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Research Papers

Parameter Estimation by Parameter Signature Isolation in the Time-Scale Domain

[+] Author and Article Information
Kourosh Danai1

Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003danai@ecs.umass.edu

James R. McCusker

Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003

1

Corresponding author.

J. Dyn. Sys., Meas., Control 131(4), 041008 (May 18, 2009) (11 pages) doi:10.1115/1.3117197 History: Received February 08, 2008; Revised February 19, 2009; Published May 18, 2009

It is shown that output sensitivities of dynamic models can be better delineated in the time-scale domain. This enhanced delineation provides the capacity to isolate regions of the time-scale plane, coined as parameter signatures, wherein individual output sensitivities dominate the others. Due to this dominance, the prediction error can be attributed to the error of a single parameter at each parameter signature so as to enable estimation of each model parameter error separately. As a test of fidelity, the estimated parameter errors are evaluated in iterative parameter estimation in this paper. The proposed parameter signature isolation method (PARSIM) that uses the parameter error estimates for parameter estimation is shown to have an estimation precision comparable to that of the Gauss–Newton method. The transparency afforded by the parameter signatures, however, extends PARSIM’s features beyond rudimentary parameter estimation. One such potential feature is noise suppression by discounting the parameter error estimates obtained in the finer-scale (higher-frequency) regions of the time-scale plane. Another is the capacity to assess the observability of each output through the quality of parameter signatures it provides.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Impulse response prediction error of the nonlinear mass-spring-damper system in Eq. 13 (top plot solid line) and its approximation by the weighted sum of parameter effects according to Eq. 12 (top plot dashed line). The lower plots are the parameter effects of m, c, and k in Eq. 13 at the nominal parameter values Θ¯=[m¯,c¯,k¯]T=[340,10500,125×103]T.

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Figure 2

Gauss WT of the prediction error in Fig. 1

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Figure 3

The location of pixels included in the parameter signatures of m, c, and k of the nonlinear mass-spring-damper model using Gauss WT and η=0.1 in Eq. 26

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Figure 4

The parameter signatures of m, c, and k of the mass-spring-damper model in Eq. 13 by Gauss WT at η=0.2 in Eq. 26

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Figure 6

Two uncorrelated signals and the difference between the absolute values of their Gauss WT

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Figure 7

The parameter signatures of hypothetical parameters corresponding to the parameter effects ζ1 and ζ2 in Fig. 5 and ζ3 and ζ4 in Fig. 6 shown, respectively, in the top and bottom subfigures. As expected, there are very few pixels included in the top parameter signatures due to the high correlation of ζ1 and ζ2. In contrast, the extracted parameter signatures associated with the uncorrelated signals ζ3 and ζ4 comprise many pixels.

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Figure 8

Prediction error during the 100 estimation runs of the nonlinear mass-spring-damper model parameters by PARSIM and the Gauss–Newton method

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Figure 9

Estimated parameters of the drug kinetics model in Eq. 33 by PARSIM (left) and the Gauss–Newton method (right)

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Figure 5

Two highly correlated signals and the difference between the absolute values of their Gauss WT

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