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Methods for reliability based design optimization of structural components
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Cost and quality are key properties of a product, possibly even the two most important. Onedefinition of quality is fitness for purpose. Load-bearing products, i.e. structural components,loose their fitness for purpose if they fail. Thus, the ability to withstand failure is a fundamentalmeasure of quality for structural components. Reliability based design optimization(RBDO) is an approach for development of structural components which aims to minimizethe cost while constraining the probability of failure. However, the computational effort ofan RBDO applied to large-scale engineering problems has prohibited it from employment inindustrial applications. This thesis presents methods for computationally efficient RBDO.A review of the work presented on RBDO algorithms reveals that three constituentsof an RBDO algorithm has rendered significant attention; i ) the solution strategy for andnumerical treatment of the probabilistic constraints, ii ) the surrogate model, and iii) theexperiment design. A surrogate model is ”a model of a model”, i.e. a computationally cheapapproximation of a physics-based but computationally expensive computer model. It is fittedto responses from the physics-motivated model obtained via a thought-through combinationof experiments called an experiment design.In Paper A, the general algorithm for RBDO employed in this work, including the sequentialapproximation procedure used to treat the probabilistic constraints, is laid out. A singleconstraint approximation point (CAP) is used to save computational effort with acceptablelosses in accuracy. The approach is used to optimize a truck component and incorporatesthe effect that production related design variables like machining and shot peening have onfatigue life.The focus in Paper B is on experiment design. An algorithm employed to construct anovel experiment design for problems with multiple constraints is presented. It is based onan initial screening and uses the specific problem structure to combine one-factor-at-a-timeexperiments to a several-factors-at-a-time experiment design which reduces computationaleffort.In Paper C, a surrogate model tailored for RBDO is introduced. It is motivated by appliedsolid mechanics considerations and the use of the first order reliability method to evaluate theprobabilistic constraint. An optimal CAP is furthermore deduced from the surrogate model.In Paper D, the paradigm to use sets of experiments rather than one experiment at atime is challenged. A new procedure called experiments on demand (EoD) is presented. TheEoD procedure utilizes the core of RBDO to quantify the demand for new experiments andaugments it by a D-optimality criterion for added robustness and numerical stability.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. , 86 p.
Series
Trita-HFL. Report / Royal Institute of Technology, Solid mechanics, ISSN 1654-1472 ; 0520
Keyword [en]
Reliability
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-90753OAI: oai:DiVA.org:kth-90753DiVA: diva2:506434
Public defence
2012-03-12, F3, Linstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20120229

Available from: 2012-02-29 Created: 2012-02-28 Last updated: 2013-01-14Bibliographically approved
List of papers
1. Reliability Based Design Optimization Using a Single Constraint Approximation Point
Open this publication in new window or tab >>Reliability Based Design Optimization Using a Single Constraint Approximation Point
2011 (English)In: Journal of mechanical design (1990), ISSN 1050-0472, E-ISSN 1528-9001, Vol. 133, no 3, 031006- p.Article in journal (Refereed) Published
Abstract [en]

The computational effort for reliability based design optimization (RBDO) is no longer prohibitive even for detailed studies of mechanical integrity. The sequential approximation RBDO formulation and the use of surrogate models have greatly reduced the amount of computations necessary. In RBDO, the surrogate models need to be most accurate in the proximity of the most probable point. Thus, for multiply constrained problems, such as fatigue design problems, where each finite element (FE)-model node constitutes a constraint, the computational effort may still be considerable if separate experiments are used to fit each constraint surrogate model. This paper presents an RBDO algorithm that uses a single constraint approximation point (CAP) as a starting point for the experiments utilized to establish all surrogate models, thus reducing the computational effort to that of a single constraint problem. Examples of different complexities from solid mechanics applications are used to present the accuracy and versatility of the proposed method. In the studied examples, the ratio of the computational effort (in terms of FE-solver calls) between a conventional method and the single CAP algorithm was approximately equal to the number of constraints and the introduced error was small. Furthermore, the CAP-based RBDO is shown to be capable of handling over 10,000 constraints and even an intermittent remeshing. Also, the benefit of considering other objectives than volume (mass) is shown through a cost optimization of a truck component. In the optimization, fatigue-specific procedures, such as shot peening and machining to reduce surface roughness, are included in the cost as well as in the constraints.

National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-32003 (URN)10.1115/1.4003410 (DOI)000288390200008 ()2-s2.0-79953059654 (Scopus ID)
Note
QC 20110407Available from: 2011-04-07 Created: 2011-04-04 Last updated: 2017-12-11Bibliographically approved
2. Efficient design of experiments for structural optimization using significance screening
Open this publication in new window or tab >>Efficient design of experiments for structural optimization using significance screening
2012 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 45, no 2, 185-196 p.Article in journal (Refereed) Published
Abstract [en]

When performing structural optimization of large scale engineering problems, the choice of experiment design is important. However, classical experiment designs are developed to deal with undesired but inevitable scatter and are thus not ideal for sampling of deterministic computational responses. In this paper, a novel screening and design of computer experiments algorithm is presented. It is based on the concept of orthogonal design variable significances and is applicable for problems where design variables do not simultaneously have a significant influence on any of the constraints. The algorithm presented uses significance orthogonality to combine several one-factor-at-a-time experiments in one several-factors-at-a-time experiment. The procedure results in a reduced experiment design matrix. In the reduced experiment design, each variable is varied exactly once but several variables may be varied simultaneously, if their significances with respect to the constraints are orthogonal. Moreover, a measure of influence, as well as an influence significance threshold, is defined. In applications, the value of the threshold is left up to the engineer. To assist in this choice, a relation between model simplification, expressed in terms of the significance threshold, and computational cost is established in a screening. The relation between efficiency and loss of accuracy for the proposed approach is discussed and demonstrated. For two solid mechanics type problems studied herein, the necessary number of simulations could be reduced by 25% and 64%, respectively, with negligible losses in accuracy.

Keyword
Screening, Design of experiments, Significance orthogonality, Multiple constraints
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-63229 (URN)10.1007/s00158-011-0677-0 (DOI)000298500500003 ()2-s2.0-84859590341 (Scopus ID)
Note
QC 20120127Available from: 2012-01-27 Created: 2012-01-23 Last updated: 2017-12-08Bibliographically approved
3. A directional surrogate model tailored for efficient reliability based design optimization
Open this publication in new window or tab >>A directional surrogate model tailored for efficient reliability based design optimization
2012 (English)Report (Other academic)
Abstract [en]

Reliability based design optimization (RBDO) aims at minimizing an objective while constraining the failure probability of structural components. Due to the iterative nature of both the minimization and the failure probability validation, there is considerable computational effort associated with it. In this paper, a computationally inexpensive approach for RBDO is presented. The key contribution is the directional surrogate model and its associated advantages; a sound balance between accuracy and computational cost, including the possibility to fit model coefficients based on an optimal experiment design, high fidelity modeling of representative structural responses, treatment of multiple constraints without added computational cost, and straightforward sequential linear programming implementation. The directional surrogate model is of power type with nonlinear behaviour only in the gradient direction, thus balancing accuracy and computational cost. Moreover, information from prior iterations are used in every iteration in a weighted least squares optimization. When benchmarked against existing approaches from the literature using a well known reference problem, it is shown to be highly efficient. It also shows promising stability and convergence rate for additional challenging problems to which it has been applied.

Publisher
15 p.
Series
Trita-HFL, ISSN 1104-6813 ; 518
Keyword
FORM, Surrogate Model, Design of Experiments, Multiple Constraints
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-90799 (URN)
Note
QC 20120229Available from: 2012-02-29 Created: 2012-02-29 Last updated: 2012-03-01Bibliographically approved
4. Reliability based design optimization with experiments on demand
Open this publication in new window or tab >>Reliability based design optimization with experiments on demand
2012 (English)Report (Other academic)
Abstract [en]

In this paper, an algorithm for reliability based design optimization (RBDO) is presented. It incorporates a novel procedure in which experiments are performed one at a time where and when they are needed. The procedure is called experiments on demand. The experiment procedure utilizes properties specific to RBDO and the problem at hand augmented by the concept of D-optimality familiar from traditional design of experiments. Furthermore, an adaptive surrogate model fitting scheme is proposed which balances numerical stability and convergence rate as well as accuracy. Benchmarked against algorithms in the literature, the number of experiments needed for convergence was reduced by up to 80 % for a frequently used analytical problem and by up to 19 % for an application example. The accuracy of the reliability index is in line with the most efficient algorithm against which it was benchmarked but up to 3 % lower than the most accurate algorithm.

Publisher
13 p.
Series
Trita-HFL, ISSN 1104-6813 ; 519
Keyword
Experiments on demand, Reliability based design optimization, Surrogate model
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-90800 (URN)
Note
QC 20120229Available from: 2012-02-29 Created: 2012-02-29 Last updated: 2012-03-01Bibliographically approved

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