Weighted Multivariate Mean Square Error for processes optimization: A case study on flux-cored arc welding for stainless steel claddings

A mathematical programming technique developed recently that optimizes multiple correlated characteristics is the Multivariate Mean Square Error (MMSE). The MMSE approach has obtained noteworthy results, by avoiding the production of inappropriate optimal points that can occur when a method fails to take into account a correlation structure. Where the MMSE approach is deficient, however, is in cases where the multiple correlated characteristics need to be optimized with varying degrees of importance. The MMSE approach, in treating all responses as having the same importance, is unable to attribute the desired weights. This paper thus introduces a strategy that weights the responses in the MMSE approach. The method, called the Weighted Multivariate Mean Square Error (WMMSE), utilizes a weighting procedure that integrates Principal Component Analysis (PCA) and Response Surface Methodology (RSM). In doing so, WMMSE obtains uncorrelated weighted objective functions from the original responses. After being mathematically programmed, these functions are optimized by employing optimization algorithms. We applied WMMSE to optimize a stainless steel cladding application executed via the flux-cored arc welding (FCAW) process. Four input parameters and eight response variables were considered. Stainless steel cladding, which carries potential benefits for a variety of industries, takes low cost materials and deposits over their surfaces materials having anti-corrosive properties. Optimal results were confirmed, which ensured the deposition of claddings with defect-free beads exhibiting the desired geometry and demonstrating good productivity indexes.

► This paper presents the method Weighted Multivariate Mean Square Error (WMMSE).
► The WMMSE optimizes multiple correlated responses.
► A cladding application with four input parameters and eight responses was optimized.
► All characteristics were modeled according to Response Surface Methodology.
► Confirmation runs showed the results to be close to the theoretical values.