## 1 Introduction
### Physical Background of the Method
The use of low frequencies (several tens of hertz) for scanning moving magnetic objects does not allow for the use of the FEM, since the wavelength for low sound frequencies is about 10 m. This limits the minimum size of the object being examined. Additionally, this leads to a few areas, each with a very large size, being partitioned, which does not allow for compiling of the correct system of equations. Therefore, to date, we are not aware of any attempts to create low-frequency magnetic scanning devices that can be used for large-sized ferromagnetic objects with a high magnetic signal. Thus, for the first time, in this work we propose a new device and a new algorithm for processing a low-frequency electromagnetic signal from an object, which mainly consists of a magnetic fraction, with the addition of non-magnetic inclusions. The principle of scanning such an object is to consistently measure the magnetic signal and to measure the total mass of the object. Non-magnetic inclusions do not contribute to the magnetic component of the signal, but they contribute to the total mass of the object. In some cases, this allows us to estimate the mass fractions of the magnetic and non-magnetic fractions. The best method for measuring a low-frequency magnetic signal is a conventional high-inductance solenoid (inductance coil). The express control process, which is based on the measurement of the parameters of the inductor coil, through which the inspected freight passes at its core, is free from the aforementioned drawbacks. The dimensions of the solenoid compared to the length of the object being measured,with an approximation sufficient for our purposes, enable application of the equations describing the inductance of a long solenoid (Figure 1). Solenoid coil inductance can be calculated with the following equation [15]:  
\[L=A_{L}\mu_{r}N^{2} \tag{1}\]  
where \(N\) is the turn number of the coil, \(\mu_{r}\) is the relative magnetic permeability of the coil core (when there is a core), and \(A_{L}\) is the coefficient defined by the coil geometric parameters:  
\[A_{L}=\mu_{0}\frac{S_{e}}{l_{e}}, \tag{2}\]  
where \(\mu_{0}\) is the vacuum magnetic permeability, \(S_{e}\) is the cross-section area of the coil (core), and \(l_{e}\) is the effective magnetic path length. Equations (1) and (2) show that coil inductance is directly proportional to the core magnetic permeability (susceptibility), and the core cross-section area. Thus, any non-magnetic or weakly magnetic inclusions in the core (freight) will add to the coil inductance to an extent that can be calculated when measuring this parameter (or values related to it) and will connect it with the mass-dimensional characteristics of the inspected freight. The application of a sinusoidal alternating voltage to the ideal inductance coil, i.e., to the coil with zero ohmic resistance, the zero capacity, and no core, results in the appearance of an alternating current in the coil that changes with time according to sinusoidal law and lags behind the voltage by which it was caused by \(\pi/2\). The actual coil with no core is characterized by finite ohmic resistance and capacity, so the circuit equivalent to the coil may be presented as active (ohmic) resistance \(R\), connected in a series with inductive resistance \(X_{L}\), both of them connected in parallel to reactive capacitive resistance \(R_{C}\), the two latter values being calculated via the following equations respectively [15]:  
\[X_{L}=\omega L, \tag{3}\]  
\[R_{C}=\frac{1}{\omega C_{k}}, \tag{4}\]  
where \(L\) is the coil inductance, \(C_{k}\) is the coil capacity, \(\omega=2\pi f\) is the cyclic frequency, and \(f\) is the alternating voltage (current) frequency. Figure 1: Experimental setup diagram. 1. Railway car, 2. Measuring coil system, 3. Building construction elements, 4. Platform car weights, 5. Signal reception and processing system.