Wstępna analiza zebranych sygnałów oraz zdefiniowanie odpowiedniej dla nich nowej klasy Autorzy: Urbanek J., Jabłoński A.

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1 Wstępna analiza zebranych sygnałów oraz zdefiniowanie odpowiedniej dla nich nowej klasy Autorzy: Urbanek J., Jabłoński A., Barszcz T Sprawozdanie z wykonania zadania nr 5 projektu badawczego IP pt. Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych warunkach operacyjnych Dokument zawiera wyniki pracy badawczej, która pozwoliła opracować unikatową, nową klasę sygnałów, umożliwiającą opisywanie sygnałów generowane przez maszyny wirnikowe pracujące w silnie zmiennych warunkach eksploatacyjnych. W trakcie realizacji zadania 5 i 6 (następnego), zespół badawczy będzie pracował nad czterema publikacjami naukowymi odzwierciedlającymi zakres prowadzonych prac. W raporcie zestawiono abstrakty artykułów. Dokument sporządzono w języku angielskim Urbanek J., Jabłoński A., Barszcz T ssswedfsdfurbanek J., Jabłoński A., Barszcz T., Wykonanie pomiarów sygnałów wibroakustycznych przy stałych oraz zmiennych warunkach eksploatacyjnych na 0 stanowisku testowym. Część II: Analiza poprawności pomiarów.

2 Outline 1 Introduction Preliminary analysis of recorded data Application for visualization of long speed profiles Application for visualization of speed and load profiles in sessions Application for visualization of time and frequency signal characteristics Classification of vibration signals Problem definition Classification of signals first approach The concept of stationarity of real signals Classification of signals second approach The concept of cyclo-stationarity Proposition of a novel class of vibration signals Bibliography Appendix A Sessions with a damaged bearing Appendix B Sessions with a damaged bearing and imbalance Appendix D Abstracts

3 1 Introduction The main goal of the current task of the project is to propose a definition of a novel class of signals, which would encapsulate signals generated by machinery working under highly fluctuating operational parameters. In order to achieve this goal, the task includes: preliminary analysis of recorded data (supplementary to analysis described in section 5.5 in the report from task No.4), study of available classes of vibration signals with emphasis on non-stationary signals, development of a proposition of a novel class of signals, verification of the developed class on simulated signals. As a results of the realization of the task, we achieved the following: development of attributes and constraints of a novel class of signals, development of conceptual scheme for a mathematical model of the signals, which is to be investigated in details in next task of the project, conceptual development and submission of four abstracts of publications to the 4th International Conference on Condition Monitoring of Machinery in Non-Stationary Operations (CMMN0'2014) will be held in Lyon (France) during the 15th, 16th and 17th of December 2014: Varying-coefficient based modeling of wind turbine vibration features and its application to condition monitoring, Application of angular-temporal spectrum for detection of rolling-element bearing faults operating under varying speed regime, Blind separation of vibration components for rotor machinery operating under highly nonstationary regime, Modeling of rotating machine vibration signals operating under highly varying speed and load. During the tasks 5 and 6, we have worked on the listed four papers. 2

4 2 Preliminary analysis of recorded data The goal of the preliminary analysis of the data was to verify the contents of the recorded data in all channels and observe the relationship (and degree of its repeatability) between the highly fluctuating process parameters and the values of wideband diagnostic estimators. The verification of the frequency contents is illustrated in chapter 5 in report from task No.4, part II: - verification of vibration levels with respect to machine vibration level, sensors sensitivity, and data acquisition unit gain settings (section 5.1), - verification of time-domain characteristics with respect to single-to-noise (SNR) ratio and measurement channel offset characteristics (section 5.2), - verification of frequency-domain characteristics in terms of detection of resonant frequency ranges (section 5.3), - verification of time-frequency characteristics in terms of assessment of signal stationarity level (section 5.4) A partial preliminary analysis of has been conducted in advance to the project schedule and has been reported section 5.5 in report from task No.4, part II (pages 14-17). The current chapter illustrates a supplementary analysis of data, including additionally recorded data, which is a set of 60-second signals with extreme fluctuations of speed. Within the current task, the team has developed a three stand-alone applications for rapid data analysis. 2.1 Application for visualization of long speed profiles The application view_txt_manual enables visualization of the real phase marker signal along with resulting instantaneous speed profile. 3

5 Figure 1. Visualization of speed profile from session 001 (bottom; raw phase marker signal, zoom (top) The applications enables verification of the phase marker signal and display of the instantaneous speed profile. The application accepts raw files recorded with National Instruments DAQ stored as text files with comma-separated values. The instantaneous speed profile implies that the test rig purchased within the project has outstanding capability of simulation extremely fluctuating operational parameters of rotary machinery. 4

6 2.2 Application for visualization of speed and load profiles in sessions The application view_txt_session enables visualization of the instantaneous speed profile and averaged torque profile. Figure 2. Visualization of exemplary properly recorded session The exemplary session illustrates a correctly recorded data, where the speed and torque have been monotonically increased according to the a predefined scheme described in task No. 4. 5

7 Figure 3. Visualization of exemplary of improperly recorded session The exemplary session illustrates a incorrectly recorded data, where the speed and torque have been monotonically increased according to the a predefined scheme described in task No. 4. The incorrect values of instantaneous speed are marked with two black arrows. This errors have occurred as a result of errors in the control application of the test rig. 2.3 Application for visualization of time and frequency signal characteristics The application view_txt_session enables visualization of the instantaneous speed profile and averaged torque profile. 6

8 Figure 4. Visualization of exemplary time signal (top), frequency spectrum (center), and envelope spectrum (bottom) The exemplary signal (No. 121 form session 001) shows a time view, frequency spectrum, and envelope spectrum for a signal recorded with a maximum braking motor torque (100%) and maximum running motor speed (nominally 3000 rpm). The time signal is scaled in second, whereas frequency and envelope spectra are scaled in Hertz. Figure 4 clearly shows that the dominant component in the spectrum is the gear meshing frequency, whereas the dominant component in the envelope spectrum is the characteristic frequency of the ball passing through the outer race (BPFO). The developed applications shown in chapter 2 are necessary for efficient preliminary analysis of the data because they: - enable rapid visualization and grasping of recorded signals, - enable easy rejection of improperly signals, - aided in formulation of preliminary conclusions about relationship between signal contents and instantaneous values of process parameters, - enable a quick review of recorded signals at any future part of the project as well any following scientific activities with the data. 7

9 3 Classification of vibration signals 3.1 Problem definition The classification of signals is a well-developed branch of interdisciplinary science, which overlaps among telecommunication, mathematics, signal processing, and machine exploitation. Within the general problem of signal classification, two basic concerns are to be listed: a) formulation of analytical description of a signal, b) selection of proper tools. The first concern is a classical scientific theoretical problem, because it get backs to development of mathematical formulas, which enable description of a signal. The description of a signal is actually a recipe for any value of a signal in the very same way as it is done in case of well-known signal description, e.g. x(t) = sin(t). In this case, the formula enables calculation of the value of x for every t. Naturally, formulation of analytical description of a signal is a trivial task only for a limited group of signals, generally deterministic, 1-dimensional signals. In case of real signal from physical objects, a number of constraints must be taken into account. For analysis of vibration signals recorded from rotor machinery, the most significant aspects, which ought to be taken into account include: - finite length of all signals, - degree of stationarity of signals, - visible periodicity of deterministic components, - relationship of visible deterministic components to phase, - frequency description of the signal in terms of local resonant ranges, - hidden periodicity of deterministic components, - relationship of visible deterministic components to phase, - relationship of stochastic components to phase. Sections 3.2 and 3.3 illustrate two very different concepts of signal classification currently accepted in scientific world. The red ellipse shows the place of non-stationary signals in both classifications, whereas the blue ellipse shows the random class in both graphs. The team members opinion sates that the differentiation between the two classification is a result of a trial of classification of non-tree structure via a classical tree structure. The second concern aids in signal analysis by helping in selection of proper tools, transforms, and 8

10 techniques for data analysis. For instance, if a steady-state signal is to be analyzed, Fourier Transform precisely determines frequency content. If a machine run-up is analyzed for determination of critical speed values, a waterfall plots would be a proper tool. 3.2 Classification of signals first approach The classification of vibration signals has been presented in scientific literature in general different ways. Figure 5. Classification according to Prof. R.B. Randall (UNSW, Australia) According to Prof. Randall, all signals are classified either as stationary or non-stationary. Within the stationary class, Prof. Randall differentiates between random signals (e.g. noise) and deterministic signals, Random signals are such that their value at any time cannot be predicted, but for stationary random signals their statistical properties are unchanging with time [5]. On the other hand, deterministic signals are composed entirely of discrete frequency sinusoids and thus their frequency spectrum consists of discrete lines at the frequencies of those sinusoids. Once the frequency, amplitude and initial phase (i.e. at time zero) of these components is known, the value of the signal can be predicted at any time in the future or past; hence the term deterministic [5]. 9