TY - JOUR

T1 - Development of fuzzy probability based random fields for the numerical structural design

AU - Schietzold, Friedemann N.

AU - Schmidt, Albrecht

AU - Dannert, Mona M.

AU - Fau, Amelie

AU - Fleury, Rodolfo M.N.

AU - Graf, Wolfgang

AU - Kaliske, Michael

AU - Könke, Carsten

AU - Lahmer, Tom

AU - Nackenhorst, Udo

N1 - Funding information: This research was supported by the Deutsche Forschungsgemeinschaft, KA 1163/36-1, GR 1504/10-1, LA 2869/6-1, KO 1267/22-1, NA 330/12-1. The demonstrated results and research activities arise from a cooperation of the three projects “Multi-objective optimization of wooden structures with polymorphic uncertain parameters” (GR 1504/10-1 and KA 1163/36-1), “Polymorphic uncertainty modeling of heterogeneous thermo-hydro-mechanical coupled systems under vague assumptions of parameter correlations” (LA 2869/6-1 and KO 1267/22-1), and “Sophisticated computational techniques for damage mechanics with mixed uncertain input fields” (NA 330/12-1). They are part of Priority Programme SPP 1886. The funding by the German Research Foundation (DFG) is gratefully acknowledged.

PY - 2019/3/21

Y1 - 2019/3/21

N2 - In structural analysis with multivariate random fields, the underlying distribution functions, the autocorrelations, and the crosscorrelations require an extensive quantification. While those parameters are difficult to measure in experiments, a lack of knowledge is included. Therefore, polymorphic uncertainty models are attained by involving uncertainty models with epistemic characteristic for the quantification of the stochastic models in this contribution. Three extensions for random fields with polymorphic uncertainty modeling are introduced. Interval probability based random fields, fuzzy probability based random fields, and structural dependent autocorrelations for random fields are shown. Applications for engineering problems are shown for each extension, where uncertainty analysis of structures with different materials is performed. In this contribution, a damage simulation of a concrete beam with interval valued parametrization of stochastic models, an application for porous media in a multiphysical structural analysis with fuzzy valued parametrization and an uncertainty analysis with structural dependent autocorrelations for timber structures are presented.

AB - In structural analysis with multivariate random fields, the underlying distribution functions, the autocorrelations, and the crosscorrelations require an extensive quantification. While those parameters are difficult to measure in experiments, a lack of knowledge is included. Therefore, polymorphic uncertainty models are attained by involving uncertainty models with epistemic characteristic for the quantification of the stochastic models in this contribution. Three extensions for random fields with polymorphic uncertainty modeling are introduced. Interval probability based random fields, fuzzy probability based random fields, and structural dependent autocorrelations for random fields are shown. Applications for engineering problems are shown for each extension, where uncertainty analysis of structures with different materials is performed. In this contribution, a damage simulation of a concrete beam with interval valued parametrization of stochastic models, an application for porous media in a multiphysical structural analysis with fuzzy valued parametrization and an uncertainty analysis with structural dependent autocorrelations for timber structures are presented.

KW - fuzzy probability based randomness

KW - interval probability based randomness

KW - multivariate random fields

KW - polymorphic uncertainty

KW - structural depending correlation

UR - http://www.scopus.com/inward/record.url?scp=85063326245&partnerID=8YFLogxK

U2 - 10.1002/gamm.201900004

DO - 10.1002/gamm.201900004

M3 - Article

AN - SCOPUS:85063326245

VL - 42

JO - GAMM Mitteilungen

JF - GAMM Mitteilungen

SN - 0936-7195

IS - 1

M1 - e201900004

ER -