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.

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Keywords Combinatorial space, Pipe girth weld, Sequence optimization, Surrogate model, Weld distortion, Welding simulation
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Journal International Journal of Mechanics and Materials in Design
Asadi, M. (Mahyar), & Goldak, J.A. (John A.). (2011). Combinatorial optimization of weld sequence by using a surrogate model to mitigate a weld distortion. International Journal of Mechanics and Materials in Design, 7(2), 123–139. doi:10.1007/s10999-011-9154-6