Investigating computational geometry for failure prognostics
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Published
Nov 1, 2020
Emmanuel Ramasso
Abstract
Prognostics and Health Management (PHM) is a multidisciplinary field aiming at maintaining physical systems in their optimal functioning conditions. The system under study is assumed to be monitored by sensors from which are obtained measurements reflecting the system’s health state. A health indicator (HI) is estimated to feed a data-driven PHM solution developed to predict the remaining useful life (RUL). In this paper, the values taken by an HI are assumed imprecise (IHI). An IHI is interpreted as a planar figure called polygon and a case-based reasoning (CBR) approach is adapted to estimate the RUL. This adaptation makes use of computational geometry tools in order to estimate the nearest cases to a given testing instance. The proposed algorithm called RULCLIPPER is assessed and compared on datasets generated by the NASA’s turbofan simulator (C-MAPSS) including the four turbofan testing datasets and the two testing datasets of the PHM’08 data challenge. These datasets represent 1360 testing instances and cover different realistic and difficult cases considering operating conditions and fault modes with unknown characteristics. The problem of feature selection, health indicator estimation, RUL fusion and ensembles are also tackled. The proposed algorithm is shown to be efficient with few parameter tuning on all datasets.
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Keywords
Data Uncertainty, CMAPPS datasets, Prediction method, Pattern matching, Geometry, Similar-based modeling, Computational geometry
References
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Beer, M., Ferson, S., & Kreinovich, V. (2013). Imprecise probabilities in engineering analyses. Mechanical Systems and Signal Processing, 37(1-2), 4-29.
Bentley, J., & Ottmann, T. (1979). Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput., C28, 643-647.
Bonissone, P., Varma, A., & Aggour, K. (2005). A fuzzy instance-based model for predicting expected life: A locomotive application. In IEEE int. conf. on computational intelligence for measurement systems and applications (p. 20-25).
Celaya, J., Kulkarni, C., Biswas, G., & Goebel, K. (2012). Towards a model based prognostics methodology for electrolytic capacitors a case study based on electrical overstress accelerated aging. Int. Journal of Prognostics and Health Management, 3(2-004), 1-19.
Chazelle, B., & Edelsbrunner, H. (1992). An optimal algorithm for intersecting line segments in the plane. J. Assoc. Comput. Mach, 39, 1-54.
Chen, C., Zhang, B., Vachtsevanos, G., & Orchard, M. (2011). Machine condition prediction based on adaptive neuro-fuzzy and high-order particle filtering. IEEE Trans. on Industrial Electronics, 58(9), 4353-4364.
Coble, J. (2010). Merging data sources to predict remaining useful life - an automated method to identify prognostic parameters (Unpublished doctoral dissertation). University of Tennessee, Knoxville.
Coble, J., & Hines, J. W. (2011). Applying the general path model to estimation of remaining useful life. Int. Journal on Prognostics and Health Management, 2, 326-337.
Daigle, M., & Goebel, K. (2011). A model-based prognostics approach applied to pneumatic valves. Int. Journal of Prognostics and Health Management, 2(2-008), 1-16.
Filippov, A. (1950). An elementary proof of Jordan’s theorem. Uspekhi Mat. Nauk, 5, 173-176.
Gelman, I., Patel, T., Murray, B., & Thomson, A. (2013). Rolling bearing diagnosis based on the higher order spectra. Int. Journal of Prognostics and Health Management, 4(2-022), 1-9.
Goharrizi, A. Y., & Sepehri, N. (2010). A wavelet-based approach to internal seal damage diagnosis in hydraulic actuators. IEEE Trans. on Industrial Electronics, 57(5), 1755-1763.
Gouriveau, R., Ramasso, E., & Zerhouni, N. (2013). Strategies to face imbalanced and unlabelled data in PHM applications. Chemical Engineering Trans., 33, 115-120.
Gouriveau, R., & Zerhouni, N. (2012). Connexionistsystems- based long term prediction approaches for prognostics. IEEE Trans. on Reliability, 61, 909-920.
Greiner, G., & Hormann, K. (1998). Efficient clipping of arbitrary polygons. ACM Trans. on Graphics, 17, 71-83.
Gucik-Derigny, D., Outbib, R., & Ouladsine, M. (2011). Prognosis applied to an electromechanical system, a nonlinear approach based on sliding mode observer. In Annual conf. on european safety and reliability association.
Gustafson, E., & Kessel, W. (1978). Fuzzy clustering with a fuzzy covariance matrix. In IEEE conf. on decision and control.
He, D., & Bechhoefer, E. (2008). Development and validation of bearing diagnostic and prognostic tools using HUMS condition indicators. In IEEE aerospace conf.
He, D., Bechhoefer, E., & Saxena, A. (2013). Editorial: Special issue on wind turbine phm. Int. Journal of Prognostics and Health Management, 4(4-031), 2.
Heimes, F. (2008). Recurrent neural networks for remaining useful life estimation. In IEEE int. conf. on prognostics and health management.
Hu, C., Youn, B., Wang, P., & Yoon, J. (2012). Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life. Reliability Engineering and System Safety, 103, 120 - 135.
Javed, K., Gouriveau, R., & Zerhouni, N. (2013). Novel failure prognostics approach with dynamic thresholds for machine degradation. In IEEE industrial electronics conf.
Khelif, R., Malinowski, S., Morello, B., & Zerhouni, N. (2014). Rul prediction based on a new similarityinstance based approach. In IEEE ISIE. Istambul, Turkey.
Klir, G., & Wierman, M. (1999). Uncertainty-based information. elements of generalized information theory. In (chap. Studies in fuzzyness and soft computing). Physica-Verlag.
Kuncheva, L. I. (2004). Combining pattern classifiers: Methods and algorithms. Wiley-Interscience.
Lapira, E., Siegel, D., Zhao, W., Brisset, D., Su, J., Wang, C., . . . Lee, J. (2011). A systematic framework for wind turbine health assessment under dynamic operating conditions. In 24th int. congress on condition monitoring and diagnostics engineering management.
Liu, K., Gebraeel, N. Z., & Shi, J. (2013). A data-level fusion model for developing composite health indices for degradation modeling and prognostic analysis. IEEE Trans. on Automation Science and Engineering.
Longley, P., de Smith, M., & Goodchild, M. (2007). Geospatial analysis : A comprehensive guide to principles, techniques and software tools. Matador, Leicester.
Margalit, A., & Knott, G. (1989). An algorithm for computing the union, intersection or difference of two polygons. Computers & Graphics, 13, 167-183.
Mulligan, K., Yang, C., Quaegebeur, N., & Masson, P. (2013). A data-driven method for predicting structural degradation using a piezoceramic array. Int. Journal of Prognostics and Health Management, 4(2-037), 1-14.
Orchard, M., Cerda, M., Olivares, B., & Silva, J. (2012). Sequential monte carlo methods for discharge time prognosis in lithium-ion batteries. Int. Journal of Prognostics and Health Management, 3(2-010), 1-12.
Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vachtsevanos, G. (2008). Advances in uncertainty representation and management for particle filtering applied to prognostics. In Int. conf. on prognostics and health management.
Peel, L. (2008). Data driven prognostics using a Kalman filter ensemble of neural network models. In Int. conf. on prognostics and health management.
Peng, T., He, J., Liu, Y., Saxena, A., Celaya, J., & Goebel, K. (2012). Integrated fatigue damage diagnosis and prognosis under uncertainties. In Annual conf. of prognostics and health management.
Powers, D. (2011). Evaluation: From precision, recall and F-factor to ROC, informedness, markedness & correlation. Journal of Machine Learning Technologies, 2,37-63.
Ramasso, E. (2014). Investigating computational geometry for failure prognostics in presence of imprecise health indicator: results and comparisons on CMAPSS datasets. In European conference of the prognostics and health management society (Vol. 5, p. 1-13).
Ramasso, E., & Denoeux, T. (2013). Making use of partial knowledge about hidden states in hidden Markov models: an approach based on belief functions. IEEE Trans. on Fuzzy Systems, 22(2), 395-405.
Ramasso, E., & Gouriveau, R. (2013). RUL estimation by classification of predictions: an approach based on a neuro-fuzzy system and theory of belief functions. IEEE Trans. on Reliability, Accepted.
Ramasso, E., Rombaut, M., & Zerhouni, N. (2013). Joint prediction of observations and states in time-series based on belief functions. IEEE Trans. on Systems, Man and Cybernetics - Part B: Cybernetics, 43, 37-50.
Riad, A., Elminir, H., & Elattar, H. (2010). Evaluation of neural networks in the subject of prognostics as compared to linear regression model. Int. Journal of Engineering & Technology, 10, 52-58.
Richter, H. (2012). Engine models and simulation tools. In Advanced control of turbofan engines (p. 19-33). Springer New York.
Rigaux, P., Scholl, M., & Voisard, A. (2002). Spatial databases with application to gis (E. Science, Ed.). Kauffman Publishers.
Rosen, K. (2004). Handbook of discrete and computational geometry, second edition (J. E. Goodman & J. O’Rourke, Eds.). Chapman and Hall/CRC.
Saha, B., Goebel, K., & Christophersen, J. (2008). Comparison of prognostic algorithms for estimating remaining useful life of batteries. Trans. of the Royal UK Institute on Measurement & Control, special issue on Intelligent Fault Diagnosis & Prognosis for Engineering Systems, 293-308.
Saha, B., Goebel, K., Poll, S., & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a Bayesian framework. IEEE Trans. on Instrumentation and Measurement, 58, 291-296.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2009). Uncertainty quantification in fatigue damage prognosis. In Annual conf. of the prognostics and health management society.
Sarkar, S., Jin, X., & Ray, A. (2011). Data-driven fault detection in aircraft engines with noisy sensor measurements. Journal of Engineering for Gas Turbines and Power, 133, 081602.
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In Int. conf. on prognostics and health management (p. 1-17).
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine runto- failure simulation. In Int. conf. on prognostics and health management (p. 1-9). Denver, CO, USA.
Saxena, A., Wu, B., & Vachtsevanos, G. (2005). Integrated diagnosis and prognosis architecture for fleet vehicles using dynamic case-based reasoning. In Autotestcon (p. 96-102).
Serir, L., Ramasso, E., & Zerhouni, N. (2013). E2GKpro: An evidential evolving multi-modeling approach for system behavior prediction with applications. Mechanical Systems and Signal Processing, 37(1-2), 213-228. doi: 10.1016/j.ymssp.2012.06.023
Simon, D. (2012). Challenges in aircraft engine gas path health management. (Tutorial on Aircraft Engine Control and Gas Path Health Management Presented at 2012 Turbo Expo)
Vachtsevanos, G. (2006). Intelligent fault diagnosis and prognosis for engineering systems. Wiley, Hoboken, NJ.
Vatti, B. R. (1992). A generic solution to polygon clipping. Communications of the ACM, 35, 56-63.
Wang, P., Youn, B., & Hu, C. (2012). A generic probabilistic framework for structural health prognostics and uncertainty management. Mechanical Systems and Signal Processing, 28, 622 - 637.
Wang, T. (2010). Trajectory similarity based prediction for remaining useful life estimation (Unpublished doctoral dissertation). University of Cincinnati.
Wang, T., Yu, J., Siegel, D., & Lee, J. (2008). A similaritybased prognostics approach for remaining useful life estimation of engineered systems. In Ieee int. conf. on prognostics and health management (p. 1-6).
Zein-Sabatto, S., Bodruzzaman, J., & Mikhail, M. (2013). Statistical approach to online prognostics of turbine engine components. In Proc. of IEEE southeastcon (p. 1-6).
Zhang, X., & Pisu, P. (2014). Prognostic-oriented fuel cell catalyst aging modeling and its application to healthmonitoring and prognostics of a PEM fuel cell. Int. Journal of Prognostics and Health Management, 5(1- 003), 1-16.
Beer, M., Ferson, S., & Kreinovich, V. (2013). Imprecise probabilities in engineering analyses. Mechanical Systems and Signal Processing, 37(1-2), 4-29.
Bentley, J., & Ottmann, T. (1979). Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput., C28, 643-647.
Bonissone, P., Varma, A., & Aggour, K. (2005). A fuzzy instance-based model for predicting expected life: A locomotive application. In IEEE int. conf. on computational intelligence for measurement systems and applications (p. 20-25).
Celaya, J., Kulkarni, C., Biswas, G., & Goebel, K. (2012). Towards a model based prognostics methodology for electrolytic capacitors a case study based on electrical overstress accelerated aging. Int. Journal of Prognostics and Health Management, 3(2-004), 1-19.
Chazelle, B., & Edelsbrunner, H. (1992). An optimal algorithm for intersecting line segments in the plane. J. Assoc. Comput. Mach, 39, 1-54.
Chen, C., Zhang, B., Vachtsevanos, G., & Orchard, M. (2011). Machine condition prediction based on adaptive neuro-fuzzy and high-order particle filtering. IEEE Trans. on Industrial Electronics, 58(9), 4353-4364.
Coble, J. (2010). Merging data sources to predict remaining useful life - an automated method to identify prognostic parameters (Unpublished doctoral dissertation). University of Tennessee, Knoxville.
Coble, J., & Hines, J. W. (2011). Applying the general path model to estimation of remaining useful life. Int. Journal on Prognostics and Health Management, 2, 326-337.
Daigle, M., & Goebel, K. (2011). A model-based prognostics approach applied to pneumatic valves. Int. Journal of Prognostics and Health Management, 2(2-008), 1-16.
Filippov, A. (1950). An elementary proof of Jordan’s theorem. Uspekhi Mat. Nauk, 5, 173-176.
Gelman, I., Patel, T., Murray, B., & Thomson, A. (2013). Rolling bearing diagnosis based on the higher order spectra. Int. Journal of Prognostics and Health Management, 4(2-022), 1-9.
Goharrizi, A. Y., & Sepehri, N. (2010). A wavelet-based approach to internal seal damage diagnosis in hydraulic actuators. IEEE Trans. on Industrial Electronics, 57(5), 1755-1763.
Gouriveau, R., Ramasso, E., & Zerhouni, N. (2013). Strategies to face imbalanced and unlabelled data in PHM applications. Chemical Engineering Trans., 33, 115-120.
Gouriveau, R., & Zerhouni, N. (2012). Connexionistsystems- based long term prediction approaches for prognostics. IEEE Trans. on Reliability, 61, 909-920.
Greiner, G., & Hormann, K. (1998). Efficient clipping of arbitrary polygons. ACM Trans. on Graphics, 17, 71-83.
Gucik-Derigny, D., Outbib, R., & Ouladsine, M. (2011). Prognosis applied to an electromechanical system, a nonlinear approach based on sliding mode observer. In Annual conf. on european safety and reliability association.
Gustafson, E., & Kessel, W. (1978). Fuzzy clustering with a fuzzy covariance matrix. In IEEE conf. on decision and control.
He, D., & Bechhoefer, E. (2008). Development and validation of bearing diagnostic and prognostic tools using HUMS condition indicators. In IEEE aerospace conf.
He, D., Bechhoefer, E., & Saxena, A. (2013). Editorial: Special issue on wind turbine phm. Int. Journal of Prognostics and Health Management, 4(4-031), 2.
Heimes, F. (2008). Recurrent neural networks for remaining useful life estimation. In IEEE int. conf. on prognostics and health management.
Hu, C., Youn, B., Wang, P., & Yoon, J. (2012). Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life. Reliability Engineering and System Safety, 103, 120 - 135.
Javed, K., Gouriveau, R., & Zerhouni, N. (2013). Novel failure prognostics approach with dynamic thresholds for machine degradation. In IEEE industrial electronics conf.
Khelif, R., Malinowski, S., Morello, B., & Zerhouni, N. (2014). Rul prediction based on a new similarityinstance based approach. In IEEE ISIE. Istambul, Turkey.
Klir, G., & Wierman, M. (1999). Uncertainty-based information. elements of generalized information theory. In (chap. Studies in fuzzyness and soft computing). Physica-Verlag.
Kuncheva, L. I. (2004). Combining pattern classifiers: Methods and algorithms. Wiley-Interscience.
Lapira, E., Siegel, D., Zhao, W., Brisset, D., Su, J., Wang, C., . . . Lee, J. (2011). A systematic framework for wind turbine health assessment under dynamic operating conditions. In 24th int. congress on condition monitoring and diagnostics engineering management.
Liu, K., Gebraeel, N. Z., & Shi, J. (2013). A data-level fusion model for developing composite health indices for degradation modeling and prognostic analysis. IEEE Trans. on Automation Science and Engineering.
Longley, P., de Smith, M., & Goodchild, M. (2007). Geospatial analysis : A comprehensive guide to principles, techniques and software tools. Matador, Leicester.
Margalit, A., & Knott, G. (1989). An algorithm for computing the union, intersection or difference of two polygons. Computers & Graphics, 13, 167-183.
Mulligan, K., Yang, C., Quaegebeur, N., & Masson, P. (2013). A data-driven method for predicting structural degradation using a piezoceramic array. Int. Journal of Prognostics and Health Management, 4(2-037), 1-14.
Orchard, M., Cerda, M., Olivares, B., & Silva, J. (2012). Sequential monte carlo methods for discharge time prognosis in lithium-ion batteries. Int. Journal of Prognostics and Health Management, 3(2-010), 1-12.
Orchard, M., Kacprzynski, G., Goebel, K., Saha, B., & Vachtsevanos, G. (2008). Advances in uncertainty representation and management for particle filtering applied to prognostics. In Int. conf. on prognostics and health management.
Peel, L. (2008). Data driven prognostics using a Kalman filter ensemble of neural network models. In Int. conf. on prognostics and health management.
Peng, T., He, J., Liu, Y., Saxena, A., Celaya, J., & Goebel, K. (2012). Integrated fatigue damage diagnosis and prognosis under uncertainties. In Annual conf. of prognostics and health management.
Powers, D. (2011). Evaluation: From precision, recall and F-factor to ROC, informedness, markedness & correlation. Journal of Machine Learning Technologies, 2,37-63.
Ramasso, E. (2014). Investigating computational geometry for failure prognostics in presence of imprecise health indicator: results and comparisons on CMAPSS datasets. In European conference of the prognostics and health management society (Vol. 5, p. 1-13).
Ramasso, E., & Denoeux, T. (2013). Making use of partial knowledge about hidden states in hidden Markov models: an approach based on belief functions. IEEE Trans. on Fuzzy Systems, 22(2), 395-405.
Ramasso, E., & Gouriveau, R. (2013). RUL estimation by classification of predictions: an approach based on a neuro-fuzzy system and theory of belief functions. IEEE Trans. on Reliability, Accepted.
Ramasso, E., Rombaut, M., & Zerhouni, N. (2013). Joint prediction of observations and states in time-series based on belief functions. IEEE Trans. on Systems, Man and Cybernetics - Part B: Cybernetics, 43, 37-50.
Riad, A., Elminir, H., & Elattar, H. (2010). Evaluation of neural networks in the subject of prognostics as compared to linear regression model. Int. Journal of Engineering & Technology, 10, 52-58.
Richter, H. (2012). Engine models and simulation tools. In Advanced control of turbofan engines (p. 19-33). Springer New York.
Rigaux, P., Scholl, M., & Voisard, A. (2002). Spatial databases with application to gis (E. Science, Ed.). Kauffman Publishers.
Rosen, K. (2004). Handbook of discrete and computational geometry, second edition (J. E. Goodman & J. O’Rourke, Eds.). Chapman and Hall/CRC.
Saha, B., Goebel, K., & Christophersen, J. (2008). Comparison of prognostic algorithms for estimating remaining useful life of batteries. Trans. of the Royal UK Institute on Measurement & Control, special issue on Intelligent Fault Diagnosis & Prognosis for Engineering Systems, 293-308.
Saha, B., Goebel, K., Poll, S., & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a Bayesian framework. IEEE Trans. on Instrumentation and Measurement, 58, 291-296.
Sankararaman, S., Ling, Y., Shantz, C., & Mahadevan, S. (2009). Uncertainty quantification in fatigue damage prognosis. In Annual conf. of the prognostics and health management society.
Sarkar, S., Jin, X., & Ray, A. (2011). Data-driven fault detection in aircraft engines with noisy sensor measurements. Journal of Engineering for Gas Turbines and Power, 133, 081602.
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In Int. conf. on prognostics and health management (p. 1-17).
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine runto- failure simulation. In Int. conf. on prognostics and health management (p. 1-9). Denver, CO, USA.
Saxena, A., Wu, B., & Vachtsevanos, G. (2005). Integrated diagnosis and prognosis architecture for fleet vehicles using dynamic case-based reasoning. In Autotestcon (p. 96-102).
Serir, L., Ramasso, E., & Zerhouni, N. (2013). E2GKpro: An evidential evolving multi-modeling approach for system behavior prediction with applications. Mechanical Systems and Signal Processing, 37(1-2), 213-228. doi: 10.1016/j.ymssp.2012.06.023
Simon, D. (2012). Challenges in aircraft engine gas path health management. (Tutorial on Aircraft Engine Control and Gas Path Health Management Presented at 2012 Turbo Expo)
Vachtsevanos, G. (2006). Intelligent fault diagnosis and prognosis for engineering systems. Wiley, Hoboken, NJ.
Vatti, B. R. (1992). A generic solution to polygon clipping. Communications of the ACM, 35, 56-63.
Wang, P., Youn, B., & Hu, C. (2012). A generic probabilistic framework for structural health prognostics and uncertainty management. Mechanical Systems and Signal Processing, 28, 622 - 637.
Wang, T. (2010). Trajectory similarity based prediction for remaining useful life estimation (Unpublished doctoral dissertation). University of Cincinnati.
Wang, T., Yu, J., Siegel, D., & Lee, J. (2008). A similaritybased prognostics approach for remaining useful life estimation of engineered systems. In Ieee int. conf. on prognostics and health management (p. 1-6).
Zein-Sabatto, S., Bodruzzaman, J., & Mikhail, M. (2013). Statistical approach to online prognostics of turbine engine components. In Proc. of IEEE southeastcon (p. 1-6).
Zhang, X., & Pisu, P. (2014). Prognostic-oriented fuel cell catalyst aging modeling and its application to healthmonitoring and prognostics of a PEM fuel cell. Int. Journal of Prognostics and Health Management, 5(1- 003), 1-16.
Section
Technical Papers