# SimuTools - Split and merge strategies for solving uncertain equations using affine arithmetic

 dc.identifier.uri http://dx.doi.org/10.15488/5036 dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/5080 dc.contributor.author Scharf, Oliver dc.contributor.author Olbrich, Markus dc.contributor.author Barke, Erich dc.date.accessioned 2019-06-26T12:57:11Z dc.date.available 2019-06-26T12:57:11Z dc.date.issued 2015 dc.identifier.citation Scharf, Oliver; Olbrich, Markus; Barke, Erich: SimuTools - Split and merge strategies for solving uncertain equations using affine arithmetic. In: inis 16 (9), e1. DOI: https://doi.org/10.4108/eai.24-8-2015.2260594 dc.description.abstract The behaviour of systems is determined by various parameters. Due to several reasons like e. g. manufacturing tolerances these parameters can have some uncertainties. Corner Case and Monte Carlo simulations are well known approaches to handle uncertain systems. They sample the corners and random points of the parameter space, respectively. Both require many runs and do not guarantee the inclusion of the worst case. As alternatives, range based approaches can be used. They model parameter uncertainties as ranges. The simulation outputs are ranges which include all possible results created by the parameter uncertainties. One type of range arithmetic is the affine arithmetic, which allows to maintain linear correlations to avoid over-approximation. An equation solver based on affine arithmetic has been proposed earlier. Unlike many other range based approaches it can solve implicit non-linear equations. This is necessary for analog circuit simulation. For large uncertainties the solver suffers from convergence problems. To overcome these problems it is possible to split the parameter ranges, calculate the solutions separately and merge them again. For higher dimensional systems this leads to excessive runtimes as each parameter is split. To minimize the additional runtime several split and merge strategies are proposed and compared using two analog circuit examples. eng dc.language.iso eng dc.publisher New York, NY : A C M Special Interest Group dc.relation.ispartof Eighth EAI International Conference on Simulation Tools and Techniques 2015 dc.relation.ispartofseries inis 16 (9) dc.rights CC BY 3.0 Unported dc.rights.uri https://creativecommons.org/licenses/by/3.0/ dc.subject Parametric statistics eng dc.subject Mathematical optimization eng dc.subject Nonlinear system eng dc.subject Affine arithmetic eng dc.subject Monte Carlo method eng dc.subject Corner case eng dc.subject Solver eng dc.subject Computer science eng dc.subject Convergence (routing) eng dc.subject Parameter space eng dc.subject.ddc 600 | Technik ger dc.title SimuTools - Split and merge strategies for solving uncertain equations using affine arithmetic eng dc.type article dc.type Text dc.relation.doi https://doi.org/10.4108/eai.24-8-2015.2260594 dc.bibliographicCitation.volume 2015 dc.bibliographicCitation.firstPage 1 dc.bibliographicCitation.lastPage 8 dc.description.version publishedVersion tib.accessRights frei zug�nglich
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