Radial basis functional model for multi-objective sheet metal forming optimization

Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases

“…(19). The MOPSO algorithm proposed by Coello et al [48,50] has been successfully employed to solve the numerous crashworthiness optimization problems such as functionally graded foam-filled structures [29] and the sheet metal forming problems [51], which has demonstrated the major advantages of fast convergence and well-distributed Pareto frontier, over other multiobjective optimization algorithms, such as NSGA [52], PEAS etc. [53,54].…”

Variable fidelity design based surrogate and artificial bee colony algorithm for sheet metal forming process

“…Various surrogate models, including polynomial response surface, Kriging (KG), radial basis function (RBF), artificial neural network (ANN) and support vector regression (SVR) have been successfully applied to approximate the responses of complicated engineering problems such as sheet metal forming [14,39,40] and vehicle crashworthiness [15,36,[41][42][43][44]. Therefore, to capture such sophistication, we attempt to adopt different surrogate models to formulate correction function C j (x,a j ) in this paper.…”

“…Of these possible basis functions, the most commonly used basis functions include: f(r)¼r 3 (cubic); f(r)¼r 2 ln(r) (thin-plate spline); fðrÞ ¼ e Àcr 2 , c 4 0 (Gaussian); fðrÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 2 þ c 2 p (multiquadric) and fðrÞ ¼ ðr 2 þ c 2 Þ À1=2 (inverse multiquadric). In this study, we chose the thin-plate spline formulation of RBF because it has proved to perform very well for sheet metal forming problems [39]. Given the M vectors of design variables and their corresponding functional values at the sampling points, we can obtain the following M equations:…”

Numerical and experimental case study on simultaneous optimization of blank shape and variable blank holder force trajectory in deep drawing

“…Design optimization using the SAO for drawbead forces can be found in Refs. (Breitkopf et al 2005;Jansson et al 2003;Liu & Yang 2008;Sun et al 2011;Wang et al 2009a;Wang et al 2010), in which note that a constant BHF is used. Optimization of VBHF trajectory using the SAO is recognized as an attractive and crucial approach for successful sheet metal forming in industry (Kitayama et al 2013;Wang et al 2008), but the practical application is rarely reported.…”