A new hybrid reliability‐based design optimization method under random and interval uncertainties

Using a sampling-based reliability-based design optimization method, we present a shape reliability-based design optimization method for coupled fluid–solid interaction problems. For the fluid–solid interaction problem in arbitrary Lagrangian–Eulerian formulation, a coupled variational equation is derived from a steady state Navier–Stokes equation for incompressible flows, an equilibrium equation for geometrically nonlinear solids, and a traction continuity condition at interfaces. The fluid–solid interaction problem is solved using the finite element method and the Newton–Raphson scheme. For the fluid mesh movement, we formulated and solved a pseudo-structural sub-problem. The shape of the solid is modeled using the Non-Uniform Rational B-Spline (NURBS) surface, and the coordinate components of the control points are selected as random design variables. The sensitivity of the probabilistic constraint is calculated using the first-order score functions obtained from the input distributions and from the Monte Carlo simulation on the surrogate model constructed by using the Dynamic Kriging method. The sequential quadratic programming algorithm is used for the optimization. In two numerical examples, the proposed optimization method is applied to the shape design problems of solid structure which is loaded by prescribed fluid flow, and this proves that the sampling-based reliability-based design optimization can be successfully utilized for obtaining a reliable optimum design in highly nonlinear multi-physics problems.

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Development of a Multistage Reliability-Based Design Optimization Method

Journal of Mechanical Design ◽

10.1115/1.4025492 ◽

2013 ◽

Vol 136 (1) ◽

Cited By ~ 4

Author(s):

Eric J. Paulson ◽

Ryan P. Starkey

Keyword(s):

Objective Function ◽

Design Optimization ◽

Technology Development ◽

Computational Cost ◽

Optimization Method ◽

Comparison Method ◽

Reliability Based Design Optimization ◽

Numerical Example ◽

Reliability Based Design ◽

System Acquisition

Complex system acquisition and its associated technology development have a troubled recent history. The modern acquisition timeline consists of conceptual, preliminary, and detailed design followed by system test and production. The evolving nature of the estimates of system performance, cost, and schedule during this extended process may be a significant contribution to recent issues. The recently proposed multistage reliability-based design optimization (MSRBDO) method promises improvements over reliability-based design optimization (RBDO) in achieved objective function value. In addition, its problem formulation more closely resembles the evolutionary nature of epistemic design uncertainties inherent in system design during early system acquisition. Our goal is to establish the modeling basis necessary for applying this new method to the engineering of early conceptual/preliminary design. We present corrections in the derivation and solutions to the single numerical example problem published by the original authors, Nam and Mavris, and examine the error introduced under the reduced-order reliability sampling used in the original publication. MSRBDO improvements over the RBDO solution of 10–36% for the objective function after first-stage optimization are shown for the original second-stage example problem. A larger 26–40% improvement over the RBDO solution is shown when an alternative comparison method is used than in the original. The specific implications of extending the method to arbitrary m-stage problems are presented, together with a solution for a three-stage numerical example. Several approaches are demonstrated to mitigate the computational cost increase of MSRBDO over RBDO, resulting in a net decrease in calculation time of 94% from an initial MSRBDO baseline algorithm.

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

Volume 2B: 42nd Design Automation Conference ◽

10.1115/detc2016-60505 ◽

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.

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