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Abstract This paper considers a class of nonlinear filtering algorithms based on variational Bayesian (VB) theory to settle the unknown measurement noise problem in target tracking system. When the unknown measurement noise is conditionally independent of states, based on the variational idea, estimate of probability density function of state is converted into approximation two probability density functions for both unknown noise and nonlinear states. Then, an iterative algorithm is established to jointly estimate the state and the unknown measurement noise using variational Bayesian inference. Thus, the unknown measurement noise could be estimated as hidden state. The convergence result of the proposed nonlinear probability density function approximation algorithm is also given. The simulation results of typical examples show that the proposed VB based methods have superior performance to these classic algorithms in target tracking problems. [ABSTRACT FROM AUTHOR]

Abstract A cantilever with an open surface crack excited by the pedestal movement with the form of the Gaussian white noise was modeled in this paper. The open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained. The dynamical equation governing the transverse motion was gained with the Kane's method after sufficient consideration of the geometrical nonlinearity and the axial inertia. Both quasi-conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically. The stationary probability density function (PDF) of the amplitude, as well as the joint stationary PDF of the displacement and velocity, was investigated. For the purpose of exploring the reliability of the cantilever, the reliability function was established to avoid the potential fatigue or damage. Numerical simulations were carried out to vindicate the theoretical analysis. The advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary PDF of the amplitude and the joint PDF of displacement and velocity. Furthermore, the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation (Monte Carlo method) of the reliability. [ABSTRACT FROM AUTHOR]

Flow regime map is often used in choosing constitutive correlations for the two-phase flow model. The related research mainly concentrates on the vertical upward and horizontal flow, while it is not sufficient in the vertical downward flow. Downward flow is very important as it is frequently encountered in the industrial applications. To enrich the downward flow research, an experiment is performed on a piping system with an inner diameter of 0.1524 m. Four different flow patterns (bubbly flow, cap bubbly flow, churn turbulent flow, and annular flow) are classified with the artificial neural network method. The probability density function (PDF) profile of each flow pattern is discussed. The proposed flow regime map is compared with the other experiments and the effect of the pipe size is discussed. The existing downward flow regime boundary criteria are assessed with the experiment results. It is found that these criteria cannot fit the experiment results well. A set of general boundary criteria are still needed. In this paper, the criteria for the boundary of the bubbly flow, the boundary between the cap bubbly flow and the slug flow, and the boundary of the falling film regime are proposed. They are verified with the experiments on different size pipes. A significant inlet effect on the flow regime boundary is found. The falling film boundary criterion proposed cannot be applied when a sparger is used to inject gas into the downward test section. [ABSTRACT FROM AUTHOR]

Over the years, combinations of different methods that use multi-satellites and multi-sensors have been developed for estimating global precipitation. Recently, studies that have evaluated Integrated Multi-satellite Retrievals for GPM (IMERG) Final-Run (FR) version V-03D and other precipitation products have indicated better performance for IMERG-FR compared to other similar products in different climate regimes. This study comprehensively evaluates the two GPM-IMERG products, specifically IMERG-FR and IMERG-Real-Time (RT) late-run, against a dense station network (62 stations) in northeast Austria from mid-March 2015 to the end of January 2016 using different time-scales. Both products are examined against station data in capturing the occurrence and statistical characteristics of precipitation intensity. With regard to probability density functions (PDFs), the satellite precipitation estimate (SPE) products have detected more heavy and extreme precipitation events than the ground measurements. Both precipitation products at all time-scales, except for IMERG-RT 12-hourly and daily precipitation, capture less occurrence of precipitation than the station dataset for light precipitation. This partially explains the under-detection of precipitation events. For all time-scales, both IMERG products' CDFs (Cumulative Distribution Function) are well above that of the stations' precipitation. For lower precipitation levels, IMERG-RT is slightly below the IMERG-FR whereas IMERG-RT is above IMERG-FR at higher precipitation levels. Furthermore, for entire spectrum precipitation rates (P ≥ 0.1 mm), 1, 3, 6-hourly, IMERG-FR did not show a clear improvement of the Bias over IMERG-RT, while for 12-hourly and daily precipitation estimates, the bias in IMERG-FR has improved compared to IMERG-RT. In addition, IMERG-FR shows a considerable improvement in RMSE as compared to IMERG-RT. IMERG-FR, however, systematically underestimates moderate to extreme precipitation and overestimates light precipitation for all time scales against rain-gauges in northeast Austria. When comparing the bias, RMSE, and correlation coefficients, IMERG-FR has outperformed IMERG-RT particularly for 6-hourly, 12-hourly, and daily precipitation. Despite the general low probability of detection (POD) and threat score (TS) and the high false alarm ratio (FAR) within specified precipitation thresholds, the contingency table shows relatively acceptable values of the POD, TS and FAR for precipitation without classification. [ABSTRACT FROM AUTHOR]

We discuss several features of the classical quantum potential appearing in Covariant Quantum Mechanics. In particular, we compare the “observed potential” A [ K , G , o ] of the joined spacetime connection K with the potential A ↑ of the cosymplectic phase 2-form Ω [ K , G ] and with the potential A ↑ of the upper quantum connection Ч ↑ . Moreover, we discuss the distinguished observer o [ Ψ ] and the distinguished timelike potential A [ Ψ ] associated with a non-vanishing quantum section Ψ. We show that the above objects play a natural role in the context of the kinetic quantum momentum Q [ Ψ ] , of the quantum probability current J [ Ψ ] , of the Schrödinger operator S [ Ψ ] and of the classical fluid associated with a non-vanishing quantum section Ψ. [ABSTRACT FROM AUTHOR]

Based on the random theory of the probability density evolution method (PDEM), a refined random wheel/rail contact model for train-track-bridge systems is proposed. The trace line method with the law of equal slopes is developed to determine the wheel/rail contact locations, which are described by probability density functions on the wheel/rail surface. The number theoretic method (NTM) and stochastic harmonic functions (SHFs) are employed to generate the representative random track irregularities. Considering the excitation of random track irregularities and the wheel/rail contact geometry, the wheel/rail normal contact force and the tangential creep force are accurately calculated and analyzed using the proposed wheel/rail contact model. A high-speed railway case study is presented to reveal the random dynamic characteristics of a train-track-bridge system and the wheel/rail interaction. The results show that the time-varying probability density evolution functions of the wheel/rail contact points can effectively indicate both the phenomenon of wear on the rail surface and its distribution characteristics. Additionally, some significant conclusions are obtained. [ABSTRACT FROM AUTHOR]

There are relatively few publications that assess capacity decline in enough commercial cells to quantify cell-to-cell variation, but those that do show a surprisingly wide variability. Capacity curves cross each other often, a challenge for efforts to measure the state of health and predict the remaining useful life (RUL) of individual cells. We analyze capacity fade statistics for 24 commercial pouch cells, providing an estimate for the time to 5% failure. Our data indicate that RUL predictions based on remaining capacity or internal resistance are accurate only once the cells have already sorted themselves into “better” and “worse” ones. Analysis of our failure data, using maximum likelihood techniques, provide uniformly good fits for a variety of definitions of failure with normal and with 2- and 3-parameter Weibull probability density functions, but we argue against using a 3-parameter Weibull function for our data. pdf fitting parameters appear to converge after about 15 failures, although business objectives should ultimately determine whether data from a given number of batteries provides sufficient confidence to end lifecycle testing. Increased efforts to make batteries with more consistent lifetimes should lead to improvements in battery cost and safety. [ABSTRACT FROM AUTHOR]

Results related to the filtered non-premixed turbulent flame statistics are presented. Considering non-premixed turbulent combustion modeling in the framework of large eddy simulations (LES), a turbulent flamelet equation is derived based on the filtered governing equations. Using a direct numerical simulation (DNS) data set, the statistical properties of two important parameters, the scalar dissipation and chemical source term, are analyzed in details. Numerical results show that for the scalar dissipation term, the probability density function (PDF) of the magnitude of the mixture fraction gradient changes is strongly dependent on the filter scale, whereas the PDF of the turbulent diffusivity is almost invariant. Theoretically from the scalar structure function a scaling law can be expected for the conditional mean of the difference between the filtered and nonfiltered scalars with respect to the filter scale, which is important for estimating the chemical source in the subgrid scale models. [ABSTRACT FROM AUTHOR]