Multivariate steepest ascent method based on latent variables

Abstract

This paper presents a multivariate steepest ascent method based on the gradient of the first order principal component score model, with direction, step sizes and shifts driven by an integrated variance mapping. Using a random initial center point guess within regions of minimal prediction error, gradual improvements are done towards the curvature region where a response surface may be properly fitted. Experimentations carried out in such regions allow a large step size since coefficients standard error are very low. In order to illustrate this approach, a Flux-Cored arc welding cladding process of AISI 1020 carbon steel sheets with AISI 316L stainless steel tubular wires was studied considering a full factorial design with four input parameters for correlated pairs of responses. The case study and additional simulations highlights the suitable optimization results obtained with the method and its practical and successful implementation in a real-word manufacturing problem.