A Comparative Study of Inversion Optimization Algorithms for Underground Metal Target Detection

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. INDEX TERMS electromagnetic induction (EMI), least-squares inversion, optimization algorithm, sensitivity analysis, underground metal target detection.

MicEMD: An open-source platform for modeling, inversion, and classification in electromagnetic underground metal target detection

“…The least-squares inversion is used to estimate the attributes of underground metal targets by minimizing the objective function. The objective function measures the misfit between observed values and the fitted values provided by a forward model (Wan et al, 2020), and it is minimized by the optimization algorithms.…”

“…Rodi and Mackie (2001) used the nonlinear conjugate gradient method to solve the magnetotelluric 2-D inversion problem. Wan et al (2020) used the numerical optimization algorithms to acquire the least-squares solution to identify the underground metal targets. As for the classification problems, Kappler and Gasperikova (2011) utilized the features extracted from the polarizabilities curve and Bayesian classification algorithm to classify unexploded ordnance and harmless scrap metal.…”

Modeling and forecasting of at home activity in older adults using passive sensor technology

“…Thus to estimate $$$ \hat{\alpha} $$$, we use a common numerical optimization method called Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS), see Fletcher 16 . This optimization method and versions of it are widely used in many research areas to find a local minimum of a differentiable function 17‐19 . We provide the derivatives for the log‐likelihood, $$$ \nabla l\left(\alpha \right) $$$, which given in Appendix C for reference.…”

“…16 This optimization method and versions of it are widely used in many research areas to find a local minimum of a differentiable function. 17 , 18 , 19 We provide the derivatives for the log‐likelihood, , which given in Appendix C for reference. Due to the logarithms within the gradient function, the iterative optimization algorithms are prone to exploding gradients.…”

Robust and Efficient Classification for Underground Metal Target Using Dimensionality Reduction and Machine Learning

“…U NDERGROUND metal target detection is the process of estimating the properties of subsurface metal items based on the observed data. It has been widely applied in resource exploration [1], engineering construction [2], military fields [3], and many other fields [4]- [6]. Geophysical exploration systems such as infrared remote sensing (RS) system [7], [8], electromagnetic induction (EMI) system [9]- [12] and ground-penetrating radar (GPR) [2], [13], [14] have proven to be successful in underground target detection.…”