Electromagnetic induction (EMI) detection technology detects target based on the principle of electromagnetic induction, which was proposed by Harry W Conklin, Lundberg A and Sundberg, and it has been widely used in geophysical detection, security, military, medical, aerospace, and other fields. The framework for underground target electromagnetic detection that is applicable to multi-frequency bands, as shown in Fig. 1.
Fig.1. Technical framework of the underground target electromagnetic detection
In underground metal target detection, the metal target first generates eddy current in the changing magnetic field, also named primary field. Then the electromagnetic induction technology uses the inversion optimization algorithms to obtain the position and orientation information of the metal target from the data by detecting and analyzing the secondary field generated by the eddy current.
EMI detection technology can be divided into time domain electromagnetic (TDEM) detection and frequency domain electromagnetic (FDEM) detection according to the difference in conductivity and permeability between soil and metal targets. The TDEM method transmits pulse signals and determines the parameters of the metal target by analyzing the amplitude and attenuation characteristics of the received magnetic field signal. The TDEM method is commonly used to distinguishing and classify the material of the underground metal target due to the attenuation curve is highly susceptible to material. Different from the TDEM method, the FDEM method transmits continuous signals, and obtains the parameters of the metal target by analyzing the amplitude and phase of the secondary field signal received at multiple locations.
The process of underground metal target detection is shown in Fig. 2. The metal target is located at a specific position in the underground space. Researchers collect the observed data by sequentially placing the EMI detector at different data acquisition positions. The response of a metal target correlates with metal’s position, size, shape, orientation, and material properties. Based on these observed data and the forward model, the objective function could be constructed.
Fig.2. Process of underground metal target detection.
The principle model of electromagnetic induction detection system can be described as three-loop mutual inductance model, as shown in Fig.3. In this model, the transmitting coil can be equivalent to TX, the target is equivalent to Object, the receiving coil is equivalent to RX. TX is a loop with current.
Fig.3.** **Three-loop mutual inductance model
The forward model describes the relationship between the electromagnetic response and physical properties of targets. To obtain parameter information of underground target by observing magnetic field data, it is necessary to select an appropriate forward model for detection.
The process of underground target electromagnetic detection involves two kinds of problems: inversion and classification. Parameters about underground target such as material, shape, size, position, and orientation can be estimated by further processing the observed data collected by GPR or EMI method.
Inversion refers to estimating the properties of underground targets based on observed data obtained by electromagnetic detection methods. As discussed above, forward modeling is a process of using different models to calculate the observed values from given parameters such as position, material, and attitude. However, inversion can obtain physical parameters of underground targets from observed data.
The purpose of inversion based on EMI is to obtain the position, principal axes, polarizability, and orientation of underground targets from observed data. Typical inversion methods include filtering, least-squares, and neural networks (NN). The detection of a metal target by the filtering method can be abstracted into a dynamic state space model (DSSM). Therefore, the parameter optimization problem can be transformed into a Bayesian estimation problem, which can be solved mainly by either of two methods, the Kalman filter (KF) or the particle filter (PF). The PF method solves the problem by sequential Monte Carlo simulation, which is prone to “the curse of dimensionality” when solving the problem of high-dimensional parameter estimation. Therefore, it is not suitable for electromagnetic detection of underground targets. However, the Kalman filter method solves the problem by assuming that the posterior probability density function satisfies the Gaussian distribution. KF method still has good performance even under the Gaussian noise distribution. The difficulty inherent in any filtering method is the determination of the initial conditions. The initial conditions are the key factor to determine the convergence and efficiency of the filtering method.
The least-squares inversion algorithm involves constructing an objective function and optimization algorithm. An appropriate objective function measures the misfit between observed values and the fitted values provided by a forward model. Least-squares inversion estimates the parameters of underground targets by minimizing the objective function using the optimization algorithms. Optimization algorithms are numerous and broadly fall into two categories, heuristic and numerical. Heuristic optimization algorithms include differential evolution algorithms (DEA), genetic algorithms (GA), and simulated annealing algorithms (SAA). These algorithms have higher computational complexity when the EMI model has higher dimensions. Numerical optimization algorithms, however, use the gradient information of the objective function to obtain the optimal solution directly. Compared with heuristic optimization algorithms, numerical optimization algorithms have a faster convergence speed and lower computational cost. Numerical optimization algorithms include gradient descent, steepest descent, Newton’s method, BroydenFletcher-Goldfarb-Shanno (BFGS) algorithm, conjugate gradient method and Levenberg-Marquardt (LM) algorithm. Among these numerical optimization algorithms, the most used is the LM iterative algorithm, which is also named the damped least-squares method. LM algorithm is a blend of vanilla gradient descent and Gauss-Newton iteration and has the advantage of being less sensitive to initial values.
To obtain the optimal value of a nonlinear function, neural networks have been widely applied to the inversion problem. One of the most widely used neural network structures is the BP neural network. This neural network can learn and save the input-output mapping relationship of each neuron without knowing the equation of the function mapping relationship. The radial basis function (RBF) neural network is an ANN with an activation function of radial basis function. Here, the problem of minimizing the cost function can be abstracted into the optimal solution to solving the weight and bias. That is to use the optimization method to make the NN have a fast convergence speed and high prediction accuracy.
Classification aims to distinguish targets from other objects by analyzing the electromagnetic characteristics of the targets, and generally, a repetition and overlap between underground targets and other objects will lead to a high false positive alarm rate. Therefore, the underground target needs to be classified during the process of underground target electromagnetic detection to reduce the chance of this happening.
Underground target classification algorithms can be roughly divided into three categories: (1) Supervised classification algorithm represented by NN and SVM; (2) Un-supervised classification algorithm represented by cluster analysis; (3) Semi-supervised algorithm represented by deep learning.
The purpose of classification based on EMI is to classify underground targets based on different parameters. These parameters principally generally consist of model-based parameters, most of which are parameters of forward models and data-based parameters, which refer to parameters obtained from electromagnetic data directly, such as magnetic field amplitude and energy.
According to the categories of parameters, the existing classification strategies for underground targets focus on two aspects: model-based methods and data-based methods. Model-based methods classify underground targets by taking model parameters as the input and can include clustering, Gauss, and K-nearest neighbor (KNN) methods. Common models can be summarized into simple dipole models and physically complete models. Examples, of the latter ones include the normalized surface magnetic source (NSMS) model and the ortho-normalized volume magnetic sources (ONVMS) model. The NSMS model is an extension of the magnetic dipole model and can be considered as a generalized surface dipole model, and the ONVMS model is a further extension of the NSMS model, which can simultaneously detect multiple abnormal targets. In addition, other models have also been studied, such as the surface magnetic charge (SMC) model and the normalized surface magnetic charge (NSMC) model. Data-based methods take data features as the classification features directly and some examples of these are the SVM and random forest algorithms, and NNs. Underground targets can also be classified by the magnetic polarizability tensor. The magnetic polarizability tensor contains information about the size, shape, and material of a target. The polarizability attenuation curve has been demonstrated to be an effective classification feature.
Due to the diversity and complexity of underground targets, the generality of existing methods still needs to be improved. Therefore, deep learning, as a mature technology of data processing, is used for further processing of data collected by GPR or EMI to solve the problems of inversion and classification. In a variety of deep learning models, CNN can significantly reduce the number of training weights through local connection and weight sharing, which has already been applied extensively. Inversion strategy based on CNN can be used for multi-dimensional underground feature representation from deep electromagnetic measurements. The use of CNN for EMI inversion provides a new solution for geophysical inversions that simplifies the process of underground target electromagnetic detection. For the problem of underground target classification, CNN can greatly improve performance and are also widely used in the field of underground target electromagnetic detection. Compared with the two-stage algorithm, single-stage algorithms have more significant advantages in real-time detection.