A Single-Loop Method for Reliability-Based Design Optimization

2004 ◽  
Author(s):  
Jinghong Liang ◽  
Zissimos P. Mourelatos ◽  
Jian Tu
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Computational Effort ◽  
Side Impact ◽  
Double Loop ◽  
Reliability Based Design Optimization ◽  
Deterministic Optimization ◽  
Single Loop ◽  
Reliability Based Design ◽  
Reliability Assessments

Reliability-Based Design Optimization (RBDO) can provide optimum designs in the presence of uncertainty. It can therefore, be a powerful tool for design under uncertainty. The traditional, double-loop RBDO algorithm requires nested optimization loops, where the design optimization (outer) loop, repeatedly calls a series of reliability (inner) loops. Due to the nested optimization loops, the computational effort can be prohibitive for practical problems. A single-loop RBDO algorithm is proposed in this paper for both normal and non-normal random variables. Its accuracy is the same with the double-loop approach and its efficiency is almost equivalent to deterministic optimization. It collapses the nested optimization loops into an equivalent single-loop optimization process by imposing the Karush-Kuhn-Tucker optimality conditions of the reliability loops as equivalent deterministic equality constraints of the design optimization loop. It therefore, converts the probabilistic optimization problem into an equivalent deterministic optimization problem, eliminating the need for calculating the Most Probable Point (MPP) in repeated reliability assessments. Several numerical applications including an automotive vehicle side impact example, demonstrate the accuracy and superior efficiency of the proposed single-loop RBDO algorithm.

The Response Surface Single Loop Reliability-Based Design Optimization Method With Reliability Requirement on System Failure

2016 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Optimization Problem ◽  
Optimization Method ◽  
Reliability Based Design Optimization ◽  
Single Loop ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method ◽  
Deterministic Solution

In reliability-based design optimization (RBDO), an optimal design which minimizes an objective function while satisfying a number of probabilistic constraints is found. As opposed to deterministic optimization, statistical uncertainties in design variables and design parameters have to be taken into account in the design process in order to achieve a reliable design. In the most widely used RBDO approaches, the First-Order Reliability Method (FORM) is used in the probability assessment. This involves locating the Most Probable Point (MPP) of failure, or the inverse MPP, either exactly or approximately. If exact methods are used, an optimization problem has to be solved, typically resulting in computationally expensive double loop or decoupled loop RBDO methods. On the other hand, locating the MPP approximately typically results in highly efficient single loop RBDO methods since the optimization problem is not necessary in the probability assessment. However, since all these methods are based on FORM, which in turn is based on a linearization of the deterministic constraints at the MPP, they may suffer inaccuracies associated with neglecting the nonlinearity of deterministic constraints. In a previous paper presented by the authors, the Response Surface Single Loop (RSSL) Reliability-based design optimization method was proposed. The RSSL-method takes into account the non-linearity of the deterministic constraints in the computation of the probability of failure and was therefore shown to have higher accuracy than existing RBDO methods. The RSSL-method was also shown to have high efficiency since it bypasses the concept of an MPP. In RSSL, the deterministic solution is first found by neglecting uncertainties in design variables and parameters. Thereafter quadratic response surface models are fitted to the deterministic constraints around the deterministic solution using a single set of design of experiments. The RBDO problem is thereafter solved in a single loop using a closed-form second order reliability method (SORM) which takes into account all elements of the Hessian of the quadratic constraints. In this paper, the RSSL method is used to solve the more challenging system RBDO problems where all constraints are replaced by one constraint on the system probability of failure. The probabilities of failure for the constraints are assumed independent of each other. In general, system reliability problems may be more challenging to solve since replacing all constraints by one constraint may strongly increase the non-linearity in the optimization problem. The extensively studied reliability-based design for vehicle crash-worthiness, where the provided deterministic constraints are general quadratic models describing the system in the whole region of interest, is used to demonstrate the capabilities of the RSSL method for problems with system reliability constraints.

A Single-Loop Approach for System Reliability-Based Design Optimization

2006 ◽  
Author(s):  
Jinghong Liang ◽  
Zissimos P. Mourelatos ◽  
Efstratios Nikolaidis
Keyword(s):  
Design Optimization ◽  
System Reliability ◽  
Failure Modes ◽  
Optimization Problems ◽  
Side Impact ◽  
Sequential Optimization ◽  
Reliability Based Design Optimization ◽  
Single Loop ◽  
Reliability Based Design ◽  
Probable Failure

An efficient single-loop approach for series system reliability-based design optimization problems is presented in this paper. The approach enables the optimizer to apportion the system reliability among the failure modes in an optimal way by increasing the reliability of those failure modes whose reliability can be increased at low cost. Furthermore, it identifies the critical failure modes that contribute the most to the overall system reliability. A previously reported methodology uses a sequential optimization and reliability approach. It also uses a linear extrapolation to determine the coordinates of the most probable points of the failure modes as the design changes. As a result, the approach can be slow and may not converge if the location of the most probable failure point changes significantly. This paper proposes an alternative system RBDO approach that overcomes the above difficulties by using a single-loop approach where the searches for the optimum design and for the most probable failure points proceed simultaneously. An easy to implement active set strategy is used. The maximum allowable failure probabilities of the failure modes are considered as design variables. The efficiency and robustness of the method is demonstrated on three design examples involving a beam, an internal combustion engine and a vehicle side impact. The results are compared with deterministic optimization and the conventional component RBDO formulation.

scholarly journals Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

2021 ◽  
Author(s):  
Yoshihiro Kanno
Keyword(s):  
Design Optimization ◽  
Optimization Problem ◽  
Structural Reliability ◽  
Reliability Based Design Optimization ◽  
Input Distribution ◽  
Reliability Based Design ◽  
Optimal Value ◽  
Reliability Constraint ◽  
Distributionally Robust ◽  
Robust Reliability

AbstractThis study considers structural optimization under a reliability constraint, in which the input distribution is only partially known. Specifically, when it is only known that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, it is required that the failure probability of a structure should be no greater than a specified target value for any realization of the input distribution. We demonstrate that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can handle a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization; in particular, nonlinear semidefinite programming. Two numerical examples are solved to demonstrate the relation between the optimal value and either the target reliability or the uncertainty magnitude.

Reliability-Based Design Optimization of Microstructures With Analytical Formulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Pinar Acar
Keyword(s):  
Design Optimization ◽  
Material Properties ◽  
Optimization Problem ◽  
Optimization Under Uncertainty ◽  
Reliability Based Design Optimization ◽  
Case Scenario ◽  
Worst Case ◽  
Analytical Formulation ◽  
Reliability Based Design ◽  
Safe Approach

Microstructures are stochastic by their nature. These aleatoric uncertainties can alter the expected material performance substantially and thus they must be considered when designing materials. One safe approach would be assuming the worst case scenario of uncertainties in design. However, design under the worst case conditions can lead to over-conservative solutions that provide less effective material properties. Here, a more powerful design approach can be developed by implementing reliability constraints into the optimization problem to achieve superior material properties while satisfying the prescribed design criteria. This is known as reliability-based design optimization (RBDO), and it has not been studied for microstructure design before. In this work, an analytical formulation that models the propagation of microstructural uncertainties to the material properties is utilized to compute the probability of failure. Next, the analytical uncertainty solution is integrated into the optimization problem to define the reliability constraints. The presented optimization under uncertainty scheme is exercised to maximize the yield stress of α-Titanium and magnetostriction of Galfenol, respectively.

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