New Equation-based Method for Parameter and State Estimation

Abstract

To get reliable simulation results from a Modelica model it is important to parametrize and initialize the model using the best estimate of the state of the system. Commonly, this state estimation is done by inverse calculation on a square system of equations requiring as many known values as states to be computed. In practice this constraint is an important limitation and, in addition, this method does not provide any information on the uncertainties or confidence level associated to the estimated state. Taking advantage of the mathematical formulation of Modelica equations, this paper presents a new method to cope with the difficulties associated to the inverse calculation method. This approach adapts and extends the framework of data assimilation to provide a fully-integrated Modelica tool, which efficiently can handle every type of state estimation problem for static models. This method has been successfully tested with simple and complex Modelica models. Finally, the Modelica implementation of this technique allows to easily extend it to further applications.