibited an increasing trend denoted by “N” and “M”, respectively. (2) The coupling coordination level has undergone a development phase of “Moderate disorder–Bare coordination–Moderate disorder”. (3) The level of coordination has been enhanced, with intra-regional differences identified as the primary source of variation. (4) The number of Internet users, the number of students in institutions of higher learning, per capita public financial expenditure, science and technology expenditures as a share of fiscal expenditures, urban per capita disposable income, foreign exchange earnings from tourism, and the number of inbound tourists is the main factors affecting the CCD of urban resilience and tourism economy.

DATED HOLOCENE HUMAN REMAINS FROM SOUTH AFRICA: RECALIBRATION AND BROAD CONTEXTUALIZATION

ABSTRACTThe study of human remains can provide valuable information about aspects of past populations. Here we present an updated database consisting of 590 radiocarbon (14C) dates for human remains from Holocene South Africa before European contact. We calibrated or recalibrated all the previously published dates using the most recent calibration curve for the southern hemisphere. Each date is roughly georeferenced and plotted according to their Stone Age or Iron Age contexts, revealing the broad distribution pattern of dated Holocene human remains across South Africa—perhaps reflecting aspects of past population distribution and densities, but also underscoring historical collection practices, archaeological research focus, and preservation conditions. We use Kernel Density Estimation models to show peaks and troughs of dated remains through time, with Later Stone Age peaks at ∼5.5 ka cal BP, ∼2 ka cal BP and ∼0.5 ka cal BP, and Iron Age peaks ∼1.1 ka cal BP and ∼0.5 ka cal BP, some of which show broad correspondence to climatic data. Our data, based on dated remains only, do not provide a full reflection of past populations, and our large-scale, coarse-grained analysis cannot yet assess the reasons for the peaks in dated human remains in detail. Yet, the study provides a new resource, and a data-driven overview that highlights aspects to be explored with further contextual analyses against the available archaeological records, population histories and climatic indicators through time and across space.

Probabilistic Graph Modeling based Safety Classifier Algorithm for Smart Transportation

This research introduces a novel Probabilistic Graph Modeling-based Safety Classifier Algorithm designed for the purpose of classifying road safety in smart transportation systems. Leveraging a combination of numerical integration methods and Gaussian kernel density estimation models, the proposed algorithm offers an effective approach to assess and categorizing the safety levels of roads. The integration of these techniques enables a comprehensive analysis, allowing for a more nuanced understanding of the complex interactions within transportation networks. The algorithm's efficacy in road safety classification holds promising implications for enhancing traffic management and promoting safer urban environments.

Research and evaluation of high-quality development of pearl River Delta and urban conglomeration based on energy consumption

In the framework of “dual carbon,” the correlation between energy usage and the enduring advancement of the Pearl River Delta (PRD) urban cluster, emblematic of China’s reform and opening policies, has garnered considerable interest across different segments of society. The problem of measuring regional high-quality development is related to many indicators and variables, and the quantitative measurement of this topic is a complex systematic project. Based on the high degree of specificity of the region, we have constructed a dynamic and comprehensive measurement system of advanced development for the nine cities in the PRD region using the degree of intensive socio-economic development, the construction of a regional social security system, the structure and efficiency of energy consumption, and the degree of harmony between human beings and the natural environment as the secondary indicators. Utilizing relevant data throughout the period spanning from 2005 to 2020, encompassing the nine cities within the PRD region. The study utilized various methodologies including the kernel density estimation model, GIS spatial model, Dagum Gini coefficient method, and simulation calculations to delve into the current status and trends of advanced development in the PRD urban conglomeration. It also examined the primary barriers to high-quality development in the PRD urban conglomeration and the mechanisms underlying internal coordination development within the urban conglomeration. The research suggests that enhancing the advanced development level in the PRD urban conglomeration relies on improving energy utilization efficiency, transitioning traditional industries, and promoting the development of eco-friendly industries. These findings offer decision-makers valuable insights and practical guidance for advancing high-quality development in the PRD urban conglomeration.

Larval instars determination for the twig borer weevil (Coleoptera: Curculionidae) of Falcataria moluccana (Miq.) Barneby & Grimes in Moluccas, Indonesia

In establishing an integrated pest control strategy, it is important first to discover the life history of a potential agent, including the number of larval instars. The snout-weevil of the tribe Ithyporini Genus species (Coleoptera: Curculionidae) is a holometabolous insect that attacks Falcataria moluccana, a native tree of the Moluccas (Maluku), Indonesia. Preliminary observations show that their larvae feed and develop as a twig borer, making direct observation of their development complicated. This study aimed to determine the number of larval instars by measuring the head capsule width (HCW) and the growth pattern of larvae. As many as 940 larvae of all sizes were collected from three islands in Maluku Province: Ambon, Seram, and Haruku. Kernel density estimation (KDE) and Gaussian mixture model (GMM) were used for data analysis. The growth instars were verified using Brooks-Dyar’s rule. The results indicated four peaks in the frequency distribution from KDE, and cluster four showed the best-fit model from GMM. The growth ratio of HCW was 1.47, which also agrees with Brooks-Dyar’s rule that the growth ratio was consistent and followed a constant geometric. Thus, this research concluded that there were four instars for Ithyporini Gen. sp. larvae.

Spatiotemporal differences in and influencing effects of per-capita carbon emissions in China based on population-related factors

Intensive human activities and resource consumption in China have led to increasing carbon emissions, placing enormous pressure on achieving sustainable development goals. Nonetheless, the effects of population-related factors and carbon emissions remain controversial. This study focuses on the spatiotemporal differences in and influencing effects of per-capita carbon emissions using 2010–2019 panel data covering 30 regions in China. Differing from previous studies, population-related factors are employed to classify the 30 regions into 4 classes, and kernel density estimation, σ convergence and spatial econometric models are used to analyse the spatiotemporal differences in and influencing effects of per-capita carbon emissions. The results demonstrate that overall per-capita carbon emissions rose, but there was heterogeneity in the change in per-capita carbon emissions in the 4 classes of regions. The difference in regional per-capita carbon emissions has been widening, but the change rate of the difference stabilized. Overall, per-capita carbon emissions are heavily affected by household size; however, the driving forces behind per-capita carbon emissions in the 4 classes of regions vary. These results suggest that precise and coordinated governance of carbon emissions and reverting to the traditional household structure should be considered to meet the dual carbon goal.

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.

GIS-Based Analysis of Wildlife Habitat Suitability and Conservation Strategies in Maasai Mara Reserve

The significance of conducting an animal habitats suitability analysis is to enhance sustainable management in the face of land use modification, population growth, and changing settlement patterns, thereby safeguarding Kenya's natural resources, tourism, biodiversity, resource utilization, and community livelihoods. This paper establishes a habitat suitability analysis of specific animal habitats based on GIS technology. Firstly, key indicators were identified and subjected to the single factor analysis. Secondly, the AHP model was employed to calculate the weights of the indicators. A comprehensive evaluation was then carried out to visualize the animal habitat suitability map. Finally, the results of the animal habitat suitability analysis were overlaid with the spatial data of the road network. Overall, the results show that the suitable habitat for wildlife habitat is concentrated in the eastern and western corners of the Masai Mara Reserve, evenly distributed in the south-eastern corner, with a small amount in the north. The impact of lost opportunities for people living near the reserve will be significantly reduced. A kernel density estimation model was introduced to make predictions based on the first law of geography. The visualized predictions show that the habitable range of animals is relatively close to the results of model 1, which proves that animal populations and the quality of human life are secure.