Two-Level Approximation Method for Reliability-Based Design Optimization

2004 ◽  
Author(s):  
Kunjal Oza ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Approximation Method ◽  
Order Approximation ◽  
Optimal Solution ◽  
Design Tool ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Dominant Design ◽  
Practical Engineering ◽  
The Cost

In order to model uncertainties and achieve the required reliability, Reliability Based Design Optimization (RBDO) has evolved as a dominant design tool. Many methods have been introduced in solving the RBDO problem. However, the computational expense associated with the probabilistic constraint evaluation still limits the applicability of the RBDO to practical engineering problems. In this paper, a Two-Level Approximation method (TLA) is proposed. At the first level, a reduced second order approximation is used for better optimization solution; at the second level a linear approximation is used for faster reliability assessment. The optimal solution is obtained interatively. The proposed method is tested on certain numerical examples, and results obtained are compared to evaluate the cost-effectiveness.

First-Order Approximation Methods in Reliability-Based Design Optimization

2004 ◽  
Vol 127 (5) ◽  
pp. 851-857 ◽  
Author(s):  
Anukal Chiralaksanakul ◽  
Sankaran Mahadevan
Keyword(s):  
Design Optimization ◽  
Order Approximation ◽  
Mathematical Optimization ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Inverse Form ◽  
Numerical Studies ◽  
Reliability Method ◽  
First Order Approximation

Efficiency of reliability-based design optimization (RBDO) methods is a critical criterion as to whether they are viable for real-world problems. Early RBDO methods are thus based primarily on the first-order reliability method (FORM) due to its efficiency. Recently, several first-order RBDO methods have been proposed, and their efficiency is significantly improved through problem reformulation and/or the use of inverse FORM. Our goal is to present these RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO reformulations. Through the formalization, their relationships are revealed. Using reported numerical studies, we discuss their numerical efficiency, convergence, and accuracy.

Bayesian Reliability Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method

2007 ◽  
Author(s):  
Pingfeng Wang ◽  
Byeng D. Youn ◽  
Lee J. Wells
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Engineering Design ◽  
Mean Deviation ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Practical Engineering ◽  
Eigenvector Dimension Reduction

In the last decade, considerable advances have been made in Reliability-Based Design Optimization (RBDO). It is assumed in RBDO that statistical information of input uncertainties is completely known (aleatory uncertainty), such as a distribution type and its parameters (e.g., mean, deviation). However, this assumption is not valid in practical engineering applications, since the amount of uncertainty data is restricted mainly due to limited resources (e.g., man-power, expense, time). In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, this paper proposes an integration of RBDO with Bayes Theorem, referred to as Bayesian Reliability-Based Design Optimization (Bayesian RBDO). However, when a design problem involves a large number of epistemic variables, Bayesian RBDO becomes extremely expensive. Thus, this paper presents a more efficient and accurate numerical method for reliability method demanded in the process of Bayesian RBDO. It is found that the Eigenvector Dimension Reduction (EDR) Method is a very efficient and accurate method for reliability analysis, since the method takes a sensitivity-free approach with only 2n+1 analyses, where n is the number of aleatory random parameters. One mathematical example and an engineering design example (vehicle suspension system) are used to demonstrate the feasibility of Bayesian RBDO. In Bayesian RBDO using the EDR method, random parameters associated with manufacturing variability are considered as the aleatory random parameters, whereas random parameters associated with the load variability are regarded as the epistemic random parameters. Moreover, a distributed computing system is used for this study.

scholarly journals Reliability-Based Design Optimization for Crane Metallic Structure Using ACO and AFOSM Based on China Standards

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoning Fan ◽  
Xiaoheng Bi
Keyword(s):  
Design Optimization ◽  
Optimal Solution ◽  
Probabilistic Constraints ◽  
Metallic Structure ◽  
Reliability Based Design Optimization ◽  
Metallic Structures ◽  
Practical Applications ◽  
Reliability Indices ◽  
Uncertain Variables ◽  
Reliability Based Design

The design optimization of crane metallic structures is of great significance in reducing their weight and cost. Although it is known that uncertainties in the loads, geometry, dimensions, and materials of crane metallic structures are inherent and inevitable and that deterministic structural optimization can lead to an unreliable structure in practical applications, little amount of research on these factors has been reported. This paper considers a sensitivity analysis of uncertain variables and constructs a reliability-based design optimization model of an overhead traveling crane metallic structure. An advanced first-order second-moment method is used to calculate the reliability indices of probabilistic constraints at each design point. An effective ant colony optimization with a mutation local search is developed to achieve the global optimal solution. By applying our reliability-based design optimization to a realistic crane structure, we demonstrate that, compared with the practical design and the deterministic design optimization, the proposed method could find the lighter structure weight while satisfying the deterministic and probabilistic stress, deflection, and stiffness constraints and is therefore both feasible and effective.

Reliability-Based Design Optimization Using Confidence-Based Model Validation for Insufficient Experimental Data

2016 ◽  
Author(s):  
Min-Yeong Moon ◽  
K. K. Choi ◽  
Hyunkyoo Cho ◽  
Nicholas Gaul ◽  
David Lamb ◽  
...  
Keyword(s):  
Experimental Data ◽  
Simulation Model ◽  
Design Optimization ◽  
Model Validation ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Validation Process ◽  
Target Problem ◽  
Reliability Based Design ◽  
The Cost

The conventional reliability-based design optimization (RBDO) methods assume that a simulation model is able to represent the real physics accurately. However, the simulation model could be biased. Accordingly, when the conventional RBDO design is manufactured, the product may not satisfy the target reliability. Therefore, model validation, which corrects model bias, should be integrated in the RBDO process by incorporating experimental data. The challenge is that only a limited number of experimental data is usually available due to the cost of actual product testing. Consequently, model validation for RBDO needs to account for the uncertainty induced by insufficient experimental data as well as variability inherently existing in the products. In this paper, a confidence-based model validation process that captures the uncertainty and corrects model bias at user-specified target conservativeness level is developed. Thus, RBDO can be performed using confidence-based model validation to obtain conservative RBDO design. It is found that RBDO with model bias correction becomes a moving-target problem because the feasible domain changes as the design moves. Consequently, the RBDO optimum may not be easily found due to the convergence problem. To resolve the issue, an efficient process is proposed by carrying out deterministic design optimization (DDO) and RBDO without validation, followed by RBDO with confidence-based model validation. Finally, we demonstrate that the proposed RBDO approach can achieve a conservative and practical optimum design given a limited number of experimental data.

Role of Conservative Moving Least Squares Methods in Reliability Based Design Optimization: A Mathematical Foundation

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Jongsoo Lee ◽  
Chang Yong Song
Keyword(s):  
Design Optimization ◽  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Function ◽  
Optimal Solution ◽  
Moving Least Squares ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Moving Least Squares Method

The response surface method (RSM) and the moving least squares method (MLSM) are extensively used due to their computational efficiency in solving reliability based design optimization (RBDO) problems. Since traditional RSM and MLSM are described by second-order polynomials, approximated constraints are sometimes unable to ensure feasibility when highly nonlinear and/or nonconvex constraint functions are approximated in RBDO. We explore the development of a new MLSM based meta-model that ensures the constraint feasibility of an optimal solution in RBDO. A constraint-feasible MLSM (CF-MLSM) is devised to realize feasibility regardless of the multimodality/nonlinearity of the constraint function in all approximation processes as well as the variation of random characteristics in RBDO. The usefulness of the proposed approach is verified by examining a nonlinear function problem and an actively controlled structure problem.

Augmented Single Loop Single Vector Algorithm Using Nonlinear Approximations of Constraints in Reliability-Based Design Optimization

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Petter N. Lind ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Order Approximation ◽  
Nonlinear Problems ◽  
Probability Of Failure ◽  
Reliability Based Design Optimization ◽  
Performance Function ◽  
Single Loop ◽  
Nonlinear Approximations ◽  
Reliability Based Design ◽  
Probe Point

Reliability-based design optimization (RBDO) aims at minimizing a function of probabilistic design variables, given a maximum allowed probability of failure. The most efficient methods available for solving moderately nonlinear problems are single loop single vector (SLSV) algorithms that use a first-order approximation of the probability of failure in order to rewrite the inherently nested structure of the loop into a more efficient single loop algorithm. The research presented in this paper takes off from the fundamental idea of this algorithm. An augmented SLSV algorithm is proposed that increases the rate of convergence by making nonlinear approximations of the constraints. The nonlinear approximations are constructed in the following way: first, the SLSV experiments are performed. The gradient of the performance function is known, as well as an estimate of the most probable failure point (MPP). Then, one extra experiment, a probe point, per performance function is conducted at the first estimate of the MPP. The gradient of each performance function is not updated but the probe point facilitates the use of a natural cubic spline as an approximation of an augmented MPP estimate. The SLSV algorithm using probing (SLSVP) also incorporates a simple and effective move limit (ML) strategy that also minimizes the heuristics needed for initiating the optimization algorithm. The size of the forward finite difference design of experiment (DOE) is scaled proportionally with the change of the ML and so is the relative position of the MPP estimate at the current iteration. Benchmark comparisons against results taken from the literature show that the SLSVP algorithm is more efficient than other established RBDO algorithms and converge in situations where the SLSV algorithm fails.

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