Moving least squares response surface approximation: Formulation and metal forming applications

By Piotr Breitkopf, H. Naceur, A. Rassineux, Pierre Villon. 2005

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Multi-fidelity optimization for sheet metal forming process (2011, methodology): “It has been developed and continuously improved since 1990 ( Breitkopf et al. 2005 ).”
New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares (2008, unknown): “in [3], and stochastic analyses, e.”
Multiobjective robust optimization method for drawbead design in sheet metal forming (2010, methodology): “[17] developed a new RSM involving Moving Least Squares regression models and pattern search algorithms for achieving uniform thickness, where a one step solver is used in optimization procedure and the incremental solver for final verification.”
Metamodeling in Multidisciplinary Design Optimization: How Far Have We Really Come? (2014, unknown): “least squares [77–79].”
Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment (2017, background): “The local MLS approximation at x is formulated as [20] ~Lðx; xiÞ ¼ bðxiÞTaðxÞ ð65Þ where xi denotes experimental points and the basis functions BðxÞ are commonly chosen as bðxÞ ¼ 1x1 . . . xnx2 . . . x2n T ð66Þ The vector of unknown coefficients aðxÞ is determined by minimizing the error between the”