Modelling of Uncertainties with Modelica

Many industrial applications, e.g. in power systems, need to use uncertain information (e.g. coming from sensors). The influence of uncertain measurements on the behavior of the system must be assessed, for safety reasons for instance. Also, by combining information given by physical models and sensor measurements, the accuracy of the knowledge of the state of the system can be improved, leading to better plant monitoring and maintenance. Three well established techniques for handling uncertainties using physical models are presented: data reconciliation, propagation of uncertainties and interpolation techniques. Then, the requirements for handling these techniques in Modelica environments are given. They apply to the Modelica language itself: how to specify the uncertainty problem to be solved directly in the Modelica model. They also apply to model processing: what are the pieces of information that must be automatically extracted from the model and provided to the standard algorithms that compute the uncertainties. Modelica language extensions in terms of two new pre-defined attributes, uncertain and distribution, are introduced for Real and Integer variables. This is needed to differentiate between certain (the usual kind) variables and uncertain variables which have associated probability distributions. An algorithm for extracting from the Modelica model the auxiliary conditions needed by the data reconciliation algorithm is given. These new features have been partially implemented in the MathModelica tool (and soon OpenModelica).