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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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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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