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Research Papers

Stochastic Subspace Identification Applied to the Weave Mode of Motorcycles

[+] Author and Article Information
James C. Brendelson

Product Development Center,
Harley-Davidson Motor Company,
Wauwatosa, WI 53222
e-mail: jim.brendelson@harley-davidson.com

Anoop K. Dhingra

Department of Mechanical Engineering,
University of Wisconsin—Milwaukee,
Milwaukee, WI 53201-0784
e-mail: dhingra@uwm.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 22, 2011; final manuscript received November 2, 2012; published online February 21, 2013. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 135(2), 021019 (Feb 21, 2013) (9 pages) Paper No: DS-11-1159; doi: 10.1115/1.4023068 History: Received May 22, 2011; Revised November 02, 2012

This paper presents a safe and practical method for the identification of the weave mode of motorcycles without the need for the test rider to provide a deliberate lateral input to excite a large perceptible weave response. The solution utilizes stochastic subspace identification (SSI) and relies on the smooth surface of the road under normal steady-state running conditions to randomly excite the steering system. Three SSI variants: covariance (COV), unweighted principal component (UPC), and the canonical variate analysis (CVA) are outlined and pole selection via stabilization diagrams is discussed. Then a motorcycle test protocol necessary to collect quality data for identification analysis is described. Strong correlation between stochastic identifications and traditional impulse-based weave testing of several straight running motorcycles under multiple trim states is shown. Because of the ability to use data collected under normal steady-state running conditions, the proposed stochastic technique has the potential for allowing the identification of weave modal properties under trim state conditions that are not possible with traditional weave testing, like hands-on the handlebars in straight running or when the motorcycle is cornering. Results from identifications under these hands-on trim states are presented, demonstrating the potential for deeper understanding of these conditions.

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References

Cossalter, V., 2006, Motorcycle Dynamics, 2nd ed., Lulu, Raleigh, NC, pp. 241–281 .
Singh, D. V., 1964, “Advanced Concepts of the Stability of Two-Wheeled Vehicles: Application of Mathematical Analysis to Actual Vehicles,” Ph.D. thesis, University of Wisconsin, Madison, WI.
Roland, R. D., 1973, “Simulation Study of Motorcycle Stability at High Speed,” Proceedings of the 2nd International Congress on Automotive Safety, San Francisco, CA, July 16–18, SAE Paper No. 73020.
Eaton, D. J., 1973, “Man-Machine Dynamics in the Stabilization of Single-Track Vehicles,” Ph.D. thesis, University of Michigan, Ann Arbor, MI.
Weir, D. H., and Zellner, J. W., 1978, “Motorcycle Handling. Volume I: Summary Report,” National Highway Traffic Safety Administration, Washington, DC.
Weir, D. H., and Zellner, J. W., and Teper, G. L., 1978, “Motorcycle Handling. Volume II: Technical Report,” National Highway Traffic Safety Administration, Washington, DC.
Weir, D. H., and Zellner, J. W., 1979, “Experimental Investigation of the Transient Behavior of Motorcycles,” SAE, Paper No. 790266. [CrossRef]
Roe, G. E., and Thorpe, T. E., 1980, “Improvements to the Stability, Handling and Braking of High-Performance Motorcycles,” International Motorcycle Safety Conference Proceedings, Motorcycle Safety Foundation, Linthicum, MD, Vol. 2, pp. 565–597.
Roe, G. E., and Thorpe, T. E., 1989, “The Influence of Frame Structure on the Dynamics of Motorcycle Stability,” SAE Small Engine Technology: Conference Proceeding, Paper No. 891772. [CrossRef]
Otto, W. M., 1980, “Effect of Motorcycle Accessories on Stability,” International Motorcycle Safety Conference Proceedings,” Motorcycle Safety Foundation, Linthicum, MD, Vol. 4, pp. 1559–1581.
Takahashi, T., Yamada, T., and Nakamura, T., 1984, “Experimental and Theoretical Study of the Influence of Tires on Straight-Running Motorcycle Weave Response,” SAE, Paper No. 840248. [CrossRef]
Kageyama, I., 1993, “On a Testing Method for Two Wheeled Vehicle Handling,” Proceedings of SETC, Vol. 2, SAE Paper No. 931554, pp. 679–684.
Iwamatsu, S., Nishimura, H., Sekine, T., Kageyama, I., Baba, M., Okabe, Y., Makita, T., Watanabe, H., Tsukahara, K., and Tamano, A., 2006, “Verification of Motorcycles Riding Test Procedure for Common Data of Dynamic Characteristics,” Proceedings, JSAE, Tokyo, Japan, May, No. 60-06, Paper No. 20065321, pp. 17–20.
Van Overschee, P., and De Moor, B., 1996, Subspace Identification for Linear Systems: Theory Implementation and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Peeters, B., and De Roeck, G., 1999, “Reference Based Stochastic Subspace Identification in Civil Engineering,” Proceedings of the 2nd International Conference on Identification in Engineering Systems, Swansea, UK, March, pp. 639–648.
Peeters, B., and De Roeck, G., 1999, “Reference-Based Stochastic Subspace Identification for Output-Only Modal Analysis,” Mech. Syst. Signal Process, 13(6), pp. 855–878. [CrossRef]
Peeters, B., 2000, “System Identification and Damage Detection in Civil Engineering,” Ph.D. thesis, Department of Civil Engineering, Katholieke Universiteit Leuven, Belgium.
Peeters, B., and De Roeck, G., 2001, “Stochastic System Identification for Operational Modal Analysis: A Review,” ASME J. Dyn. Sys., Meas., Control, 123(4), pp. 659–667. [CrossRef]
Peeters, B., Maeck, J., and De Roeck, G., 2000, “Excitation Sources and Dynamic System Identification in Civil Engineering,” Proceedings of the European COSTF3 Conference on System Identification & Structural Health Monitoring, Madrid, Spain, June, pp. 341–350.
Nishimi, T., Aoki, A., and Katayama, T., 1985, “Analysis of Straight Running Stability of Motorcycles,” SAE Paper No. 856124.
Katayama, T., Aoki, A., Nishimi, T., and Okayama, T., 1987, “Measurement of Structural Properties of Riders,” SAE Paper No. 871229.
Sharp, R. S., and Limebeer, D. J. N., 2004, “On Steering Oscillations of Motorcycles,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 18, pp. 1449–1456. [CrossRef]
Marumo, Y., and Katayama, T., 2005, “Effect of Motorcycle Tandem Riding on Weave Mode Stability,” Trans. Soc. Automot. Eng. Japan, 36(6), pp. 199–204.
Cossalter, V., Lot, R., and Massaro, M., 2007, “The Influence of Frame Compliance and Rider Mobility on the Scooter Stability,” Veh. Syst. Dyn., 45, pp. 315–326. [CrossRef]
Cossalter, V., Doria, A., Lot, R., and Massaro, M., 2011, “The Effect of Rider's Passive Steering Impedance on Motorcycle Stability: Identification and Analysis,” Meccanica, 46(2), pp. 279–292. [CrossRef]
Fujino, Y., and Siringoringo, D. M., 2007, “Monitoring of Bridges and Transportation Infrastructures Using Vibration Techniques,” Experimental Vibration Analysis for Civil Engineering Structures Conference (EVACES), Porto, Portugal.
Faurre, P. L., 1976, “Stochastic Realization Algorithms,” System Identification: Advances and Case Studies. Mathematics in Science and Engineering, Vol. 126, R. K.Mehra, and D. G.Lainiotis, eds., Academic Press, New York, pp. 1–25.
Kung, S. Y., 1978, “A New Identification and Model Reduction Algorithm via Singular Value Decomposition,” Proceedings of the 12th Asilomar Conference on Circuits, Systems and Computers, Asilomar, CA, pp. 705–714,.
De Cock, K., and De Moor, B., 2003, “Subspace Identification Methods,” UNESCO Encyclopedia of Life Support Systems, Vol. 1, H. D.Unbehauen, ed., EOLSS Publishers Co., Ltd., Oxford, UK, pp. 933–979.
Van Overschee, P., and De Moor, B., 1996, “sto_stat.m,” Companion MATLAB® m-Function From Subspace Identification for Linear Systems: Theory Implementation and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands.
De Cock, K., 2002, “Principal Angles in System Theory, Information Theory and Signal Processing,” Ph.D thesis, Faculty of Engineering, Katholieke Universiteit Leuven, Belgium.
Brendelson, J. C., 2010, “Stochastic Subspace Identification Applied to Motorcycle Lateral Dynamics,” Ph.D. thesis, University of Wisconsin—Milwaukee, WI.
Lanslots, J., Rodiers, B., and Peeters, B., 2004, “Automated Pole Selection: Proof-of-Concept & Validation,” Proceedings of the ISMA International Conference on Noise and Vibration Engineering, Leuven, Belgium.
LMS International, 2005, “Automatic Modal Analysis: Reality or Myth?” Leuven, Belgium.

Figures

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Fig. 1

(a) Real-time trace of a rider induced free response weave event. (b) Typical segment of stochastic response due to road surface excitation under normal running. Note the steering angle amplitude differences between (a) and (b).

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Fig. 2

Stabilization diagram constructed from system identifications of the same motorcycle “hands-off” measured data over ascending model orders. Note the weave mode identified between 2 and 4 Hz and the wobble mode identified between 8 and 10 Hz.

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Fig. 3

Correlation plots of stochastic testing versus traditional weave testing

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Fig. 4

Straight running comparison of hands-off versus hands-on stochastic identifications

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Fig. 5

“Hands-on” stabilization diagram for the same motorcycle, rider and speed as the “hands-off” stabilization diagram shown in Fig. 2

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Fig. 6

Comparison of hands-on cornering versus hands-on straight running stochastic identifications

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Fig. 7

Cornering stabilization diagram

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