Analysis of the Nonstationary Response of Vehicles With Multiple Wheels

1986 ◽  
Vol 108 (1) ◽  
pp. 69-73 ◽  
Author(s):  
R. F. Harrison ◽  
J. K. Hammond
Keyword(s):  
Random Processes ◽  
Time Variable ◽  
Variable Delay ◽  
Excitation Process ◽  
Nonstationary Random Process ◽  
Nonstationary Response ◽  
The Mean ◽  
Autocovariance Matrix ◽  
Ground Profile ◽  
Mean Vector

Vehicles moving on rough surfaces are subject to inputs which are often conveniently regarded as random processes. In general, the excitation process is “perceived” by the vehicle as a nonstationary random process either due to inhomogeneity in the ground profile or variations in the vehicle’s velocity, or both, Hitherto this second case has not been tractable analytically due to the time variable delay between inputs. In this paper this difficulty is overcome and expressions are derived for the propagation of the mean vector and zero-lag autocovariance matrix. An example of a vehicle modelled by a bicycle configuration is discussed.

The Analysis of Dynamic Stresses in Aircraft Structures During Landing as Nonstationary Random Processes

1955 ◽  
Vol 22 (4) ◽  
pp. 449-457
Author(s):  
Y. C. Fung
Keyword(s):  
Maximum Stress ◽  
Impact Load ◽  
Bending Moment ◽  
Random Processes ◽  
Dynamic Loads ◽  
Dynamic Stresses ◽  
Nonstationary Random Process ◽  
Time Histories ◽  
Drop Tests ◽  
The Mean

Abstract The basic fact is recognized that throughout the service life of an airplane there occurs a variety of landing conditions and, consequently, it is subjected to transient dynamic loads of varied time histories. Accordingly, a statistical analysis is proposed. The landing-gear impact load is regarded as a nonstationary random process. In this paper the ensemble means and the correlation functions of landing impacts are defined and their experimental determination from flight or drop tests is illustrated. From these the mean response (displacement, bending moment, shear, or stress), the root mean square deviation from the mean, and higher statistical moments are computed. The results are used to find the most probable maximum stress (at any point in the structure) attained in a given number of landings, or the most probable total number of landings a given aircraft can withstand. A stress envelope can be derived which represents the distribution of the severest stress in the structure for a large number of landings. A design based on such an envelope, statistically, will have a uniform factor of safety over the entire aircraft with respect to landings.

Characterization and Simulation of Gunfire with Karhunen-Loeve Expansion

2004 ◽  
Vol 47 (1) ◽  
pp. 47-50
Author(s):  
David Smallwood
Keyword(s):  
Random Process ◽  
Time History ◽  
Nonstationary Random Process ◽  
Random Events ◽  
The Matrix ◽  
History Of ◽  
The Mean ◽  
Autocovariance Matrix ◽  
The Individual

Gunfire is used as an example to illustrate how the Karhunen-Loeve (K-L) expansion can be used to characterize and simulate nonstationary random events. This paper will develop a method to describe the nonstationary random process in terms of a K-L expansion. The gunfire record is broken up into a sequence of transient waveforms, each representing the response to the firing of a single round. First, the mean is estimated and subtracted from each waveform. The mean is an estimate of the deterministic part of the gunfire. The autocovariance matrix is estimated from the matrix of these single-round gunfire records. Each column is a realization of the firing of a single round. The gunfire is characterized with the K-L expansion of the autocovariance matrix. The gunfire is simulated by generating realizations of records of a single-round firing from the expansion and the mean waveform. The individual realizations are then assembled into a realization of a time history of many rounds firing. The method is straightforward and easy to implement, and produces a simulated record very much like the original measured gunfire record.

Tests for the mean vector under intraclass covariance structure

1981 ◽  
Vol 12 (3-4) ◽  
pp. 237-245 ◽  
Author(s):  
Bernard Clement ◽  
Sukharanyan Chakraborty ◽  
Bimal K. Sinha ◽  
Narayan C. Giri
Keyword(s):  
Covariance Structure ◽  
The Mean ◽  
Mean Vector

The solution of theoretical seismic problems by best rational function approximations for Laplace transform inversion

1975 ◽  
Vol 65 (4) ◽  
pp. 927-935
Author(s):  
I. M. Longman ◽  
T. Beer
Keyword(s):  
Laplace Transform ◽  
Rational Function ◽  
High Accuracy ◽  
Time Variable ◽  
Inversion Method ◽  
The Laplace Transform ◽  
Previously Treated ◽  
The Mean ◽  
Function Approximations ◽  
Laplace Transform Inversion

Abstract In a recent paper, the first author has developed a method of computation of “best” rational function approximations ḡn(p) to a given function f̄(p) of the Laplace transform operator p. These approximations are best in the sense that analytic inversion of ḡn(p) gives a function gn(t) of the time variable t, which approximates the (generally unknown) inverse f(t) of f̄(p in a minimum least-squares manner. Only f̄(p) but not f(t) is required to be known in order to carry out this process. n is the “order” of the approximation, and it can be shown that as n tends to infinity gn(t) tends to f(t) in the mean. Under suitable conditions on f(t) the convergence is extremely rapid, and quite low values of n (four or five, say) are sufficient to give high accuracy for all t ≧ 0. For seismological applications, we use geometrical optics to subtract out of f(t) its discontinuities, and bring it to a form in which the above inversion method is very rapidly convergent. This modification is of course carried out (suitably transformed) on f̄(p), and the discontinuities are restored to f(t) after the inversion. An application is given to an example previously treated by the first author by a different method, and it is a certain vindication of the present method that an error in the previously given solution is brought to light. The paper also presents a new analytical method for handling the Bessel function integrals that occur in theoretical seismic problems related to layered media.

scholarly journals BAYESIAN INFERENCE FOR THE TANGENT PORTFOLIO

2018 ◽  
Vol 21 (08) ◽  
pp. 1850054 ◽  
Author(s):  
DAVID BAUDER ◽  
TARAS BODNAR ◽  
STEPAN MAZUR ◽  
YAREMA OKHRIN
Keyword(s):  
Bayesian Inference ◽  
Point Of View ◽  
Posterior Distributions ◽  
Conditional Distributions ◽  
Linear Combinations ◽  
Conjugate Priors ◽  
Mean And Variance ◽  
The Mean ◽  
Stochastic Representations ◽  
Mean Vector

In this paper, we consider the estimation of the weights of tangent portfolios from the Bayesian point of view assuming normal conditional distributions of the logarithmic returns. For diffuse and conjugate priors for the mean vector and the covariance matrix, we derive stochastic representations for the posterior distributions of the weights of tangent portfolio and their linear combinations. Separately, we provide the mean and variance of the posterior distributions, which are of key importance for portfolio selection. The analytic results are evaluated within a simulation study, where the precision of coverage intervals is assessed.

scholarly journals ‘Hardcastle Hollows’ in loess landforms: Closed depressions in aeolian landscapes – in a geoheritage context

2018 ◽  
Vol 10 (1) ◽  
pp. 58-63
Author(s):  
Roger Fagg ◽  
Ian Smalley
Keyword(s):  
Monte Carlo ◽  
Random Processes ◽  
Ground Subsidence ◽  
Shape Classification ◽  
Random Shape ◽  
Side Ratio ◽  
Landscape Processes ◽  
Stage Process ◽  
The Mean ◽  
Loess Deposits

Abstract Loess landscapes sometimes contain isolated depressed areas, which often appear as lakes. The outline shape (and distribution) of these depressions could be controlled by random processes, particularly if the depressions are caused by loess hydroconsolidation and ground subsidence. By applying the Zingg system of shape classification it is possible to propose a mean random shape for the closed depressions. A Zingg rectangle with a side ratio of about 2:1 is produced by a very simple Monte Carlo method, which had been used previously to calculate the mean random shape of a loess particle. The Zingg rectangle indicates the basic shape of the mean closed depression. A simple four stage process for the formation of the depressions is proposed. They might be called ‘Hardcastle Hollows’ in honour of John Hardcastle who first reported them, in New Zealand. Studies on Ukrainian deposits suggest that there might be some stratigraphic value in the observation of closed depressions; they are often not superimposed in successive depositions of loess. Hydroconsolidation is important in landscape processes. The hollows provide interesting habitats and enlarge the ecological interest of loess deposits; the geoheritage scene is enhanced.

Structured Antedependence Models for Functional Mapping of Multiple Longitudinal Traits

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Wei Zhao ◽  
Wei Hou ◽  
Ramon C. Littell ◽  
Rongling Wu
Keyword(s):  
Genetic Correlations ◽  
Covariance Matrices ◽  
Growth Trajectories ◽  
Relative Importance ◽  
Hybrid Progeny ◽  
Linkage Groups ◽  
Stem Height ◽  
Pleiotropic Qtl ◽  
The Mean ◽  
Mean Vector

In this article, we present a statistical model for mapping quantitative trait loci (QTL) that determine growth trajectories of two correlated traits during ontogenetic development. This model is derived within the maximum likelihood context, incorporated by mathematical aspects of growth processes to model the mean vector and by structured antedependence (SAD) models to approximate time-dependent covariance matrices for longitudinal traits. It provides a quantitative framework for testing the relative importance of two mechanisms, pleiotropy and linkage, in contributing to genetic correlations during ontogeny. This model has been employed to map QTL affecting stem height and diameter growth trajectories in an interspecific hybrid progeny of Populus, leading to the successful discovery of three pleiotropic QTL on different linkage groups. The implications of this model for genetic mapping within a broader context are discussed.

Sign in / Sign up

Export Citation Format

Share Document