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In this paper, an analytical model is proposed to predict magnetic flux leakage (MFL) signals from the surface defects in ferromagnetic tubes. The analytical expression consists of elliptic integrals of first kind based on the magnetic dipole model. The radial (B z ) component of leakage fields is computed from the cylindrical holes in ferromagnetic tubes. The effectiveness of the model has been studied by analyzing MFL signals as a function of the defect parameters and lift-off. The model predicted results are verified with experimental results and a good agreement is observed between the analytical and the experimental results. This analytical expression could be used for quick prediction of MFL signals and also input data for defect reconstructions in inverse MFL problem.

This paper proposes a nonlinear optimal-function-based algorithm which can be utilized to replace electronic circuitry traditionally employed to linearize the characteristics of commonly used temperature transducers such as resistance temperature detectors, thermistors and thermocouples. The function exploits ratiometric-logarithmic operation for linearization. The optimal parameters of the function are determined using a covariance matrix adopted evolutionary strategy (CMAES) algorithm. Transducers' input–output data are derived from the Yokogawa handy calibrator model CA 150 and subjected to the proposed algorithm to evaluate the performance of the method. The performance measures such as full-scale error and mean square error are considered to compare the performance of the proposed technique with other methods reported for transducers. The present linearization algorithm was implemented using LabVIEW 7.1 Professional Development System in a personal computer that provides the facility to interface with the National Instruments data acquisition module NI DAQCard PCI-6221. Experimental results reveal that the proposed evolutionary optimized nonlinear function based software linearizer does its job efficiently in a better way than that of the conventional hardware and software methods. Also, the results obtained using the CMAES algorithm are compared with the results of a real-coded genetic algorithm. The comparison shows that the CMAES algorithm is more consistent in determining the best solution for the proposed ratiometric-logarithmic function with reasonable computation time.