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.

scholarly journals Multi-Dimensional Moving Least Squares Method for Elasticity Problems

2012 ◽  
Vol 78 (786) ◽  
pp. 142-151
Author(s):  
Kohei SAKIHARA ◽  
Hitoshi MATSUBARA ◽  
Takaaki EDO ◽  
Hisao HARA ◽  
Genki YAGAWA
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Moving Least Squares ◽  
Moving Least Squares Method ◽  
Elasticity Problems

scholarly journals An Improved Moving Least Squares Method for Curve and Surface Fitting

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Lei Zhang ◽  
Tianqi Gu ◽  
Ji Zhao ◽  
Shijun Ji ◽  
Ming Hu ◽  
...  
Keyword(s):  
Least Squares ◽  
Random Error ◽  
Least Squares Method ◽  
Surface Fitting ◽  
Measured Data ◽  
Moving Least Squares ◽  
Generate Curve ◽  
Moving Least Squares Method ◽  
Curve And Surface Fitting ◽  
Mls Method

The moving least squares (MLS) method has been developed for the fitting of measured data contaminated with random error. The local approximants of MLS method only take the error of dependent variable into account, whereas the independent variable of measured data always contains random error. Considering the errors of all variables, this paper presents an improved moving least squares (IMLS) method to generate curve and surface for the measured data. In IMLS method, total least squares (TLS) with a parameterλbased on singular value decomposition is introduced to the local approximants. A procedure is developed to determine the parameterλ. Numerical examples for curve and surface fitting are given to prove the performance of IMLS method.

RESPONSE SURFACE MODEL USING MOVING LEAST SQUARES METHOD

2000 ◽  
Vol 2000.4 (0) ◽  
pp. 181-186
Author(s):  
Akihiro KAMINAGA ◽  
Katsuyuki SUZUKI ◽  
Daiji FUJII ◽  
Hideomi OHTSUBO
Keyword(s):  
Least Squares ◽  
Response Surface ◽  
Least Squares Method ◽  
Response Surface Model ◽  
Moving Least Squares ◽  
Surface Model ◽  
Moving Least Squares Method

Reliability-based design optimization of fluid–solid interaction problems

2013 ◽  
Vol 228 (10) ◽  
pp. 1724-1742 ◽  
Author(s):  
Hong-Lae Jang ◽  
Hyunkyoo Cho ◽  
Kyung K Choi ◽  
Seonho Cho
Keyword(s):  
Design Optimization ◽  
Incompressible Flows ◽  
Variational Equation ◽  
Optimization Method ◽  
Programming Algorithm ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Highly Nonlinear ◽  
Fluid Solid Interaction ◽  
Interaction Problem

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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