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The non-Gaussian feature of seismic ground motion has been reported in some works. However, there remains a lack of research on the influence of the ground motion non-Gaussianity on the seismic performance of buildings, which motivates this study. By employing a non-Gaussian non-stationary random process simulation method previously proposed by the authors, 40,000 ground motion acceleration signals are efficiently generated, including 20,000 Gaussian and 20,000 non-Gaussian records. As computational examples, a four-story frame building and a three-tower super-tall building are selected. The generated acceleration signals serve as external excitations for the two buildings, allowing for a comparison of the differences in seismic structural responses caused by the Gaussian and non-Gaussian earthquake groups. Probability analysis is performed using top-layer displacement and maximum inter-story drift ratio as damage indicators. The results show that the structural responses induced by both Gaussian and non-Gaussian earthquake groups have identical first- and second-order moments but different higher-order moments. The responses from non-Gaussian earthquakes display distinct non-Gaussian traits, with their distribution of extreme values exhibiting a longer tail compared to the Gaussian counterparts. This leads to a notably larger value of non-Gaussian responses under high crossing probabilities, with an amplification that can surpass 18%. [ABSTRACT FROM AUTHOR]

Non-stationary non-Gaussian random vibration problems of structures are challenging and drawing increasing attention. In the present study, firstly, an explicit time-domain method (ETDM) is proposed to determine the higher-order response statistics of linear systems subjected to non-stationary non-Gaussian random excitations, in which the first four orders of cumulants of dynamic responses are directly formulated through the cumulant operation rule based on the explicit expressions of responses. Secondly, an equivalent linearization – explicit time-domain method (EL-ETDM) is further developed to solve the non-stationary non-Gaussian random vibration problems of Duffing systems, in which the equivalent linear system is derived discarding the assumption of Gaussian response, and the corresponding higher-order cumulant analyses of the linearized system are accomplished by the efficient ETDM. The present approach can account for non-Gaussian random excitations with arbitrary forms, and two specific applications to the Poisson white noise and the square form of Gaussian random process are investigated. Four numerical examples are presented to demonstrate the effectiveness of the proposed methods.

In recent decades, the outcrossing rate method has gained popularity for structural time-dependent reliability assessments (TRA). Despite numerous efforts, developing a general analytical outcrossing rate method for a nonstationary non-Gaussian performance function to estimate the failure probability within the forecast time interval remains a significant challenge. This paper introduces an analytical outcrossing rate method for non-Gaussian cases, named the three-moments-based outcrossing rate (TMO) method. The outcrossing rate is formulated based on the third-moment outcrossing rate with no assumption of the correlation between the performance function and its derivative process, allowing for a comprehensive understanding of the performance characteristics of a structure. Following the development of the proposed outcrossing rate, a TRA methodology is established to evaluate the failure probability of the nonstationary non-Gaussian performance function. Notably, the TMO method only requires statistical moments of the nonstationary non-Gaussian performance function, which are easy to calculate, facilitating efficient implementation. Three numerical examples are presented to demonstrate the applicability, efficiency, and accuracy of the proposed TMO method. It can be concluded that the proposed TMO method provides an accurate and useful approach for TRA in engineering applications. [ABSTRACT FROM AUTHOR]

AbstractMarkov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to consider finding expressions of the posterior distribution that are computationally straightforward to obtain independent replicates from directly. We focus on a broad class of Bayesian hierarchical models for spatially dependent data, which are often modeled via a latent Gaussian process (LGP). First, we derive a new class of distributions referred to as the generalized conjugate multivariate (GCM) distribution. The GCM distribution’s theoretical development follows that of the conjugate multivariate (CM) distribution with two main differences: the GCM allows for latent Gaussian process assumptions, and the GCM explicitly accounts for hyperparameters through marginalization. The development of GCM is needed to obtain independent replicates directly from the exact posterior distribution, which has an efficient regression form. Hence, we refer to our method as Exact Posterior Regression (EPR). Simulation studies with weakly stationary spatial processes and spatial basis function expansions are provided. We provide an analysis of poverty incidence from the U.S. Census Bureau, and an analysis of high-dimensional remote sensing data. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In the power system, failure interruption hugely compromises the power system reliability. Therefore, an efficient method to correctly predict how long the power outage last would significantly improve the efficiency. To address this problem, we propose a method based on a suitable stochastic motion. First, we introduce linear multifractional Lévy stable motion (LMLSM). Then, by computing the global and local fractal characteristics we show that the LMLSM is multifractal and possesses the long-range dependence (LRD) property. Besides, the non-Gaussian characteristics of the LMLSM are analyzed, which means it can better describe the constant peak values in the stochastic time series. Furthermore, a discrete iterative prediction model is derived with fractional Black-Scholes differential equation. At last, a case study is provided based on the real failure interruption duration (FID) dataset in the power grid, by illustrating the validity of the proposed prediction method for power grid reliability. • A prediction method of power outage length is provided. • A multifractal model is derived to describe the local irregularity of the multifractal Levy stable motion. • The expression of the increment distribution of the multifractal Levy stable motion is derived. • Compared with existing models of time series prediction model, the prediction accuracy is better. [Display omitted] [ABSTRACT FROM AUTHOR]

In the classical theory of locally optimal designs, which is developed within the framework of the center+error model, the most efficient design is the one based on MGLE, the maximum Gaussian likelihood estimator. However, practical scenarios often lack of complete information as to the governing probability model for the response measure and deviate from Gaussianity and homoscedasticity assumptions, in which, MqLE, the maximum quasi-likelihood estimator, has been advocated in the literature. In this work, we examine the locally optimal design based on the novel oracle-SLSE, the second-order least-square estimator, in the case where the underlying probability model is incompletely specified. We find that in a general setting, our oracle SLSE-based optimal design, incorporating skewness and kurtosis information, outperforms those based on MqLE or MGLE. Our numerical experiment supports this, with locally D-optimal designs based on MqLE approaching the efficiency of oracle-SLSE designs in some cases. This research guides the choice of estimators in practical scenarios departing from ideal assumptions. [ABSTRACT FROM AUTHOR]

We present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve. [ABSTRACT FROM AUTHOR]

The Hermite polynomial model based on the first-four central moments of non-Gaussian distribution is widely applied to simulate non-Gaussian stochastic processes due to its simplicity and efficiency. Although a variety of expressions have been developed to approximate the coefficients of the Hermite polynomial model, unsatisfactory accuracy and limited applicability could still be encountered. Compared to the central moments, probability-weighted moments possess abundant characteristics of probability distribution. In this paper, a new form of Hermite polynomial model is proposed based on probability-weighted moments for simulating non-Gaussian stochastic processes. The coefficients of the Hermite polynomial model can be conveniently determined via a linear system of equations, leading to a wide application range of the model. More importantly, the sample accuracy for simulating non-Gaussian processes can be significantly improved, and the incompatibility problem can be avoided to some extent by using the proposed model. In addition, a fast strategy for determining the Gaussian auto-correlation function is also suggested, which avoids the complicated manipulations of cubic equations of Gaussian and non-Gaussian auto-correlation functions. A classical example is investigated to demonstrate the better accuracy and applicability over conventional Hermite polynomial models for simulating non-Gaussian stochastic processes. Two engineering cases are also investigated to demonstrate practical applications of the proposed model. [ABSTRACT FROM AUTHOR]

A new approach is proposed to analyze the non‐Gaussian random vibration of hyperbolic tangent package. Firstly, the non‐Gaussian vibration noise of specified mean, variance, skewness, and kurtosis is developed by Hermite polynomial and verified by Gaussian mixture model theory. Secondly, next to analyzing an analytical and numerical response of the two degrees of freedom linear package, the acceleration response of the two degrees of freedom hyperbolic tangent package system under non‐Gaussian vibration excitation is obtained though the Hermite polynomial and Runge–Kutta method, and the effects of the external excitation and system parameters are investigated. Finally, on the basis of the first‐passage probability of the acceleration response, the reliability analysis method is introduced. The analysis provides a guidance to the vibration reliability analysis and packaging optimization design. [ABSTRACT FROM AUTHOR]

With increasing recognition of randomness and time-variance of variables in structural assessment, time-dependent reliability (TdR) methods have gained popularity among researchers and practitioners. This paper critically reviews commonly used TdR methods, with focuses on analytical solutions, hybrid solutions and simulation solutions. Through this review and analysis, research challenges for TdR methods are identified and future research directions are proposed. It is found that Rice formula-based solutions are accurate but have limited solutions, hybrid solutions are efficient but affected by non-Gaussianity and nonlinearity of limit state functions, and simulation solutions are robust but time-consuming for complex structure systems. It is also found that the effectiveness of TdR methods depends highly on the complexity of limit state functions and types of stochastic processes involved, in particular, the stationarity, Gaussianity and correlation. The contribution of this review is that different TdR methods are elucidated and future research directions are proposed. [ABSTRACT FROM AUTHOR]

Background and purpose: The differential diagnosis between solid glioma and brain inflammation is necessary but sometimes difficult. We assessed the effectiveness of multiple diffusion metrics of diffusion-weighted imaging (DWI) in differentiating solid glioma from brain inflammation and compared the diagnostic performance of different DWI models. Materials and methods: Participants diagnosed with either glioma or brain inflammation with a solid lesion on MRI were enrolled in this prospective study from May 2016 to April 2023. Diffusion-weighted imaging was performed using a spin-echo echo-planar imaging sequence with five b values (500, 1,000, 1,500, 2000, and 2,500 s/mm2) in 30 directions for each b value, and one b value of 0 was included. The mean values of multiple diffusion metrics based on diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), mean apparent propagator (MAP), and neurite orientation dispersion and density imaging (NODDI) in the abnormal signal area were calculated. Comparisons between glioma and inflammation were performed. The area under the curve (AUC) of the receiver operating characteristic curve (ROC) of diffusion metrics were calculated. Results: 57 patients (39 patients with glioma and 18 patients with inflammation) were finally included. MAP model, with its metric non-Gaussianity (NG), shows the greatest diagnostic performance (AUC = 0.879) for differentiation of inflammation and glioma with atypical MRI manifestation. The AUC of DKI model, with its metric mean kurtosis (MK) are comparable to NG (AUC = 0.855), followed by NODDI model with intracellular volume fraction (ICVF) (AUC = 0.825). The lowest value was obtained in DTI with mean diffusivity (MD) (AUC = 0. 7 58). Conclusion: Multiple diffusion metrics can be used in differentiation of inflammation and solid glioma. Non-Gaussianity (NG) from mean apparent propagator (MAP) model shows the greatest diagnostic performance for differentiation of inflammation and glioma. [ABSTRACT FROM AUTHOR]

We derive a generalization of the Kalman filter that allows for non‐Gaussian background and observation errors. The Gaussian assumption is replaced by considering that the errors come from a mixed distribution of Gaussian, lognormal, and reverse lognormal random variables. We detail the derivation for reverse lognormal errors and extend the results to mixed distributions, where the number of Gaussian, lognormal, and reverse lognormal state variables can change dynamically every analysis time. We test the dynamical mixed Kalman filter robustly on two different systems based on the Lorenz 1963 model, and demonstrate that non‐Gaussian techniques generally improve the analysis skill if the observations are sparse and uncertain, compared with the Gaussian Kalman filter. [ABSTRACT FROM AUTHOR]

The gust factor commonly is used in wind engineering community to convert mean wind speeds into gusty winds, which exhibit significant variability in real observations of typhoon winds. This study proposes a probabilistic gust factor model that accounts for uncertainties of wind speed statistics. The statistical characteristics of wind speed from nine typhoons, including the mean, standard deviation, skewness, kurtosis, power spectral density (PSD) parameter, peak factor, and gust factor, were examined. The effects of nonstationary characteristics in terms of time-varying mean wind speed and non-Gaussian attributes of fluctuating winds on the gust factor are discussed. These wind speed statistics were incorporated into a non-Gaussian moment-based translation model to perform the Monte Carlo simulation of peak factor and gust factor. The simulation results for different gust durations were juxtaposed with observations to substantiate the accuracy of the probabilistic model. Subsequently, a standardization framework for estimating site-specific probabilistic gust factor curves was developed. This approach was applied to determine the gust typhoon wind speed hazard curve at a real bridge site with flat open terrain. The present model enables the consideration of gust factor dispersion to achieve a probabilistic gust wind hazard curve and facilitate the development of performance-based wind engineering. [ABSTRACT FROM AUTHOR]

This study exploits the non-Gaussianity for identification of a Bayesian SVAR model on newly unexplored monthly Indonesian data from 2007M1–2022M12, where we disentangle the commodity-related revenue from the total government revenues. Our main contribution is in labeling the statistically identified structural shocks as economic shocks by conducting a formal assessment of a set of proposed sign constraints. We simultaneously label a commodity price and three fiscal policy shocks, i.e. fiscal income tax, investment-spending, and consumption-spending shocks. Having evaluated their impacts, among the fiscal policy shocks, we find income tax shock the most impactful on output. Moreover, during the Covid crisis 2020–2021, the launched fiscal economic stimulus package (PEN program) positively contributed to the output. The recession of the Covid crisis could have deepened had the fiscal policymaker not responded at all. Albeit so, we should not overlook the contribution of the rising commodity prices to the output recovery. We also evaluate the commodity boom period in 2007–2009, the tax amnesty program in 2016–2017 and 2022, and the infrastructure spending boost in 2015. Our results suggest that output and retail sales would have been lower without the commodity price shock's contribution during the commodity boom. Then, we find that tax amnesty and infrastructure spending boost policies contribute to higher retail sales. [ABSTRACT FROM AUTHOR]

Multivariate monitoring plays an important role in process monitoring. Among the multivariate monitoring methods, the projection to latent structure method (PLS) has been most widely used in the fields of quality control and fault diagnosis. To improve the monitoring capability of traditional PLS methods in nonlinear and non‐Gaussian multivariate systems, this paper proposes an innovative multivariate monitoring strategy, which combines adversarial autoencoder (AAE) and the concurrent projection to latent structure method (CPLS). In the proposed strategy, the original data are mapped to the high‐dimensional space using the AAE method with the Gaussian prior distribution to realize data transformation. The mapped data are linearly divisible and approach the Gaussian distribution. Then, the projection with orthogonality is realized using the CPLS method. In addition, the reconstruction error and distribution properties are used as evaluation indexes of the high‐dimensional mapping performance. The corresponding monitoring strategy is established using the traditional statistical method based on the Gaussian distribution. Finally, the simulations are performed on the Tennessee‐Eastman process platform, and the results show that the proposed method could efficiently extract the principal components, especially in quality‐relevant fault monitoring. [ABSTRACT FROM AUTHOR]

The non-Gaussian feature of seismic ground motion has been reported in some works. However, there remains a lack of research on the influence of the ground motion non-Gaussianity on the seismic performance of buildings, which motivates this study. By employing a non-Gaussian non-stationary random process simulation method previously proposed by the authors, 40,000 ground motion acceleration signals are efficiently generated, including 20,000 Gaussian and 20,000 non-Gaussian records. As computational examples, a four-story frame building and a three-tower super-tall building are selected. The generated acceleration signals serve as external excitations for the two buildings, allowing for a comparison of the differences in seismic structural responses caused by the Gaussian and non-Gaussian earthquake groups. Probability analysis is performed using top-layer displacement and maximum inter-story drift ratio as damage indicators. The results show that the structural responses induced by both Gaussian and non-Gaussian earthquake groups have identical first- and second-order moments but different higher-order moments. The responses from non-Gaussian earthquakes display distinct non-Gaussian traits, with their distribution of extreme values exhibiting a longer tail compared to the Gaussian counterparts. This leads to a notably larger value of non-Gaussian responses under high crossing probabilities, with an amplification that can surpass 18%.

In many applications of data assimilation, especially when the size of the problem is large, a substantial assumption is made: all variables are well‐described by Gaussian error statistics. This assumption has the advantage of making calculations considerably simpler, but it is often not valid, leading to biases in forecasts or, even worse, unphysical predictions. We propose a simple, but effective, way of replacing this assumption, by making use of transforming functions, while remaining consistent with Bayes' theorem. This method allows the errors to have any value of the skewness and kurtosis, and permits physical bounds for the variables. As such, the error distribution can conform better to the underlying statistics, reducing biases introduced by the Gaussian assumption. We apply this framework to a 3D variational data assimilation method, and find improved performance in a simple atmospheric toy model (Lorenz‐63), compared to an all‐Gaussian technique. Plain Language Summary: Data assimilation is the technique of combining model predictions with observations in the optimal way and is, for example, used in weather forecasting. To simplify the procedure, a crucial assumption is made on the statistics of all components. However, as models are becoming increasingly precise, and computational techniques are improving, it is becoming more and more obvious that this simple assumption is inadequate, resulting in inaccurate forecasts. We provide a very general framework that relaxes this assumption, and that allows for a much broader scope of statistics. This generalization significantly improves prevailing methods, as tested with a simple atmospheric toy model. Key Points: A general framework for non‐Gaussian data assimilation is formulatedThe proposed method allows for skewness and kurtosis and provides a straightforward approach to handling variables with physical boundsExperiments with the Lorenz‐63 model show significant improvements over an all‐Gaussian approach [ABSTRACT FROM AUTHOR]

Numerical simulation of the spatial wind field plays a very important role in the study of wind-induced response law of transmission tower structures. A reasonable construction of a numerical simulation method of the wind field is conducive to the study of wind-induced response law under the action of an actual wind field. Currently, many research studies rely on simulating spatial wind fields as Gaussian wind, often overlooking the basic non-Gaussian characteristics. This paper aims to provide a comprehensive overview of the historical development and current state of spatial wind field simulations, along with a detailed introduction to standard simulation methods. Furthermore, it delves into the composition and unique characteristics of spatial winds. The process of fluctuating wind simulation based on the linear filter AR method is improved by introducing spatial correlation and non-Gaussian distribution characteristics. The numerical simulation method of the wind field is verified by taking the actual transmission tower as a calculation case. The results show that the method summarized in this paper has a broader application range and can effectively simulate the actual spatial wind field under various conditions, which provides a valuable data basis for the subsequent research on the wind-induced response of transmission tower lines. [ABSTRACT FROM AUTHOR]

The normal inverse Gaussian (NIG) and generalized asymmetric Laplace (GAL) distributions can be seen as skewed and semi-heavy-tailed extensions of the Gaussian distribution. Models driven by these more flexible noise distributions are then regarded as flexible extensions of simpler Gaussian models. Inferential procedures tend to overestimate the degree of non-Gaussianity in the data and therefore we propose controlling the flexibility of these non-Gaussian models by adding sensible priors in the inferential framework that contract the model towards Gaussianity. In our venture to derive sensible priors, we also propose a new intuitive parameterization of the non-Gaussian models and discuss how to implement them efficiently in Stan. The methods are derived for a generic class of non-Gaussian models that include spatial Mat´ern fields, autoregressive models for time series, and simultaneous autoregressive models for aerial data. The results are illustrated with a simulation study and geostatistics application, where priors that penalize model complexity were shown to lead to more robust estimation and give preference to the Gaussian model, while at the same time allowing for non-Gaussianity if there is sufficient evidence in the data. [ABSTRACT FROM AUTHOR]

Abstract In many applications of data assimilation, especially when the size of the problem is large, a substantial assumption is made: all variables are well‐described by Gaussian error statistics. This assumption has the advantage of making calculations considerably simpler, but it is often not valid, leading to biases in forecasts or, even worse, unphysical predictions. We propose a simple, but effective, way of replacing this assumption, by making use of transforming functions, while remaining consistent with Bayes' theorem. This method allows the errors to have any value of the skewness and kurtosis, and permits physical bounds for the variables. As such, the error distribution can conform better to the underlying statistics, reducing biases introduced by the Gaussian assumption. We apply this framework to a 3D variational data assimilation method, and find improved performance in a simple atmospheric toy model (Lorenz‐63), compared to an all‐Gaussian technique.

Traditionally the power grid has been a one‐way street with power flowing from large transmission‐connected generators through the distribution network to consumers. This paradigm is changing with the introduction of distributed renewable energy resources (DERs), and with it, the way the grid is managed. There is currently a dearth of high fidelity solar irradiance datasets available to help grid researchers understand how expansion of DERs could affect future power system operations. Realistic simulations of by‐the‐second solar irradiances are needed to study how DER variability affects the grid. Irradiance data are highly non‐stationary and non‐Gaussian, and even modern time series models are challenged by their distributional properties. We develop a subordinated non‐Gaussian stochastic model whose simulations realistically capture the distribution and dependence structure in measured irradiance. We illustrate our approach on a fine resolution dataset from Hawaii, where our approach outperforms standard nonlinear time series models. [ABSTRACT FROM AUTHOR]

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The creativity and emergence of biological and psychological behavior tend to be nonlinear, and correspondingly, biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows for making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator of independence failing to hold, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance. [ABSTRACT FROM AUTHOR]

This research contributes to the literature on the effects of fiscal and monetary policy by exploiting non-Gaussianity of the time series for the identification of a Bayesian structural vector autoregression model. Using quarterly US data from 1954:IV to 2006:IV and from 1985:I to 2020:III, we formally assess the plausibility of theoretically predicted signs to label fiscal policy, monetary policy, and business cycle shocks. The impulse responses of consumption to the fiscal policy shock depend to some extent on the sample period, but the implied fiscal multiplier is always less than unity. On investment, there is a lagging crowding-out effect with a high probability, but it is not strongly evident in the latter sample. As for the responses after a contractionary monetary policy shock, we find a weakening output after some lags consistent with the leading monetary policy literature. The business cycle shock turns out to matter for government spending only in the long run, while it is already important for the federal funds rate in the short run. [ABSTRACT FROM AUTHOR]

In passive microwave remote sensing of the Earth's surface, it is essential to relate the emission to geophysical parameters. The emissivity ranges between 0 and 1. Hence, a slight emissivity variation leads to a significant change in brightness temperature. Many sources of error contribute to such tiny variations in emission. This paper quantifies microwave emission variability from a rough surface through model simulation due to the non-Gaussianity in height probability density (HPD) and power spectrum density (PSD). We considered Gaussian and exponential distributions for surface height and correlation functions, representing two extremes of asperity and skewness. Additionally, the surface under consideration contains multiscale roughness. The impact of the HPD and multiscale roughness on the polarization index of the emissivity is evaluated as a function of frequency and roughness. In general, assuming that Gaussian-distributed height leads to an underestimation of the emissivity, with V polarization being less sensitive to the non-Gaussian HPD and PSD effects than H polarization, the emissions are enhanced at high roughness with small look angles but are reduced for smooth surfaces at large look angles under non-Gaussian PSD. In a specific scenario, the dynamic range of the difference between exponential and Gaussian HPD is 0~10%, and the difference in emissivity caused by non-Gaussian PSD ranges from −2% to 16%. These results should be helpful in interpreting the radiometric measurements that exhibit fluctuations and differences with model predictions. [ABSTRACT FROM AUTHOR]

In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be viewed as a combination of the LAPF and a localized version of a Gaussian mixture filter, i.e., a "Localized Mixture Coefficients Particle Filter (LMCPF)". Here, we investigate the feasibility of the LMCPF within a global operational framework and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in a standard pre-operational experimental set-up with the full global observing system, 52 km global resolution and 106 model variables. Statistics of particle movement in the assimilation step are calculated. The mixture approach is able to deal with the discrepancy between prior distributions and observation location in a real-world framework and to pull the particles towards the observations in a much better way than the pure LAPF. This shows that using Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework. [ABSTRACT FROM AUTHOR]

Spatial structures of natural variables are often very complex due to the different physical chemical or biological processes which contributed to the emergence of the fields. These structures often show non‐Gaussian spatial dependence. Unfortunately, there are only a limited number of approaches that can explicitly consider non‐Gaussian behavior. In this contribution, a very flexible way of defining non‐Gaussian spatial dependence is presented. The approach is based on a kind of continuous deformation of fields with different Gaussian spatial dependence. Theoretical examples illustrate the methodology for a wide variety of non‐Gaussian structures. A real‐life example of groundwater quality parameters shows the practical applicability of the geostatistical model. Key Points: A method to define a wide range of non‐Gaussian spatial dependence is presentedA conditional simulation approach for these non‐Gaussian structures via Monte Carlo optimization is presentedA groundwater quality parameter study demonstrates the benefits of the approach [ABSTRACT FROM AUTHOR]

In the presence of non-Gaussian impulsive noise (IN) with a heavy tail, active noise control (ANC) algorithms often encounter stability problems. While adaptive filters based on the higher-order error power principle have shown improved filtering capability compared to the least mean square family algorithms for IN, however, the performance of the filtered-x least mean absolute third (FxLMAT) algorithm tends to degrade under high impulses. To address this issue, this paper proposes three modifications to enhance the performance of the FxLMAT algorithm for IN. To improve stability, the first alteration i.e. variable step size FxLMAT (VSSFxLMAT)algorithm is suggested that incorporates the energy of input and error signal but has slow convergence. To improve its convergence, the second modification i.e. filtered x robust normalized least mean absolute third (FxRNLMAT) algorithm is presented but still lacks robustness. Therefore, a third modification i.e. modified filtered-x RNLMAT (MFxRNLMAT) is devised, which is relatively stable when encountered with high impulsive noise. With comparable computational complexity, the proposed MFxRNLMAT algorithm gives better robustness and convergence speed than all variants of the filtered-x least cos hyperbolic algorithm, and filtered-x least mean square algorithm.

Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.

In mechanical, civil and chemical engineering systems the accuracies of flow measurement instruments is conventionally specified by certified measurement capabilities (CMCs) that are symmetric, however it is physically possible for some flow instruments and equipment to exhibit asymmetric non-Gaussian behaviour. In this paper the influence of non-Gaussian uncertainties is investigated using direct Monte Carlo simulations to construct a probability density function (PDF) using representative non-Gaussian surface roughness data for a commercial steel pipe friction factor. Actual PDF results are compared and contrasted with a symmetric Gaussian PDF, and reveal inconsistencies in the statistical distributions that cannot be neglected in high accuracy flow measurements. The non-Gaussian PDF is visualized with a kernel density estimate (KDE) scheme to infer an initial qualitative shape of the actual PDF using the approximate locations of the normalized peaks as a initial metrologist estimate of the measurement density. This is then utilized as inputs in a maximum statistical entropy functional to optimize the actual non-Gaussian PDF using a nonlinear optimization of Lagrange multipliers for a mathematically unique PDE. Novelties in the present study is that a new methodology has been developed for statistical sampling from non-monotonic non-Gaussian distributions with accompanying Python and Matlab/GNU Octave computer codes, and a new methodology for utilizing metrologist's expert prior knowledge of PDF peaks and locations for constructing an a priori estimate of the shape of unknown density have been incorporated into the maximum statistical entropy nonlinear optimization problem for a faster and more efficient approach for generating statistical information and insights in constructing high accuracy non-Gaussian PDFs of real world messy engineering measurements.

This study proposes a multi-rank range-spread target detection method for multi-channel array radar under a non-Gaussian clutter background. The method aims to detect the target from real clutter using the multi-channel array radar. First, a multi-rank range-spread target model was formulated using a subspace matrix with a rank greater than one and the coordinate vectors of corresponding range bins. Then, by exploiting the persymmetric structure information of the clutter covariance matrix under the detection scenario, wherein the radar receiver units were central symmetric in space or time, a small sample estimation strategy for the parameters to be solved through the unitary transformation was constructed. Further, a non-Gaussian clutter background multi-rank range-spread target detection method was designed based on the generalized likelihood ratio, Rao, and Wald tests. Finally, a theoretical derivation proved that the proposed detection method has the constant false alarm rate property. The experimental results based on both the simulated and measured data showed that the proposed detection method can ensure the constant false alarm rate property of the clutter covariance matrix. Additionally, compared with the existing detection methods, the proposed detection method improves the target detection performance under small sample support. Besides, the proposed detection method effectively improves the robustness of target detection under the condition of steering vector mismatch.

This paper focuses on the non-Gaussian properties of tornado pressure loading on a Texas Tech University (TTU) building model. External pressures of the model were measured at multiple radial positions in a two-celled tornado-like vortex generated by a tornado-like vortex simulator. High-order statistical moments of pressure coefficients were studied. The spatial distributions of non-Gaussian zones were presented and compared with the figure for boundary layer wind. Four exponential models were used to fit the probability density of tornado pressures. The peak factors obtained by five methods were also investigated. Results indicate that non-Gaussian regions of a low-rise building in a tornado-like vortex significantly differ from that in boundary layer wind. The peak pressure coefficients exhibit a maximum value near the end of windward eaves when the model is located at a tornadic core radius. The probability density of tornado pressure time series cannot be fitted by a single exponential distribution. The gamma distribution and generalized extreme value (GEV) distribution can describe the probabilistic behavior of pressure coefficients at the most unfavorable load position. Compared with other methods, the skewness-dependent peak factor method exhibits the advantages of reliable results, easy calculation, and wide applicability. [ABSTRACT FROM AUTHOR]

This paper evaluates the real‐time forecast performance of alternative Bayesian autoregressive (AR) and vector autoregressive (VAR) models for the Australian macroeconomy. To this end, we construct an updated vintage database and compare the predictive ability of a wide set of specifications that takes into account almost all possible combinations of nonstandard errors existing in the current literature. In general, we find that the models with flexible covariance structures can improve the forecast accuracy as compared with the standard variant. For forecasting GDP, both point and density forecasts consistently suggest small VARs tend to outperform their counterparts while AR models often predict inflation better. With the unemployment rate, large VAR models provide superior forecasts to the alternatives at almost all forecast horizons. The forecasting performance of these models slightly changes when we consider the first, second, and latest‐available vintage as actual values, highlighting the importance of using real‐time data vintages in forecasting. [ABSTRACT FROM AUTHOR]

Network models of rubber elasticity are based on the conformational entropy of an idealized chain and mostly motivated by the non-Gaussian statistical theory by Kuhn and Grün. However, the non-Gaussian probability distribution function cannot be expressed in a closed form and requires an approximation. All such approximations applied in the literature demonstrate pronounced inaccuracies in comparison to the analytical solution. The ideal choice of the approximation function depends on a variety of factors, such as the chain parameters or the desired application of the approximation (the probability distribution function itself, the corresponding entropic energy, or the force developed by the chain). In addition, when making a choice regarding the best approximation for a given application, the applied error measure plays a significant role since the approximation that grants, for example, the best maximal relative error is not necessarily the same that provides the best mean absolute error. In the literature, this application-specific evaluation of available approximations is commonly disregarded. In this paper, we evaluate previously proposed approximations on the application-specific basis and develop an approach to derive a family of approximations for the free energy of a polymer chain in a broader range of the number of its chain segments. The analytical method based on the Padé technique delivers an approximation of the non-Gaussian probability distribution function that can be easily tailored depending on the desired application. The proposed approach is capable to provide much stronger predictions in comparison to the Kuhn and Grün model in a wide range of chain segment numbers. [ABSTRACT FROM AUTHOR]

It is necessary to investigate the identification of structural systems and unknown inputs under non‐Gaussian measurement noises. In recent years, a few scholars have proposed methods of particle filter (PF) with unknown input for such task. However, these PF with unknown input require that unknown inputs appear in structural measurement equations. Such requirement may not always met, which restrict their practical application. To overcome this limitation, a generalized extended Kalman particle filter with unknown input (GEKPF‐UI) is proposed for the simultaneous identification of structural systems and unknown inputs under non‐Gaussian measurement noises. The proposed method is more general than the existing methods of PF with unknown input as it is applicable whether measurement equations contain or do not contain unknown inputs. It is proposed to establish the importance density function of PF by the generalized extended Kalman filter with unknown input (GEKF‐UI) recently developed by the authors, in which GEKF‐UI is utilized to generate particles and allow particles to carry the latest observational information. The effectiveness of the proposed method is verified through two numerical identification examples of a nonlinear hysteretic structure under two types of unknown inputs, including unknown external excitation and unknown seismic inputs, respectively. [ABSTRACT FROM AUTHOR]

In order to explore the formation mechanism of the nonstationary wind speed in the eye wall regions and eye region of a typhoon, taking the measured data of No. 0814 strong typhoon Hagupit as the research object, we identify and extract the coherent structure of the measured wind field by discrete wavelet transform combined with hypothesis testing, and analyze the influence of the coherent structure on the nonstationary and non-Gaussian wind speed and study the influence of the coherent structure on the wind turbulence characteristics. The results show that for the 0814 typhoon Hagupit process, the coherent structure is the main reason that leads to the nonstationary and non-Gaussian fluctuating winds in the typhoon field, and with the coherent structures being exacted from the original winds, the nonstationary and non-Gaussian characteristics of the nonstationary wind samples are significantly weakened. The average contribution of the coherent structure to the turbulence parameters ranges from 6. 42% to 32. 40%. The duration of the coherent structure is about 10. 60% of the sample duration, however, its contribution to turbulent kinetic energy is up to 40. 50%. The coherent structure has the characteristics of short duration and high energy content, which is the cause of the abnormally large turbulence parameter value. This study can provide a reference for the refined wind resistance design of structures under the action of nonstationary wind. [ABSTRACT FROM AUTHOR]

Engineering surfaces exhibit asymmetrical height distributions due to certain types of surface finishing and running-in process. This non-Gaussian surface reflects different contact performances and tribological properties. In this paper, the influence of non-Gaussian surface parameters on contact performance and friction is investigated. First, the computer program for generating rough surfaces with given parameters is developed; then, contact analysis for rough surfaces are conducted through a deterministic contact model; finally, friction coefficient can be derived from friction model using the results of the contact model. The simulation analyses indicate that the skewness and amplitude of non-Gaussian surface have significant effects on contact performance and friction. The contact characteristic parameters and friction coefficient become slightly changed when kurtosis becomes relatively large. [ABSTRACT FROM AUTHOR]

Beam-driven plasma wakefield accelerators typically use the external injection to ensure controllable beam quality at injection. However, the externally injected witness bunch may exhibit a non-Gaussian transverse density distribution. Using particle-in-cell simulations, we show that the common beam quality factors, such as the normalized RMS emittance and beam radius, do not strongly depend on the initial transverse shapes of the witness beam. Nonetheless, a beam with a highly-peaked transverse spatial profile can achieve a higher fraction of the total beam charge in the core. The same effect can be seen when the witness beam's transverse momentum profile has a peaked non-Gaussian distribution. In addition, we find that an initially non-axisymmetric beam becomes symmetric due to the interaction with the plasma wakefield. [ABSTRACT FROM AUTHOR]

To address the challenges posed by known heavy-tailed non-Gaussian noise characteristics in multi-sensor fusion, such as complex modeling, reduced estimation accuracy, and inadequate real-time performance, a non-Gaussian cubature particle filter sequential fusion method based on Gradient Descent (GD) and Maximum Correntropy Criterion (MCC) is proposed. Firstly, the proposed approach employs the gradient descent technique to minimize the Pseudo-Huber loss function. This optimization aims to approximate a known heavy-tailed non-Gaussian distribution to a Gaussian distribution, thereby reducing the complexity associated with modeling non-Gaussian noise. Furthermore, by incorporating the MCC into the Cubature Particle Filtering (CPF) process, we achieve real-time optimal estimation of the state, leading to a further improvement in the accuracy of the filter. Finally, a sequential fusion approach is employed for multi-sensor fusion, ensuring real-time filtering and fusion of measurement values. The simulation results demonstrate that in the multi-sensor fusion problem under non-Gaussian noise, the proposed fusion method in this paper can effectively reduce the algorithm's time complexity while ensuring accuracy. [ABSTRACT FROM AUTHOR]

• An innovative deep learning parameterization method (DLPM) is proposed to parameterize non-Gaussian conductivity fields. • Integrated two DLPMs with data assimilation for groundwater inverse modeling. • Both DLPM-based inversion frameworks successfully identify model parameters for a complex contaminated site. • Analysis in four scenarios demonstrated the proposed DLPM's efficacy in extracting crucial information from measurements. 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. [ABSTRACT FROM AUTHOR]

• Propose an analytical method for determining the outcrossing rate of nonstationary and strong non-Gaussian processes. • Combine a two-components parallel system model with higher order moments-based reliability indexes. • This method is more computation efficient than Monte Carlo simulation. • This method is robust for different types of stochastic processes, and for both linear and nonlinear limit state functions. For time-dependent reliability methods, there is a lack of analytical solutions to outcrossing rates of nonstationary and non-Gaussian processes. This paper aims to propose an analytical method to determine this type of outcrossing rate with improved accuracy and efficiency. The novelty of this proposed method is that it can consider the probabilistic properties of non-Gaussian processes by combining a two-component parallel system model with higher-order moments-based reliability indexes. The main contributions of this method are: (1) compared with PHI2+ method, it is more accurate for the calculation of the outcrossing rate of nonstationary and non-Gaussian processes with nonlinear limit state functions; (2) compared with MPHI2 method, it is analytical and not only applicable for the nonstationary stochastic processes but also insensitive to time increments; and (3) it is not only more accurate than the existing methods for nonstationary and non-Gaussian processes but also more computation efficient than the Monte Carlo simulation method. The proposed method has shown its advantages for practical structures with neither Gaussian processes nor linear limit state functions, which are beneficial for both researchers and asset managers to evaluate the time-dependent reliability of structures accurately and to develop risk-informed maintenance schemes with a view to prolonging their service life. [ABSTRACT FROM AUTHOR]

The article highlights the development of a Non-Gaussian Process Monitoring Strategy for a Steel Billet Manufacturing Unit (SBMU). The non-Gaussian monitoring strategy being proposed is based on Modified Independent Component Analysis (ICA) which is a variant of the widely employed conventional ICA. The Independent Components(IC) being extracted by modified ICA technique are ordered as per the variance explained akin to that of Principle Component Analysis (PCA). Whereas in conventional ICA the variance explained by the ICs are not known and thereby causes hindrance in the selection of influential ICs for eventual building of the nominal model for the ensuing monitoring strategy. Hotelling T2 control chart based on modified ICA scores was used for detection of fault(s) whose control limit was estimated via Bootstrap procedure owing to the non-Gaussian distribution of the underlying data. The Diagnosis of the Detected Fault(s) was carried out by employment of Fault Diagnostic Statistic. The Diagnosis of the Fault(s) involved determination of the contribution of the responsible Process and Feedstock characteristics. The non-Gaussian strategy thus devised was able to correctly detect and satisfactory diagnose the detected fault(s)

In modeling a rough surface, it is common to assume a Gaussian height distribution. This hypothesis cannot describe an eventual asymmetry between crests and troughs of natural surfaces. We analyzed the bistatic scattering from a rough surface with non-Gaussian height distributions using the Kirchhoff scattering theory. Two extreme cases of Gamma-distributed surfaces were compared in particular: exponential and Gaussian distributions. The bistatic angular dependence was examined under various root mean square (RMS) heights and power spectrum densities. Contribution sources to the coherent and incoherent scattering components were singled out relating to the surface height distribution. For an exponential height surface, the coherent scattering strengthens even as the surface becomes rough. The non-Gaussian effect on the incoherent scattering is connected with surface power spectrum density. The height distribution impacts differ in the different regions of the bistatic scattering plane and thus complicate the differentiation of the scattering patterns due to height distribution. [ABSTRACT FROM AUTHOR]

In the last years, a few experiments in the fields of biological and soft matter physics in colloidal suspensions have reported "normal diffusion" with a Laplacian probability distribution in the particle's displacements (i.e., Brownian yet non-Gaussian diffusion). To model this behavior, different stochastic and microscopic models have been proposed, with the former introducing new random elements that incorporate our lack of information about the media and the latter describing a limited number of interesting physical scenarios. This incentivizes the search of a more thorough understanding of how the media interacts with itself and with the particle being diffused in Brownian yet non-Gaussian diffusion. For this reason, a comprehensive mathematical model to explain Brownian yet non-Gaussian diffusion that includes weak molecular interactions is proposed in this paper. Based on the theory of interfaces by De Gennes and Langevin dynamics, it is shown that long-range interactions in a weakly interacting fluid at shorter time scales leads to a Laplacian probability distribution in the radial particle's displacements. Further, it is shown that a phase separation can explain a high diffusivity and causes this Laplacian distribution to evolve towards a Gaussian via a transition probability in the interval of time as it was observed in experiments. To verify these model predictions, the experimental data of the Brownian motion of colloidal beads on phospholipid bilayer by Wang et al. are used and compared with the results of the theory. This comparison suggests that the proposed model is able to explain qualitatively and quantitatively the Brownian yet non-Gaussian diffusion. [ABSTRACT FROM AUTHOR]

There are potential sources of uncertainty when using default or generic profiles for vibration testing, particularly for large and complex payloads (Warren and Joiner, 2019). Replacing these severities with custom profiles generated using measured data offers one alternative; however, care must be taken not to select an inappropriate or inaccurate method. This research details the methodology and results of a trial which involved the design and implementation of a series of vibration tests, each to simulate a mixed-terrain environment applied to a complex payload. A systematic approach was used to develop and execute a test plan via the design of experiments method. An estimate of the damage potential for each was formed using Miner's rule (linear damage accumulation) applied to direct strain gauge data. This approach was compared with damage measured during a time waveform replication style test to be used as a baseline. The results of this test can be used to guide test specifiers and programme-level acceptance test guidelines and may be useful in implementing or guiding standards in this space. In addition, the damage measured in a series of increasing amplitude vibration tests (with an identical power spectral density) was compared with predicted values to assess the gain linearity assumptions often used in accelerated vibration testing. The research is unique as the authors could not source a thorough trial comparing the damage produced using a range of different profile development methods with a complex, real-world payload. Test houses and test specifiers seeking to improve the accuracy of their tests should consider the key findings and guidance in this article. [ABSTRACT FROM AUTHOR]

By dealing with the non-Gaussian measurement and slow-change faults in running gear systems, this paper presents a fault detection (FD) scheme named time-series independent component analysis (TsICA), where the time-series characteristic is taken into account. Time-series algorithms can extract slow-change information in the data. The advantages of the proposed method are: 1) it can improve the FD power; 2) it considers the information in the data 3) it is suitable for non-Gaussian systems; 4) it is sensitive to slow-change faults; 5) it can effectively shorten the first time of fault detection. The feasibility of the proposed scheme is verified through a case study on running gear systems. [ABSTRACT FROM AUTHOR]