Analyzing the Influence of Measurements in Dynamical Parameter Identification Using Parametric Sensitivities

Abstract

Abstract In many modern applications, a central task is to model a dynamical behavior with ordinary differential equations. A common way to identify parameters within such a model is to fit its output against given measurements. Since it can be difficult to understand the connection between measurements and the parameter identification result, it is desirable to develop methods for analyzing this aspect. In this paper, we show how information from parametric sensitivity analysis can be used to gain a better insight into the impact of certain measurement regions on the identified model parameters. We parameterize the measurements by a B-spline regression and formulate the task of parameter identification using a collocation approach. In the resulting nonlinear optimization problem, we consider the B-spline coefficients as perturbation parameters. Next, we identify the model parameters and compute their parametric sensitivities with respect to these perturbations. In a final step, we evaluate a newly developed measure to characterize the desired influence. The corresponding optimization problems are solved with the nonlinear programming solver WORHP in combination with its integrated module WORHP Zen, which computes the required parametric sensitivities efficiently. We demonstrate the proposed approach by applying it to the example of parameter identification of a driving car.