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Technical Brief

Selecting Sensitive Parameter Subsets in Dynamical Models With Application to Biomechanical System Identification

[+] Author and Article Information
Ahmed Ramadan

Mem. ASME
Department of Mechanical Engineering,
MSU Center for Orthopedic Research (MSUCOR),
Michigan State University,
428 S. Shaw Ln,
East Lansing, MI 48824
e-mail: ramadana@msu.edu

Connor Boss

Mem. ASME
Department of Electrical and Computer Engineering,
MSU Center for Orthopedic Research (MSUCOR),
Michigan State University,
East Lansing, MI 48824
e-mail: bossconn@egr.msu.edu

Jongeun Choi

Mem. ASME
School of Mechanical Engineering,
Yonsei University,
Seoul 03722, Republic of Korea
e-mail: jongeunchoi@yonsei.ac.kr

N. Peter Reeves

Sumaq Life LLC,
East Lansing, MI 48823;
Department of Osteopathic Surgical Specialities,
MSU Center for Orthopedic Research (MSUCOR),
East Lansing, MI 48824
e-mail: reevesn@icloud.com

Jacek Cholewicki

Department of Osteopathic Surgical Specialties,
MSU Center for Orthopedic Research (MSUCOR),
Michigan State University,
East Lansing, MI 48824
e-mail: cholewic@msu.edu

John M. Popovich,, Jr.

Department of Osteopathic Surgical Specialties,
MSU Center for Orthopedic Research (MSUCOR),
Michigan State University,
East Lansing, MI 48824
e-mail: popovi16@msu.edu

Clark J. Radcliffe

Fellow ASME
Department of Mechanical Engineering,
MSU Center for Orthopedic Research (MSUCOR),
Michigan State University,
East Lansing, MI 48824
e-mail: radcliffe@egr.msu.edu

1Corresponding author.

Manuscript received October 5, 2017; final manuscript received March 2, 2018; published online May 8, 2018. Assoc. Editor: Guy M. Genin.

J Biomech Eng 140(7), 074503 (May 08, 2018) (8 pages) Paper No: BIO-17-1452; doi: 10.1115/1.4039677 History: Received October 05, 2017; Revised March 02, 2018

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

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Figures

Grahic Jump Location
Fig. 2

The best-fit model output (during a trial) when estimating the FIM- and LASSO-selected sensitive parameters. The experimental (EXP) output is a subject's response.

Grahic Jump Location
Fig. 1

(a) Experimental setup for head position tracking. The reference marker is r(t) and the head position marker is y(t). (b) The block diagram of the head position tracking model adopted from Refs. [3] and [4]. The transfer functions come from Refs. [2] and [4] after accounting for the change in output from acceleration to position.

Grahic Jump Location
Fig. 3

An outline of model-based bootstrap [25] using 1000 replicates to estimate 95% confidence interval (CI) of the parameter vector θ

Grahic Jump Location
Fig. 4

Results of applying the FIM method (Appendix C) with nmin=2 to the experimental data. The optimal number of sensitive parameters per subset is nθ*. The number of subsets (each with nθ* parameters) is Ncandidate.

Grahic Jump Location
Fig. 5

Comparing the 95% confidence interval (CI) between estimating ALL parameters, FIM-selected parameters (θFIM), and LASSO-selected parameters (θLASSO). • is the mean point-estimate and the error bars are the mean CI (across subjects) for (a) Kvis, (b) Kccr, and (c) τ that were selected as sensitive parameters by both FIM and LASSO methods.

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