The identification of the aerodynamic coefficients, based on free flight measurements, remains a difficult task for flying vehicles like space vehicles, munitions, UAV. This is mainly due to the nonlinear structure of the mathematical model describing the behavior of the vehicle in flight, the absence of an input signal, the unknown initial conditions and the nonlinear dependence of the aerodynamic coefficients on several state variables. Under these conditions, the estimation of the model parameters must be processed with caution.In this paper, we propose a new procedure for the identification of the aerodynamic coefficients, and more precisely the pitch damping coefficient, Cmq of a re-entry space vehicle. This approach is based on system identification techniques and several steps are required, like the polynomial description of the coefficient as a function of the Mach number and the total angle of attack, the a priori and a posteriori identifiability study, followed by the estimation of the parameters in question based on real experimental free flight measurements. This model-based method improves the accuracy of the estimated coefficient.
In systems biology, a common approach to model biological processes is to use large systems of nonlinear differential equations. The associated parameter estimation problem then requires a prior handling of the global identifiability question in a realistic experimental framework. The lack of a method able to solve this issue has indirectly encouraged the use of global sensitivity analysis to select the subset of parameters to estimate. Nevertheless, the links between these two global analyses are not yet fully explored.The present work reveals new bridges between sensitivity analyses and global non-identifiability, through the use of functions derived from the Sobol' high dimensional representation of the model output. We particularly specify limits of variance-based sensitivity tools to completely conclude on global non-identifiability of parameters in a given experimental context.
In systems biology, a common approach to model biological processes is to use large systems of differential equations.The associated parameter estimation problem requires to prior handle identifiability and sensitivity issues in a practical biological framework. The lack of method to assess global practical identifiability has leaded us to analyze and establish bridges between global sensitivity and identifiability measures. Specifically, we are interested in deriving conditions of global practical non-identifiability in association with global sensitivity results. Two cases are considered: i) insensitive (or non-observable) parameters ; ii) two (or more) correlated sensitivity measures of the model output with respect to model parameters. Propositions of relationships between sensitivity and identifiability, and their proofs are developped herein. Academic examples are also treated in order to illustrate contents of these propositions.
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