Density Estimation Method Research Articles

Chance-Constrained Optimal Design of PV-Based Microgrids under Grid Blackout Uncertainties

A grid blackout is an intractable problem with serious economic consequences in many developing countries. Although it has been proven that microgrids (MGs) are capable of solving this problem, the uncertainties regarding when and for how long blackouts occur lead to extreme difficulties in the design and operation of the related MGs. This paper addresses the optimal design problem of the MGs considering the uncertainties of the blackout starting time and duration utilizing the kernel density estimator method. Additionally, uncertainties in solar irradiance and ambient temperature are also considered. For that, chance-constrained optimization is employed to design residential and industrial PV-based MGs. The proposed approach aims to minimize the expected value of the levelized cost of energy (LCOE), where the restriction of the annual total loss of power supply (TLPS) is addressed as a chance constraint. The results show that blackout uncertainties have a considerable effect on calculating the size of the MG’s components, especially the battery bank size. Additionally, it is proven that considering the uncertainties of the input parameters leads to an accurate estimation for the LCOE and increases the MG reliability level.

Failure precursors recognition method for loading coal and rock using the fracture texture features of infrared thermal images

Early warning of the catastrophic failure of rocks is a challenging rock mechanics problem. This article proposed a failure precursor recognition method based on infrared thermal image texture features for coal and rock. Based on spatiotemporal background noise correction for infrared thermal images, a new thermal image parameter of loading coal and rock, Contrast Texture Feature Values (CTFV), is proposed to extract subtle changes in the thermal image caused by crack evolution based on the Gray Level Co-occurrence Matrix (GLCM). The cumulative Crack Texture Thermal Image (CTTI) is reconstructed using CTFV, which can accurately reflect the spatial evolution process of loading coal and rock cracks. The CTFV remains at 0 in the early stage of loading and gradually increases with stress increase at the unstable crack propagation stage, which can serve as a reference for precursor warning of coal and rock failure. For shale, sandstone, and limestone, the precursor of CTFV at grayscale levels of 7, 8, and 9, can be classified into high failure risk, medium failure risk, and low failure risk, respectively. For coal samples, the CTFV is only applicable for the critical warning of high failure risk when the grayscale level is 7. Then, an adaptive identification method for failure precursors based on the sliding window probability density estimation method is proposed. The research results can enhance the reliability of IR monitoring technology for rock failure and instability early warning and can provide support for the prevention and control of rock engineering and geological disasters.

Velocity Dispersion of the Open Cluster NGC 2571 by Radial Velocities and Proper Motions

We use a kernel density estimator method to evaluate the stellar velocity dispersion in the open cluster NGC 2571. We derive the 3D velocity dispersion using both proper motions as extracted from Gaia Data Release 3 and single-epoch radial velocities as obtained with the instrument FLAMES at ESO's Very Large Telescope. The mean-square velocity along the line of sight is found to be larger than the one in the tangential direction by a factor of 6–8. We argue that the most likely explanation for such an occurrence is the presence of a significant quantity of unresolved binary and multiple stars in the radial velocity sample. Special attention should be paid to single-line spectroscopic binaries (SB1) since in this case we observe the spectral lines of the primary component only, and therefore the derived radial velocity is not the velocity of the binary system center of mass. To investigate this scenario, we performed numerical experiments varying the fractional abundance of SB1 in the observed sample. These experiments show that the increase of the mean-square radial velocity depends on the fractional abundance of SB1 to a power in the range [0.39, 0.45]. We used the 3D velocity dispersion obtained by the dispersions in the tangential directions and the assumption that the radial velocity dispersion is the same as a tangential one to estimate the virial cluster mass and the cluster mass, taking into account the gravitational field of the Galaxy and the nonstationarity of the cluster. These estimates are 650 ± 30 M ⊙ and 310 ± 80 M ⊙, respectively, in substantial agreement with the photometric cluster mass.

Identifying spatio-temporal pattern of electric vehicles involved traffic accidents

The increasing popularity of electric vehicles (EVs) has given rise to concerns regarding emerging safety challenges. To address this, an enhanced spatio-temporal kernel density estimation (STKDE) method is developed, which leverages GIS technologies to analyze the temporal evolution of EV accidents across different locations. Our approach introduces several innovations: (1) The incorporation of network distance to address overestimation associated with the conventional Euclidean distance; (2) Integration of a Severity Index (SI) to rationalize accident weighting; (3) Utilization of a likelihood cross-validation method to determine optimal bandwidths for simplified computation. Additionally, statistical significance tests and a ranking system based on cluster strength are implemented to enhance the accuracy and stability of hotspot identification compared to the traditional kernel density estimation (KDE) method. Empirical analyses reveal spatial trends, indicating a higher likelihood of EV accidents occurring near city administrative centers and along arterial roads. Temporally, our findings show increased daytime hotspot density with distinct morning and evening peaks compared to nighttime. Furthermore, a total of 209 hazardous locations, containing 907 accidents, representing 23.4% of all accidents are filtered. Our improved STKDE approach demonstrates a mean hit rate of 0.553 and a PAI of 5.573, which are 3.5% and 27.5% higher, respectively, than those achieved with SKDEKDE. These insights can assist transportation agencies in implementing targeted interventions and resource allocation strategies.

Click detection rate variability of central North Pacific sperm whales from passive acoustic towed arrays.

Passive acoustic monitoring (PAM) is an optimal method for detecting and monitoring cetaceans as they frequently produce sound while underwater. Cue counting, counting acoustic cues of deep-diving cetaceans instead of animals, is an alternative method for density estimation, but requires an average cue production rate to convert cue density to animal density. Limited information about click rates exists for sperm whales in the central North Pacific Ocean. In the absence of acoustic tag data, we used towed hydrophone array data to calculate the first sperm whale click rates from this region and examined their variability based on click type, location, distance of whales from the array, and group size estimated by visual observers. Our findings show click type to be the most important variable, with groups that include codas yielding the highest click rates. We also found a positive relationship between group size and click detection rates that may be useful for acoustic predictions of group size in future studies. Echolocation clicks detected using PAM methods are often the only indicator of deep-diving cetacean presence. Understanding the factors affecting their click rates provides important information for acoustic density estimation.

Spatial-temporal characteristics analysis and ecological environment quality evaluation of forest health care bases in Yunnan, Guizhou and Sichuan provinces

As the forest health care in China is still in the early stage of development, the construction standards of forest health care base are not unified yet, resulting in large differences in the evaluation criterion for the ecological environment of forest health care bases. So, it is urgent to develop a new forest health care ecological environment quality assessment method. Yunnan, Guizhou and Sichuan provinces of China were selected as the study area, the previous 6 batches of 165 national forest health care pilot construction bases were selected as the main data source. This study explored the spatial and temporal distribution characteristics of forest health care bases in the study area using standard deviation ellipses, kernel density estimation method and cold and hot spot analysis. Furthermore, this study evaluated the ecological environment quality of the forest health care bases with a new ecological environment quality evaluation index model, which assembled Fraction Vegetation Coverage (FVC), Wetness (WET), Evapotranspiration (ET), Land Surface Temperature (LST) and Normalized Difference Bare Soil Index (NDBSI). The results are as follows: (1) the forest health bases in the study area are mainly located by the east of the Hu Line with a northeast-southwest distribution direction characteristics, and gradually expanded into a shape of “high in the east and low in the west, multi-point development”. (2) the area with ecological environment quality in excellent, good and medium grade accounts for about 87.73 % in the study area, indicating that most of the study area is suitable for the construction of forest health care base. These results can provide a practical guidance for the further rational layout and balanced development of forest health care bases in the study area.

A Weakly-Supervised Crowd Density Estimation Method Based on Two-Stage Linear Feature Calibration

A Weakly-Supervised Crowd Density Estimation Method Based on Two-Stage Linear Feature Calibration

The mode I fracture toughness and acoustic emission characteristics of hot dry rock under temperature effects

The application of liquid nitrogen fracturing technology exhibits promising potential in the exploitation of hot dry rock (HDR). Therefore, studying the variation in granite's fracture characteristics under rapid cooling with liquid nitrogen is highly significant. In this study, the mode I fracture characteristics and acoustic emission (AE) characteristics of thermally treated granite under liquid nitrogen cooling were investigated experimentally. The results indicate that as the temperature increases, both the natural cooling group and liquid nitrogen cooling group exhibit a gradual decrease in granite's fracture toughness, and the cooling effect of liquid nitrogen will further damage the granite. When heated from 25 °C to 600 °C, the natural cooling fracture toughness decreased from 1.089 MPa·m1/2 to 0.1631 MPa·m1/2, with a reduction of 85.0 %; the liquid nitrogen cooling fracture toughness decreased from 1.089 MPa·m1/2 to 0.1493 MPa·m1/2, with a reduction of 86.3 %. Additionally, both the peak load and fracture energy are reduced; intragranular fracture behavior is observed within the granite, resulting in a rougher fracture surface. The integration of a crack classification method based on the rise angle (RA) and average frequency (AF) of AE parameters with the kernel density estimation (KDE) method effectively validates the fracture mechanism of semi-circular bend (SCB) specimens. Meanwhile, based on the AE results during granite fracturing, a method is proposed to discriminate crack types using RA and AF thresholds.

Large-Area Thickness Measurement of Transparent Films Based on a Multichannel Spectral Interference Sensor

Thickness measurement of thin films is essential for quality control in the manufacturing process of the semiconductor and display industries. Real-time monitoring of film thickness during production is an urgent technical problem to be solved. In this study, a method for large-area thickness measurement of transparent films based on a multichannel spectral interference sensor is proposed. The sensor simultaneously acquires multichannel spectral interference signals through a combination of fan-out fiber optic bundles, detection probes, and an imaging spectrometer. The spectral data are calibrated and transformed into the wavenumber dimension, and then the power spectral density estimation method is used to demodulate the data frequency to swiftly derive the film thickness. The thickness measurement capacity of the proposed system is successfully validated on two standard film samples with a relative deviation of less than 0.38% and a relative standard deviation of less than 0.044%. The total spectral acquisition and calculation time for a single multichannel measurement was approximately 7.5 ms. The experimental results on polyimide films show that the measurement efficiency of the system is at least 4 times higher than that of the traditional system, indicating the potential of the multichannel spectral interference sensor for online monitoring in film production.

Compressing Image-to-Image Translation GANs Using Local Density Structures on Their Learned Manifold

Generative Adversarial Networks (GANs) have shown remarkable success in modeling complex data distributions for image-to-image translation. Still, their high computational demands prohibit their deployment in practical scenarios like edge devices. Existing GAN compression methods mainly rely on knowledge distillation or convolutional classifiers' pruning techniques. Thus, they neglect the critical characteristic of GANs: their local density structure over their learned manifold. Accordingly, we approach GAN compression from a new perspective by explicitly encouraging the pruned model to preserve the density structure of the original parameter-heavy model on its learned manifold. We facilitate this objective for the pruned model by partitioning the learned manifold of the original generator into local neighborhoods around its generated samples. Then, we propose a novel pruning objective to regularize the pruned model to preserve the local density structure over each neighborhood, resembling the kernel density estimation method. Also, we develop a collaborative pruning scheme in which the discriminator and generator are pruned by two pruning agents. We design the agents to capture interactions between the generator and discriminator by exchanging their peer's feedback when determining corresponding models' architectures. Thanks to such a design, our pruning method can efficiently find performant sub-networks and can maintain the balance between the generator and discriminator more effectively compared to baselines during pruning, thereby showing more stable pruning dynamics. Our experiments on image translation GAN models, Pix2Pix and CycleGAN, with various benchmark datasets and architectures demonstrate our method's effectiveness.

Investigating the temporal dynamics of motor vehicle collision density patterns in urban road networks – A case study of New York

Introduction: Motor vehicle collisions are a leading source of mortality and injury on urban highways. From a temporal perspective, the determination of a road segment as being collision-prone over time can fluctuate dramatically, making it difficult for transportation agencies to propose traffic interventions. However, there has been limited research to identify and characterize collision-prone road segments with varying collision density patterns over time. Method: This study proposes an identification and characterization framework that profiles collision-prone roads with various collision density variations. We first employ the spatio-temporal network kernel density estimation (STNKDE) method and time-series clustering to identify road segments with different collision density patterns. Next, we characterize collision-prone road segments based on spatio-temporal information, consequences, vehicle types, and contributing factors to collisions. The proposed method is applied to two-year motor vehicle collision records for New York City. Results: Seven clusters of road segments with different collision density patterns were identified. Road segments frequently determined as collision-prone were primarily found in Lower Manhattan and the center of the Bronx borough. Furthermore, collisions near road segments that exhibit greater collision densities over time result in more fatalities and injuries, many of which are caused by both human and vehicle factors. Conclusions: Collision-prone road segments with various collision density patterns over time have distinct differences in the spatio-temporal domain and the collisions that occur on them. Practical Applications: The proposed method can help policymakers understand how collision-prone road segments change over time, and can serve as a reference for more targeted traffic treatment.

Structural EEG signal analysis for sleep apnea classification.

Diagnosing the sleep apnea can be critical in preventing the person having sleep disorder from unhealthy results. The aim of this study is to obtain a sleep apnea scoring approach by comparing parametric and non-parametric power spectral density (PSD) estimation methods from EEGsignals recorded from different brain regions (C4-M1 and O2-M1) for transient signal analysis of sleep apnea patients. Power Spectral Density (PSD) methods (Burg, Yule-Walker, periodogram, Welch and multi-taper) are examined for the detection of apnea transition states including pre-apnea, intra-apnea and post-apnea together with statistical methods. In the experimental studies, EEG recordings available in the database were analyzed with PSD methods. Results showed that there are statistically significant differences between parametric and non-parametric methods applied for PSD analysis of apnea transition states in delta, theta, alpha and beta bands. Moreover, it was also revealed that PSD of EEG signals obtained from C4-M1 and O2-M1 channels were also found statistically different as proved by classification using the K-nearest neighbour (KNN) method. It was concluded that not only applying different PSD methods, but also EEG signals from different brain regions provided different statistical results in terms of apnea transition states as obtained from KNN classification.

Spatial differences, distribution dynamics and driving factors of the synergy between marine ecological security and high-quality development in three major marine economic circles of China

IntroductionIn China, the sustainable development of the marine is facing a prominent contradiction between ecological security and economic development, as well as unbalanced and non-coordinated regional development. Exploring the regional differences in the synergy between marine ecological security (MES) and high-quality development of the marine economy (MHQD) and its driving mechanism is the key to optimizing the spatial distribution of marine development, promoting the synergistic and balanced development of the regional marine composite system during the “14th Five-Year Plan” period.MethodsIn this article, we employed the Dagum Gini coefficient decomposition model and Kernel density estimation methods to reveal the evolution of regional differences, sources, and distributional dynamics of synergistic development of the composite system from 2009 to 2020. Meanwhile, spatial econometric analyses were applied to identify the influencing factors and spatial spillover effects.ResultsThe level of synergistic development of composite system has a fluctuating upward trend, with a significant positive spatial correlation and a significant “polarization effect”. Inter-regional differences in the synergistic development of the composite system are the main source of the overall differences. Factors such as innovation-driven, human capital, and opening up to the outside world are important driving factors for the synergistic development of the composite system.DiscussionThe MES-MHQD composite system exhibits a low level of synergistic development, with significant differences in the level of synergy both among the 3MMECs and within each circle. We infer that the expansion trend of overall difference will constrain the exploration of a sustainable development path for China’s coastal regions in the future. It is necessary to optimize the spatial layout of the composite system, establish robust mechanisms for regional cooperation and communication, accurately identify the development bottlenecks of the regional composite systems. This study provides a theoretical basis and decision-making reference for the promotion of the synergistic development of the composite system of the Three Major Marine Economic Circles (3MMECs) in China.

Home range size of Tengmalm’s owl offspring during the post-fledging dependence period in Central and North Europe

A greater knowledge of the intrinsic and extrinsic factors of animal home range (HR) formation can help us to understand the fundamental biological issues underlying, for instance, movement patterns, habitat selection and survival. However, very little is known about the HRs of birds of prey fledglings, even though the post-fledging phase is recognised as crucial due to the high mortality of juvenile birds. We radio-tracked 138 Tengmalm’s owl (Aegolius funereus) fledglings from 43 broods to determine their HRs during the post-fledging dependence period and to investigate the factors affecting their sizes. The study was conducted during four breeding seasons in Czechia and two seasons in Finland. The mean fledglings’ HR size calculated according to the 95% IID Kernel Density Estimation method was 63.7 ± 43.9 ha (± SD; n = 71) during nocturnal activity and 52.0 ± 46.1 ha (n = 63) during diurnal roosting. The sizes of both nocturnal activity and diurnal roosting HRs increased with the longer individual duration of the post-fledging dependence period and also the higher rank of hatching within a brood. Diurnal roosting HRs were two times smaller in the Czech site, probably because of the very limited number of dense forest patches suitable for roosting as a legacy of the air pollution calamity in the 1970s, during which most coniferous stands died out. There was no difference in the size of nocturnal activity HR between the two study areas, although they differed markedly in terms of night length, altitude, weather, and forest age, structure and composition. This suggests that environmental factors are not decisive in determining the size of nocturnal activity HRs of Tengmalm’s owl fledglings. Since the diurnal HRs always occurred within the area of the nocturnal HRs, we suggest that conservation of the densest and preferably oldest forest stands within the areas of the study species occurrence may offer straightforward conservation tasks for protecting Tengmalm’s owl fledglings and also other species.

High-dimensional and permutation invariant anomaly detection

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

Dynamic evolution and obstacle factor analysis of green development in China's agriculture and rural areas based on entropy-based TOPSIS model

Green development of agriculture and rural areas (GDARA) is an essential part of rural revitalization and high-quality development. Based on 2011 to 2020 provincial panel data from China, the entropy-based Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model is constructed to measure the level of GDARA, finding that the overall level during the sample period was positive. Then the regional differences mainly from intra-regional were revealed by the methods of Dagum Gini coefficient and Kernel density estimation and were shrinking overall. Besides, the results of Markov chain transfer matrix show the dynamic characteristics clearly, which the low-level regions shift to the middle and high levels with a greater probability. The results of the spatial autocorrelation test display that GDARA has a spatial clustering effect. Finally, the industrial upgrading and the business income of leisure agriculture are respectively proven to hinder GDARA at most by the Obstacle degree model empirically. Based on a series of empirical tests, a few relevant policy recommendations are proposed to promote the road to strong agriculture and rural areas in China.

Maximum likelihood estimation of log-concave densities on tree space

Phylogenetic trees are key data objects in biology, and the method of phylogenetic reconstruction has been highly developed. The space of phylogenetic trees is a nonpositively curved metric space. Recently, statistical methods to analyze samples of trees on this space are being developed utilizing this property. Meanwhile, in Euclidean space, the log-concave maximum likelihood method has emerged as a new nonparametric method for probability density estimation. In this paper, we derive a sufficient condition for the existence and uniqueness of the log-concave maximum likelihood estimator on tree space. We also propose an estimation algorithm for one and two dimensions. Since various factors affect the inferred trees, it is difficult to specify the distribution of a sample of trees. The class of log-concave densities is nonparametric, and yet the estimation can be conducted by the maximum likelihood method without selecting hyperparameters. We compare the estimation performance with a previously developed kernel density estimator numerically. In our examples where the true density is log-concave, we demonstrate that our estimator has a smaller integrated squared error when the sample size is large. We also conduct numerical experiments of clustering using the Expectation-Maximization algorithm and compare the results with k-means++ clustering using Fréchet mean.

Not All Probability Density Functions Are Tomograms.

This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be "quantum".

Probabilistic En Route Sector Traffic Demand Prediction Based on Quantile Regression Neural Network and Kernel Density Estimation

With the development of civil aviation in China, airspace congestion has become more and more serious and has gradually spread from airport terminal areas to en route networks. Traditionally, most prediction methods that obtain traffic flow data are based on the number of aircraft passing through an en route sector and require flight data to meet strict assumptions and conditions. While these methods are normally used in the actual operation of air traffic flow management departments in China, the results are not satisfactory due to the nonlinearity of traffic demand along en route sectors and the change in high-frequency noise. In order to refine aircraft control in airspace, it is necessary to predict traffic flow accurately. Thus, this paper proposes the quantile regression neural network and kernel density estimation method to obtain some quantiles of continuous traffic demand data in the future, which combines the strong nonlinear adaptive ability of neural networks with the ability of quantile regression to describe explanatory variables. By using these continuous conditional quantiles, we obtain the probability density function and probability density curve of the continuous traffic demand in the future using the kernel density estimation method. In this way, we can obtain not only a specific point prediction value and its change interval but also the probability of each value in the prediction change interval of traffic demand in the en route sector as well as a more accurate point prediction value for a specific day.

Learning transfer operators by kernel density estimation.

Inference of transfer operators from data is often formulated as a classical problem that hinges on the Ulam method. The conventional description, known as the Ulam-Galerkin method, involves projecting onto basis functions represented as characteristic functions supported over a fine grid of rectangles. From this perspective, the Ulam-Galerkin approach can be interpreted as density estimation using the histogram method. In this study, we recast the problem within the framework of statistical density estimation. This alternative perspective allows for an explicit and rigorous analysis of bias and variance, thereby facilitating a discussion on the mean square error. Through comprehensive examples utilizing the logistic map and a Markov map, we demonstrate the validity and effectiveness of this approach in estimating the eigenvectors of the Frobenius-Perron operator. We compare the performance of histogram density estimation (HDE) and kernel density estimation (KDE) methods and find that KDE generally outperforms HDE in terms of accuracy. However, it is important to note that KDE exhibits limitations around boundary points and jumps. Based on our research findings, we suggest the possibility of incorporating other density estimation methods into this field and propose future investigations into the application of KDE-based estimation for high-dimensional maps. These findings provide valuable insights for researchers and practitioners working on estimating the Frobenius-Perron operator and highlight the potential of density estimation techniques in this area of study.