Detection of branching points in noisy processes

Abstract

Processes in engineering mechanics often contain branching points at which the system can follow different physical paths. In this paper a method for the detection of these branching points is proposed for processes that are affected by noise. It is assumed that a bundle of process records are available from numerical simulations or from experiments, and branching points are concealed by the noise of the process. The bundle of process records is then evaluated at a series of discrete values of the independent process coordinates. At each discrete point of the process, the associated point set of process values is investigated with the aid of cluster analysis. The detected branching points are verified with a recursive algorithm. The revealed information about the branching points can be used to identify the physical and mechanical background for the branching. This helps to better understand a mechanical system and to design it optimal for a specific purpose. The proposed method is demonstrated by means of both a numerical example and a practical example of a crashworthiness investigation.

Title pages

“…Selected developments are discussed with focus on the added value for engineering analyses and are demonstrated on industrial examples. These developments include processing of vague information as fuzzy sets with evolutionary concepts [1,2] and their use in design [3], efficient stochastic analysis with meta models [4,5] and process simulation [6,7] based on neural networks, robust design [3] and identification of critical mechanical behavior [8] with the aid of cluster analysis methods. The examples include dynamical analyses of civil engineering structures and of an aerospace structure, as well as nonlinear dynamical problems in crashworthiness analysis.…”