Kernel Distribution Research Articles

Short-time adaptive compact kernel distribution for fault diagnosis under variable working condition bearing

Time-frequency distribution (TFD) methods are extensively employed in the diagnosis of bearings operating under variable working conditions. However, these methods often face high computational complexity, limited time-frequency resolution, and cross-terms. To address these issues, this paper presents a new approach called Short-Time Adaptive Compact Kernel Distribution (STACKD). Based on the characteristics of the vibration signals, we designed Chirp-modulated Gaussian Window and used them to segment the overall signal into small segments. Then, we used a two-step Bayesian optimization method to obtain adaptive compact kernel distributions (ACKD) for these small segments of the signal. Finally, we recombined the ACKD of these small segments into a global STACKD. Results from simulations and experiments demonstrate that STACKD offers improved robustness against interference signals, lower computational complexity, and higher time-frequency resolution without cross-term effects. This method is tailored for diagnosing rolling bearings under variable working conditions, providing enhanced visualization of diagnostic processes with superior time-frequency resolution.

Statistical downscaling model for future projection of daily IDF relationship by Markov chain and kernel density estimator

ABSTRACT Changes in climate might have a significant impact on rainfall characteristics, including extreme rainfall. This study aims to project the future daily rainfall, preserving most of the rainfall characteristics, including extreme rainfall incorporating climate changes. This paper presents two hybrid semi-parametric statistical downscaling models for future projection of IDF curves. The precipitation flux from seven scenarios of ten GCMs and observed daily rainfall data are considered as predictors and predictand variables, respectively. At site, daily rainfall occurrence is modeled using a two-state first-order Markov chain. Rainfall amounts on each wet day are modelled using a univariate nonparametric kernel density estimator. Two types of amount generation models are presented in this study. The bounded model (KDE-SP) is developed, considering the support for the kernel distribution as positive. In the unbounded model (KDE-Ext), the wet days are reclassified as extreme and non-extreme rainy days. A significant increasing trend can be observed in the future projected intensity–duration–frequency relationships. The maximum increment using empirical distribution is observed as 93.21 and 80.93% on a 5-year return period in the far future for the SSP5-8.5 scenario, using KDE-Ext and KDE-SP models, respectively. Although both methods show similar results, the KDE-Ext model performs better in simulating extreme rainfall.

Producer Welfare Benefits of Rating Area Yield Crop Insurance

Index-based insurance is an innovative concept for evaluating agricultural risks and payouts, which uses an index instead of traditional on-site loss assessment. Area yield insurance, as an index-based approach, is an effective strategy to mitigate moral hazard and adverse selection issues. This study aims to develop area yield insurance as a new insurance plan in Iran for two major crops: wheat and barley. It utilized kernel and joint kernel distributions to price the insurance and assessed producer welfare benefits by comparing the certainty equivalence (CE) of farmers’ utility with and without the policy. Data were collected from East Azerbaijan Province, including county-level yield data for irrigated and rainfed wheat and barley from 1975 to 2019 and 446 individual-level yield data from 2015 to 2019. A two-stage method was used to model yield risk: the first stage fits a trend model, while the second estimates the yield distributions with the detrended data. The results showed a significant difference in premiums calculated by the two distributions, with joint kernel distribution offering the best empirical fit and reasonable premiums. The findings indicate that area yield crop insurance provides positive welfare benefits and should serve as a viable alternative or complement to existing yield insurance plans. The successful implementation of this policy in various countries suggests it can be a suitable risk management program for developing countries like Iran.

On the stability of a single-species model with a generic delay distribution kernel

The delayed logistic equation, also known as Hutchinson’s equation, is a simple and elegant model commonly used to capture critical features of complex phenomena in biology, medicine, and economics. This paper studies the stability of a single-species logistic model with a general delay distribution and a constant inflow of nutritional resources. We provide conditions for the linear stability of the positive equilibrium and the occurrence of Hopf bifurcation. The findings complement existing literature and are applied to specific delay distributions: Uniform, Dirac-delta, and gamma distributions. Without resource inflow, we find that the positive equilibrium is stable for short delays but loses stability through Hopf bifurcation as the mean delay increases. The model’s dynamics vary with resource inflow based on the delay distribution: in uniform and Dirac-delta distributions, the dynamics are similar to the no-inflow case, whereas for the gamma distribution, stability depends on the delay order p=1,2,3.

Statistical inference for innovation distribution in ARMA and multi-step-ahead prediction via empirical process

The kernel distribution estimator (KDE) is proposed based on residuals of the innovation distribution in the autoregressive moving-average (ARMA) time series. The deviation between KDE and the innovation distribution function is shown to converge to the Brownian bridge, leading to the construction of a Kolmogorov–Smirnov smooth simultaneous confidence band for the innovation distribution function. Additionally, an empirical cumulative distribution function (CDF) based on prediction residuals is introduced for the multi-step-ahead prediction error distribution function. This empirical process weakly converges to a Gaussian process with a specific covariance function. Furthermore, a quantile estimator is derived from the empirical CDF of prediction residuals, and multi-step-ahead prediction intervals (PIs) for future observations are established using these estimated quantiles. The PIs achieve the nominal prediction level asymptotically for the finite variance ARMA model. Simulation studies and analysis of crude oil price data confirm the validity of the asymptotic theory.

A Principled Distributional Approach to Trajectory Similarity Measurement and its Application to Anomaly Detection

This paper aims to solve two enduring challenges in existing trajectory similarity measures: computational inefficiency and the absence of the ‘uniqueness’ property that should be guaranteed in a distance function: dist(X, Y ) = 0 if and only if X = Y , where X and Y are two trajectories. In this work, we present a novel approach utilizing a distributional kernel for trajectory representation and similarity measurement, based on the kernel mean embedding framework. It is the very first time a distributional kernel is used for trajectory representation and similarity measurement. Our method does not rely on point-to-point distances which are used in most existing distances for trajectories. Unlike prevalent learning and deep learning approaches, our method requires no learning. We show the generality of this new approach in anomalous trajectory and sub-trajectory detection. We identify that the distributional kernel has (i) a data-dependent property and the ‘uniqueness’ property which are the key factors that lead to its superior task-specific performance, and (ii) runtime orders of magnitude faster than existing distance measures.

Detecting Change Intervals with Isolation Distributional Kernel

Detecting abrupt changes in data distribution is one of the most significant tasks in streaming data analysis. Although many unsupervised Change-Point Detection (CPD) methods have been proposed recently to identify those changes, they still suffer from missing subtle changes, poor scalability, or/and sensitivity to outliers. To meet these challenges, we are the first to generalise the CPD problem as a special case of the Change-Interval Detection (CID) problem. Then we propose a CID method, named iCID, based on a recent Isolation Distributional Kernel (IDK). iCID identifies the change interval if there is a high dissimilarity score between two non-homogeneous temporal adjacent intervals. The data-dependent property and finite feature map of IDK enabled iCID to efficiently identify various types of change-points in data streams with the tolerance of outliers. Moreover, the proposed online and offline versions of iCID have the ability to optimise key parameter settings. The effectiveness and efficiency of iCID have been systematically verified on both synthetic and real-world datasets.

Latest Technologies on Dataset Distillation: A Survey

Dataset distillation refers to the process of constructing a smaller dataset based on a larger dataset, so that the training model with the smaller dataset can obtain similar results to the larger dataset. In this paper, we first briefly review the basic methods and some recent advances in this field from the perspectives of meta-learning framework and data matching framework, including the backpropagation through time(BPTT), kernel ridge regression(KRR), decoupled techniques, gradient matching(DC), trajectory matching(MTT) and distribution matching(DM). The results of the plug-and-play approach in recent years are then presented. Finally, we discuss possible future developments from the perspectives of data distillation algorithms on large datasets, the relationship between compress ratio and information contained, more tasks and data modalities, and the use of generative models to improve the distillation results of datasets.

Considering spatial constraints to identify areas for new species sampling: A species-specific prioritization approach

Currently, many regions of the world are under-sampled, which means our knowledge about biodiversity has gaps. Many studies proposed methods to identify areas for new specimen sampling; however, none considered the application of spatial constraints for this prioritization, which does not consider logistical issues. Here, we propose an approach to identify priority areas for new specimen sampling, considering distributional aspects based on species distribution models and kernel density estimation for species occurrences. We also used different species weights (e.g., endemicity degree) and spatial constraints (e.g., proximity to roads or land cover). Our method applies to one or several species since our approach separately considers the interaction between the distribution and density of occurrences of each species. We used the Gran Chaco biome as the study area and Leguminosae as a target species group to exemplify the use of our approach. We verified that Gran Chaco presents low sample coverage. Paraguay and Bolivia should be prioritized for new samples, especially considering the endemicity degree of the species. The Gran Chaco is one of the most extensive formations of dry forests on the planet and one of the regions with the highest levels of deforestation, exposing the urgency of field research in the region. Our approach identifies conserved priority areas for new specimen sampling accessible through roads, with a low density of occurrences and high suitability for different species. Our method will help scientists in the field work, reducing costs and facilitating the planning to prioritize regions for new specimen sampling.

Food and nutrition public establishments: assessment of the food environment.

This article aims to assess the community food environment around areas with and without Food and Nutrition Public Establishments (FNPE). Cross-sectional study carried out in Belo Horizonte, Brazil. The unit of analysis was the buffer (500m) around the FNPE and the census tracts without FNPE. The investigated establishments should market food for consumption at home and be located within the buffer of the areas with and without FNPE. Data collection performed by direct observation (active search) in August to October 2019. Data collected were location and type of commercial establishments, the density of the establishments was calculated. Descriptive analysis, spatial distribution (Kernel estimator) and Nearest Neighbor analysis were performed. Of the evaluated establishments, 60.5% were in the areas without FNPE and 39.6% in the areas with FNPE, showing a random distribution pattern. Of these, 24.2% were convenience stores and bakeries, 21.0% butcher stores, and 19.0% street markets. Seven FNPE were close to commercial establishments. There were fewer establishments around the FNPE, with convenience stores and bakeries predominating.

SAKS: Sampling Adaptive Kernels From Subspace for Point Cloud Graph Convolution

Convolution on 3D point clouds has been extensively explored in geometric deep learning, but it is far from perfect. Convolution operations on point clouds with the fixed kernel indistinguishably capture correspondences between feature pairs, thereby raising an inherent drawback of limited distinctive feature learning. This paper proposes a novel approach to Sampling Adaptive Kernels from Subspace (SAKS) for graph convolution. It adaptively constructs convolution kernels for different feature correspondences according to the unique coordinate representations under the learned subspace. Associating the subspace design with the deep network is a novel concept, providing different viewpoints on feature learning. Specifically, incomplete orthogonal bases are learned at each convolution layer to span a linear subspace in an elaborately designed manner. Subsequently, adaptive kernels are sampled from the learned subspace via unique coordinates parameterized by feature pairs. Unlike existing adaptive convolution methods in a bruteforce manner, the low-rank property of the subspace reduces the computational complexity of this method. Moreover, we theoretically prove that the proposed SAKS derives the principal components of the kernel distribution, which is similar to principal component analysis under some prior assumptions. Extensive experimental results on point cloud classification and segmentation tasks show that SAKS outperforms state-of-the-arts on various benchmark datasets.

CFD Simulation of Biomass Combustion in an Industrial Circulating Fluidized Bed Furnace

ABSTRACT In this study, a three-dimensional computational fluid dynamics (CFD) model is employed to investigate the hydrodynamic and combustion characteristics of biomass particles in an industrial-scale circulating fluidized bed (CFB) furnace. The CFD model considered here is based on the Eulerian-Lagrangian framework, the multi-phase particle-in-cell (MP-PIC) collision model, the coarse grain method (CGM), and a recently developed distribution kernel method (DKM). The challenge of simulating industrial-scale CFB furnaces using CFD lies in the large number of particles in the system. MP-PIC and CGM showed that local particle overloading could occur, causing the numerical simulation to diverge. The combination of MP-PIC with CGM and DKM was shown to overcome this problem. The CFD predictions werecompared with onsite temperature experiments in the furnace, and the predicted furnace temperature agreed fairly well with the measured data. Using the CFD results, the study analyzed the transient solids mixing and fluidization characteristics, as well as the thermochemical process in biomass combustion. The simulated individual particle provided insight into the physical and chemical processes of the granular flow in the dilute/dense regions of the CFB furnace. The simulated results revealed the CO and NOx emission processes in the furnace.

Reliability of Ensemble Climatological Forecasts

AbstractEnsemble climatological forecasts play a critical part in benchmarking the predictive performance of hydroclimatic forecasts. Accounting for the skewness and censoring characteristics of hydroclimatic variables, ensemble climatological forecasts can be generated by the log, Box‐Cox and log‐sinh transformations, by the combinations of the Bernoulli distribution with the Gaussian, Gamma, log‐normal, generalized extreme value, generalized logistic and Pearson type III distributions and by the non‐parametric resampling, empirical cumulative distribution function and kernel density estimation methods. This paper is concentrated on the reliability of the 12 types of ensemble climatological forecasts. Specifically, mathematical formulations are presented and large‐sample tests are devised to verify the forecast reliability for the Multi‐Source Weighted‐Ensemble Precipitation version 2 across the globe. Climatological forecasts of monthly precipitation over 18,425 grid cells are generated for 30 years under leave‐one‐year‐out cross validation, leading to 6,633,000 (12 × 18425 × 30) sets of ensemble climatological forecasts. The results point out that the reliability of climatological forecasts considerably varies across the 12 methods, particularly in regions with high hydroclimatic variability. One observation is that climatological forecasts tend to deviate from the distributions of observations when there is inadequate flexibility to fit precipitation data. Another observation is that ensemble spreads can be overly wide when there exist overfits of sample‐specific noises in cross validation. Through the tests of global precipitation, the robustness of the log‐sinh transformation and the Bernoulli‐Gamma distribution is highlighted. Overall, the investigations can serve as a guidance on the uses of transformations, distributions and non‐parametric methods in generating climatological forecasts.

Distributionally robust chance‐constrained optimization with Sinkhorn ambiguity set

AbstractA novel distributionally robust chance‐constrained optimization (DRCCP) method is proposed in this work based on the Sinkhorn ambiguity set. The Sinkhorn ambiguity set is constructed based on the Sinkhorn distance, which is a variant of the Wasserstein distance with the entropic regularization. The proposed method can hedge against more general families of uncertainty distributions than the Wasserstein ambiguity set‐based methods. The presented approach is formulated as a tractable conic model based on the Conditional value‐at‐risk (CVaR) approximation and the discretized kernel distribution relaxation. This model is compatible with more general constraints that are subject to uncertainty than the Wasserstein‐based methods. Accordingly, the presented Sinkhorn DRCCP is a more practical approach that overcomes the limitations of the traditional Wasserstein DRCCP approaches. A numerical example and a nonlinear chemical process optimization case are studied to demonstrate the efficacy of the Sinkhorn DRCCP and its advantages over the Wasserstein DRCCP.

A Study on the Suitable Areas for Growing Apricot Kernels in China Based on the MaxEnt Model

Research on the climatic adaptation of the apricot kernels (Prunus armeniaca L.) has significant meaning for optimizing their cultivation and utilizing climatic resources effectively. This research utilizes geographical distribution data, climatic environmental factors, soil data, and altitude data of the apricot kernel in China. By employing the maximum entropy model (MaxEnt) and geographic information system (ArcGIS), we identify the key factors influencing the distribution of apricot kernels in China and suitable areas for their cultivation. Our findings reveal that annual precipitation, frequency of frost days in April, altitude, soil pH, and effective soil water content are the primary environmental factors impacting the distribution of apricot kernels in China. We classify the planting suitability zones into four categories. The areas characterized by annual precipitation ranging from 330.54 mm to 616.42 mm, frost day frequency of 2.68 to 19.15 days in April, altitude between 84.22 m and 831.81 m, pH values ranging from 7.5 to 8.6, and effective soil water content of 1.16 to 3.88 are deemed most suitable for growing apricot kernels. The most suitable areas correspond to the main growing areas in reality. Given the limited existing research on suitable areas for apricot kernel cultivation, this study provides a scientific foundation for promoting the cultivation of apricot kernels.

Measurement of Urban Green Total Factor Productivity and Analysis of Its Temporal and Spatial Evolution in China

This paper uses the Super SBM-DEA model and GML index method with undesirable output indicators to measure GTFP in 288 cities in China. Furthermore, we divide Chinese land into east, central, west, and northeast parts, and analyze their temporal and spatial evolution trends. It is shown that, firstly, China’s overall GTFP shows an upward fluctuating trend, in which green technical efficiency contributes more to the improvement of GTFP in Chinese cities, while green technological progress contributes less. Secondly, the urban GTFP in the eastern, central, western, and northeastern regions shows obvious differences, with the source of GTFP growth in the eastern region being mainly green technological progress, the source of growth in the central region being green efficiency improvement in the early stage and green technological progress in the later stage, while the source of growth in the western and northeastern regions is green efficiency improvement. Finally, combined with spatial distribution characteristic maps and kernel density estimation, GTFP shows spatial disequilibrium characteristics in China.

Modal analysis under jittering and kernel clock distribution: single-output identification

Smartphones have attracted attention in the structural health monitoring community due to their embedded multisensory platforms suitable for crowdsourcing innovation. Despite their advantages, smartphone sensors are originally designed for user utility rather than technical engineering applications (e.g. vibration analysis and modal identification). Sampling jitter is among those problems adversely influencing smartphone performance as a scientific device that can be used for characterising civil infrastructure dynamic characteristics. With inconsistencies in the sampling period due to jitter effects, the identified modal frequencies of a structure can deviate from the actual value, which is artificially introduced by smartphone clock errors. In this study, the authors formulate the statistical characteristics of the smartphone sampling period through kernel distribution and apply a digital reconstruction remedy to the sampling jitter problem. Through introductory simulations of a sine wave and physical implementations through shaking table tests equipped with smartphones, the efficiency of kernel distribution diagnosis and the signal-reconstruction remedy is presented. Following the simulation and laboratory applications, the proposed techniques are applied to vibration monitoring of a steel pedestrian bridge in terms of the auto power spectral density and short-time Fourier transform of single-output signals. The results show successful rehabilitation of accelerometer data from smartphones, removing jitter-induced errors to a significant extent and accordingly improving the identification accuracy currently in a single-output setting.

Mehler–Fock transforms and retarded radiative Green functions in hyperbolic and spherical spaces

We develop the theory of causal radiation Green functions on hyperbolic and hyperspherical spaces using a constructive approach based on generalized Mehler–Fock transforms. This approach focuses for HRd on the kernel of the transformation expressed in terms of hyperbolic angles θ with 0 ≤ θ < ∞. The kernel provides an explicit representation for the generalized delta distribution, which acts as the source term for the radiation, and allows for an easy implementation of the causality or retardation condition and determination of the Green function. We obtain the corresponding kernel distribution on SRd by analytic continuation of the kernel distribution of an appropriate Helmholtz equation on HRd and then show that this construction leads to the proper retarded Green function for the wave equation. That result is then used to establish the validity of a new generalized Mehler–Fock transformation for 0 ≤ θ < π. The present results clarify and extend those obtained recently by Cohl et al. [SIGMA 14, 136 (2018)].

Linear Quadratic Regulator for Delayed Systems Using the Hamiltonian Approach and Exact Closed-Loop Poles for First-Order Systems

Abstract We consider the linear quadratic regulator (LQR) for linear constant-coefficient delay differential equations (DDEs) with multiple delays. The Hamiltonian approach is used instead of an algebraic Riccati partial differential equation. Two coupled DDEs governing the state and control input are derived using the calculus of variations. This coupled system, with infinitely many roots in both left and right half-planes, defines a boundary value problem. Its left half-plane roots are the exact closed-loop poles of the controlled system. These closed-loop poles have not been used to compute the optimal feedback before. Here, the distributed delay kernel that yields exactly those poles is first computed using an eigenfunction expansion. Increasing the number of terms in the truncated expansion yields a highly oscillatory kernel. However, the oscillatory kernel's antiderivative converges to a piecewise smooth function on the delay interval plus a Dirac delta function at zero. Discontinuities in the kernel coincide with discrete delay values in the original DDE. Using this insight, a fitted piecewise polynomial kernel matches the exact closed-loop poles very well. The twofold contribution of the Hamiltonian approach is thus clarity on the form of the feedback kernel as well as the exact closed-loop poles. Subsequently, the fitted piecewise polynomial kernel can be used for a much simpler control calculation. The polynomial coefficients can be fitted by solving a few simultaneous linear equations. Two detailed numerical examples of the LQR for DDEs, one with two delays and one with three delays, show excellent results.

Effect of wind speed distribution and site assessment on pitch bearing loads and life

In this paper, the wind speed distribution at thirteen onshore and offshore wind sites has been studied. Different probability distributions are used to estimate the wind speed distribution. Several goodness-of-fit indicators were used to assess the suitability of the fitting. The highest results were achieved by Kernel distribution in both onshore and offshore wind sites. Onshore wind sites did not fit well compared to offshore wind sites. Rayleigh distribution results at onshore wind sites were worse than at offshore wind sites. Onshore and offshore wind distributions result in various load duration distributions in pitch bearing. The concept of life ratio was introduced to compare the long-term fatigue life of the pitch bearing in different wind speed conditions. It is observed that the fatigue life of the pitch bearings in some wind sites is less than that of related IEC classes, and the risk of failure of the pitch bearing before the end of its expected designed fatigue life exists.