A Recursive Bayesian Solution for the Excess Over Threshold Distribution with Stochastic Parameters

In this paper, the stochastic parameters of the effective thermal conductivity of multilayer composites are considered. The examined specimens of composites were built with a different number of layers and each had a different saturation density of a composite matrix with fibers. For each case of laminate built with a prescribed number of layers and assumed saturation density, 10,000 tests of its effective thermal conductivity were carried out using numerical experiments. It was assumed that the fibers located in each layer were rectilinear, had a circular cross-section and that they could take random positions in their repeatable volume elements (RVEs). In view of the mentioned assumptions, the heat flux passing throughout a cross-section of a composite sample, perpendicular to the fibers’ direction, was considered. The probability density functions were fitted to the obtained data and then the chosen stochastic parameters of the effective thermal conductivity coefficients were determined.

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Empirical Stochastic Model of Multi-GNSS Measurements

Sensors ◽

10.3390/s21134566 ◽

2021 ◽

Vol 21 (13) ◽

pp. 4566

Author(s):

Dominik Prochniewicz ◽

Kinga Wezka ◽

Joanna Kozuchowska

Keyword(s):

Stochastic Model ◽

Density Ratio ◽

Functional Model ◽

Optimal Solution ◽

Global Navigation Satellite Systems ◽

Unknown Parameters ◽

Short Baseline ◽

Stochastic Parameters ◽

Dependent Model ◽

The Impact

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

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A fast simulation algorithm for the wheel profile wear of high-speed trains considering stochastic parameters

Wear ◽

10.1016/j.wear.2021.203942 ◽

2021 ◽

pp. 203942

Author(s):

Ren Luo ◽

Binbin Liu ◽

Sheng Qu

Keyword(s):

High Speed ◽

Simulation Algorithm ◽

Fast Simulation ◽

Stochastic Parameters ◽

High Speed Trains ◽

Wheel Profile ◽

Wheel Profile Wear

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Enough is too much: the excessiveness objection to sufficientarianism

Economics and Philosophy ◽

10.1017/s0266267121000171 ◽

2021 ◽

pp. 1-25

Author(s):

Carl Knight

Keyword(s):

Distributive Justice ◽

Standard Version ◽

Threshold Distribution

Abstract The standard version of sufficientarianism maintains that providing people with enough, or as close to enough as is possible, is lexically prior to other distributive goals. This article argues that this is excessive – more than distributive justice allows – in four distinct ways. These concern the magnitude of advantage, the number of beneficiaries, responsibility and desert, and above-threshold distribution. Sufficientarians can respond by accepting that providing enough unconditionally is more than distributive justice allows, instead balancing sufficiency against other considerations.

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