Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach

Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications.

Bayesian Classifier Based on Robust Kernel Density Estimation and Harris Hawks Optimisation

In real-world applications, datasets frequently contain outliers, which can hinder the generalization ability of machine learning models. Bayesian classifiers, a popular supervised learning method, rely on accurate probability density estimation for classifying continuous datasets. However, achieving precise density estimation with datasets containing outliers poses a significant challenge. This paper introduces a Bayesian classifier that utilizes optimized robust kernel density estimation to address this issue. Our proposed method enhances the accuracy of probability density distribution estimation by mitigating the impact of outliers on the training sample’s estimated distribution. Unlike the conventional kernel density estimator, our robust estimator can be seen as a weighted kernel mapping summary for each sample. This kernel mapping performs the inner product in the Hilbert space, allowing the kernel density estimation to be considered the average of the samples’ mapping in the Hilbert space using a reproducing kernel. M-estimation techniques are used to obtain accurate mean values and solve the weights. Meanwhile, complete cross-validation is used as the objective function to search for the optimal bandwidth, which impacts the estimator. The Harris Hawks Optimisation optimizes the objective function to improve the estimation accuracy. The experimental results show that it outperforms other optimization algorithms regarding convergence speed and objective function value during the bandwidth search. The optimal robust kernel density estimator achieves better fitness performance than the traditional kernel density estimator when the training data contains outliers. The Naïve Bayesian with optimal robust kernel density estimation improves the generalization in the classification with outliers.

Robust state of charge estimation of lithium-ion battery via mixture kernel mean p-power error loss LSTM with heap-based-optimizer

The state of charge(SOC)estimation of lithium-ion battery is an important function in the battery management system(BMS)of electric vehicles.The long short term memory(LSTM)model can be employed for SOC estimation,which is capable of estimating the future changing states of a nonlinear system.Since the BMS usually works under complicated operating conditions,i.e the real measurement data used for model training may be corrupted by non-Gaussian noise,and thus the performance of the original LSTM with the mean square error(MSE)loss may deteriorate.Therefore,a novel LSTM with mixture kernel mean p-power error(MKMPE)loss,called MKMPE-LSTM,is developed by using the MKMPE loss to replace the MSE as the learning criterion in LSTM framework,which can achieve robust SOC estimation under the measurement data contaminated with non-Gaussian noises(or outliers)because of the MKMPE containing the p-order moments of the error distribution.In addition,a meta-heuristic algorithm,called heap-based-optimizer(HBO),is employed to optimize the hyper-parameters(mainly including learning rate,number of hidden layer neuron and value of p in MKMPE)of the proposed MKMPE-LSTM model to further improve its flexibility and generalization performance,and a novel hybrid model(HBO-MKMPE-LSTM)is established for SOC estimation under non-Gaussian noise cases.Finally,several tests are performed under various cases through a benchmark to evaluate the performance of the proposed HBO-MKMPE-LSTM model,and the results demonstrate that the proposed hybrid method can provide a good robustness and accuracy under different non-Gaussian measurement noises,and the SOC estimation results in terms of mean square error(MSE),root MSE(RMSE),mean absolute relative error(MARE),and determination coefficient R2are less than 0.05%,3%,3%,and above 99.8%at 25℃,respectively.

Heat Kernel Estimates on Simple Random Walks and On-Diagonal Upper Bounds

We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

Real-time road traffic states estimation based on kernel-KNN matching of road traffic spatial characteristics

The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial characteristics is presented to estimate road traffic states. Firstly, the representative road traffic state data were extracted to establish the reference sequences of road traffic running characteristics(RSRTRC). Secondly, the spatial road traffic state data sequence was selected and the kernel function was constructed, with which the spatial road traffic data sequence could be mapped into a high dimensional feature space. Thirdly, the referenced and current spatial road traffic data sequences were extracted and the Euclidean distances in the feature space between them were obtained. Finally, the road traffic states were estimated from weighted averages of the selected k road traffic states, which corresponded to the nearest Euclidean distances. Several typical links in Beijing were adopted for case studies. The final results of the experiments show that the accuracy of this algorithm for estimating speed and volume is 95.27% and 91.32% respectively, which prove that this road traffic states estimation approach based on kernel-KNN matching of road traffic spatial characteristics is feasible and can achieve a high accuracy.

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

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

Hazard Rate Function Estimation Using Weibull Kernel

In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.

Image Motion Deblurring Based on Salient Structure Selection and L0-2 Norm Kernel Estimation

Single image motion deblurring has been a very challenging problem in the field of image processing. Although there are many researches had been proposed to solve this problem, it still has problems on kernel accuracy. In order to improve the kernel accuracy, an effective structure selection method was used to select the salient structure of the blur image. Then a novel kernel estimation method based on L0-2 norm was proposed. To guarantee the sparse kernel and eliminate the negative influence of details L0-norm was used. And L2-norm was used to ensure the continuity of kernel. Many experiments were done to compare proposed method and state-of-the-art methods. The results show that our method can estimate a better kernel and use less time than previous work, especially when the size of blur kernel is large.

Kernel Density Estimation of Tropical Cyclone Frequencies in the North Atlantic Basin

Previous research has identified specific areas of frequent tropical cyclone activity in the North Atlantic basin. This study examines long-term and decadal spatio-temporal patterns of Atlantic tropical cyclone frequencies from 1944 to 2009, and analyzes categorical and decadal centroid patterns using kernel density estimation (KDE) and centrographic statistics. Results corroborate previous research which has suggested that the Bermuda-Azores anticyclone plays an integral role in the direction of tropical cyclone tracks. Other teleconnections such as the North Atlantic Oscillation (NAO) may also have an impact on tropical cyclone tracks, but at a different temporal resolution. Results expand on existing knowledge of the spatial trends of tropical cyclones based on storm category and time through the use of spatial statistics. Overall, location of peak frequency varies by tropical cyclone category, with stronger storms being more concentrated in narrow regions of the southern Caribbean Sea and Gulf of Mexico, while weaker storms occur in a much larger area that encompasses much of the Caribbean Sea, Gulf of Mexico, and Atlantic Ocean off of the east coast of the United States. Additionally, the decadal centroids of tropical cyclone tracks have oscillated over a large area of the Atlantic Ocean for much of recorded history. Data collected since 1944 can be analyzed confidently to reveal these patterns.

Kernel density estimation and marginalized-particle based probability hypothesis density filter for multi-target tracking

In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.

AN EFFECTIVE IMAGE RETRIEVAL METHOD BASED ON KERNEL DENSITY ESTIMATION OF COLLAGE ERROR AND MOMENT INVARIANTS

In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

Diversity Sampling Based Kernel Density Estimation for Background Modeling

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

Density Estimation Using Gumbel Kernel Estimator

In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (pdf). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibull kernel estimator, where performance of newly proposed kernel is outstanding.

Improved Logistic Regression Algorithm Based on Kernel Density Estimation for Multi-Classification with Non-Equilibrium Samples

Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.

Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring

The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many investigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a heavy-tailed distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.

Performance Evaluation of Various Functions for Kernel Density Estimation

There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally best among possible background models. For KDE, the selection of kernel functions and their bandwidths greatly influence the performance. There were few attempts to compare the adequacy of functions for KDE. In this paper, we evaluate the performance of various functions for KDE. Functions tested include almost everyone cited in the literature and a new function, Laplacian of Gaussian(LoG) is also introduced for comparison. All tests were done on real videos with vary-ing background dynamics and results were analyzed both qualitatively and quantitatively. Effect of different bandwidths was also investigated.

我国护理人力资源区域差异的演变特征——基于Dagum基尼系数分解和Kernel核密度估计的实证研究

目的分析我国护理人力资源的区域差异及分布动态演进,为我国护理人力资源的合理配置和规划提供参考。方法基于2011-2022年省级护理人力资源面板数据,通过测算Kernel密度和Dagum基尼系数对我国护理人力资源的区域差异及分布动态演进进行分析评价。结果2011-2022年,在空间分布上,全国及各地区护理人力资源总量呈增加趋势,各区域差异逐步降低,且两极化特征明显;在区域差异上,我国护理人力资源总体差异均值为0.1149;区域内呈东部>西部>中部>东北区域的梯度逐步递增趋势;区域间差异占总体差异的40.61%。结论全国护理人力资源总体差异处于相对合理状态,区域间差异是主要来源,均等化水平逐步提升;政府应针对各区域精准施策,进一步稳定护理人力资源队伍,完善护理人力资源结构以促进护理人力资源的优质均衡发展。

ESSENTIAL RELATIONSHIP BETWEEN DOMAIN-BASED ONE-CLASS CLASSIFIERS AND DENSITY ESTIMATION

One-class support vector machine （OCSVM） and support vector data description （SVDD） are two main domain-based one-class （kernel） classifiers. To reveal their relationship with density estimation in the case of the Gaussian kernel, OCSVM and SVDD are firstly unified into the framework of kernel density estimation, and the essential relationship between them is explicitly revealed. Then the result proves that the density estimation induced by OCSVM or SVDD is in agreement with the true density. Meanwhile, it can also reduce the integrated squared error （ISE）. Finally, experiments on several simulated datasets verify the revealed relationships.