Developing an Adaptive Fractional Model of a Magnetic Structure using Evolutionary Algorithm

Magnetic flux leakage technique is used extensively to detect and characterize defects in natural gas and oil transmission pipelines. The amount of magnetic flux introduced into the test sample is an important factor in the resolution of flaw detection. It depends on the power of permanent magnets and the geometrical design of the magnetic yoke. Finite element method (FEM) is the most widely used method of analyzing magnetic yoke due to its power, accuracy and straightforwardness. On the other hand its calculations are so complicated and time consuming, and every single modification in the parameters of the problem requires a new run. In this paper, we present an innovative method to overcome the problem of heavy calculations. In this method an adaptive fractional model (AFM) is fitted, to the calculated values of FEM, to simulate the behavior of the magnetic yoke for different design parameters with an acceptable error. Tolerating an acceptable amount of error, AFM can be replaced by FEM. This replacement brings about flexibility besides reducing the heavy calculations considerably. Finally, setting the parameters of the model according to the nature of data, the FEM results can be reproduced.