First-order Moment Research Articles

Uncertainty in risk of highway bridges assessed for integrated seismic and flood hazards

Probabilistic risk assessment for bridges under natural hazards is of great interest to engineers for the development of risk mitigation strategies and implementation plans. The present study evaluates risk of an existing highway bridge in California, USA, under the integrated impact of regional seismic and flood hazards. A sensitivity study combining tornado diagram and first-order second moment reliability analyses is conducted to screen significant uncertain parameters to which bridge response is mostly sensitive. A rigorous uncertainty analysis, employing random sampling and Monte Carlo simulation techniques, is performed to obtain variations in fragility and risk curves of the bridge. Observed variations in risk curves at various risk levels are quantified through 90% confidence intervals and coefficients of variation (COV) of risk. It is observed that uncertainty in the estimated risk increases due to the presence of flood hazard at the bridge site, although mean risk does not vary with flood hazard level. Research outcome signifies that the variation in risk due to parameter uncertainty and varied flood hazard level should not be ignored to ensure bridge safety under the stated multi-hazard condition.

Uncertainty analysis of a 2D sediment transport model: an example of the Lower River Salzach

In sediment transport modeling, several sources of uncertainty exist that impinge on the variability of model results. Therefore, it is essential to conduct an uncertainty analysis to quantify the impact of these uncertainties, to detect regions of enhanced sensitivity and subsequently to determine a range of possible model outcomes. The first-order second moment method with numerical differentiation is applied to assess the uncertainties of a 2D sediment transport model Hydro_FT-2D at the Lower River Salzach. In comparison to other methods, the first-order second moment method has benefits in terms of total time requirement since it uses considerably less simulation runs to determine model uncertainty. In total, eight uncertain parameters are investigated including both model and river specific parameters. For this purpose, only 2n + 1 simulation runs are necessary leading to a total of 17 simulations. The results are evaluated against a reference simulation regarding bed elevation changes, bed load transport rates, grain size distribution, and total riverbed evolution volume. The results of the total riverbed evolution volume indicate a large influence of the investigated river specific parameters roughness of river channel (k st ), grain roughness (k s ), and bed load input rate of the upstream River Saalach (QS SAAL). Among the model specific parameters, the critical Shields parameter (θ crit) and the scaling factor of Meyer-Peter and Mueller equation (MPM) have a significant effect on the model results. Moreover, a spatial evaluation of the maximum and minimum parameter-specific deviation from the reference indicates sensitive areas in regions with poor descriptive data as well as in close vicinity to weirs, ramps, and lateral inflows. In these areas, the model predictions are subject to a high degree of uncertainty and have to be taken with caution. The applied first-order second moment method with numerical differentiation is a powerful method to identify sensitive areas within the numerical model and to gain knowledge on both uncertain model and river specific parameters. Based on the results, the variability of model outputs can be evaluated and assessed with respect to the uncertainty in the input parameters and can thus contribute to a deeper understanding of the model behavior, which is highly beneficial for long-term morphodynamic studies. The method is found to be applicable for sediment transport models especially in an applied engineering context and for long-term simulation runs due to the simplicity of implementation as well as the reasonable total time requirement.

The Impact of Layer Perturbation Potential Energy on the East Asian Summer Monsoon

This paper analyzes the relationship between the 1000–850-hPa layer perturbation potential energy (LPPE) as the difference in local potential energy between the actual state and the reference state and the East Asian summer monsoon (EASM) using reanalysis and observational datasets. The EASM is closely related to the first-order moment term of LPPE (LPPE1) from the preceding March to the boreal summer over three key regions: the eastern Indian Ocean, the subtropical central Pacific, and midlatitude East Asia. The LPPE1 pattern (−, +, +), with negative values over the eastern Indian Ocean, positive values over the subtropical central Pacific, and positive values over East Asia, corresponds to negative LPPE1 anomalies over the south of the EASM region but positive LPPE1 anomalies over the north of the EASM region, which lead to an anomalous downward branch over the southern region but an upward branch over the northern region. The anomalous vertical motion affects the local meridional circulation over East Asia that leads to a southwesterly wind anomaly over East Asia (south of 30°N) at 850 hPa and anomalous downward motion over 100°–120°E (along 25°–35°N), resulting in a stronger EASM, more kinetic energy over the EASM region, and less boreal summer rainfall in the middle and lower reaches of the Yangtze River valley (24°–36°N, 90°–125°E). These LPPE1 anomalies in the eastern Indian Ocean and subtropical central Pacific appear to be connected to changes in local sea surface temperature through the release of latent heat.

Reliability prediction of large fuel cell stack based on structure stress analysis

The aim of this paper is to improve the reliability of Proton Electrolyte Membrane Fuel Cell (PEMFC) stack by designing the clamping force and the thickness difference between the membrane electrode assembly (MEA) and the gasket. The stack reliability is directly determined by the component reliability, which is affected by the material property and contact stress. The component contact stress is a random variable because it is usually affected by many uncertain factors in the production and clamping process. We have investigated the influences of parameter variation coefficient on the probability distribution of contact stress using the equivalent stiffness model and the first-order second moment method. The optimal contact stress to make the component stay in the highest level reliability is obtained by the stress-strength interference model. To obtain the optimal contact stress between the contact components, the optimal thickness of the component and the stack clamping force are optimally designed. Finally, a detailed description is given how to design the MEA and gasket dimensions to obtain the highest stack reliability. This work can provide a valuable guidance in the design of stack structure for a high reliability of fuel cell stack.

Random Set Approach to Distributed Multivehicle SLAM

This paper deals with the simultaneous localization and mapping (SLAM) problem for autonomous vehicles or mobile robots. More specifically, a multi-vehicle scenario is considered wherein a team of vehicles explore the scene of interest in order to cooperatively construct the map of the environment by locally updating and exchanging map information in a neighbor-wise fashion. A random-set approach is undertaken by regarding the map as a random finite set (RFS) and updating the first-order moment, called probability hypothesis density (PHD), of its multi-object density. Consensus on PHDs is adopted in order to spread the map information through the team of vehicles also taking into account the different and time-varying fields of view (FoVs) of the team members. The developed algorithm represents - to the best of the authors’ knowledge - the first attempt to solve in a fully decentralized way the multi-vehicle SLAM problem within the RFS framework. The effectiveness of the proposed approach is tested by means of simulation experiments.

Polarization property changes of optical beam transmission in atmospheric turbulent channels.

We theoretically analyze and experimentally verify the performance of multiple polarization parameters in the presence of atmospheric turbulence for a terrestrial optical transmission. First, both the first- and second-moment characteristic of polarization parameters are derived based on the extended Huygens-Fresnel principle. Then, numerical simulations are presented for different propagating distances, optical source properties, and turbulent strengths. Finally, a series of well-designed experiments are carried out to verify the theory with turbulence-controlled conditions, where the polarization states are measured at two wavelengths, respectively. As a result, the theoretical predictions conform closely to the experimental data, and both show that with the increasing turbulent strength, the first-order moment of polarization parameters varies in different trends, while their second-order moment increases. The proposed approach is promising for building a comprehensive statistical model of polarization and improving the performance of a free-space optical communication link.

Expected and unexpected values of individual Mahalanobis distances

ABSTRACTThis paper derives first-order sampling moments of individual Mahalanobis distances (MDs) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c, 0 ⩽ c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second-order moments are also supplied to give some additional insight to the matter.

A Second-Order PHD Filter With Mean and Variance in Target Number

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters.

A hybrid relaxed first-order reliability method for efficient structural reliability analysis

The Hasofer-Lind and Rakwitz-Fiessler (HL-RF) algorithm is widely used for structural reliability analysis in first-order moment method (FORM). However, it meets non-convergence problem including generating periodic and chaotic solutions for highly nonlinear limit state function. In this paper, relaxed HL-RF (RHL-RF) is developed based on a relaxed factor, which is dynamically computed by the second-order interpolation between zero and one. A hybrid relaxed HL-RF (HRHL-RF) method is proposed, in which the HL-RF and RHL-RF are adaptively implemented by using an angle criterion to improve the robustness and efficiency of FORM formula. The angle condition is simply calculated based on the results from the new and previous points. Finally, the performances in terms of robustness and efficiency of the HRHL-RF are compared with several existing FORM methods through five mathematical and structural examples. The results indicate that HRHL-RF method is more robust than the HL-RF and more efficient than other existing methods.

Distributed multi‐sensor fusion using generalised multi‐Bernoulli densities

A new method for distributed multi-target tracking with multistatic radar systems is presented.The proposed method is based on using generalised covariance intersection (GCI) of multi-object densities for fusion of the posteriors within a multi-object Bayesian filtering scheme. The presented solution is particularly formulated for sensor fusion with posterior densities that are parameterised as generalised multi-Bernoulli (GMB) distributions which are the unlabelled version of VoCVo densities by discarding the labels. To obtain a closed-form solution for fusing GMB densities, the authors use an efficient approximation to the densities. The approximated density is another GMB density that preserves both the first-order moment (intensity or PHD) and the cardinality distribution of the original density. As such, it is called the second-order approximation of the GMB (SO-GMB) density. The resulting explicit expressions for the GCI fusion using SO-GMB approximations allow distributed sensor fusion, not only with VoCVo filters, but also with M-generalised labelled multi-Bernoulli and labelled multi-Bernoulli filters being in place as local filters in the multistatic radar system. In two challenging multi-target tracking scenarios, the tracking performance of the proposed method is shown to outperform the state of art.

Dimension-by-dimension moment-based central Hermite WENO schemes for directly solving Hamilton-Jacobi equations

In this paper, a class of high-order central Hermite WENO (HWENO) schemes based on finite volume framework and staggered meshes is proposed for directly solving one- and two-dimensional Hamilton-Jacobi (HJ) equations. The methods involve the Lax-Wendroff type discretizations or the natural continuous extension of Runge-Kutta methods in time. This work can be regarded as an extension of central HWENO schemes for hyperbolic conservation laws (Tao et al. J. Comput. Phys. 318, 222–251, 2016) which combine the central scheme and the HWENO spatial reconstructions and therefore carry many features of both schemes. Generally, it is not straightforward to design a finite volume scheme to directly solve HJ equations and a key ingredient for directly solving such equations is the reconstruction of numerical Hamiltonians to guarantee the stability of methods. Benefited from the central strategy, our methods require no numerical Hamiltonians. Meanwhile, the zeroth-order and the first-order moments of the solution are involved in the spatial HWENO reconstructions which is more compact compared with WENO schemes. The reconstructions are implemented through a dimension-by-dimension strategy when the spatial dimension is higher than one. A collection of one- and two- dimensional numerical examples is performed to validate high resolution and robustness of the methods in approximating the solutions of HJ equations, which involve linear, nonlinear, smooth, non-smooth, convex or non-convex Hamiltonians.

An Analysis of Adaptive Recursive Smoothing with Applications to Noise PSD Estimation

First-order recursive smoothing filters using a fixed smoothing constant are in general unbiased estimators of the mean of a random process. Due to their efficiency in terms of memory consumption and computational complexity, they are of high practical relevance and are also often used to track the first-order moment of nonstationary random processes. However, in single-channel speech-enhancement applications, e.g., for the estimation of the noise power spectral density, an adaptively changing smoothing factor is often employed. Here, the adaptivity is used to avoid speech leakage by raising the smoothing factor when speech is likely to be present. In this paper, we investigate the properties of adaptive first-order recursive smoothing factors applied to noise power spectral density estimators. We show that in contrast to a smoothing with fixed smoothing factors, adaptive smoothing is in general biased. We propose different methods to quantify and to compensate for the bias. We demonstrate that the proposed correction methods reduce the estimation error and increases the perceptual evaluation of speech quality scores in a speech enhancement framework.

INFLUENCE OF THE GALACTIC GRAVITATIONAL FIELD ON THE POSITIONAL ACCURACY OF EXTRAGALACTIC SOURCES

ABSTRACT We investigate the influence of random variations of the Galactic gravitational field on the apparent celestial positions of extragalactic sources. The basic statistical characteristics of a stochastic process (first-order moments, an autocorrelation function and a power spectral density) are used to describe a light ray deflection in a gravitational field of randomly moving point masses as a function of the source coordinates. We map a 2D distribution of the standard deviation of the angular shifts in positions of distant sources (including reference sources of the International Celestial Reference Frame) with respect to their true positions. For different Galactic matter distributions the standard deviation of the offset angle can reach several tens of μas (microarcsecond) toward the Galactic center, decreasing down to 4–6 μas at high galactic latitudes. The conditional standard deviation (“jitter”) of 2.5 μas is reached within 10 years at high galactic latitudes and within a few months toward the inner part of the Galaxy. The photometric microlensing events are not expected to be disturbed by astrometric random variations anywhere except the inner part of the Galaxy as the Einstein–Chvolson times are typically much shorter than the jittering timescale. While a jitter of a single reference source can be up to dozens of μas over some reasonable observational time, using a sample of reference sources would reduce the error in relative astrometry. The obtained results can be used for estimating the physical upper limits on the time-dependent accuracy of astrometric measurements.

A study on the effect of atorvastatin on the pharmacokinetic and antidepressant activity of fluoxetine

Background: Polypharmacy is of wide concern in drug interaction. It is the leading cause of adverse drug reaction, and consequently, increasing the possibility of hospitalization and escalating the cost of care. The incidence of coexisting depression and hyperlipidemia in patients is generally managed by providing numerous drugs for a longer period of time. Aims and Objectives: This study was conducted to observe the effect of atorvastatin on pharmacokinetic parameters of fluoxetine in healthy albino rabbits and to find possible interactions of atorvastatin on the antidepressant activity of fluoxetine using animal screening test. Materials and Methods: Two drugs: Fluoxetine and atorvastatin used concurrently were selected. Healthy male albino rabbits were used to determine the effect of atorvastatin on fluoxetine addressing its pharmacokinetic parameters, whereas rats and mice were used to assess the antidepressant activity of fluoxetine. Two animal models were used to determine its antidepressant activity. Forced swim test (FST) and tail suspension test (TST) were employed in exploring antidepressant activity. High-performance liquid chromatography was used to estimate fluoxetine concentration. Results: The concentration of serum fluoxetine showed slight increment after the atorvastatin treatment for 7 days at 2nd, 4th, 8th, 16th, and 24th h. The pharmacokinetic parameters: Area under the curve, area under first-order moment curve, t1/2, and Cmax of fluoxetine varied after atorvastatin treatment for 1 week in healthy albino rabbits. ‘’Furthermore, atorvastatin treatment for a week revealed a reduction in immobility time in rats and mice as shown by the FST and TST respectively. Conclusion: The results revealed the possibility of drug-drug interaction between fluoxetine and atorvastatin.

Distributed Fusion With Multi-Bernoulli Filter Based on Generalized Covariance Intersection

In this paper, we propose a distributed multi-object tracking algorithm through the use of multi-Bernoulli (MB) filter based on generalized Covariance Intersection (G-CI). Our analyses show that the G-CI fusion with two MB posterior distributions does not admit an accurate closed-form expression. To solve this challenging problem, we firstly approximate the fused posterior as the unlabeled version of $\delta$-generalized labeled multi-Bernoulli ($\delta$-GLMB) distribution, referred to as generalized multi-Bernoulli (GMB) distribution. Then, to allow the subsequent fusion with another multi-Bernoulli posterior distribution, e.g., fusion with a third sensor node in the sensor network, or fusion in the feedback working mode, we further approximate the fused GMB posterior distribution as an MB distribution which matches its first-order statistical moment. The proposed fusion algorithm is implemented using sequential Monte Carlo technique and its performance is highlighted by numerical results.

On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach

This paper is motivated by recent results in the design of signal plans for Manhattan that highlight the importance of providing signal control algorithms with an analytical description of between-link dependencies. This is particularly important for congested networks prone to the occurrence of spillbacks. This paper formulates a probabilistic network model that proposes an aggregate description of the queue-length, and then approximates the joint aggregate queue-length distribution of subnetworks. The goal is to model between-queue dependencies beyond first-order moments, yet to do so in a tractable manner such that these techniques can be used for optimization purposes.This paper models an urban road network as a finite space capacity Markovian queueing network. Exact evaluation of the stationary joint queue-length distribution of such a network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the network state space, which is exponential in the number of queues. This paper proposes to address the dimensionality issue by: 1) describing the state of the network aggregately, and 2) decomposing the network into overlapping subnetworks. We propose an analytical approximation of the stationary aggregate joint queue-length distribution of a subnetwork. The model consists of a system of nonlinear equations with a dimension that is linear, instead of exponential, in the number of queues and that is independent of the space capacity of the individual queues. The method is derived for tandem Markovian finite capacity queueing networks. The proposed model is computationally tractable and scalable, it can be efficiently used for the higher-order distributional analysis of large-scale networks. The model is validated versus simulation estimates and versus other decomposition methods. We then use it to address an urban traffic control problem. We show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested urban networks.

A Gini-based time series analysis and test for reversibility

Time reversibility is a fundamental hypothesis in time series. In this paper, Gini-based equivalents for time series concepts that enable to construct a Gini-based test for time reversibility under merely first-order moment assumptions are developed. The key idea is that the relationship between two variables using Gini (as measured by Gini autocorrelations and partial autocorrelations) can be measured in two directions, which are not necessarily equal. This implies a built-in capability to discriminate between looking at forward and backward directions in time series. The Gini creates two bi-directional Gini autocorrelations (and partial autocorrelations), looking forward and backward in time, which are not necessarily equal. The difference between them may assist in identifying models with underlying heavy-tailed and non-normal innovations. Gini-based test and Gini-based correlograms, which serve as visual tools to examine departures from the symmetry assumption, are constructed. Simulations are used to illustrate the suggested Gini-based framework and to validate the statistical test. An application to a real data set is presented.

Dynamic reliability prediction of bridge member based on Bayesian dynamic nonlinear model and monitored data

Bridge monitoring systems provide a huge number of stress data used for reliability prediction. In this article, the dynamic measure of structural stress over time is considered as a time series, and considering the limitation of the existing Bayesian dynamic linear models only applied for short-term performance prediction, Bayesian dynamic nonlinear models are introduced. With the monitored stress data, the quadratic function is used to build the Bayesian dynamic nonlinear model. And two methods are proposed to handle with the built Bayesian dynamic nonlinear model and the corresponding probability recursion processes. One method is to transform the built Bayesian dynamic nonlinear model into Bayesian dynamic linear model with Taylor series expansion technique; then the corresponding probability recursion processes are completed based on the transformed Bayesian dynamic linear model. The other one is to directly handle with the built Bayesian dynamic nonlinear model and the corresponding probability recursion processes with Markov chain Monte Carlo simulation method. Based on the predicted stress information (means and variances) of the above two methods, first-order second moment method is adopted to predict the structural reliability indices. Finally, an actual engineering is provided to illustrate the application and feasibility of the above two methods.

The frequency domain approach to analyse field-scale miscible flow transport experiments in the soils

A new approach to the estimate of the parameters u (advective velocity) and λ (dispersivity) characterizing solute transport in soils is presented. The pair (u, λ) is estimated by matching in the frequency domain (FD) the theoretical expression of moments pertaining to the breakthrough curve (BTC) against to the one evaluated by means of the experimental data. In particular, we demonstrate that to reduce the impact of the random measurement-errors upon such an estimate, it is worth retaining in the Fourier's expansion of the moments only the harmonics associated to the smaller frequencies. This is due to the fact that the Fourier transform moves most of the measurement-errors affecting moments in the high-frequency range. As a consequence, by adopting a relatively small number of harmonics to compute the Fourier transform of the experimental moments, one may filter out most of the noise. It is also shown that the number of harmonics to retain (cut-off) depends upon the soil's water content as well as the magnitude of the characteristic length l E of the error relative to the dispersivity λ. The proposed methodology has been applied to a recently conducted plot-scale transport experiment. For comparison purposes, we have also estimated the pair (u, λ) by the classical method of moments (MM). Both the methods lead to the same value of the advective velocity u. This is explained by recalling that u depends upon the first-order moment, a quantity that is scarcely influenced by the measurement-errors. Instead, the estimate of the dispersivity λ (which is related to the second-order moment) is largely different (with the value achieved by the MM larger than the one obtained by the FD approach). Such a difference is addressed to the fact that in the MM the distortion-effect due to the measurement-errors amplifies with the increasing order of the moments, a phenomenon which is completely avoided in the FD approach by adopting the above mentioned cut-off.

A random cell splitting scheme on the sphere

A random recursive cell splitting scheme of the 2-dimensional unit sphere is considered, which is the spherical analogue of the STIT tessellation process from Euclidean stochastic geometry. First-order moments are computed for a large array of combinatorial and metric parameters of the induced splitting tessellations by means of martingale methods combined with tools from spherical integral geometry. The findings are compared with those in the Euclidean case, making thereby transparent the influence of the curvature of the underlying space. Moreover, the capacity functional is computed and the point process that arises from the intersection of a splitting tessellation with a fixed great circle is characterized.