In systems for monitoring, diagnostics and recognition of the state of various types of objects, an important aspect is the reduction of the volume of measured signal data for its transmission or accumulation in information bases with the ability to restore it without significant distortion. A special type of signals in this case are packet signals, which represent sets of harmonics with multiple frequencies and are truly periodic with a clearly distinguishable period. Signals of this type are typical for mechanical, electromechanical systems with rotating elements: reducers, gearboxes, electric motors, internal combustion engines, etc. The article considers a number of models for reducing these signals and cases of priority application of each of them. In particular, the following are highlighted: the discrete Fourier transform model with a modified formula for restoring a continuous signal, the proposed model based on decomposition by bordering functions and the discrete cosine transform model. The first two models ideally provide absolute accuracy of signal restoration after reduction, the last one refers to reduction models with information loss. The main criteria for evaluating the models are: computational complexity of the implemented transformations, the degree of implemented signal reduction, and the error in restoring the signal from the reduced data. It was found that in the case of application to packet signals, each of the listed models can be used, the choice being determined by the priority indicators of the reduction assessment. The application of the considered reduction models is possible in information and measuring systems for monitoring the state, diagnostics, and control of the above-mentioned objects.

Keywords: reduction model, measured packet signal, discrete cosine transform, decomposition into bordering functions, reduction quality assessment, information-measuring system

The article considers a variant of constructing a digital twin model for diagnostics of operation of a mechanical gear transmission - a reducer consisting of a pair of cylindrical gears. The basis of the considered digital twin model is an adaptive learning vibration mathematical model of the static operating mode when gears rotate at a constant speed. The vibration signals of the reducer, recorded by accelerometers and effective for detecting and diagnosing faults, are used as the main information measured at the facility. The detected faults are cracking, wear, chipping and pitting of teeth. A special feature of the implemented digital twin is the ability to simultaneously detect faults of several teeth at once, both on the driving and driven gears, by time and frequency characteristics, as well as the ability to determine the main technical data of a specific reducer by vibration characteristics.

Keywords: diagnostic mathematical model, digital twin, vibration diagnostics, mechanical gearbox, tooth defect, diagnostic signal, vibration power spectrum, synchronously averaged time characteristic