Combinatorial optimization of weld sequence by using a surrogate model to mitigate a weld distortion

  • Mahyar Asadi
  • John A. Goldak


Choosing an optimal sequence from the set of all possible combinations of a weld’s sub-passes is always a challenge for designers. The solution of such combinatorial optimization problems is limited by the available resources. For example, having n sub-passes leads to choosing from 2 n  × n! possible combinations of the sub-passes, e.g., 46,080 for n = 6. It is not feasible to choose the optimal sequence by evaluating all possible combinations either experimentally or by simulation models. The purpose of using a surrogate model based on a simulation model is to find the solution in the space of all possible combinations with a significant decrease in computational expenses. In effect, the surrogate model constructs an approximation model from some combinations of solutions of a more expensive model to mimic the behavior of the simulation model as closely as possible but at a much lower computational cost. This surrogate model, then, could be used to approximate the behavior of the other combinations. In this paper, a surrogate model is demonstrated that minimizes the distortion in a pipe girth weld with six sub-passes by analyzing only 14 combinations of sub-passes from total of 48 possible combinations. A comparison between the results of the surrogate model and the full transient FEM analysis all possible combinations shows the accuracy of the algorithm/model.


Sequence optimization Combinatorial space Welding simulation Surrogate model Pipe girth weld Weld distortion 



The authors wish to acknowledge technical supports from Daniel Downy, Stainslav Tchernov and Jianguo Zhou from Goldak Technologies Inc.


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Copyright information

© Springer Science+Business Media, B.V. 2011

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringCarleton UniversityOttawaCanada

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