Multivariate Stochastic Optimization Approach Applied in a Flux-Cored Arc Welding Process

Abstract

One of the main goals in flux-cored arc welding processes is the optimization of bead geometry, in which multiple geometric characteristics of the welding bead are important; therefore, multiobjective optimization programming is often applied. However, several optimization problems that use stochastic programming do not consider the impact of the correlation between the output variables on their probabilistic constraints. In this context, this paper aims to present a multiobjective optimization method based on multivariate stochastic programming. To demonstrate the applicability of the proposal, we conducted a design of experiments to optimize a flux-cored arc welding process for stainless-steel claddings. The weighting-sums method was applied to formulate the multiobjective optimization problem. It was possible to formulate a multivariate probability distribution for the penetration and dilution. In addition, a 95% probability to meet the predefined specification limits of the geometric characteristics was achieved. INDEX TERMS Bead geometry, bivariate normal distribution, flux-cored arc welding, multiobjective optimization programming, stainless steel claddings, stochastic programming.

A Gage Study Through the Weighting of Latent Variables Under Orthogonal Rotation

“…(2). The formula considers the independent normally distributed data with null mean and the variances 2…”

“…In Eq. (19), μ is the expected value for WRF and τi, βj, τβij, and εijk refer to random effects with null expected values and variances στ 2 , σβ 2 , στβ 2 , and σε 2 respectively. For scenarios in which the interaction is not significant, then WRF is estimated using Eq.…”

“…Such methods have been applied in many engineering problems to improve the interpretation of extensive and correlated data. In fact, several studies already use multivariate strategies in a handful of applications, such as flux-cored arc welding process [2], moving average control chart [3], design of experiments on clustering methods [4] and applications in process monitoring [5,6]. Such approaches are also used in the energy [7], healthcare [8] and economy [9] sectors.…”

Improved Method for Determining the Feed Influence on the Tangential Cutting Force During Re-drilling, Countersinking and Boring Based on the Small Sample Theory

“…Probability-statistical methods of processing the results of real-life experiments of the cutting process have become widespread. For example, in paper [26] the problem of multicriteria optimization of the turning process using probabilistic-statistical approach is solved, in paper [27] optimization of the turning process of hardened steel AISI 52100 using stochastic programming is carried out, and in paper [28] the stochasticity of various criteria on the optimization process is taking into account. A great number of papers is devoted to the analysis of stochasticity of cutting forces occurring during metal layer cutting in turning [29] and milling [30].…”

Plasticity of Bead-on-Plate Welds Made with the Use of Stored Flux-Cored Wires for Offshore Applications

“…The consumption of flux-cored wires for ocean and marine structures is still increasing. This is the result of many unquestionable advantages of the FCAW welding process: high welding efficiency, penetration depth, good arc stability and relative ease of training of welders [ 15 , 20 , 21 , 22 ].…”