Premium
Autoregressive model for a finite random sequence on the unit circle for investigating the fluctuations of residual stresses in the rims of new railroad wheels
Author(s) -
Koshulyan Alexey V.,
Malajchuk Valentin P.
Publication year - 2014
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2022
Subject(s) - autoregressive model , independent and identically distributed random variables , unit circle , sequence (biology) , mathematics , estimator , residual , transformation (genetics) , random variable , least squares function approximation , statistics , mathematical analysis , algorithm , biochemistry , chemistry , biology , gene , genetics
This paper presents an autoregressive model for a finite sequence of random variables that are observed at points equally spaced on the unit circle. The proposed model is an extension of the well‐known autoregressive model of time series. We demonstrate that this model amounts to a linear transformation of a vector of independent and identically distributed random variables. The second‐order properties of the multivariate distribution were examined. The least squares estimators of the model parameters were obtained. The connection between the proposed first‐order model and a second‐order, stationary, mean‐square‐continuous, real‐valued random process on the unit circle was considered. We used the model presented to describe the fluctuations of hoop residual stresses in the rims of new railroad wheels. The stress measurement was performed using an ultrasonic method. The stress fluctuation model allowed us to determine the number of measurement points required to assess residual stress levels in the wheels. Copyright © 2014 John Wiley & Sons, Ltd.