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# Miscellaneous

This page provides miscellaneous papers on optimization, stochastic analysis and related topics
• Detection of branching points in noisy processes

Michael Beer, Martin Liebscher

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 evalu- ated at a series of discrete values of the independent process coordinates. At each discrete point of the process, the associ- ated 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 bet- ter 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 exam- ple of a crashworthiness investigation.

• Efficiency Improvement of Stochastic Simulations by Means of Subset Sampling

M. Liebscher, S. Pannier, W. Graf (TU Dresden)

The design of engineering systems requires a sophisticated structural analysis close to reality. The uncertainty of structural parameters, such as loads, material parameters, and geometrical properties must be taken into account. Based on the framework of probabilistics a structural behavior may be assessed by a failure probability. The failure probability can be computed with the aid of Monte Carlo simulation. Especially in the case of complex nonlinear structures the Monte Carlo simulation meets their limits. The more advanced simulation method subset sampling, which promises to compensate this drawback, is investigated in this paper. The main idea of subset sampling is the subdivision of the failure event into a sequence of partial failure events, which are denoted as subsets. The numerical efﬁcient sampling within the subset is realized with aid of the Markov chain Monte Carlo simulation. Subset sampling is demonstrated by means of examples. Keywords: subset sampling, Monte Carlo simulation, reliability analysis