Improved Differential Evolution Algorithm for Multi-Target Response Inversion Detected by a Portable Transient Electromagnetic Sensor

The superimposed response of multi-target causes difficulty in locating and characterizing each target when detecting unexploded ordnance with a portable transient electromagnetic sensor, constructed with a single-layer transmitting coil and five three-component receiving coils. Differential evolution (DE) algorithm is improved here with Gram–Schmidt orthogonalization and position rearrangement for superimposed response inversion based on the multisource model, which represents the multi-target response with a set of magnetic dipoles distributed over the interrogated area. The Gram–Schmidt orthogonalization turns the coefficient matrix of each target into an orthonormal basis. Accordingly, the best magnetic polarization tensor can be directly extracted from the superimposed response without inverting large and potentially ill-conditioned matrices. The position rearrangement groups the positions of individuals in the contemporary population to maximize the likelihood that the positions in the same group belong to the same target. The convergence speed of multi-target inversion is accelerated with the crossover operation of DE algorithm performed within the groups. Simulated experiment results show that the error in estimated position and characteristic response for improved DE algorithm is only 10% of that of the conventional DE algorithm. Field experiment is also conducted, and its results show that the error in estimated position for improved DE algorithm is only 20% of that of the conventional DE algorithm. The improved DE algorithm can accurately estimate the position and characteristic response of each target from superimposed response.