Stochastic analysis of surface roughness

Abstract

For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method was applied to different road surface profiles which were measured with high resolution. Evidence of Markov properties is shown. Estimations for the parameters of the Fokker-Planck equation are based on pure, parameter free data analysis.

Deterministic and stochastic features of rhythmic human movement

“…Since its introduction , the extraction procedure has found application in physics (e.g., Waechter et al 2003), engineering (Gradisek et al 2000(Gradisek et al , 2002b, economics , sociology (Kriso et al 2002) and meteorology (Sura 2003). The method has been successfully tested by analyzing simulated data from known dynamical systems such as nonlinear oscillators and chaotic systems (see, e.g., Gradisek et al 2000;2002a, 2002bSiegert et al 1998).…”

Multiscale reconstruction of time series

“…Successful attempts have been made to describe these systems as processes in scale rather than time or space itself. Examples are the description of roughness of surfaces [1,2], turbulence [3,4,5], earthquakes [6] and finance [7,8]. These successful attempts are characterised by the fact, that they can correctly provide the joint probability density function p(y 1 (τ 1 ), ..., y n (τ n )) of the increments y(τ ) of the process variable x at different scales τ , y(t, τ ) := x(t) − x(t − τ ).…”

Stochastic analysis of different rough surfaces

“…It is possible that the range of ∆r < l M where no Markov properties are given is in most cases large enough that approximations for small ∆r are inaccurate. We would like to note that there are also data sets which did not require any adjustment of the estimated coefficients, see Road 2 and [12]. A last remark concerns the latest results in the case of Road 1, see fig.…”

“…In this paper we want to give a deeper introduction into a new approach to surface roughness analysis which has recently been introduced by us [11,12] and by [13]. This method is based on stochastic processes which should grasp the scale dependency of surface roughness in a most general way.…”

“…Among these examples is a collection of road surfaces measured with a specially designed profile scanner. Preliminary results of the analysis of one of these surfaces have already been presented [12]. AFM measurement data from an evaporated gold film have already been analysed in an earlier stage of the method [11].…”