Adaptive Kernel Density Estimation Research Articles

Uncovering the progressive failure process of primary coal-rock mass specimens: Insights from energy evolution, acoustic emission crack patterns, and visual characterization

The failure and instability of deep coal-rock mass structures, which are influenced by mining disturbances, are major contributors to disasters like rock bursts. This study involved conducting indoor experiments using uniaxial loading test and acoustic emission (AE) experiments on indigenous primary coal-rock mass (PCRM). We utilize chaotic bifurcation based on strain energy to characterize the progressive damage stages of PCRM, demonstrating the chaotic characteristics of energy evolution during the gradual destruction process. The degree of damage resulting from PCRM failure was evaluated by jointly applying P-wave velocity tomography and AE event localization. Additionally, the classification of crack patterns in PCRM was conducted using the RA-AF correlation analysis method. The segmentation boundaries of crack classification patterns were then redefined using the Gaussian mixture model (GMM) algorithm. The research findings indicate that the chaotic bifurcation model of strain energy classifies stress into four stages: the stable region (Ⅰ), the metastable region (Ⅱ), the bifurcation region (Ⅲ), and the chaotic region (Ⅳ). The presence of a low-velocity zone in P-waves may indicate crack accumulation and damage within the system. Additionally, areas with abnormal P-wave velocities exhibit numerous AE events. The crack classification patterns of the four stages undergo an evolution from predominantly tensile cracks to a mixture of tensile and shear cracks, and the GMM algorithm successfully identifies the optimal separation path for crack classification boundaries. We propose an adaptive kernel density estimation (AKDE) algorithm to quantify the spatial distribution of AE events, thus offering a visual representation of the damage patterns at various stages.

A novel framework for high resolution air quality index prediction with interpretable artificial intelligence and uncertainties estimation

Accurate air quality index (AQI) prediction is essential in environmental monitoring and management. Given that previous studies neglect the importance of uncertainty estimation and the necessity of constraining the output during prediction, we proposed a new hybrid model, namely TMSSICX, to forecast the AQI of multiple cities. Firstly, time-varying filtered based empirical mode decomposition (TVFEMD) was adopted to decompose the AQI sequence into multiple internal mode functions (IMF) components. Secondly, multi-scale fuzzy entropy (MFE) was applied to evaluate the complexity of each IMF component and clustered them into high and low-frequency portions. In addition, the high-frequency portion was secondarily decomposed by successive variational mode decomposition (SVMD) to reduce volatility. Then, six air pollutant concentrations, namely CO, SO2, PM2.5, PM10, O3, and NO2, were used as inputs. The secondary decomposition and preliminary portion were employed as the outputs for the bidirectional long short-term memory network optimized by the snake optimization algorithm (SOABiLSTM) and improved Catboost (ICatboost), respectively. Furthermore, extreme gradient boosting (XGBoost) was applied to ensemble each predicted sub-model to acquire the consequence. Ultimately, we introduced adaptive kernel density estimation (AKDE) for interval estimation. The empirical outcome indicated the TMSSICX model achieved the best performance among the other 23 models across all datasets. Moreover, implementing the XGBoost to ensemble each predicted sub-model led to an 8.73%, 8.94%, and 0.19% reduction in RMSE, compared to SVM. Additionally, by utilizing SHapley Additive exPlanations (SHAP) to assess the impact of the six pollutant concentrations on AQI, the results reveal that PM2.5 and PM10 had the most notable positive effects on the long-term trend of AQI. We hope this model can provide guidance for air quality management.

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

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

A new method for analysis of marine sustainable energy systems

This paper proposes to utilise a new adaptive kernel density estimation (KDE) methodology based on linear diffusion processes for predicting the probability distribution tails of sea-state parameters. A key conclusion was reached that the proposed new methodology can lead to more accurate prediction results than traditional methods based on fittings to a measured significant wave height data set at National Data Buoy Center station 46014. This proposed methodology was subsequently utilised for deriving an accurate 50-year environmental contour line that was used in the dynamic analysis of a two-body point absorber wave energy converter. After systematically analysing the calculation results, another key conclusion was drawn that it is advantageous to use a more reliable contour line derived using the proposed new methodology for long-term dynamic analysis of wave energy converters. In summary, the proposed new adaptive KDE methodology is recommended to be utilised and to be refined continuously in future research work in the field of long-term reliability analysis of marine sustainable energy systems.

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.

A new method for long-term safety analysis of marine structures

This paper proposes to utilise a new adaptive kernel density estimation (KDE) method based on a linear diffusion process for fitting the significant wave height data in order to calculate the sea state parameter distribution tails more accurately, particularly the higher, more extreme values. The accuracy of the proposed method has been demonstrated based on fittings to two measured ocean wave datasets. This proposed method has subsequently been utilised for deriving accurate 50-year and 500-year environmental contour lines. The advantages of using a more reliable contour line derived from using the proposed new method for long-term safety analysis of marine structures have been substantiated.

Research on a Deep Ensemble Learning Model for the Ultra-Short-Term Probabilistic Prediction of Wind Power

An accurate method for predicting wind power is crucial in effectively mitigating wind energy fluctuations and ensuring a stable power supply. Nevertheless, the inadequacy of the stability of wind energy severely hampers the consistent functioning of the power grid and the reliable provision of electricity. To enhance the accuracy of wind power forecasting, this paper proposes an ensemble model named the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and convolutional bidirectional long short-term memory (CNN-BiLSTM), which incorporates a data preprocessing technique, feature selection method, deep ensemble model, and adaptive control. Initially, CEEMDAN is utilized to decompose wind speed and power sequences and hence obtain decomposed subsequences for further analysis. Subsequently, the CNN is used to extract features from each subsequence, whereas each subsequence is processed by BiLSTM to obtain an ultra-short-term deterministic prediction model. Additionally, the adaptive kernel density estimation (AKDE) method is employed to estimate the probabilistic distribution of prediction error, enabling ultra-short-term probabilistic wind power prediction. Finally, based on real datasets, the reliability of the model in probabilistic prediction is verified through the evaluation metrics of multi-step prediction intervals (PIs).

Probabilistic Load Flow Analysis Using Nonparametric Distribution

In the pursuit of sustainable energy solutions, this research addresses the critical need for accurate probabilistic load flow (PLF) analysis in power systems. PLF analysis is an essential tool for estimating the statistical behavior of power systems under uncertainty. It plays a vital part in power system planning, operation, and dependability studies. To perform accurate PLF analysis, this article proposes a Kernel density estimation with adaptive bandwidth for probability density function (PDF) estimation of power injections from sustainable energy sources like solar and wind, reducing errors in PDF estimation. To reduce the computational burden, a Latin hypercube sampling approach was incorporated. Input random variables are modeled using kernel density estimation (KDE) in conjunction with Latin hypercube sampling (LHS) for probabilistic load flow (PLF) analysis. To test the proposed techniques, IEEE 14 and IEEE 118 bus systems are used. Two benchmark techniques, the Monte Carlo Simulation (MCS) method and Hamiltonian Monte Carlo (HMC), were set side by side for validation of results. The results illustrate that an adaptive bandwidth kernel density estimation with the Latin hypercube sampling (AKDE-LHS) method provides better performance in terms of precision and computational efficiency. The results also show that the suggested technique is more feasible in reducing errors, uncertainties, and computational time while depicting arbitrary distributions of photovoltaic and wind farms for probabilistic load flow analysis. It can be a potential solution to tackle challenges posed by sustainable energy sources in power systems.

Scenario-based ultra-short-term rolling optimal operation of a photovoltaic-energy storage system under forecast uncertainty

The rapid development of renewable energy sources (RESs) facilitates the coordinated operation of different energy sources to hedge against the uncertain and non-dispatchable nature of RESs. In this paper, we propose an effective approach for ultra-short-term optimal operation of a photovoltaic-energy storage hybrid generation system (PV-ES HGS) under forecast uncertainty. First, a generic approach for modelling forecast uncertainty is designed to capture PV output characteristics in the form of scenarios. Then, stochastic model predictive control (SMPC) is utilized in the coordinated operation of PV-ES HGS for load shifting under forecast uncertainty. Finally, a PV-ES power station located in Northeast China is selected as a case study to validate the feasibility and effectiveness of the proposed method in detail. The results show that: (1) The forecast uncertainty modelling method, which incorporates adaptive kernel density estimation (KDE) and two-layer nested copula, could capture the characteristics of PV output effectively. (2) The proposed sampling procedure ensures the representativeness and temporal dependence of scenarios extracted from the joint predictive density, leading to stability and efficiency in solving the stochastic optimization problems. (3) The SMPC-based coordinated operation strategy exhibits significant superiority in load shifting performance and resistance to risks. The standard deviation of residual load (SDORL) is reduced by 17.5% on average compared to the conventional scheme. Thus, this work provides operators with guidance in the ultra-short-term optimal operation of a PV-ES HGS under forecast uncertainty.

Risk Assessment Based on KDE of Ship Collision Candidates for Ship Routing Waterway

To study the geographical distribution characteristics of maritime traffic risks, statistical representations of potential accident scenarios and macro collision risk models were established, and the waters with higher maritime traffic risks were generated. To better evaluate the risk of ship collision candidates during routing waterways, an improved adaptive bandwidth kernel density estimation (KDE) is proposed. This proposed algorithm is used for evaluating risk reduction of the ship routing system, which schedules and adjusts maritime traffic in congested harbor waterways. Larger bandwidth can make the hot spot region more obvious on a global scale. Moreover, the bandwidth is positively correlated with the dispersion of points. Concerning the data with sparse point distribution, a larger bandwidth should be used whereas, for data with dense points of interest, a smaller bandwidth should be considered. The results show that the KDE, with optimized bandwidth, can fit the ship encountering distribution and obtain the frequent spots for ship encountering. The comparison between KDE results before and after the ship routing system shows that the hot spots of ship collision candidates are reduced after the ship routing waterway is established.

Adaptive kernel density estimation weighted twin support vector machine and its sample screening method

SummaryIn twin support vector machines (TSVM), noise blurs the boundary between positive and negative samples, increasing the probability of classification errors. In this article, we propose an adaptive kernel density estimation weighted twin support vector machine(AKWTSVM). AKWTSVM uses KDE based on K‐nearest neighbor estimation to calculate the probability density of samples. It automatically selects the optimal bandwidth based on the local density of the samples to improve the robustness of the algorithm. However, TSVM has high time complexity, to reduce the time costs, a sample screening method is proposed for AKWTSVM, named AKWTSVM‐SSM, which is based on the overall distance and local density, and reduces the time costs of the algorithm by reducing the sample size while ensuring the accuracy of the algorithm. The experiment with differently scaled noise environments of 0%, 5%, 10%, 15%, and 20% on 12 UCI datasets validate the accuracy and running time of AKWTSVM and AKWTSVM‐SSM. Experimental results prove the effectiveness and robustness of AKWTSVM, the robustness of AKWTSVM‐SSM, and its applicability to large‐scale datasets.

TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation.

Real-time density estimation is ubiquitous in many applications, including computer vision and signal processing. Kernel density estimation is arguably one of the most commonly used density estimation techniques, and the use of "sliding window" mechanism adapts kernel density estimators to dynamic processes. In this article, we derive the asymptotic mean integrated squared error (AMISE) upper bound for the "sliding window" kernel density estimator. This upper bound provides a principled guide to devise a novel estimator, which we name the temporal adaptive kernel density estimator (TAKDE). Compared to heuristic approaches for "sliding window" kernel density estimator, TAKDE is theoretically optimal in terms of the worst-case AMISE. We provide numerical experiments using synthetic and real-world datasets, showing that TAKDE outperforms other state-of-the-art dynamic density estimators (including those outside of kernel family). In particular, TAKDE achieves a superior test log-likelihood with a smaller run-time.

Incipient Fault Detection in a Hydraulic System Using Canonical Variable Analysis Combined with Adaptive Kernel Density Estimation.

Incipient fault detection in a hydraulic system is a challenge in the condition monitoring community. Existing research mainly monitors abnormal working conditions in hydraulic systems by separately detecting the key working parameter, which often causes a high miss warning rate for incipient faults due to the oversight of parameter dependence. A principal component analysis provides an effective method for incipient fault detection by taking the correlation of multiple parameters into consideration, but this technique assumes the systems are Gaussian-distributed, making it invalid for a dynamic non-Gaussian system. In this paper, we combine a canonical variable analysis (CVA) and adaptive kernel density estimation (AKDE) for the early fault detection of nonlinear dynamic hydraulic systems. The collected hydraulic system data set was used to construct the typical variable space, and the state space and residual space are divided to represent the characteristics of different correlations between the two variables, which are quantitatively described using Hotelling's T2 and Q. In order to investigate the proper upper control limits, AKDE was utilised to estimate the underlying probability density functions of T2 and Q by taking the nonlinearity of the hydraulic system variables into consideration. The advantages of the proposed approach for incipient fault detection are illustrated via a marine power plant lubrication system.

Spatial and temporal trends of overweight/obesity and tobacco use in East Africa: subnational insights into cardiovascular disease risk factors

BackgroundCardiovascular disease (CVD) is increasing in Sub-Saharan Africa (SSA). Overweight/obesity and tobacco use are modifiable CVD risk factors, however literature about the spatiotemporal dynamics of these risk factors in the region at subnational or local scales is lacking. We describe the spatiotemporal trends of overweight/obesity and tobacco use at subnational levels over a 13-year period (2003 to 2016) in five East African nations.MethodsCross-sectional, nationally representative Demographic and Health Surveys (DHS) were used to explore the subnational spatiotemporal patterns of overweight/obesity and tobacco use in Burundi, Kenya, Rwanda, Tanzania, and Uganda, five East African Community (EAC) nations with unique cultural landscapes influencing CVD risk factors. Adaptive kernel density estimation and logistic regression were used to determine the spatial distribution and change over time of CVD risk factors on a subnational and subpopulation (rural/urban) scale.ResultsSubnational analysis shows that regional and national level analysis masks important trends in CVD risk factor prevalence. Overweight/obesity and tobacco use trends were not similar: overweight/obesity prevalence increased across most nations included in the study and the inverse was true for tobacco use prevalence. Urban populations in each nation were more likely to be overweight/obese than rural populations, but the magnitude of difference varied widely between nations. Spatial analysis revealed that although the prevalence of overweight/obesity increased over time in both urban and rural populations, the rate of change differed between urban and rural areas. Rural populations were more likely to use tobacco than urban populations, though the likelihood of use varied substantially between nations. Additionally, spatial analysis showed that tobacco use was not evenly distributed across the landscape: tobacco use increased in and around major cities and urban centers but declined in rural areas.ConclusionsWe highlight the importance of de-homogenizing CVD risk factor research in SSA. Studies of national or regional prevalence trends mask important information about subpopulation and place-specific behavior and drivers of risk factor prevalence. Spatially explicit studies should be considered as a vital tool to understand local drivers of health, disease, and associated risk factor trends, especially in highly diverse yet low-resourced, marginalized, and often homogenized regions.

Ensemble water quality forecasting based on decomposition, sub-model selection, and adaptive interval

The prediction of effluent quality for wastewater treatment plants (WWTPs) has caused widespread concern due to its essential role in ensuring water quality standards and reducing energy consumption. However, the complex nonlinearity of WWTPs leads to difficulties in forecasting and less attention to forecast uncertainty. A novel ensemble water quality forecasting (EWQF) system is proposed that incorporates data preprocessing, point prediction and interval prediction. The system provides an accurate prediction of effluent quality and analyses this uncertainty, for enabling feed-forward control of WWTPs. Specifically, the original water quality data is decomposed into subsequences containing more information and less noise based on improved variational modal decomposition (IVMD). The optimal sub-model for each sub-series is selected from six prediction models based on the sub-model selection strategy, and the point prediction results for water quality are obtained by combining the prediction results of the sub-models. Robust and reliable prediction interval construction based on adaptive kernel density estimation. The results demonstrate that the EWQF achieves optimal point prediction results (R2 = 0.955). The EWQF interval prediction achieves the optimal coverage width criterion (CWC) for different confidence intervals and decision objectives. These results demonstrate that EWQF systems can perform excellent point and interval prediction.

An adaptive selective ensemble algorithm for fault classification

With the aim of improving the classification performance of a single extreme learning machine (ELM) for fault diagnosis, an adaptive selective ensemble classification algorithm is proposed based on the idea of ensemble learning. The proposed algorithm achieves better classification performance than a single model and the selected ELM subnetworks are selected adaptively and the ensemble weights of selected ELM subnetworks are calculated adaptively, which avoids the complex process of manually selecting subnetworks and calculating ensemble weights. First, a regularized error weight adjustment ELM is constructed by introducing regularization parameters and error weight adjustment matrix to a standard ELM, where the error weight adjustment matrix is obtained by the method of adaptive Gaussian kernel density estimation. Then, discrepancy subnetworks are constructed using six different activation functionsand the ensemble weights of subnetworks are obtained adaptively according to the normalized ratio of mean and variance of subnetwork F-scores to achieve the ensemble of subnetworks. Finally, the adaptive selective ensemble classification algorithm is validated using the UCI dataset and experimental acoustic emission signals of gearbox faults. The results show that the adaptive selective ensemble method can improve the stability and accuracy of classification algorithms and the achieved classification accuracy for experimental acoustic emission was 0.9773.

Adaptive First-Crossing Approach for Life-Cycle Reliability Analysis

Abstract Life-cycle reliability analysis can effectively estimate and present the changes in the state of safety for structures under dynamic uncertainties during their lifecycle. The first-crossing approach is an efficient way to evaluate time-variant reliability-based on the probabilistic characteristics of the first-crossing time point (FCTP). However, the FCTP model has a number of critical challenges, such as computational accuracy. This paper proposes an adaptive first-crossing approach for the time-varying reliability of structures over their whole lifecycle, which can provide a tool for cycle-life reliability analysis and design. The response surface of FCTP regarding input variables is first estimated by performing support vector regression. Furthermore, the adaptive learning algorithm for training support vector regression is developed by integrating the uniform design and the central moments of the surrogate model. Then, the convergence condition, which combines the raw moments and entropy of the first-crossing probability distribution function (PDF), is constructed to build the optimal first-crossing surrogate model. Finally, the first-crossing PDF is solved using the adaptive kernel density estimation to obtain the time-variant reliability trend during the whole lifecycle. Examples are demonstrated to specify the proposed method in applications.

An adaptive binned kernel density estimation method for analysis of wave energy converters

ABSTRACT This research proposes a new adaptive binned Kernel Density Estimation (KDE) method to fit significant wave height data in order to more accurately calculate the sea state parameter distribution tails. The brief details of the proposed new methodology are to utilize the fast Fourier transform to perform the convolution of the data with the kernel to find the kernel density estimates on the bin nodes. The Crámer-von Mises test statistic for the proposed adaptive KDE distribution is calculated to be 0.0926 based on a measured wave data set. The Crámer-von Mises test statistic value for the fitted 3-parameter Weibull distribution based on the identical measured data set is 251.2463, indicating a much poorer fit to the empirical distribution function. The advantages of using a more reliable and accurate contour line derived using the proposed new method for long term reliability analysis of wave energy converters have been finally substantiated.

Density-Distance Outlier Detection Algorithm Based on Natural Neighborhood

Outlier detection is of great significance in the domain of data mining. Its task is to find those target points that are not identical to most of the object generation mechanisms. The existing algorithms are mainly divided into density-based algorithms and distance-based algorithms. However, both approaches have some drawbacks. The former struggles to handle low-density modes, while the latter cannot detect local outliers. Moreover, the outlier detection algorithm is very sensitive to parameter settings. This paper proposes a new two-parameter outlier detection (TPOD) algorithm. The method proposed in this paper does not need to manually define the number of neighbors, and the introduction of relative distance can also solve the problem of low density and further accurately detect outliers. This is a combinatorial optimization problem. Firstly, the number of natural neighbors is iteratively calculated, and then the local density of the target object is calculated by adaptive kernel density estimation. Secondly, the relative distance of the target points is computed through natural neighbors. Finally, these two parameters are combined to obtain the outlier factor. This eliminates the influence of parameters that require users to determine the number of outliers themselves, namely, the top-n effect. Two synthetic datasets and 17 real datasets were used to test the effectiveness of this method; a comparison with another five algorithms is also provided. The AUC value and F1 score on multiple datasets are higher than other algorithms, indicating that outliers can be found accurately, which proves that the algorithm is effective.

Probabilistic Power Flow Method for Hybrid AC/DC Grids Considering Correlation among Uncertainty Variables

For a new power system using high-penetration renewable energy, the traditional deterministic power flow analysis method cannot accurately represent the stochastic characteristics of each state variable. The aggregation of renewable energy with different meteorological characteristics in the AC/DC interconnected grid significantly increases the difficulty of establishing a steady-state model. Therefore, this study proposes an improved Latin hypercube sampling algorithm using the van der Waerden scores and diffusion kernel density estimation to overcome the limitations of a priori assumption on probability distributions in uncertainty modeling and to retain the correlations among random variables in the sampling data. Interconnected grids are constructed with IEEE 9-bus and IEEE 14-bus and modified with IEEE 57-bus to describe common application cases of aggregated renewable energy. On this basis, the approximation errors of the proposed probabilistic power flow algorithm to the statistical characteristics of the power parameters are evaluated by setting the Nataf algorithm and the Latin hypercube algorithm using adaptive kernel density estimation as the control group. The results show that the improved Latin hypercube sampling algorithm can exhibit high computational accuracy and strong adaptability, both in severe operating scenarios with large amplitude of load fluctuations and with nonlinear power balance equations incorporating high dimensional random variables.