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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Symbolic observability coefficients for univariate and multivariate analysis.

Christophe Letellier1, Luis A Aguirre

  • 1Analyse Topologique et de Modélisation de Systèmes Dynamiques, Université de Rouen-CORIA, BP 12, F-76801 Saint-Etienne du Rouvray Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary

This study introduces symbolic observability coefficients to identify optimal observables and reconstruction methods for system analysis. These coefficients enhance system observability by guiding the selection of measurements and their combinations for improved accuracy.

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Area of Science:

  • Control Theory
  • System Identification
  • Mathematical Modeling

Background:

  • System observability is crucial for analysis and control.
  • Reconstructed space uniqueness is not guaranteed with given observables.
  • Multivariate measurements offer flexibility but require optimal combination strategies.

Purpose of the Study:

  • To develop a method for selecting optimal observables and reconstruction strategies.
  • To enhance system observability in practical applications.
  • To provide tools for analyzing systems in higher dimensions.

Main Methods:

  • Analytical computation of symbolic observability coefficients.
  • Utilizing a recently introduced graphical approach.
  • Applying coefficients to scalar and multivariate reconstructions.

Main Results:

  • Symbolic observability coefficients are computed analytically.
  • The coefficients guide the selection of the best observable for scalar reconstructions.
  • Optimal combination methods for multivariate reconstructions are identified.
  • The coefficients prove useful for higher-dimensional system analysis.

Conclusions:

  • The proposed coefficients offer a systematic way to improve system observability.
  • This method aids in choosing optimal measurements and reconstruction techniques.
  • The approach is applicable to various system dimensions and complexities.