Modelling of Uncertainties with Modelica

Abstract

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).

Stochastic Simulation and Inference using Modelica

“…The fixed schedule strategy operates the under-floor heating for 5 hours every night, between 3 am and 8 am. Moreover, it does not differentiate between weekdays and weekends 1 . Our control strategy, instead, tries to minimize the error between set-point and room temperature, and thus will tend to turn off the under-floor heating during weekends, when the set-point is lower.…”

“…We argue that, in order to gain acceptance for real-world applications, Modelica must ex-tend its langauge and computational tools to incorporate methods for dealing with these two deficiencies. Bouskela et al [1] propose a language extension to partially deal with the first deficiency, but further work is necessary.…”

“…Little work has focused on stochastic methods in Modelica. Most recently, Bouskela et al [1] have described (a) methods for stochastic analysis and (b) proposals for identifying stochastic Modelica variables and performing appropriate inference. [11] discusses how a Modelica model can be used as a simulation model within computational design, such that the probability of a feasible design is explictly computed.…”

On the Simulation of Offshore Oil Facilities at the System Level.

“…For instance in the context of Building Performance Simulation [14] to model weather and room occupancy as stochastic processes. Propositions were recently submitted by Bouskela et al [3] to enrich the Modelica language with the possibility to define uncertain variables with user-configurable probability law. The authors exposed some applications in power plant or combustion engine field to perform data reconciliation or uncertainty propagation.…”

On Credibility Assessment in Aircraft System Simulation

“…To clarify, uncertainties in parameters and inputs need to be handled separately from the Modelica model. Bouskela et al (2011) propose a set of requirements concerning the Modelica language that enable parameter uncertainties to be defined in the form of PDFs. Future developments of the Modelica language and related tools towards better support T for handling uncertainty and performing efficient stochastic simulations will be followed with great interest.…”