Abstract
Underground metal target detection refers to estimating the properties of underground metal targets based on a set of observed data. Electromagnetic induction (EMI) method and the least-squares inversion provide the data acquisition method and the parameter estimation method for the detection, respectively. As an important part of least-squares inversion, optimization algorithms directly affect the efficiency of the least-squares inversion. To improve the efficiency of underground metal target detection, it is necessary to compare the performance of different optimization algorithms. In this paper, we analyzed the characteristic of the complex EMI forward model using sensitivity analysis and inverse sensitivity analysis at first. Then, the EMI forward model and least squares were used to build the objective function. The estimation error, run time and number of iterations of six numerical optimization algorithms were compared under different signal-to-noise ratios (SNRs) and under different data acquisition spacing. The algorithms include gradient descent, steepest descent, Newton's method, Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, conjugate gradient method and Levenberg-Marquardt (LM) algorithm. A simulation platform was established to generate observed data and compare the optimization algorithms. The results of algorithm comparison showed that the BFGS, conjugate gradient and LM algorithm can efficiently and accurately estimate the properties of underground metal targets and the LM algorithm has the shortest run time and the least number of iterations. Finally, we carefully analyzed the time consumption of each optimization algorithm. The results show that the calculation of the gradient and step length selection greatly affect the efficiency of the optimization algorithms.
Highlights
As one of the geophysical inversion problems, underground metal target detection aims to estimate the properties of underground metal targets based on a set of observed data and it has been widely implemented in military, archeology, prospecting, and many other fields [1]–[4]
The inverse sensitivity analysis results indicate that the position of the target estimated by the optimization algorithms is more accurate than that of the principal axes polarizability and orientation
Overall, we gave the results of the variance-based sensitivity analysis and the inverse sensitivity analysis of the cylinder forward model and the results of the performance comparison of six numerical optimization algorithms in underground metal detection
Summary
As one of the geophysical inversion problems, underground metal target detection aims to estimate the properties of underground metal targets based on a set of observed data and it has been widely implemented in military, archeology, prospecting, and many other fields [1]–[4]. Based on the observed data, the properties of underground metal targets can be estimated by inversion algorithms [8]–[10]. In order to improve the efficiency of least-squares inversion, it is necessary to compare the performance of common numerical optimization algorithms and analyze the time-consuming calculations during the procedure of these algorithms. The BFGS algorithm, conjugate gradient method and LM algorithm can efficiently and accurately estimate the properties of underground metal targets, and the LM algorithm has the shortest run time and the least number of iterations. The sensitivity analysis and inverse sensitivity are performed to analyze cylinder forward model in underground metal target detection. The performances of six numerical optimization algorithms, which include gradient descent, steepest descent, Newton’s method, BFGS algorithm, conjugate gradient method and LM algorithm, are compared and the time-consuming calculations in these algorithms are analyzed.
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