High-order Differencing Research Articles

Random Dynamic Analysis of Wind-Vehicle-Bridge System Based on ARMAX Surrogate Model and High-Order Differencing

To investigate the stochastic characteristics of vehicle-bridge (VB) system under crosswind, an efficient method which combines AutoRegressive Moving Average with eXogenous inputs (ARMAX) model, high-order differencing (HOD) and important sample was proposed in this paper. First, the wind turbulence spectra relative to a moving vehicle and equivalent static gust load method were adopted to simplify the turbulent wind field of VB system, and a wind-vehicle-bridge (WVB) model was established and verified. Then, an analysis framework for WVB system based on ARMAX model was proposed, and HOD method and important sample were used to improve the prediction performance of the surrogate model. Prediction accuracy and calculation efficiency of proposed AMRAX model were verified and compared by Monte Carlo simulation (MCS). Finally, the impacts of vehicle speed and wind velocity on the stochastic characteristics of train response were discussed. Results indicate that the HOD method has significantly improved the prediction performance of ARMAX model for lateral response of trains, and the train responses predicted by ARMAX model based on HOD and important sample show perfect agreement with target results. Compared with MCS, the calculation efficiencies of proposed ARMAX model are improved by about two orders of magnitude. The extreme values of the train response with different vehicle speed and wind velocity gradually obey right skewness distribution, especially the lateral acceleration.

Robust estimation and moment selection in dynamic fixed-effects panel data models

Considering linear dynamic panel data models with fixed effects, existing outlier–robust estimators based on the median ratio of two consecutive pairs of first-differenced data are extended to higher-order differencing. The estimation procedure is thus based on many pairwise differences and their ratios and is designed to combine high precision and good robust properties. In particular, the proposed two-step GMM estimator based on the corresponding moment equations relies on an innovative weighting scheme reflecting both the variance and bias of those moment equations, where the bias is assumed to stem from data contamination. To estimate the bias, the influence function is derived and evaluated. The robust properties of the estimator are characterized both under contamination by independent additive outliers and the patches of additive outliers. The proposed estimator is additionally compared with existing methods by means of Monte Carlo simulations.

MODELING MULTIPHASE FLOWS SUBJECTED TO CENTRIFUGAL ACCELERATION WITH A MIXTURE-AVERAGED DRIFT-FLUX ALGORITHM

ABSTRACT A mixture-averaged multiphase flow model has been developed to predict local variations in individual phase concentrations arising from centrifugal accelerations in the fluid. This centrifugal acceleration can be caused by swirl or by flow streamline curvature. The model has been developed for turbulent, compressible, nonisothermal flows. Higher-order differencing was used to discretize the transport equations; however, the effect of differencing the particle acceleration model on model performance is shown. For a sample case, comparisons are made with results using a Eulerian/Eulerian two-phase model. Discrete phase mass fraction concentration profiles compare favorably between the modified, mixture-averaged model and a two-phase model.

Determining the Order of Differencing in Autoregressive Processes

One way of handling nonstationarity in time series is to compute first differences and fit a model to the differenced series unless the differenced series also looks nonstationary. In that case, second- or higher-order differencing is done. To decide if the current degree of differencing is sufficient, one can look at the autocorrelation function for slow decay. A formal statistical test for the need to difference further is available if one is willing to assume that at most one more difference will render the series stationary. In this article, we present a proper sequence of statistical tests that allows the practitioner to handle cases in which a high order of differencing may be needed. The proper sequence is not the traditional sequence, which begins with a test for a single unit root.

An elementary estimator of the partial linear model

Given y= z β+ f( x)+ ε where dim( x)≤3, we propose an elementary and asymptotically efficient estimator of β. Data are reordered so that the x's are “close”, then higher order differencing is applied to remove f( x). A simple specification test of f is included.

A convection scheme sensitized to the convection direction of a scalar quantity

It is generally believed that higher order differencing schemes for the convection transport term, e.g., the QUICK scheme and its variants, are superior to the first order simple upwind differencing scheme in the sense that the former produces less numerical diffusion than the latter. In this paper it is shown that this conclusion is no more correct when the flow changes its direction quite rapidly and the grid density is not sufficient. In this situation the simple upwind differencing returns much steeper change of convective variables than higher order schemes. The failure of usual higher order schemes for this flow condition is attributed to the ignorance of convection direction of variables, and a new convection scheme sensitized to the direction of convective transport of a scalar quantity is devised and applied to typical benchmark flows. Results show that the proposed scheme is sufficiently accurate for computation of scalar fields, and also show the optimum behavior for tested problems.

High-Order Numerics in an Unstaggered Three-Dimensional Time-Split Semi-Lagrangian Forecast Model

Abstract Traditional finite-difference numerical forecast models usually employ relatively low-order approximations on grids staggered in both the horizontal and the vertical. In a previous study, Purser and Leslie (1988) demonstrated that high-order differencing on an unstaggered horizontal grid led to improved forecast accuracy. The present investigation has two aims. The first aim simply is to extend the earlier work to a three-dimensional formulation, by using high-order horizontal numerics in a time-split, three-dimensional, semi-Lagrangian model on a grid that is unstaggered in both the horizontal and vertical. The choice of an unstaggered grid is very effective in a semi-Lagrangian model as it ensures that a single set of interpolations suffices for all variables at each advection step. The second aim specifically is to increase the accuracy of the vertical discretization of key quantities such as the vertically integrated divergence, and the computation of the geopotential from the hydrostatic equ...