Robust parameter optimization based on multivariate normal boundary intersection

Lopes, Luiz Gustavo Dias; Brito, Tarcísio Gonçalves; Paiva, Anderson Paulo de; Peruchi, Rogério Santana; Balestrassi, Pedro Paulo

doi:10.1016/j.cie.2015.12.023

Cited by 28 publications

(4 citation statements)

References 35 publications

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“…Normal Boundary Intersection Method (Das & Dennis, 1998); has been presented as an excellent solution to these conflicts (Costa et. al., 2016;Lopes et. al., 2016;López-Arcos, 2013;Naves et.…”

Section: Development Methodsmentioning

confidence: 99%

Design of Experiments and Computational Fluid Dynamics Approach to Improve the Product Design Process

Arcos

Camacho

Silva

et al. 2020

BJD

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Design of Experiments (DOE) techniques were applied to improve the thermal performance of a gas oven, aided with a Computational Fluid Dynamics (CFD) study in concept selection phase of Product Design Process PDP. Typical approaches to these types of activities involve developing all possible combinations of geometries changing one variable at a time, analyzing them with CFD, and predicting the main effects over the parameters surface heat flux and pressure drop, which in this application are the system responses. The develop plan for the team was to generate an script that allowed analyzing the sample space of the process variables and analyze much geometry configurations to study the geometric parameters. By utilizing DOE techniques the number of geometries was strategically reduced to 29. The metamodel of the system was obtained as a function of the input variables, with a statistical adjustment of 86.78% for the surface heat flux and 78% for the pressure drop. Subsequently we found the geometry that improves the performance of the product using the multiobjetive optimization method "Normal Boundary Intersection -NBI".

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Section: Development Methodsmentioning

confidence: 99%

Design of Experiments and Computational Fluid Dynamics Approach to Improve the Product Design Process

Arcos

Camacho

Silva

et al. 2020

BJD

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“…Lopes et al [53] proposed a similar approach for robust modelling and optimization of the arithmetic average surface roughness and the maximum roughness height. However, the present paper proposes to the experimenter the possibility of using the weighted principal component technique, avoiding loss of information, i.e., 100% of the variancecovariance structure of the original set of process outcomes is taken into consideration to estimate regression coefficients that consider all the variance-covariance influence on the response surface models.…”

Section: Normal Boundary Intersection Methodsmentioning

confidence: 99%

Multivariate robust modeling and optimization of cutting forces of the helical milling process of the aluminum alloy Al 7075

Pereira

Leite

Alvim

et al. 2017

Int J Adv Manuf Technol

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Helical milling is an advanced hole-making process and different approaches considering controllable variables have been presented addressing modelling and optimization of machining forces in helical milling. None of them considers the importance of the noise variables and the fact that machining forces components are usually correlated. Exploring this issue, this paper presents a multivariate robust modelling and optimization of cutting forces of the helical milling of the aluminum alloy Al 7075. For the study, the tool overhang length was defined as noise variable since in cavities machining there are specific workpiece geometries that constrain this variable; the controllable variables were axial feed per tooth, tangential feed per tooth and cutting speed. The cutting forces in the workpiece coordinate system were measured and the components in the tool coordinate system, i.e., the axial and radial forces, were evaluated. Since these two outcomes are correlated, the weighted principal component analysis was performed together with the robust parameter design to allow the multivariate robust modelling of the mean and variance equations. The normal boundary intersection method was used to obtain a set of Pareto robust optimal solutions related to the mean and variance equations of the weighted principal component. The optimization of the weighted principal component through the normal boundary intersection method was performed and the results evaluated in the axial and radial cutting forces components. Confirmation runs were carried out and it was possible to conclude that the models presented good fit with experimental data and that the Pareto optimal point chosen for performing the confirmation runs is robust to the tool overhang length variation. Finally, the cutting force models were also presented for mean and variance in the workpiece coordinate system in the time domain, presenting low error regarding the experimental test, endorsing the results.

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“…Taking into account that industrial processes commonly deal with multiple critical-to-quality (CTQ) characteristics [14], few researches have been conducted using multivariate approaches and DMAIC procedure to solving manufacturing problems. In such complex systems, the correlation among CTQs cannot be neglected due to its influence on the optimization results [30]. This effect destabilizes the mathematical models producing errors in the regression coefficients.…”

Section: Introductionmentioning

confidence: 99%

Integrating Multivariate Statistical Analysis Into Six Sigma DMAIC Projects: A Case Study on AISI 52100 Hardened Steel Turning

et al. 2020

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DMAIC (define, measure, analyze, improve and control) is one of the most utilized methods for guiding practitioners in the decision-making process of quality improvement projects. Industrial processes commonly deal with multiple critical-to-quality (CTQ) characteristics. When these characteristics are correlated, multivariate statistical techniques should be applied. This paper aims to propose a domainspecific Six Sigma method, the MDMAIC (multivariate DMAIC). The new stepwise procedure helps practitioners not only to reduce problem dimension but also to take account of the correlation structure among CTQs during the decision-making process. Principal component analysis has been applied for assessing the measurement system, analyzing process stability and capability, as well as modeling and optimizing multivariate manufacturing processes. A hardened steel turning case has been presented for proposal validation. The result analysis has shown that the MDMAIC was very successful in leading the practitioner during the steps and phases of the quality improvement project. The multivariate capability index of the enhanced process emphasized the substantial economic improvement. INDEX TERMS Six sigma, dmaic, quality improvement, principal component analysis, multiobjective optimization.

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Robust parameter optimization based on multivariate normal boundary intersection

Cited by 28 publications

References 35 publications

Design of Experiments and Computational Fluid Dynamics Approach to Improve the Product Design Process

Design of Experiments and Computational Fluid Dynamics Approach to Improve the Product Design Process

Multivariate robust modeling and optimization of cutting forces of the helical milling process of the aluminum alloy Al 7075

Integrating Multivariate Statistical Analysis Into Six Sigma DMAIC Projects: A Case Study on AISI 52100 Hardened Steel Turning

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