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.

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.

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.

MODERATE DEVIATIONS AND LARGEDE VIATIONS FOR A TEST OF SYMMETRY BASED ON KERNEL DENSITY ESTIMATOR

Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.

A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA

A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.

Some Improvement on Convergence Rates of Kernel Density Estimator

In this paper two kernel density estimators are introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. The second proposed density estimator is a geometric extrapolation of the first bias reduced estimator. Theoretical properties such as bias, variance and mean squared error are investigated for both estimators. To observe their finite sample performance, a Monte Carlo simulation study based on small to moderately large samples is presented.

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.

A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA

A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied.

Improved estimator of the continuous-time kernel estimator

There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases.

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.

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。

Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.

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.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

Spatiotemporal Patterns of Road Network and Road Development Pri-ority in Three Parallel Rivers Region in Yunnan,China:An Evaluation Based on Modified Kernel Distance Estimate

Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road service capacity provided by a road network composed of multi-level roads(i.e.national,provincial,county and rural roads),by taking account of the differences of effect extent and intensity for roads of different levels.Summarized at town scale,the population burden and the annual rural economic income of unit road service capacity were used as the surrogates of social and economic demands for road service.This method was applied to the road network of the Three Parallel River Region,the northwestern Yunnan Province,China to evaluate the development of road network in this region.In results,the total road length of this region in 2005 was 3.70×104km,and the length ratio between national,provincial,county and rural roads was 1∶2∶8∶47.From 1989 to 2005,the regional road service capacity increased by 13.1%,of which the contributions from the national,provincial,county and rural roads were 11.1%,19.4%,22.6%,and 67.8%,respectively,revealing the effect of′All Village Accessible′policy of road development in the mountainous regions in the last decade.The spatial patterns of population burden and economic requirement of unit road service suggested that the areas farther away from the national and provincial roads have higher road development priority(RDP).Based on the modified KDE model and the framework of RDP evaluation,this study provided a useful approach for developing an optimal plan of road development at regional scale.

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.