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Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema

  • One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of 10−4 to 10−6. Generally, it is not possible to compute the failure probability analytically. Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a fullOne of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of 10−4 to 10−6. Generally, it is not possible to compute the failure probability analytically. Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a full FE simulation. Additionally, an adaptive importance sampling scheme is used to minimize the total number of required samples. The accuracy of the failure probability depends on the accuracy of the PGD model (mainly influenced on mesh discretization and mode truncation) as well as the number of samples in the sampling algorithm. Therefore, a general iterative PGD reliability procedure is developed to automatically verify the accuracy of the computed failure probability. It is based on a goal-oriented refinement of the PGD model around the adaptively approximated design point. The methodology is applied and evaluated for 1D and 2D examples. The computational savings compared to the method based on a FE model is shown and the influence of the accuracy of the PGD model on the failure probability is studied.zeige mehrzeige weniger

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Metadaten
Autor*innen:Annika Robens-Radermacher, Jörg F. UngerORCiD
Dokumenttyp:Zeitschriftenartikel
Veröffentlichungsform:Verlagsliteratur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Advanced Modeling and Simulation in Engineering Sciences
Jahr der Erstveröffentlichung:2020
Organisationseinheit der BAM:7 Bauwerkssicherheit
7 Bauwerkssicherheit / 7.7 Modellierung und Simulation
Veröffentlichende Institution:Bundesanstalt für Materialforschung und -prüfung (BAM)
Verlag:SpringerOpen
Jahrgang/Band:7
Erste Seite:Article number: 29
DDC-Klassifikation:Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurbau
Freie Schlagwörter:Adaptive importance sampling; Probability of failure; Proper Generalized Decomposition; Reduced order models; Reliability
Themenfelder/Aktivitätsfelder der BAM:Infrastruktur
DOI:10.1186/s40323-020-00168-z
URN:urn:nbn:de:kobv:b43-510345
Verfügbarkeit des Dokuments:Datei für die Öffentlichkeit verfügbar ("Open Access")
Lizenz (Deutsch):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
Datum der Freischaltung:22.07.2020
Referierte Publikation:Nein
Schriftenreihen ohne Nummerierung:Wissenschaftliche Artikel der BAM
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