Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Yuquan Meng, Manjunath Rajagopal, Gowtham Kuntumalla, Ricardo Toro, Hanyang Zhao, Ho Chan Chang, Sreenath Sundar, Srinivasa Salapaka, Nenad Miljkovic, Placid Ferreira, Sanjiv Sinha, Chenhui Shao

Research output: Contribution to journalArticlepeer-review


Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlin-ear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)- based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial re-gression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

Original languageEnglish (US)
Pages (from-to)7411-7427
Number of pages17
JournalMathematical Biosciences and Engineering
Issue number6
StatePublished - Oct 28 2020


  • Machine learning
  • Mechanical strength
  • Process optimization
  • Response surface methodology
  • Ultrasonic metal welding

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Computational Mathematics
  • Applied Mathematics
  • Modeling and Simulation


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