Index of /rozprawy2/10621

Cyclostationarity Analysis Methods for Diagnostics of Machinery Under Varying Operational Conditions

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Table of contents

1.



Introduction ... 13



1.1



Goal and scope of the thesis ... 17



1.2



Organization of the thesis ... 18



2.



Preliminary case studies ... 21



2.1



Machinery operating in high noise disturbances ... 22



2.1.1



Object description - reciprocating compressor... 22



2.1.2



System description ... 22



2.1.3



Typical vibration signals generated by gas compressor ... 23



2.1.4



Bearing fault detection ... 24



2.1.5



Conclusions ... 27



2.2



Comparison of advanced fault detection methods for rolling bearings ... 27



2.2.1



Object description - wind turbine ... 27



2.2.2



Case study: Rolling element bearing fault ... 30



2.2.3



Comparison of fault detection methods ... 31



2.2.4



Configuration of methods ... 37



2.2.5



Conclusions ... 38



3.



Cyclostationarity in vibration analysis ... 41



3.1



What is cyclostationarity? ... 42



3.2



First order cyclostationary process ... 43



3.3



Second order cyclostationary process ... 45



3.4



Exemplary signal ... 46



3.5



Existing cyclostationarity tools used for vibration analysis ... 48



3.5.1



Power spectral density (PSD) ... 49



Jacek Urbanek

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3.5.3



Spectral correlation density ... 51



3.5.4



Instantaneous power spectrum ... 52



4.



Estimation of instantaneous shaft speed ... 55



4.1



State-of-the-art signal processing methods for speed reconstruction ... 57



4.1.1



Description of varying operational conditions of wind turbines ... 58



4.2



Wind turbine used for experiments ... 58



4.3



Concept of narrowband speed estimation methods... 61



4.3.1



Phase-based method ... 61



4.3.2



Period timing method ... 63



4.3.3



Case study ... 64



4.3.4



Conclusions ... 65



4.4



Advanced time-frequency based method ... 67



4.4.1



Experiment Description. ... 67



4.4.2



Time-frequency segmentation method description ... 69



4.4.3



Results of instantaneous frequency (IF) estimation ... 72



4.4.4



Conclusion ... 74



4.5



Two-step procedure ... 75



4.5.1



Principles of the two-step IF estimation procedure ... 75



4.5.2



Algorithmic aspects of the method... 76



4.5.3



Laboratory experiment ... 80



4.5.4



Conclusions ... 83



4.6



Comparison of methods ... 84



4.6.1



Time-frequency method ... 84



4.6.2



Phase-based method ... 85



4.6.3



Two-step speed estimation procedure ... 86



Cyclostationarity Analysis Methods for Diagnostics of Machinery Under Varying Operational Conditions

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4.6.5



Conclusions ... 94



5.



Detection of cyclostationary components in vibration signals ... 95



5.1



Detection of modulating components ... 97



5.1.1



Information carried by modulations in vibration signals ... 97



5.1.2



Types of modulations in mechanical systems ... 98



5.1.3



Proposal of a modulation intensity distribution ... 102



5.1.4



Integrated MID ... 109



5.1.5



Kurtosis of envelope spectrum as modulation intensity factor ... 111



5.1.6



Laboratory experiment ... 113



5.1.7



Conclusions ... 120



5.2



Practical aspects of Integrated MID ... 121



5.2.1



Spectral coherence as a particular case of modulation intensity distribution ... 121



5.2.2



Simulated signal example ... 124



5.2.3



Capability of spectral correlation for detection of cyclostationary components ... 128



5.2.4



Link between IMID and low-SNR maximum likelihood synchronizer. ... 130



5.2.5



Simulated signal experiment ... 132



5.2.6



Case study – wind turbine ... 134



5.2.7



Conclusions ... 141



6.



Extraction of cyclostationary components ... 143



6.1



Averaged instantaneous power spectrum ... 144



6.1.1



Influence of varying operational conditions to vibration analysis ... 144



6.1.2



The concept of Instantaneous Power Spectrum ... 146



6.1.3



The angular domain Instantaneous Power Spectrum ... 148



6.1.4



Simulated data experiment ... 151



6.1.5



Test rig experiment ... 152



Jacek Urbanek

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6.1.7



Conclusions ... 157



6.2



The time – frequency approach ... 158



6.2.1



The angular domain Averaged Instantaneous Power Spectrum ... 158



6.2.2



Extraction of selected component ... 163



6.2.3



Simulated signal experiment ... 164



6.2.4



Case study – Wind Turbine ... 170



6.2.5



Conclusions ... 171



7.



Summary ... 173



7.1



Results ... 173



7.2



Further works ... 175