Global Sensitivity Analysis applied to Model Inversion Problems: A Contribution to Rail Condition Monitoring
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Published
Nov 3, 2020
René Schenkendorf
J¨orn C. Groos
Abstract
Rising demands on railroad infrastructure operator by means of profitability and punctuality call for advanced concepts of Prognostics and Health Management. Condition based preventive maintenance aims at strengthening the rail mode of transport through an optimized scheduling of maintenance actions based on the actual and prognosticated infrastructure condition, respectively. When applying model-based algorithms within the framework of Prognostics and Health Management unknown model parameters have to be identified first. Which of these parameters should be known as precisely as possible can be figured out systematically by a sensitivity analysis. A comprehensive global sensitivity analysis, however, might be prohibitive by means of computation load when standard algorithms are implemented. In this study, it is shown how global parameter sensitivities can be calculated efficiently by combining Polynomial Chaos Expansion and Point Estimate Method principles. The proposed framework is demonstrated by a model inversion problem which aims to recalculate the track quality by measurements of the vehicle acceleration, i.e. analyzing the dynamic railway track-vehicle interaction.
##plugins.themes.bootstrap3.article.details##
Keywords
condition based maintenance (CBM), sensitivity analysis, point estimate method, uncertainty analysis, polynomial chaos expansion, railway systems
References
Alexanderian, A. (2013). On spectral methods for variance based sensitivity analysis. Probability Surveys.
Bishop, C. M. (2008). Pattern recognition and machine learning. Springer.
Bocciolone, M., Caprioli, A., Cigada, A., & Collina, A. (2007). A measurement system for quick rail inspection and effective track maintenance strategy. Mechanical Systems and Signal Processing, 21(3), 1242–1254.
Borgonovo, E. (2007). A new uncertainty importance measure. Reliab. Eng. Sys. Safety, 92, 771–784.
Buchholz, J., & v. Gr¨unhagen,W. (2007). Inversion impossible. GRIN Publishing GmbH.
Caprioli, A., Cigada, A., & Raveglia, D. (2007). Rail inspection in track maintenance: A benchmark between the wavelet approach and the more conventional fourier analysis. Mechanical Systems and Signal Processing, 21(2), 631–652.
Chiachio, J., Chiachio, M., Saxena, A., Sankararaman, S., Rus, G., & Goebel, K. (2015). Bayesian model selection and parameter estimation for fatigue damage progression models in composites. International Journal of Fatigue.
Daigle, M., & Goebel, K. (2010). Improving computational efficiency of prediction in model-based prognsotics using the unscented transformation. Procceedings of the Annual Conference of the Prognostics and Health Management Society.
Daigle, M., & Sankararaman, S. (2013). Advanced methods for determining prediction uncertainty in model-based prognostics with application to planetary rovers. Annual Conference of the Prognostics and Health Management Society.
Daigle, M., Saxena, A., & Goebel, K. (2012). An efficient deterministic approach to model-based prediction uncertainty estimation. Annual Conference of the Prognostics and Health Management Society.
Evans, D. H. (1967). An application of numerical integration techniques to statistical tolerancing. Technometrics, 9, 441-456.
Evans, D. H. (1974). Statistical tolerancing: The state of the art. Journal of Quality Technology, 6, 188-195.
Feldmann, U., Kreuzer, E., & Pinto, F. (2000). Dynamic diagnosis of railway tracks by means of the karhunen– lo`eve transformation. Nonlinear Dynamics, 22(2), 183–193.
Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1992). On differentially flat non-linear systems. C.R. de l’Académie des Sciences, 315, 619-624.
Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1995). Flatness and defect of nonlinear systems: Introductory theory and examples. Int. J. Control, 61, 1327-1361.
Gelb, A. (1974). Applied optimal estimation. The M.I.T. Press.
Gradinariu, T., Tursø-Finnich, K., Juntti-Espling, U., Mangan, C., Thill, L., Gebhardt, M., . . . Gardin, D. (2008). Lasting infrastructure cost benchmarking (licb): Summary report december 2008.
Graichen, K., Hagenmeyer, V., & Zeitz, M. (2005). A new approach for inversion-based feedforward control design of non-linear systems. Trans. Autom. Control, 41, 2033-2041.
Grigoriu, M. (2002). Stochastic calculus: Applications in science and engineering. Birkh¨auser.
Imine, H. (2011). Sliding mode based analysis and identification of vehicle dynamics. Springer.
Imine, H., & Fridman, L. (2008). Road profile estimation in heavy vehicle dynamics simulation. International Journal of Vehicle Design.
International Union of Railways (UIC). (2010). Monitoring track condition to improve asset management: Synthesis report of the uic track condition monitoring working group.
Isukapalli, S. S. (1999). Uncertainty analysis of transporttransformation models (Unpublished doctoral dissertation). Rutgers, The State University of New Jersey.
Julier, S. J., & Uhlmann, J. K. (1994). A general method for approximating nonlinear transformations of probability distributions (Tech. Rep.). Dept. of Engineering Science, University of Oxford.
Kawasaki, J., & Youcef-Toumi, K. (2002). Estimation of rail irregularities. In 2002 american control conference (pp. 3650–3660).
Kobayashi, M., Naganuma, Y., Nakagawa, M., & Okumura, T. (2008). Digital inertial algorithm for recording track geometry on commercial shinkansen trains. In Computers in railways xi (Vol. 103, pp. 683–692).
Kobayashi, T., Naganuma, Y., & Tsunashima, H. (2013). Condition monitoring of shinkansen tracks based on inverse analysis. Chemical Engineering Transactions, 33, 703–708.
Kulkarni, C. S., Biswas, G., Celaya, J. R., & Goebel, K. (2013). Physics based degradation models for electronic capacitor prognostics under thermal overstress conditions. International Journal of Prognostics and Health Management.
Lapira, E., Brisset, D., Davari, H., Siegel, D., & Lee, J. (2012). Wind turbine performance assessment using multi-regime modeling approach. Renewable Energy, 45, 86-95.
Lee, J. S., Choi, S., Kim, S.-S., Park, C., & Kim, Y. G. (2012). A mixed filtering approach for track condition monitoring using accelerometers on the axle box and bogie. IEEE Transactions on Instrumentation and Measurement, 61(3), 749–758.
Lerner, U. N. (2002). Hybrid bayesian networks for reasoning about complex systems (Unpublished doctoral dissertation). Stanford University.
Lewis, R., & Richards, A. (1988). A compensated accelerometer for the measurement of railway track crosslevel. IEEE Transactions on Vehicular Technology, 37(3), 174–178.
Lewis, R. B., & Richards, A. N. (1986). A new method for the routine measurement of railhead corrugations. Rail International(2), 37–41.
Maitre, O. P. L., & Knio, O. M. (2010). Spectral methods for uncertainty quantification. Springer.
Molodova, M., Li, Z., & Dollevoet, R. (2011). Axle box acceleration: Measurement and simulation for detection of short track defects. Wear, 271(1-2), 349–356.
Molodova, M., Li, Z., Nunez, A., & Dollevoet, R. (2014). Automatic detection of squats in railway infrastructure. IEEE Transactions on Intelligent Transportation Systems, 15(5), 1980–1990.
Mori, H., Sato, Y., Ohno, H., Tsunashima, H., & Saito, Y. (2013). Development of compact size onboard device for condition monitoring of railway tracks. Journal of Mechanical Systems for Transportation and Logistics, 6(2), 142–149.
Mori, H., Tsunashima, H., Kojima, T., Matsumoto, A., & Mizuma, T. (2010). Condition monitoring of railway track using in-service vehicle. Journal of Mechanical Systems for Transportation and Logistics, 3(1), 154–165.
Murray-Smith, D. J. (2011). Feedback mehtods for inverse simulation of dynamic models for engineering systems applications. Mathematical and Computer Modelling of Dynamical Systems, 17, 515-541.
Murray-Smith, D. J. (2013). The application of parameter sensitivity analysis methods to inverse simulation models. Mathematical and Computer Modelling of Dynamical Systems, 19, 67-90.
Naganuma, Y., Kobayashi, M., & Okumura, T. (2010). Inertial measurement processing techniques for track condition monitoring on shinkansen commercial trains. Journal of Mechanical Systems for Transportation and Logistics, 3(1), 315–325.
Naganuma, Y., Kobayashi, T., & Tsunashima, H. (2013a). Track geometry estimation for car-body motions of railway vehicle. Journal of Mechanical Systems for Transportation and Logistics.
Naganuma, Y., Kobayashi, T., & Tsunashima, H. (2013b). Track geometry estimation from car-body motions of railway vehicle. Journal of Mechanical Systems for Transportation and Logistics, 6(2), 133–141.
Saha, B., Goeble, K., Poll, S., & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a bayesian framework. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 52(2).
Saltelli, A., Ratto, M., Tarantola, S., & Campolongo, F. (2005). Sensititivity analysis for chemical models. Chemical Reviews, 105, 2811–2828.
Sankararaman, S. (2012). Uncertainty quantification and integration in engineering systems (Unpublished doctoral dissertation). Vanderbilt University.
Sankararaman, S., Daigle, M., Saxena, A., & Goebel, K. (2013). Analytical algorithms to quantify the uncertainty in remaining useful life prediction. In Aerospace conference.
Sankararaman, S., & Goebel, K. (2013). Uncertainty quantification in remaining useful life of aerospace components using state space models and inverse form (Tech. Rep.). NASA Ames Research Center; Moffett Field, CA, United States.
Schenkendorf, R. (2014). A general framework for uncertainty propagation based on point estimate methods. In Second european conference of the prognostics and health management society, phme14. Nantes, France.
Sch¨oniger, A., Nowak, W., & Franssen, H.-J. H. (2012). Parameter estimation by ensemble kalman filters with transformed data: Approach and application to hydraulic tomography. Water Resources Research, 48.
Sira-Ramirez, H., Matamoros-Sanchez, A., & Goodall, R. M. (2011). Flatness based control of a suspension system: A gpi observer approach. In 18th ifac world congress.
Sobol’, I. M. (1993). Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computational Experiment, 1, 407–414.
Sobol’, I., Tarantola, S., Gatelli, D., Kucherenko, S., & Mauntz, W. (2007). Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliability Engineering & System Safety, 92(7), 957 - 960.
Stengel, R. F. (1994). Optimal control and estimation. Dover Publications.
Sudret, B. (2007). Uncertainty propagation and sensitivity analysis in mechanical models. Universite BLAISE PASCAL - Clermont II.
Sunaga, Y., Sano, I., & Ide, T. (1997). A method to control the short wave track irregularities utilizing axlebox acceleration. Railway Technical Research Institute, Quarterly Reports, 38(4), 176–181.
Thomson, D., & Bradley, R. (2006). Inverse simulation as a tool for fight dynamics research - principles and applications. Progress in Aerospace Sciences, 42, 174-210.
Tyler, G. W. (1953). Numerical integration of functions of several variables. Canadian Jn. Math., 5, 393-412.
Ward, C., Weston, P., Stewart, E. J. C., Li, H., Goodall, R., Roberts, C., . . . Dixon, R. (2011). Condition monitoring opportunities using vehicle-based sensors. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 225(2), 202–218.
Weston, P., Ling, C., Goodman, C., Roberts, C., Li, P., & Goodall, R. (2007). Monitoring lateral track irregularity from in-service railway vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221(1), 89–100.
Weston, P., Ling, C., Roberts, C., Goodman, C., Li, P., & Goodall, R. (2007). Monitoring vertical track irregularity from in-service railway vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221(1), 75–88.
Williard, N., He, W., Osterman, M., & Pecht, M. (2013). Comperative analysis of features for determining state of health in lithium-ion batteries. International Journal of Prognostics and Health Management.
Witczak, M. (2014). Fault diagnosis and fault-tolerant control strategies for non-linear system: Analytical and soft computing approaches. Springer.
Zhang, X., & Pisu, P. (2014). Prognostic-oriented fuel cell catalyst aging modeling and its application to healthmonitoring and prognostics of a pem fuel cell. International Journal of Prognostics and Health Management, 5.
Bishop, C. M. (2008). Pattern recognition and machine learning. Springer.
Bocciolone, M., Caprioli, A., Cigada, A., & Collina, A. (2007). A measurement system for quick rail inspection and effective track maintenance strategy. Mechanical Systems and Signal Processing, 21(3), 1242–1254.
Borgonovo, E. (2007). A new uncertainty importance measure. Reliab. Eng. Sys. Safety, 92, 771–784.
Buchholz, J., & v. Gr¨unhagen,W. (2007). Inversion impossible. GRIN Publishing GmbH.
Caprioli, A., Cigada, A., & Raveglia, D. (2007). Rail inspection in track maintenance: A benchmark between the wavelet approach and the more conventional fourier analysis. Mechanical Systems and Signal Processing, 21(2), 631–652.
Chiachio, J., Chiachio, M., Saxena, A., Sankararaman, S., Rus, G., & Goebel, K. (2015). Bayesian model selection and parameter estimation for fatigue damage progression models in composites. International Journal of Fatigue.
Daigle, M., & Goebel, K. (2010). Improving computational efficiency of prediction in model-based prognsotics using the unscented transformation. Procceedings of the Annual Conference of the Prognostics and Health Management Society.
Daigle, M., & Sankararaman, S. (2013). Advanced methods for determining prediction uncertainty in model-based prognostics with application to planetary rovers. Annual Conference of the Prognostics and Health Management Society.
Daigle, M., Saxena, A., & Goebel, K. (2012). An efficient deterministic approach to model-based prediction uncertainty estimation. Annual Conference of the Prognostics and Health Management Society.
Evans, D. H. (1967). An application of numerical integration techniques to statistical tolerancing. Technometrics, 9, 441-456.
Evans, D. H. (1974). Statistical tolerancing: The state of the art. Journal of Quality Technology, 6, 188-195.
Feldmann, U., Kreuzer, E., & Pinto, F. (2000). Dynamic diagnosis of railway tracks by means of the karhunen– lo`eve transformation. Nonlinear Dynamics, 22(2), 183–193.
Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1992). On differentially flat non-linear systems. C.R. de l’Académie des Sciences, 315, 619-624.
Fliess, M., Lévine, J., Martin, P., & Rouchon, P. (1995). Flatness and defect of nonlinear systems: Introductory theory and examples. Int. J. Control, 61, 1327-1361.
Gelb, A. (1974). Applied optimal estimation. The M.I.T. Press.
Gradinariu, T., Tursø-Finnich, K., Juntti-Espling, U., Mangan, C., Thill, L., Gebhardt, M., . . . Gardin, D. (2008). Lasting infrastructure cost benchmarking (licb): Summary report december 2008.
Graichen, K., Hagenmeyer, V., & Zeitz, M. (2005). A new approach for inversion-based feedforward control design of non-linear systems. Trans. Autom. Control, 41, 2033-2041.
Grigoriu, M. (2002). Stochastic calculus: Applications in science and engineering. Birkh¨auser.
Imine, H. (2011). Sliding mode based analysis and identification of vehicle dynamics. Springer.
Imine, H., & Fridman, L. (2008). Road profile estimation in heavy vehicle dynamics simulation. International Journal of Vehicle Design.
International Union of Railways (UIC). (2010). Monitoring track condition to improve asset management: Synthesis report of the uic track condition monitoring working group.
Isukapalli, S. S. (1999). Uncertainty analysis of transporttransformation models (Unpublished doctoral dissertation). Rutgers, The State University of New Jersey.
Julier, S. J., & Uhlmann, J. K. (1994). A general method for approximating nonlinear transformations of probability distributions (Tech. Rep.). Dept. of Engineering Science, University of Oxford.
Kawasaki, J., & Youcef-Toumi, K. (2002). Estimation of rail irregularities. In 2002 american control conference (pp. 3650–3660).
Kobayashi, M., Naganuma, Y., Nakagawa, M., & Okumura, T. (2008). Digital inertial algorithm for recording track geometry on commercial shinkansen trains. In Computers in railways xi (Vol. 103, pp. 683–692).
Kobayashi, T., Naganuma, Y., & Tsunashima, H. (2013). Condition monitoring of shinkansen tracks based on inverse analysis. Chemical Engineering Transactions, 33, 703–708.
Kulkarni, C. S., Biswas, G., Celaya, J. R., & Goebel, K. (2013). Physics based degradation models for electronic capacitor prognostics under thermal overstress conditions. International Journal of Prognostics and Health Management.
Lapira, E., Brisset, D., Davari, H., Siegel, D., & Lee, J. (2012). Wind turbine performance assessment using multi-regime modeling approach. Renewable Energy, 45, 86-95.
Lee, J. S., Choi, S., Kim, S.-S., Park, C., & Kim, Y. G. (2012). A mixed filtering approach for track condition monitoring using accelerometers on the axle box and bogie. IEEE Transactions on Instrumentation and Measurement, 61(3), 749–758.
Lerner, U. N. (2002). Hybrid bayesian networks for reasoning about complex systems (Unpublished doctoral dissertation). Stanford University.
Lewis, R., & Richards, A. (1988). A compensated accelerometer for the measurement of railway track crosslevel. IEEE Transactions on Vehicular Technology, 37(3), 174–178.
Lewis, R. B., & Richards, A. N. (1986). A new method for the routine measurement of railhead corrugations. Rail International(2), 37–41.
Maitre, O. P. L., & Knio, O. M. (2010). Spectral methods for uncertainty quantification. Springer.
Molodova, M., Li, Z., & Dollevoet, R. (2011). Axle box acceleration: Measurement and simulation for detection of short track defects. Wear, 271(1-2), 349–356.
Molodova, M., Li, Z., Nunez, A., & Dollevoet, R. (2014). Automatic detection of squats in railway infrastructure. IEEE Transactions on Intelligent Transportation Systems, 15(5), 1980–1990.
Mori, H., Sato, Y., Ohno, H., Tsunashima, H., & Saito, Y. (2013). Development of compact size onboard device for condition monitoring of railway tracks. Journal of Mechanical Systems for Transportation and Logistics, 6(2), 142–149.
Mori, H., Tsunashima, H., Kojima, T., Matsumoto, A., & Mizuma, T. (2010). Condition monitoring of railway track using in-service vehicle. Journal of Mechanical Systems for Transportation and Logistics, 3(1), 154–165.
Murray-Smith, D. J. (2011). Feedback mehtods for inverse simulation of dynamic models for engineering systems applications. Mathematical and Computer Modelling of Dynamical Systems, 17, 515-541.
Murray-Smith, D. J. (2013). The application of parameter sensitivity analysis methods to inverse simulation models. Mathematical and Computer Modelling of Dynamical Systems, 19, 67-90.
Naganuma, Y., Kobayashi, M., & Okumura, T. (2010). Inertial measurement processing techniques for track condition monitoring on shinkansen commercial trains. Journal of Mechanical Systems for Transportation and Logistics, 3(1), 315–325.
Naganuma, Y., Kobayashi, T., & Tsunashima, H. (2013a). Track geometry estimation for car-body motions of railway vehicle. Journal of Mechanical Systems for Transportation and Logistics.
Naganuma, Y., Kobayashi, T., & Tsunashima, H. (2013b). Track geometry estimation from car-body motions of railway vehicle. Journal of Mechanical Systems for Transportation and Logistics, 6(2), 133–141.
Saha, B., Goeble, K., Poll, S., & Christophersen, J. (2009). Prognostics methods for battery health monitoring using a bayesian framework. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, 52(2).
Saltelli, A., Ratto, M., Tarantola, S., & Campolongo, F. (2005). Sensititivity analysis for chemical models. Chemical Reviews, 105, 2811–2828.
Sankararaman, S. (2012). Uncertainty quantification and integration in engineering systems (Unpublished doctoral dissertation). Vanderbilt University.
Sankararaman, S., Daigle, M., Saxena, A., & Goebel, K. (2013). Analytical algorithms to quantify the uncertainty in remaining useful life prediction. In Aerospace conference.
Sankararaman, S., & Goebel, K. (2013). Uncertainty quantification in remaining useful life of aerospace components using state space models and inverse form (Tech. Rep.). NASA Ames Research Center; Moffett Field, CA, United States.
Schenkendorf, R. (2014). A general framework for uncertainty propagation based on point estimate methods. In Second european conference of the prognostics and health management society, phme14. Nantes, France.
Sch¨oniger, A., Nowak, W., & Franssen, H.-J. H. (2012). Parameter estimation by ensemble kalman filters with transformed data: Approach and application to hydraulic tomography. Water Resources Research, 48.
Sira-Ramirez, H., Matamoros-Sanchez, A., & Goodall, R. M. (2011). Flatness based control of a suspension system: A gpi observer approach. In 18th ifac world congress.
Sobol’, I. M. (1993). Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computational Experiment, 1, 407–414.
Sobol’, I., Tarantola, S., Gatelli, D., Kucherenko, S., & Mauntz, W. (2007). Estimating the approximation error when fixing unessential factors in global sensitivity analysis. Reliability Engineering & System Safety, 92(7), 957 - 960.
Stengel, R. F. (1994). Optimal control and estimation. Dover Publications.
Sudret, B. (2007). Uncertainty propagation and sensitivity analysis in mechanical models. Universite BLAISE PASCAL - Clermont II.
Sunaga, Y., Sano, I., & Ide, T. (1997). A method to control the short wave track irregularities utilizing axlebox acceleration. Railway Technical Research Institute, Quarterly Reports, 38(4), 176–181.
Thomson, D., & Bradley, R. (2006). Inverse simulation as a tool for fight dynamics research - principles and applications. Progress in Aerospace Sciences, 42, 174-210.
Tyler, G. W. (1953). Numerical integration of functions of several variables. Canadian Jn. Math., 5, 393-412.
Ward, C., Weston, P., Stewart, E. J. C., Li, H., Goodall, R., Roberts, C., . . . Dixon, R. (2011). Condition monitoring opportunities using vehicle-based sensors. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 225(2), 202–218.
Weston, P., Ling, C., Goodman, C., Roberts, C., Li, P., & Goodall, R. (2007). Monitoring lateral track irregularity from in-service railway vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221(1), 89–100.
Weston, P., Ling, C., Roberts, C., Goodman, C., Li, P., & Goodall, R. (2007). Monitoring vertical track irregularity from in-service railway vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221(1), 75–88.
Williard, N., He, W., Osterman, M., & Pecht, M. (2013). Comperative analysis of features for determining state of health in lithium-ion batteries. International Journal of Prognostics and Health Management.
Witczak, M. (2014). Fault diagnosis and fault-tolerant control strategies for non-linear system: Analytical and soft computing approaches. Springer.
Zhang, X., & Pisu, P. (2014). Prognostic-oriented fuel cell catalyst aging modeling and its application to healthmonitoring and prognostics of a pem fuel cell. International Journal of Prognostics and Health Management, 5.
Section
Technical Papers