A sampling-based approach for probabilistic design with random fields

Anirban Basudhar, Samy Missoum

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

In this paper, a technique to efficiently include random fields in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit decision function in terms of the coefficients of the POD expansion, separating failure and safe regions, is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated decision function. The coefficients of the orthogonal decomposition are considered as random variables with distributions that are found from the snapshots. This allows an efficient calculation of probabilities of failure based on the explicit decision function. The methodology is demonstrated for the estimation of the probability of failure for two problems. The first example involves the linear buckling of an arch structure, for which the thickness is a random field. The second problem deals with a random field which modifies the planarity of the walls of a tube impacting a rigid wall.

Original languageEnglish (US)
Title of host publicationCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
StatePublished - 2008
Event49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference - Schaumburg, IL, United States
Duration: Apr 7 2008Apr 10 2008

Other

Other49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
CountryUnited States
CitySchaumburg, IL
Period4/7/084/10/08

Fingerprint

Sampling
Decomposition
Arches
Random variables
Buckling
Support vector machines

ASJC Scopus subject areas

  • Architecture

Cite this

Basudhar, A., & Missoum, S. (2008). A sampling-based approach for probabilistic design with random fields. In Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

A sampling-based approach for probabilistic design with random fields. / Basudhar, Anirban; Missoum, Samy.

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 2008.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Basudhar, A & Missoum, S 2008, A sampling-based approach for probabilistic design with random fields. in Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg, IL, United States, 4/7/08.
Basudhar A, Missoum S. A sampling-based approach for probabilistic design with random fields. In Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 2008
Basudhar, Anirban ; Missoum, Samy. / A sampling-based approach for probabilistic design with random fields. Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. 2008.
@inproceedings{851860ace306448e8e3daba299089d66,
title = "A sampling-based approach for probabilistic design with random fields",
abstract = "In this paper, a technique to efficiently include random fields in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit decision function in terms of the coefficients of the POD expansion, separating failure and safe regions, is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated decision function. The coefficients of the orthogonal decomposition are considered as random variables with distributions that are found from the snapshots. This allows an efficient calculation of probabilities of failure based on the explicit decision function. The methodology is demonstrated for the estimation of the probability of failure for two problems. The first example involves the linear buckling of an arch structure, for which the thickness is a random field. The second problem deals with a random field which modifies the planarity of the walls of a tube impacting a rigid wall.",
author = "Anirban Basudhar and Samy Missoum",
year = "2008",
language = "English (US)",
booktitle = "Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference",

}

TY - GEN

T1 - A sampling-based approach for probabilistic design with random fields

AU - Basudhar, Anirban

AU - Missoum, Samy

PY - 2008

Y1 - 2008

N2 - In this paper, a technique to efficiently include random fields in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit decision function in terms of the coefficients of the POD expansion, separating failure and safe regions, is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated decision function. The coefficients of the orthogonal decomposition are considered as random variables with distributions that are found from the snapshots. This allows an efficient calculation of probabilities of failure based on the explicit decision function. The methodology is demonstrated for the estimation of the probability of failure for two problems. The first example involves the linear buckling of an arch structure, for which the thickness is a random field. The second problem deals with a random field which modifies the planarity of the walls of a tube impacting a rigid wall.

AB - In this paper, a technique to efficiently include random fields in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit decision function in terms of the coefficients of the POD expansion, separating failure and safe regions, is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated decision function. The coefficients of the orthogonal decomposition are considered as random variables with distributions that are found from the snapshots. This allows an efficient calculation of probabilities of failure based on the explicit decision function. The methodology is demonstrated for the estimation of the probability of failure for two problems. The first example involves the linear buckling of an arch structure, for which the thickness is a random field. The second problem deals with a random field which modifies the planarity of the walls of a tube impacting a rigid wall.

UR - http://www.scopus.com/inward/record.url?scp=77957818036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957818036&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:77957818036

BT - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

ER -