Abstract
Multiple fields present a need to characterize what a footstep response looks like, or detect when footsteps are occurring in a periodic walking signal: localization, classification, and gait analysis among them. At the heart of this problem is a periodic signal encoded with biomechanical information of the person walking. In this work, the periodic nature of gait is used to recreate a template of the floor acceleration response to a single step for a particular person. Underfloor accelerometers positioned to measure vertical acceleration will be used. The floor acceleration response is expected to take the form of a sum of decaying sinusoidal responses, and from this assumed response the expected analytical correlation can be found. Correlation functions of the actual response over the course of multiple steps will be used to exploit the periodic nature of walking to give a clean correlation signal which represents the frequency content of each step. Next, these correlation functions are used to fit coefficients which are in turn used to recreate a template of a single step response. After recreating a template of the footstep event, the template could be used as a direct characterization of the person’s gait or to further process the response data such as footstep detection.
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References
Agarwal, Y., Balaji, B., Gupta, R., Lyles, J., Wei, M., Weng, T.: Occupancy-driven energy management for smart building automation. In: Proceedings of the 2Nd ACM Workshop on Embedded Sensing Systems for Energy-Efficiency in Building, BuildSys ’10, pp. 1–6. ACM, New York (2010)
Alajlouni, S., Albakri, M., Tarazaga, P.: Impact localization in dispersive waveguides based on energy-attenuation of waves with the traveled distance. Mech. Syst. Signal Process. 105, 361–376 (2018)
Bales, D., Tarazaga, P.A., Kasarda, M., Batra, D., Woolard, A., Poston, J.D., Malladi, V.S.: Gender classification of walkers via underfloor accelerometer measurements. IEEE Internet Things J. 3(6), 1259–1266 (2016)
Bardos, C., Garnier, J., Papanicolaou, G.: Identification of Green’s functions singularities by cross correlation of noisy signals. Inverse Prob. 24(1), 015011 (2008)
Claerbout, J.: Fundamentals of Geophysics Data Processing: With Applications to Petroleum Prospecting. 06 (1985)
Drmac, Z., Gugercin, S., Beattie, C.: Quadrature-based vector fitting for discretized h_2 approximation. SIAM J. Sci. Comput. 37(2), A625–A652 (2015)
Gustavsen, B., Semlyen, A.: Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Delivery 14(3), 1052–1061 (1999)
Hokanson, J.: Numerically Stable and Statistically Efficient Algorithms for Large Scale Exponential Fitting, PhD thesis. Rice University, Houston (2013)
Hokanson, J.M.: Projected nonlinear least squares for exponential fitting. SIAM J. Sci. Comput. 39(6), A3107–A3128 (2017)
Ljung, L.: System Identification. Prentice Hall, New Jersey (1987)
Malcolm, A., Scales, J., Tiggelen, B.: Extracting the green function from diffuse, equipartitioned waves. Phys. Rev. E Stat. Nonlin. Soft. Matter. Phys. 70, 015601 (2004)
Mayo, A., Antoulas, A.: A framework for the solution of the generalized realization problem. Linear Algebra Appl. 425(2–3), 634–662 (2007)
Pan, S., Bonde, A., Jing, J., Zhang, L., Zhang, P., Noh, H.Y.: BOES: building occupancy estimation system using sparse ambient vibration monitoring. In: Proceedings of SPIE–The International Society for Optical Engineering, vol. 9061, p. 90611O. International Society for Optics and Photonics (2014)
Peherstorfer, B., Gugercin, S., Willcox, K.: Data-driven reduced model construction with time-domain loewner models. SIAM J. Sci. Comput. 39(5), A2152–A2178 (2017)
Poston, J.D., Buehrer, R.M., Tarazaga, P.A.: Indoor footstep localization from structural dynamics instrumentation. Mech. Syst. Signal Process. 88, 224–239 (2017)
Racic, V., Chen, J., Pavic, A.: Advanced fourier-based model of bouncing loads. In: Pakzad, S. (ed.) Dynamics of Civil Structures, vol. 2, pp. 367–376. Springer International Publishing, Cham (2019)
Willford, M., Young, P., Field, C.: Improved Methodologies for the Prediction of Footfall-Induced Vibration. vol. 5933, 03 (2006)
Acknowledgements
Dr. Tarazaga would like to acknowledge the financial support of the John R. Jones Faculty Fellowship.
The authors wish to acknowledge the support as well as the collaborative efforts provided by our sponsors, VTI Instruments, PCB Piezotronics, Inc.; Dytran Instruments, Inc.; and Oregano Systems. The authors are particularly appreciative for the support provided by the College of Engineering at Virginia Tech through Dean Richard Benson and Associate Dean Ed Nelson as well as VT Capital Project Manager, Todd Shelton, and VT University Building Official, William Hinson. The authors would also like to acknowledge Gilbane, Inc. and in particular, David Childress and Eric Hotek. We are especially thankful to the Student Engineering Council (SEC) at Virginia Tech and their financial commitment to this project. The work was conducted under the patronage of the Virginia Tech Smart Infrastructure Laboratory and its members.
The work is supported in part by the National Science Foundation via grant no. DGE-1545362, UrbComp (Urban Computing): Data Science for Modeling, Understanding, and Advancing Urban Populations. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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Kessler, E., Tarazaga, P., Gugercin, S. (2020). Recreating Periodic Events: Characterizing Footsteps in a Continuous Walking Signal. In: Pakzad, S. (eds) Dynamics of Civil Structures, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12115-0_32
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DOI: https://doi.org/10.1007/978-3-030-12115-0_32
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