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Reliability Assessment and Probabilistic Optimization in Structural Design
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).ORCID iD: 0000-0001-6375-6292
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Research in the field of reliability based design is mainly focused on two sub-areas: The computation of the probability of failure and its integration in the reliability based design optimization (RBDO) loop. Four papers are presented in this work, representing a contribution to both sub-areas. In the first paper, a new Second Order Reliability Method (SORM) is presented. As opposed to the most commonly used SORMs, the presented approach is not limited to hyper-parabolic approximation of the performance function at the Most Probable Point (MPP) of failure. Instead, a full quadratic fit is used leading to a better approximation of the real performance function and therefore more accurate values of the probability of failure. The second paper focuses on the integration of the expression for the probability of failure for general quadratic function, presented in the first paper, in RBDO. One important feature of the proposed approach is that it does not involve locating the MPP. In the third paper, the expressions for the probability of failure based on general quadratic limit-state functions presented in the first paper are applied for the special case of a hyper-parabola. The expression is reformulated and simplified so that the probability of failure is only a function of three statistical measures: the Cornell reliability index, the skewness and the kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the MPP. In the last paper, an approximate and efficient reliability method is proposed. Focus is on computational efficiency as well as intuitiveness for practicing engineers, especially regarding probabilistic fatigue problems where volume methods are used. The number of function evaluations to compute the probability of failure of the design under different types of uncertainties is a priori known to be 3n+2 in the proposed method, where n is the number of stochastic design variables.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. , x, 23 p.
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 0594
Keyword [en]
Reliability-based design optimization (RBDO), First- and Second-Order Reliability Method (FORM and SORM), Response Surface Single Loop (RSSL), Probability of failure, Reliability Assessment, Probability of fatigue failure
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-183572ISBN: 978-91-7595-908-5 (print)OAI: oai:DiVA.org:kth-183572DiVA: diva2:912612
Public defence
2016-04-06, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20160317

Available from: 2016-03-17 Created: 2016-03-17 Last updated: 2016-03-29Bibliographically approved
List of papers
1. A Closed-Form Second-Order Reliability Method Using Noncentral Chi-Squared Distributions
Open this publication in new window or tab >>A Closed-Form Second-Order Reliability Method Using Noncentral Chi-Squared Distributions
2014 (English)In: Journal of mechanical design (1990), ISSN 1050-0472, E-ISSN 1528-9001, Vol. 136, no 10, 101402- p.Article in journal (Refereed) Published
Abstract [en]

In the second-order reliability method (SORM), the probability of failure is computed for an arbitrary performance function in arbitrarily distributed random variables. This probability is approximated by the probability of failure computed using a general quadratic fit made at the most probable point (MPP). However, an easy-to-use, accurate, and efficient closed-form expression for the probability content of the general quadratic surface in normalized standard variables has not yet been presented. Instead, the most commonly used SORM approaches start with a relatively complicated rotational transformation. Thereafter, the last row and column of the rotationally transformed Hessian are neglected in the computation of the probability. This is equivalent to approximating the probability content of the general quadratic surface by the probability content of a hyperparabola in a rotationally transformed space. The error made by this approximation may introduce unknown inaccuracies. Furthermore, the most commonly used closed-form expressions have one or more of the following drawbacks: They neither do work well for small curvatures at the MPP and/or large number of random variables nor do they work well for negative or strongly uneven curvatures at the MPP. The expressions may even present singularities. The purpose of this work is to present a simple, efficient, and accurate closed-form expression for the probability of failure, which does not neglect any component of the Hessian and does not necessitate the rotational transformation performed in the most common SORM approaches. Furthermore, when applied to industrial examples where quadratic response surfaces of the real performance functions are used, the proposed formulas can be applied directly to compute the probability of failure without locating the MPP, as opposed to the other first-order reliability method (FORM) and the other SORM approaches. The method is based on an asymptotic expansion of the sum of noncentral chi-squared variables taken from the literature. The two most widely used SORM approaches, an empirical SORM formula as well as FORM, are compared to the proposed method with regards to accuracy and computational efficiency. All methods have also been compared when applied to a wide range of hyperparabolic limit-state functions as well as to general quadratic limit-state functions in the rotationally transformed space, in order to quantify the error made by the approximation of the Hessian indicated above. In general, the presented method was the most accurate for almost all studied curvatures and number of random variables.

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-153249 (URN)10.1115/1.4027982 (DOI)000341298800005 ()2-s2.0-84905492687 (Scopus ID)
Note

QC 20141009

Available from: 2014-10-09 Created: 2014-10-03 Last updated: 2017-12-05Bibliographically approved
2. Response surface single loop reliability-based design optimization with higher order reliability assessment
Open this publication in new window or tab >>Response surface single loop reliability-based design optimization with higher order reliability assessment
(English)Manuscript (preprint) (Other academic)
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-183562 (URN)
Note

QS 2016

Available from: 2016-03-17 Created: 2016-03-17 Last updated: 2016-03-17Bibliographically approved
3. A novel closed-form Second-Order Reliability Method with probabilistic sensitivity analysis and application in Reliability-based Design Optimization
Open this publication in new window or tab >>A novel closed-form Second-Order Reliability Method with probabilistic sensitivity analysis and application in Reliability-based Design Optimization
2016 (Swedish)Report (Other academic)
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 592
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-183565 (URN)
Note

QC 20160317

Available from: 2016-03-17 Created: 2016-03-17 Last updated: 2016-03-17Bibliographically approved
4. An efficient reliability method applied to classical load-strength uncertainties, aleatory fatigue problems and epistemic uncertainties
Open this publication in new window or tab >>An efficient reliability method applied to classical load-strength uncertainties, aleatory fatigue problems and epistemic uncertainties
2016 (English)Report (Other academic)
Series
TRITA-HFL. Report / Royal Institute of Technology, Solid Mechanics, ISSN 1654-1472 ; 593
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-183566 (URN)
Note

QC 20160317

Available from: 2016-03-17 Created: 2016-03-17 Last updated: 2016-03-17Bibliographically approved

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