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Multi-Objective Optimization of a Magnetic Circuit for Magnetic Flux Leakage-Type Non-destructive Testing

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Abstract

The magnetic flux leakage technique is a widely used method for non-destructive testing of pipe-lines. The inspection of pipelines is typically performed with the assistance of a robotic tool called PIG, which is equipped with an array of magnetic circuits responsible for inducing a magnetic field in the pipeline wall. This magnetic field leaks out of the pipeline wall at the locations where potential anomalies are present. The optimization of the geometrical configuration of these magnetic circuits, as a method to improve the probability of detection of the technique, has been a question of great interest in recent studies. Drawing on the concept of Kirchhoff’s laws and the application of the finite elements method, this paper makes use of the forward analysis of the magnetic circuit to suggest a methodology for its design optimization. A lumped parameter model was proposed and calibrated to yield similar results as compared to the finite elements model. Following a multi-objective approach, a Genetic Algorithm was implemented in order to minimize the dimensions of the magnetic circuit while looking at the same time for the maximum magnetic flux leakage at locations with pipeline damage. The optimum design obtained by means of the Genetic Algorithm was experimentally validated. The results demonstrate the superior performance of the optimal magnetic circuit in comparison with two other non-optimal circuits.

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Acknowledgments

The authors thank Corporación para la Investigación de la Corrosión, in Piedecuesta, Colombia, for granting access to the laboratory for experimental validation of the simulation results found in this investigation.

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Authors and Affiliations

  1. Universidad Autónoma de Bucaramanga - UNAB, Bucaramanga, Colombia

    Jaime A. Parra-Raad & Sebastián Roa-Prada

Authors
  1. Jaime A. Parra-Raad
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  2. Sebastián Roa-Prada
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Corresponding author

Correspondence to Sebastián Roa-Prada.

Appendix

Appendix

This section presents the convergence graphs of the genetic algorithms used in this project. The horizontal axis shows the number of possible generations for each algorithm, along with the generations that were actually used by the algorithm, to satisfy the optimal conditions being sought. The vertical axis represents the values of the optimization function at each iteration. The crosses represent the average value of the optimization function for each generation and the points are the elite values of each generation (see Figs. 12, 13).

Fig. 13
figure 13

Failure behavior of the overall error for the design optimization algorithm

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Parra-Raad, J.A., Roa-Prada, S. Multi-Objective Optimization of a Magnetic Circuit for Magnetic Flux Leakage-Type Non-destructive Testing. J Nondestruct Eval 35, 14 (2016). https://doi.org/10.1007/s10921-015-0329-1

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  • DOI: https://doi.org/10.1007/s10921-015-0329-1

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