Spectral Analysis of a Signal Re-flected from the Lattice of Passive Reflectors Intersecting a Short-Range Radar System Beam

Abstract

Short-range radar systems (SRRS) can effectively be used for a wide range of practical applications concerned with diagnostics of equipment, mechanisms, devices and systems. Radar sensors are used in these fields as a fast, reliable, and accurate method for non-destructive contactless measurements of distances, vibrations, displacements, material thickness, and humidity for diagnosing the condition of objects. The specific feature of short-range radar systems is that the studied object is located in the antenna’s near or intermediate zone. In view of this circumstance, diffraction of electromagnetic waves caused by finite dimensions of both the antenna and the object should be taken into account. A mathematical model of the short-range radar system that takes the electromagnetic wave diffraction phenomenon into account is proposed. Hermite-Gaussian beams (HGB) are taken as the electromagnetic wave model. The object is represented as a structure consisting of a lattice of flats moving over a closed trajectory across the beam. The real structure is replaced by its involute with a period equal to the orbit length. Each flat of the lattice is turned by a certain angle with respect to its longitudinal axis. This model makes it possible to describe the motion of objects such as conveyor lines, conveyor belts, chain gears, and fans. It is shown that the reflected signal is a cross-correlation function of the radar and object functions. The product of the spectra of these functions is the spectrum of the SRRS signal. The spectrum of the radar system function in the HGB model is expressed in analytical form. The object function is defined by the shape and parameters of the object. For the lattice of flats it is expressed in analytic form; for other configurations it can be found using the FFT procedure. If necessary, the reflection coefficient time dependence is restored using the FFT. The reflection coefficient spectra for some specific configurations have been obtained. The possibility to diagnose the state of a structure from the reflected signal envelope spectrum is demonstrated, a feature that significantly reduces the calculation time and extends the possibilities of numerical simulation. It is recommended to use the model spectrum in processing a real signal as a digital filter. The characteristics of such filter can be adapted to the real signal by varying the model parameters. The use of filtration will allow more reliable diagnostics of the object state to be obtained. It is shown---within the framework of the proposed model---that structural flaws can be modeled by changing the rotation angles of flats, the coordinates of their centerlines, and the displacement of the lattice as a whole. The developed algorithm for calculating the complex reflection coefficient from the object located in the near-field region of the SRRS emitter and moving along a closed trajectory makes it possible to simulate signals reflected from specific machines and mechanisms. This will open the possibility of developing procedures for diagnosing the state of such objects.