Vibration Analysis Based on HJ-Biplots



Published Nov 20, 2020
Valter Vairinhos Rui Parreira Suzana Lampreia Vitor Lobo Purificación Galindo


Vibration Analysis (VA) is now routinely used for condition monitoring and failure diagnosis in Condition Based Maintenance (CBM). In the context of VA, a methodology is proposed, based on biplots, to simultaneously display both vibration frequencies and their measurement points, in support of monitoring and diagnostics tasks.
In this research, real observational data obtained measuring mechanical vibrations on four generators aboard a Portuguese Navy Ship in real operating conditions is used. A portable vibration collector was employed, and the measurements were taken at 13 measurement points in each one of four generators, using the same collector settings. Spectrograms resulting from vibration measurements were transformed into biplots and used for decision support according to the proposed methodology. Data analysis showed a robust stability in the macrostructure of biplots when observations resulting from different generators of the same model and at the same assumed conditions was analyzed. This invariance allows the specification of reference conditions, rules to detect changes of operating conditions and the emergence of failures. The proposed methodology, once embedded in dedicated software, will reduce the interpretation error in diagnosis and prognosis associated to variability in personnel training and experience. Consequently, it will increase the safe use of VA in an increasing number of situations.

Abstract 238 | PDF Downloads 266



CBM, vibration analysis, interpretation, sensor, Biplot, periodogram, observational data

Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods (2nd Edition). Springer Verlag, New York.
Beneke, M., Leemis, L. M., Schelegal, E., & Foote, B. (1988). Spectral analysis in quality control: A control chart based on periodogram. Technometrics, vol. 30(1), pp.63-70.
Benzécri, J. P. et Collaborateurs (1973). L’Analyse des Données. Dunod: Paris.
Emerson (2016). Process management CSI 2140 Machinery HealthTM Analyzer. User Guide.
Ferrer, Alberto (2014). Latent structures-based multivariate statistical process control: A paradigm shift. In Quality Engineering, vol. 26, pp. 72-91.
Fokianos, K., & Savvides, A. (2008). On comparing spectral densities. Technometrics, vol. 50(3), 317-331.
Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal components analysis. Biometrika, vol. 58(3), pp. 453-467.
Galindo, M. P. (1986). Una alternativa de representación simultánea: HJ-BIPLOT. Qüestiió, vol. 10(1), pp. 13-23.
García, D., & Trendafilova, I. (2014). A multivariate data-analysis approach towards vibration analysis and vabriation - based damage assessment: Application for determination detection in composite bean. Journal of Sound and Vibration, Vol. 333(25), pp. 7036-7050.
Gower, J. C., & Hand, D. J. (1996). Biplots. monographs on statistics and applied probability, vol. 54. Chapman & Hall: London.
Greenacre, M. J. (2010). Biplots in Practice. Retrieved from ([2017 January 10]).
Halliday, D. M., Rosenberg, J. R., Rigas, A., & Conway, B. A. (2009). A periodogram-based test for weak stationarity and consistency between sections in time series. In Journal of Neuroscience Methods, vol. 180, pp. 138-146.
Jones, Richard H. (1965). A reappraise of the periodogram in spectral analysis”. Technometrics, vol. 7(4), pp. 531-542.
Kolda, T. G., & Sun, J. (2008). Scalable tensor decompositions for multi-aspect data mining. In Data Mining 2008. ICDM’08, Eigtht IEEE International Conference on IEEE, 2008, pp. 363-372.
Kroonenberg, P. M. (2008). Applied multiway data analysis. Wiley: New Jersey.
Li, W., Shi, T., Liao, G., & Yang, S. (2003). Feature extraction and classification of gear faults using principal component analysis. Journal of Quality in Maintenance Engineering, vol. 9(2), pp. 132-143.
McSweeney, L. (2006). Comparison of periodogram tests. Journal of Statistical Computation and Simulation, vol. 76(4), pp. 357-369.
Mendes, S. L. C. M. (2011). Metodos multivariantes para evaluar patrones de estabilidad y cambio desde una perspectiva biplot. Tesis Doctoral. Universidad de Salamanca, España.
Mendes, S., Fernandez-Gomez, M. J., Pereira, M. J., Azeiteiro, U. M., & Galindo-Villardon, M. P. (2012), An empirical comparison of canonical correspondence analysis and atatico in the identification of spatio-temporal ecological relationships. Journal of Applied Statisticas, vol. 39(5).
Nieto, A. B., Galindo, M.P., Leiva, V., & Vicente-Galindo, P. (2014). A methodology for biplots based on bootstrapping with R. Revista Colombiana de Estadística, Current Topics in Statistical Graphics Diciembre 2014, vol. 37(2), pp. 367-397. Retrieved from ([2017 January 10]).
Papalexakis, E. E., & Faloutsos, C. (2015). Fast efficient and scalable core consistency diagnostics for the parafac decomposition for big sparse tensors. In Acoustics, Speech and Signal Processing LICASSP, 2015 IEEE International Conference on IEE.
Priestley, M.B. (1981). Spectral analysis and time series. Academic Press: London.
Ravishanker, N., Hosking, J. R. M., & Mukhopadhyay, J. (2010). Spectrum-based comparison of stationary multivariate time series. Methodol Comput Appl Probab 2010, vol. 12, pp. 749-762.
Vairinhos, V. M. (2003). Desarrollo de un sistema para minería de datos basado en los métodos biplot. Tesis Doctoral. Universidad de Salamanca (USAL), España.
Vairinhos, V. M., & Galindo, M. P. (2012). Biplots cilíndricos. Joclad 2012, XIX Jornadas de Classificação e Análise de Dados, pp. 132, Março 28-31, Tomar, Portugal.
Zhan, Y., Makis, V., & Jardine, A. K. S. (2003). Adaptive model for vibration monitoring of rotating machinery subject to random deterioration. Journal of Quality in Maintenance Engineering, vol. 9(4), pp. 351-375.
ISO 10816-3:2009 (2014). Mechanical vibration. Evaluation of machine vibration by measurements on non-rotating parts. Part 3, ISO Standards.
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