Jakub Obuchowski: Interdisciplinary PhD at the Hugo Steinhaus Center – Wroclaw University of Technology
Math students have a lot of opportunities of benefiting from their universal background. I graduated in Mathematics (Hugo Steinhaus Center, Wroclaw University of Technology) and then I started PhD studies in mining and geology (Machinery Systems Division, WrUT). In my interdisciplinary research I am applying mathematics in diagnostics of mining machines. Mining is one of the key industries in Poland. Issues related to safety and efficiency are of particular importance in every mining operation. Nowadays, in the era of mechanization, automation and robotics, performance of miners increasingly relies on condition of the machines that they are operating. Such machines are often designed exclusively for particular application, taking into account specific environment in which they will work. For instance, loaders used in specific underground mines have to be low-profiled, but they still have to carry appropriate volume of mined rock. In order to prevent from long and unexpected downtime the machines and structures are monitored using lots of sensors (temperature, pressure, current, tension, etc.). The sensors might be attached on the machine and then the measurements are performed online. Sometimes, such frequent measurements are not necessary or they are even physically impossible and then measurements might be performed e.g. on daily or monthly basis. Although, there are also machines for which diagnostic methods are still under development.
One of the most investigated problems in diagnosis of rotating machines (gears, bearings) diagnostics is local damage detection. Many methods incorporate analysis of a vibration signal acquired, for instance, using an accelerometer mounted on the considered machine. Mechanisms of damage development are rather complicated, but detection of a local damage might be simplified to searching for impulsive and cyclic (not necessarily periodic) content in the vibration signal. Such rapid and temporary increments of acceleration are related to contact between a damaged area (broken gear tooth, cracked bearing race etc., see Fig. 1) and other part of the gear or bearing. Such impulsive content is often hidden in the analyzed signal, since even a healthy gears and bearing generate vibrations. Often, the acquired signal is contaminated with vibrations of machines operating nearby the diagnosed one. Such case is revealed by mining machinery systems which are often really complex.
Application of mathematics in local damage detection comes down to vibration signal processing using several different domains, e.g. time, frequency, time-frequency or bi-frequency. These methods incorporate discrete Fourier transform and its inverse, Hilbert transform, analysis of autoregressive models in both time and frequency domains (including AR models with constant or time-varying coefficients), cyclostationarity, deconvolution under a non-Gaussianity criteria, wavelets, empirical mode decomposition etc. One of the methods for impulsive signal extraction relies on searching for a frequency band containing series of impulses. A promising approach is to quantify impulsivity of each frequency band using a specific measure (e.g. a non-Gaussianity measure) or periodicity demonstrated as an impulsive amplitude modulation of the carrier signal. The key problem related in particular to mining machines is an impulsive noise contaminating the vibration signal. Such noise might be caused by specific operation of the machine (e.g. copper ore crusher) or during data acquisition. A solution to this problem might be provided by an impulsivity measure sensitive to a series of impulses, not to a single one. Moreover, a discrimination between impulses related to local damage and those related to normal operation of the machine could be performed by assuming that the latter ones are non-cyclic. Of course, this resolves the problem only if rotational speed of the machine (bearing, gear) is approximately constant in time.
To sum up, mining is one of the industries where advanced mathematical tools have found beneficial application. Rotating machinery diagnostics is not the only one – signal processing, differential equations, statistics, etc. are also used in the mining industry. Moreover, some tools developed for one field of mining might be also applied in another one. For instance, signal processing methods developed for diagnostics of machines might be applied to seismic signals and vice versa. High requirements regarding applicability of mathematical theories are really challenging and might surely lead to new lines of research.
More on mining machinery diagnostics might be found in:
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Vibration Analysis of copper ore crushers used in Mineral Processing Plant – problem of bearings damage detection in presence of heavy impulsive noise, 2015
- Wyłomańska Agnieszka, Obuchowski Jakub, Zimroz Radosław, Hurd Harry: Influence of different signal characteristics to PAR model stability, in Applied Condition Monitoring. Cyclostationarity: Theory and Methods – II (Chaari et al. ed.), 89-104, 2015
- Obuchowski Jakub, Zimroz Radosław, Wyłomańska Agnieszka: Identification of cyclic components in presence of non-Gaussian noise application to crusher bearings damage detection, Journal of Vibroengineering, 17(3), 1242-1252, 2015
- Zimroz Radosław, Obuchowski Jakub, Wyłomańska Agnieszka: Bearings damage detection in presence of heavy non-Gaussian noise via cyclo-stationary analysis, Vibroengineering Procedia, 3, 88-92, 2014
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Recent developments in vibration based diagnostics of gear and bearings used in belt conveyors, Applied Mechanics and Materials, 683, 171-176, 2014
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Two-stage data driven filtering for local damage detection in presence of time varying signal to noise ratio, Vibration Engineering and Technology of Machinery Mechanisms and Machine Science, Vol. 23, 401-410, 2015
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Selection of informative frequency band in local damage detection in rotating machinery, Mechanical Systems and Signal Processing, 48(1-2), 138-152, 2014,
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: The local maxima method for enhancement of time-frequency map and its application to local damage detection in rotating machines, Mechanical Systems and Signal Processing, 46(2), 389-405, 2014
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: The local maxima method for enhancement of time-frequency map, Advances in Condition Monitoring of Machinery in Non-Stationary Operations, Lecture Notes in Mechanical Engineering, G. Dalpiaz et al. (eds.), 325-334, 2014
- Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Stochastic modeling of time series with application to local damage detection in rotating machinery, Damage Assessment of Structures in: Key Engineering Materials 569, 441-449, 2013
See more: http://labdiag.pwr.wroc.pl/jakobu
Contact person: Jakub Obuchowski (Machinery Systems Division, Faculty of Geoengineering, Mining and Geology, Wroclaw University of Technology, Poland)