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We study the statistical properties of Pearson correlation coefficients of Gaussian ranks, and Gaussian rank regressions – ordinary least-squares (OLS) models applied to those ranks. We show that these procedures are fully efficient when the true copula is Gaussian and the margins are non-parametrically estimated, and remain consistent for their population analogs otherwise. We compare them to Spearman and Pearson correlations and their regression counterparts theoretically and in extensive Monte Carlo simulations. Empirical applications to migration and growth across US states, the augmented Solow growth model and momentum and reversal effects in individual stock returns confirm that Gaussian rank procedures are insensitive to outliers.

The purpose of this study is to use a weak light source with spatial distribution to realize light-driven fluid by adding high-absorbing nanoparticles to the droplets, thereby replacing a highly focused strong linear light source acting on pure droplets.

First, Fe₃O₄ nanoparticles with high light response characteristics were added to the droplets to prepare nanofluid droplets, and through the Gaussian light-driven flow experiment, the Marangoni effect inside a nanofluid droplet was studied, which can produce the surface tension gradient on the air/liquid interface and induce the vortex motion inside a droplet. Then, the numerical simulation method of multiphysics field coupling was used to study the effects of droplet height and Gaussian light distribution on the flow characteristics inside a droplet.

Nanoparticles can significantly enhance the light absorption, so that the Gaussian light is enough to drive the flow, and the formation of vortex can be regulated by light distribution. The multiphysics field coupling model can accurately describe this problem.

This study is helpful to understand the flow behavior and heat transfer phenomenon in optical microfluidic systems, and provides a feasible way to construct the rapid flow inside a tiny droplet by light.

This paper aims to develop a method to improve the accuracy of tolerance analysis considering the spatial distribution characteristics of part surface morphology (SDCPSM) and local surface deformations (LSD) of planar mating surfaces during the assembly process.

First, this paper proposes a skin modeling method considering SDCPSM based on Non-Gaussian random field. Second, based on the skin model shapes, an improved boundary element method is adopted to solve LSD of nonideal planar mating surfaces, and the progressive contact method is adopted to obtain relative positioning deviation of mating surfaces. Finally, the case study is given to verify the proposed approach.

Through the case study, the results show that different SDCPSM have different influences on tolerance analysis, and LSD have nonnegligible and different influence on tolerance analysis considering different SDCPSM. In addition, the LSD have a greater influence on translational deviation along the z-axis than rotational deviation around the x- and y-axes.

The surface morphology with different spatial distribution characteristics leads to different contact behavior of planar mating surfaces, especially when considering the LSD of mating surfaces during the assembly process, which will have further influence on tolerance analysis. To address the above problem, this paper proposes a tolerance analysis method with skin modeling considering SDCPSM and LSD of mating surfaces, which can help to improve the accuracy of tolerance analysis.

The purpose of the article is to develop an equation to accurately represent OCV as a function of SoC with reduced computational burden. Dependency of open circuit voltage (OCV) on state of charge (SoC) is often represented by either a look-up table or an equation developed by regression analysis. The accuracy is increased by either a larger data set for the look-up table or using a higher order equation for the regression analysis. Both of them increase the memory requirement in the controller. In this paper, Gaussian exponential regression methodology is proposed to represent OCV and SoC relationships accurately, with reduced memory requirement.

Incremental OCV test under constant temperature provides a data set of OCV and SoC. This data set is subjected to polynomial, Gaussian and the proposed Gaussian exponential equations. The unknown coefficients of these equations are obtained by least residual algorithm and differential evolution–based fitting algorithms for charging, discharging and average OCV.

Root mean square error (RMSE) of the proposed equation for differential evolution–based fitting technique is 35% less than second-order Gaussian and 74% less than a fifth-order polynomial equation for average OCV with a 16.66% reduction in number of coefficients, thereby reducing memory requirement.

The knee structure in the OCV and SoC relationship is accurately represented by Gaussian first-order equation, and the exponential equation can accurately describe the linear relation. Therefore, this paper proposes a Gaussian exponential equation that accurately represents the OCV as a function of SoC. The results obtained from the proposed regression methodology are compared with the polynomial and Gaussian regression in terms of RMSE, mean average, variance and number of coefficients.

Ensuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.

The present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.

The efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.

The experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables. The class of models under consideration includes specifications for discrete choices, event counts and limited-dependent variables (truncation, censoring, and sample selection) among others. Our algorithm relies upon a novel implementation of efficient importance sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus, maximum likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The purpose of this study is to establish an effective numerical simulation method to describe the flow pattern and optimize the strategy of noncontact mixing induced by alternating Gaussian light inside a nanofluid droplet and analyzing the influencing factors and flow mechanism of fluid mixing inside a droplet.

First, the heat converted by the alternating incident Gaussian light acting on the nanoparticles was considered as the bulk heat source distribution, and the equilibrium equation between the surface tension and the viscous force at the upper boundary force was established; then, the numerical simulation methods for multiple-physical-field coupling was established, and the mixing index was used to quantify the mixing degree inside a droplet. The effects of the incident position of alternating Gaussian light and the height of the droplet on the mixing characteristics inside a droplet were studied. Finally, the nondimensional Marangoni number was used to reveal the flow mechanism of the internal mixing of the droplet.

Noncontact alternating Gaussian light can induce asymmetric vortex motion inside a nanofluid droplet. The incident position of alternating Gaussian light is a significant factor affecting the mixing degree in the droplet. In addition, the heat transfer caused by the surface tension gradient promotes the convection effect, which significantly enhances the mixing of the fluid in the droplet.

This study demonstrates the possibility of the chaotic mixing phenomenon induced by noncontact Gaussian light that occurs within a tiny droplet and provides a feasible method to achieve efficient mixing inside droplets at the microscale.

Control charts and process capability calculations remain fundamental techniques for statistical process control. However, it has long been realized that the accuracy of these calculations can be significantly affected when sampling from a non‐Gaussian population. Many quality practitioners are conscious of these problems but are not aware of the effects such problems might have on the integrity of their results. Considers non‐normality with respect to the use of traditional control charts and process capability calculations, so that users may be aware of the errors that are involved when sampling from a non‐Gaussian population. Use is made of the Johnson system of distributions as a simulation technique to investigate the effects of non‐normality of control charts and process control calculations. An alternative technique is suggested for process capability calculations which alleviates the problems of non‐normality while retaining computational efficiency.

Adequate resources for learning and training the data are an important constraint to develop an efficient classifier with outstanding performance. The data usually follows a biased distribution of classes that reflects an unequal distribution of classes within a dataset. This issue is known as the imbalance problem, which is one of the most common issues occurring in real-time applications. Learning of imbalanced datasets is a ubiquitous challenge in the field of data mining. Imbalanced data degrades the performance of the classifier by producing inaccurate results.

In the proposed work, a novel fuzzy-based Gaussian synthetic minority oversampling (FG-SMOTE) algorithm is proposed to process the imbalanced data. The mechanism of the Gaussian SMOTE technique is based on finding the nearest neighbour concept to balance the ratio between minority and majority class datasets. The ratio of the datasets belonging to the minority and majority class is balanced using a fuzzy-based Levenshtein distance measure technique.

The performance and the accuracy of the proposed algorithm is evaluated using the deep belief networks classifier and the results showed the efficiency of the fuzzy-based Gaussian SMOTE technique achieved an AUC: 93.7%. F1 Score Prediction: 94.2%, Geometric Mean Score: 93.6% predicted from confusion matrix.

The proposed research still retains some of the challenges that need to be focused such as application FG-SMOTE to multiclass imbalanced dataset and to evaluate dataset imbalance problem in a distributed environment.

The proposed algorithm fundamentally solves the data imbalance issues and challenges involved in handling the imbalanced data. FG-SMOTE has aided in balancing minority and majority class datasets.