non-Gaussian Distribution Research Articles

Improved stochastic linearization methods for structures with nonlinear eddy current dampers considering non-Gaussian distributions

Improved stochastic linearization methods for structures with nonlinear eddy current dampers considering non-Gaussian distributions

Quantifying the randomness and scale invariance of the repeating fast radio bursts

ABSTRACT The statistical properties of energy and waiting time carry essential information about the source of repeating fast radio bursts (FRBs). In this paper, we investigate the randomness of energy and waiting time using four data samples from three extremely active repeating FRBs observed by the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We report the deviation from complete randomness of the burst activity using three statistics, i.e. Hurst exponent, Pincus index, and non-Gaussian probability density distribution of fluctuations. First, the Hurst exponent greater than 0.5 reveals that there is long-term memory in the time series of energy and waiting time. Second, the deviation of the Pincus index from 1.0 manifests that the time series is not completely random. Finally, the fluctuations of energy and waiting time follow the scale-invariant q-Gaussian distribution. All these statistical properties imply that, although the time series of repeating FRBs seems to be irregular, they are not completely random, similar to the features of self-organized criticality.

Multitask learning of a biophysically-detailed neuron model.

The human brain operates at multiple levels, from molecules to circuits, and understanding these complex processes requires integrated research efforts. Simulating biophysically-detailed neuron models is a computationally expensive but effective method for studying local neural circuits. Recent innovations have shown that artificial neural networks (ANNs) can accurately predict the behavior of these detailed models in terms of spikes, electrical potentials, and optical readouts. While these methods have the potential to accelerate large network simulations by several orders of magnitude compared to conventional differential equation based modelling, they currently only predict voltage outputs for the soma or a select few neuron compartments. Our novel approach, based on enhanced state-of-the-art architectures for multitask learning (MTL), allows for the simultaneous prediction of membrane potentials in each compartment of a neuron model, at a speed of up to two orders of magnitude faster than classical simulation methods. By predicting all membrane potentials together, our approach not only allows for comparison of model output with a wider range of experimental recordings (patch-electrode, voltage-sensitive dye imaging), it also provides the first stepping stone towards predicting local field potentials (LFPs), electroencephalogram (EEG) signals, and magnetoencephalography (MEG) signals from ANN-based simulations. While LFP and EEG are an important downstream application, the main focus of this paper lies in predicting dendritic voltages within each compartment to capture the entire electrophysiology of a biophysically-detailed neuron model. It further presents a challenging benchmark for MTL architectures due to the large amount of data involved, the presence of correlations between neighbouring compartments, and the non-Gaussian distribution of membrane potentials.

Enhancement of DDST-MFAC for tracking performance by using dynamic data reconciliation

Abstract Model-free adaptive control (MFAC) stands out as an effective data-driven method for addressing nonlinear problems in industrial processes. To maintain good control performance, a data-driven set-point tuning (DDST) method is used to update the virtual set-point of the MFAC system. The DDST-based MFAC (i.e. DDST-MFAC) constantly approaches the target of the process through the nonlinear set-point tuning method. However, due to equipment errors and external interference, industrial sensors often suffer from measurement noise, which can have adverse effects on the control performance. In this article, an available dynamic data reconciliation (DDR) technique is adopted to improve the tracking performance of the DDST-MFAC, which suppresses the impact of process noise by using predicted information and measured data to achieve high-precision requirements for controlling nonlinear processes. Finally, considering both Gaussian and non-Gaussian distribution of measurement noise, the effectiveness of the proposed method was verified through the simulation of a nonlinear nonaffine plant. It is also applied to the steam-water heat exchange process, the control result is improved ultimately.

Closed-form solution of the peak factor of hardening non-Gaussian cross-wind response with limited time history samples

The cross-wind response generally follows an un-skewed hardening non-Gaussian distribution around vortex-resonance wind speed, a great amount of samples are required to ensure the accuracy of the peak factor. This study aims to propose a robust methodology for estimating the peak factor, even when dealing with limited samples. The accurate description of the probability distribution for cross-wind response is essential to achieve a reliable peak factor. Since both the harmonic self-excited and Gaussian buffeting components contribute to the non-Gaussianity of the cross-wind response, this study explicates the probability density function (PDF) of the composite process combining the harmonic and Gaussian elements. Subsequently, the PDF of displacement is ascertained by the energy ratio between self-excited vibration and random buffeting, also a kurtosis-based function that can be derived from limited samples. Then the cumulative distribution function (CDF) of the extreme is derived based on the displacement PDF, and a closed-form solution determined by kurtosis for peak factor is derived. Finally, the validity of the proposed method is verified through both Monte Carlo simulations and field measurements. This method offers a practical mean to estimate the extreme values of hardening non-Gaussian responses in highly flexible structures using a limited number of samples.

Information-Theoretic Bayesian Inference for Multi-Agent Localization and Tracking of an Radio Frequency Target With Unknown Waveform

Abstract Information-theoretic motion planning and machine learning through Bayesian inference are exploited to localize and track a dynamic radio frequency (RF) emitter with unknown waveform (uncooperative target). A target-state estimator handles non-Gaussian distributions, while mutual information is utilized to coordinate the motion control of a network of mobile sensors (agents) to minimize measurement uncertainty. The mutual information is computed for pairs of sensors through a four-permutation-with-replacement process. The information surfaces are combined to create a composite map, which is then used by agents to plan their motion for more efficient and effective target estimation and tracking. Simulations and physical experiments involving micro-aerial vehicles with time difference of arrival (TDOA) measurements are performed to evaluate the performance of the algorithm. Results show that when two or three agents are used, the algorithm outperforms state-of-the-art methods. Results also show that for four or more agents, the performance is as competitive as an idealized static sensor network.

Domain generalized person reidentification based on skewness regularity of higher-order statistics

The goal of domain-generalized person reidentification (DG-ReID) is to train a model in the source domain and apply it directly to unknown target domains for specific pedestrian retrieval. Existing methods rely primarily on low-order statistics (such as the mean, standard deviation, or variance), thereby ensuring the stability of the source domain data distribution for model training. However, such methods underperform when the data follow a non-Gaussian distribution, thereby reducing the generalization ability of the model on unseen target domains. To address this issue, this study proposes an instance normalization-based skewness regularity (INSR) framework that uses high-order statistics (skewness and high-order moments) to measure the skewness and regularity of the data distribution. Such measures allow further learning of the morphological features (skewness degree, trait of data near the mean, etc.) of complex data distributions for DG-ReID. Specifically, the proposed framework first extracts the skewness and third-order moments from the source domains, which provide more features (high-order moments, variance, etc.) to characterize the data distribution. Subsequently, a batch normalization-like operation was implemented to project the data into a new feature space with zero mean and unit variance, enhancing model adaption and accuracy. Extensive experiments were conducted on small-scale (VIPeR, PRID, GRID, and i-LIDS) and large-scale (Market-1501, DukeMTMC-reID, CUHK03, MSMT17) public datasets using two different protocols, demonstrating that the proposed INSR framework significantly outperforms other state-of-the-art counterparts for DG-ReID.

Control of linear motors with gas lubrication of the coordinate measurement system

The problem of the influence of non-Gaussian disturbance on the control system during the measurement of coordinate measuring system of mechanical quantities of objects with a complex spatial surface is described in the article. It is shown that the accuracy of the filtering of the random process of measuring mechanical quantities is significantly affected if to take into account the disturbing factors with non-Gaussian probability distribution density.

Assessing environmental influences on radon levels: analysis of independent variables

Regression analysis is essential for prediction analysis and variable identification since air pollution studies are complicated by competing suggestions and require careful interpretation. In the existing predictive analysis, estimating indoor radon levels is challenging due to multicollinearity issues and the existing algorithm's assumption of independent predictor variables, making it difficult to accurately assess individual effects. Hence a novel Unsupervised Bayesian Multiple Regression Analysis is used to correctly offer the specific impacts of each predictor variable by taking the complex interactions between factors in the estimation of indoor radon levels. Furthermore, in the variable identification, indoor radon levels are influenced by complex residual distributions, with existing algorithms failing to predict non-Gaussian residuals due to outlier-sensitive least squares estimation. So a novel Quadratic Discriminant Extreme Learning Machine is implemented to overcome this issue, which creates models that are better able to reliably detect the factors driving indoor radon levels and are more robust to non-Gaussian residual distributions. The proposed method demonstrates excellence in predictive analysis and variable identification achieving high coefficient of relation and low MAE.

Adaptive Bayesian speckle reduction in the 2D DOST domain using 2D MC-GARCH-M model: Preserving image edges and textural information

Image denoising and image quality enhancement are major issues in image processing. Additive and multiplicative noise removal is one of the main image enhancement approaches. In this paper, we propose a novel 2D Merged Complex Generalized Autoregressive Conditional Heteroscedasticity Mixture (MC-GARCH-M) model for 2D complex stochastic processes. This model effectively captures non-Gaussian statistics and all three types of dependencies within the processes (RRD, IID, and RID) using the proposed linear mapping transformation T. Our statistical analysis shows that the 2D MC-GARCH-M model provides the best fit to the non-Gaussian statistics of the mapped matrix of 2D DOST coefficients compared to Gaussian, Generalized Gaussian, and Stable distributions. We confirm the presence of heteroscedasticity in the mapped matrix using the Engle hypothesis test, verifying ARCH/GARCH effects. The 2D MC-GARCH-M model, with its location-dependent conditional variances, provides a flexible approach for noise removal and modeling complex stochastic processes. Experimental results on artificially speckled aerial and actual SAR images demonstrate that our method outperforms state-of-the-art approaches in terms of speckle removal and preserving the edges and textural information of the image. Key innovations include: a new statistical analysis using linear mapping T showing non-Gaussian heavy-tailed distributions; an adaptive Bayesian estimator, MCMAP, based on the heteroscedastic model for speckle noise removal; and the method's applicability to images with varying mutual information (MI) between real and imaginary parts of 2D DOST coefficients. Our method is adaptive and robust to initial parameter settings, effectively utilizing magnitude and phase information, providing an optimal closed-form solution, reducing memory and computational requirements, and demonstrating robustness to speckle power levels. While requiring more computational resources compared to thresholding methods, our approach is less demanding than other Bayesian algorithms, making it suitable for offline processing.

A GA based SVM-Bayesian technique and its application in process monitoring for mixed distributed data

Traditional data-driven fault diagnosis methods, such as principal component analysis (PCA) and independent component analysis (ICA), have significantly improved condition monitoring and fault diagnosis of industrial process by analyzing process data. However, their accuracy is limited due to the assumption that the data follows Gaussian or non-Gaussian distribution, respectively. In reality, process data is often a mixture of both Gaussian and non-Gaussian distributions, leading to reduced accuracy of the training model and fault diagnosis results. To address this issue, a genetic algorithm-based SVM-Bayesian (GSB) scheme is proposed in this paper for feature combination and model integration. The scheme first employs ICA and PCA to extract the independent/principal components of the original data, and then constructs the corresponding fault features for SVM training to obtain basic models. The extraction of fault features are optimized using genetic algorithms based on defined accuracy and diversity functions. During online monitoring, the final diagnosis result is obtained by combining the results of the basic models through Bayesian inference. The effectiveness of the proposed scheme is evaluated using a numerical example and a case study of the Tennessee Eastman process. The results show that the accuracy of fault classification is improved by about 5% compared with traditional methods.

Non-gaussian hydraulic conductivity and potential contaminant source identification: A comparison of two advanced DLPM-based inversion framework

Accurate identification of hydraulic conductivity fields (K) and contaminant source parameters is imperative for the enhanced assessment and effective remediation of polluted aquifers. Given the challenges posed by non-Gaussian distributions, high dimensionality, and ill-posed nature of groundwater inversion problems, reducing unknowns is a common strategy. Unlike conventional parameterization methods constrained by prior assumptions, this research introduces an innovative deep learning-based parameterization method (DLPM), AEdiffusion. AEdiffusion combines a Diffusion Denoising Probabilistic Model (DDPM) with a Variational Autoencoder (VAE) through a generator-refiner strategy, enabling the generation of high-dimensional K fields from low-dimensional latent representations. Additionally, this study examines the application of Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP), another advanced DLPM, in groundwater inversion. Through comparative analysis within a Data Assimilation (DA) framework, focusing on non-Gaussian K fields and three potential contaminant sources under varied data availability scenarios, this study reveals that both DLPM-based inversion frameworks are capable of identifying K fields and the true contaminant sources. Notably, the AEdiffusion-based framework excels in extracting critical information from sparse observations, delivering more stable performance, but at the cost of increased time consumption compared to WGAN-GP-based framework.

Investigation on the sampling distributions of non-Gaussian wind pressure skewness and kurtosis

Accurate estimation of skewness and kurtosis is crucial for addressing issues related to non-Gaussian wind pressure distribution fitting, signal simulation, and extreme estimation. The skewness and kurtosis determined from finite-length signals are inherent random variables characterized by obvious value fluctuations. Very limited research has been conducted on the sampling distributions of skewness and kurtosis for non-Gaussian wind pressure, motivating the present study. Firstly, the investigation focuses on the non-Gaussian white noise. The expressions of main statistical indicators such as the variance, covariance, correlation coefficient, skewness, and kurtosis of the two sampling distributions are derived and then verified using the Hermite polynomial model. The primary factors influencing the sampling distribution variance (SDV) of white noise are analyzed, including the signal length and marginal moments of the parent distribution. Secondly, the concentration shifts to colored non-Gaussian processes. The composition of SDV is analyzed through theoretical derivation. On this basis, a method for estimating SDV values using the Gaussian process regression model is proposed, with accuracy and feasibility verified based on the long-duration wind pressure data measured in wind tunnel. Furthermore, the relationship between the SDVs of wind pressure processes, signal length, higher-order correlation functions, and marginal moments of the parent process is discussed.

Entropic timescales of dynamic heterogeneity in supercooled liquid.

Non-Gaussian displacement distributions are universal predictors of dynamic heterogeneity in slowly varying environments. Here, we explore heterogeneous dynamics in supercooled liquid using molecular dynamics simulations and show the efficiency of the relative-entropy based measure, negentropy, in quantifying dynamic heterogeneity over the widely used non-Gaussian parameter. Our analysis shows that the heterogeneity quantified by the negentropy is significantly different from the one obtained using the conventional moment-based definition that considers deviation from Gaussianity up to lower-order moments. We extract the timescales of dynamic heterogeneity using the two methods and show that the differential changes diverge as the system experiences strong intermittency near the glass transition. Further, we interpret the entropic timescales and discuss the general implications of our work.

Validation of the Bond et al. (2010) SDSS-derived kinematic models for the Milky Way's disk and halo stars with Gaia Data Release 3 proper motion and radial velocity data

We validate the 2010ApJ...716....1B kinematic models for the Milky Way's disk and halo stars with Gaia Data Release 3 data. Bond et al. constructed models for stellar velocity distributions using stellar radial velocities measured by the Sloan Digital Sky Survey (SDSS) and stellar proper motions derived from SDSS and the Palomar Observatory Sky Survey astrometric measurements. These models describe velocity distributions as functions of position in the Galaxy, with separate models for disk and halo stars that were labeled using SDSS photometric and spectroscopic metallicity measurements. We find that the Bond et al. model predictions are in good agreement with recent measurements of stellar radial velocities and proper motions by the Gaia survey. In particular, the model accurately predicts the skewed non-Gaussian distribution of rotational velocity for disk stars and its vertical gradient, as well as the dispersions for all three velocity components. Additionally, the spatial invariance of velocity ellipsoid for halo stars when expressed in spherical coordinates is also confirmed by Gaia data at galacto-centric radial distances of up to 15 kpc.

Fifty shades of QE revisited

Fabo et al. (2021) use OLS regression to show that central bankers report quantitatively larger effects of QE on output and inflation than do academic researchers. We reject the null hypothesis of a Gaussian distribution of the residuals in many of these specifications, except for the language regressions. We then repeat the analysis with regression estimators that are robust to a non-Gaussian residual distribution where this is feasible. We use the median regression and the MS regression estimator. With these robust regression approaches, the null hypothesis that central bank and academic researchers report the same quantitative effect of QE on output and inflation cannot be rejected, with point estimates which are less than half as large. This statistical challenge suggests that more research is required to understand better whether central bank researchers report different QE multipliers or not.

Non-Gaussian Multivariate Process Capability Based on the Copulas Method: An Application to Aircraft Engine Fan Blades

Abstract Process capability indices (PCIs) are major tools in geometric dimensioning and tolerancing (GD&T) for quantifying the production quality, monitoring production, or prioritizing projects. Initially, PCIs were constructed for studying each characteristic of the process independently. Then, they have been extended to analyze several dependent characteristics simultaneously. Nowadays, with the increasing complexity of the production parts, for example, in aircraft engines, the conformity of one part may rely on the conformity of hundreds of characteristics. Also, because those characteristics are dependent, it may be misleading to make decisions based only on univariate PCIs. However, classical multivariate PCIs in the literature do not allow treating such amount of data efficiently, unless assuming Gaussian distribution, which may be false. Regarding those issues, we advocate for PCI based on some transformation of the conformity rates. This presents the advantage of being free from distributional assumptions, such as the Gaussian distribution. In addition, it has direct interpretation, allowing it to compare different processes. To estimate the PCIs of parts with hundreds of characteristics, we propose to use Vine Copulas. This is a very flexible class of models, which gives precise estimation even in high dimension. From an industrial perspective, the computation of the estimator can be costly. To answer this point, one explains how to compute a lower bound of the proposed PCI, which is faster to calculate. We illustrate our method adaptability with simulations under Gaussian and non-Gaussian distributions. We apply it to compare the production of fan blades of two different factories.

FGO-MFI: factor graph optimization-based multi-sensor fusion and integration for reliable localization

Reliable and precise information pertaining to the position, velocity, and attitude is essential for automated driving. This paper proposes FGO-MFI, a cost-effective and robust multi-sensor fusion and integration localization framework that utilizes factor graph optimization. Firstly, a tightly coupled Global Navigation Satellite Systems (GNSS)/on-board sensor fusion localization framework is established to estimate vehicle states, including position, velocity, and attitude. To address the large drift rate of the Inertial Measurement Unit (IMU), this study introduces a novel IMU/Dynamics pre-integration method based on the vehicle dynamics model. We establish a two-degree-of-freedom vehicle dynamics model utilizing measurements from the wheel speed sensor and steering wheel angle sensor. The IMU/Dynamics factor is devised through a close integration of the model output and IMU pre-integration, enabling the construction of precise odometry with low-cost on-board sensors. Then, to address the issue of the non-Gaussian distribution of GNSS pseudorange error, this paper employs a Gaussian Mixture Model (GMM) to characterize the pseudorange noise, which is then applied to further sensor fusion. Given the time-varying nature of pseudorange noise, the expectation maximization algorithm is utilized to estimate GMM parameters online, leveraging the pseudorange residuals within a sliding window. Comprehensive experiments, inclusive of challenging scenarios such as urban canyons, tunnels, and wooded areas, have been carried out. They affirm the superior performance of the proposed method. Experiments have shown that our method demonstrates reliable localization across different statuses of GNSS signal, exhibiting a 39.4% improvement in the root mean square error of position error when compared to the state-of-the-art. Additionally, this FGO-MFI is a general sensor data fusion framework and is able to incorporate diverse sensor measurements, for example, from cameras and LiDARs to provide more reliable and accurate localization information.

Full-Scale Observations for the Combined Wind-Induced Responses of a Cylindrical Tower

This paper presents full-scale observations of wind-induced vibrations on a 140[Formula: see text]m high cylindrical reinforced concrete tower under non-stationary and strong wind conditions. The vibration responses of the tower in two planar orthogonal axes and rotation, in conjunction with wind speed and direction data, have been utilized to extract the response characteristics. The primary focus is on discussing the correlation of wind-induced responses in three components: Along-wind, across-wind, and torsion. Throughout the varying levels of oscillation, the tower’s responses clearly exhibit correlations among these components. The correlation coefficients between along-wind and across-wind responses, as well as along-wind and torsional responses, remain negligible across the entire dataset. In contrast, during intense oscillations, there is a near-perfect correlation between the across-wind and torsional responses. Furthermore, the probability density functions (PDFs) of the response components under strong wind conditions significantly deviate from the Gaussian distribution and closely resemble the Cauchy distribution. The joint PDFs also indicate that the along-wind response is statistically independent of the other response components, while the across-wind response correlates well with the torsion, as indicated by the non-Gaussian distribution. This paper also includes distinct observations regarding dominant oscillating frequencies, torsional amplitudes, and vertical vibration amplitudes. The importance of this research lies in its examination of the relationship between different response components, a crucial aspect in understanding how structures behave under wind loading. By emphasizing the need for full-scale measurements, this study aims to provide valuable validation for previous theoretical and experimental research findings.

Phosphorescence of beta irradiated Sr4Al14O25:Eu2+,Dy3+ ─ A persistent luminescence phosphor

Phosphorescence of beta irradiated Sr4Al14O25:Eu2+,Dy3+ has been analysed. The persistent luminescence that defines this phosphor is phosphorescence hence the justification for this study. A set of phosphorescence decay curves were measured at various temperatures Tph between 20 and 352 °C following irradiation to 2 Gy. The residual thermoluminescence (R-TL) was recorded at 1 °C/s after the phosphorescence decay. A conventional TL glow curve recorded at the same rate following irradiation to 2 Gy produces two composite glow peaks P1 and P2 at 63 and 252 °C respectively. The decay curves measured between Tph = 28–60 °C and 200–240 °C associated with peaks P1 and P2 respectively give the values of the activation energy of peaks P1 and P2 as 0.59 ± 0.01 and 0.80 ± 0.04 eV. The effective frequency factors associated with the traps are 6.2 × 109 and 6.4 × 105 s−1 respectively. Peaks P1 and P2 are affected by thermal quenching with activation energy W = 0.69 ± 0.06 eV and 0.66 ± 0.03 eV respectively. The R-TL glow curves show two maxima R1 and R2 at ∼72 and 260 °C respectively. Kinetic analysis of R-TL peak R2 shows a Gaussian distribution of trap energy whereas the same analysis on R-TL peak R1 shows a non-Gaussian distribution of trap energy. The mean values of activation energy corresponding to the respective electron traps of R1 and R2 are estimated to be 0.62 ± 0.07 and 1.04 ± 0.06 eV. For peak R2, the Gaussian distribution curve shows the maximum at ∼1.06 eV which indicates that most electron traps corresponding to peak R2 have this trap depth.