Derivative-free Parameter Optimization of Functional Mock-up Units

Abstract

Representing a physical system with a mathematical model requires knowledge not only about the physical laws governing the dynamics but also about the parameter values of the system. The parameters can sometimes be measured or calculated, but some of them are often difficult or impossible to obtain directly. Never the less, finding accurate parameter values is crucial for the accuracy of the mathematical model.Estimating the parameters using optimization algorithms which attempt to minimize the error between the response from the mathematical model and the real physical system is a common approach for improving the accuracy of the model.Optimization algorithms usually require information about the derivatives which may not always be easily available or which may be difficult to compute due to, e.g., hybrid dynamics. In such cases, derivative-free optimization algorithms offer an alternative for design and parameter optimization.In this paper, we present an implementation of derivative-free optimization algorithms for parameter estimation in the JModelica.org platform. The implementation allows the underlying dynamic system to be represented as a Functional Mock-up Unit (FMU), and thus enables parameter optimization of models exported from modeling tools compliant with the Functional Mock-up Interface (FMI).

Functional Mockup Interface 2.0: The Standard for Tool independent Exchange of Simulation Models

“…In [6], an algorithm is implemented for derivative-free optimization implemented in Python and applied to parameter optimization of FMUs is introduced. The FMUs are loaded and simulated using the PyFMI package (http://www.pyfmi.org).…”

Gas Exchange and Exhaust Condition Modeling of a Diesel Engine using the Engine Dynamics Library

“…The engine system model is configured as shown in components, each separated by volume components. The compressor is connected to an inertia model (5) that is also connected to the VGT component (13).…”

“…The EGR gas path is then fed back to the inlet manifold. The exhaust manifold is also connected to the turbine component (13). Additionally, the turbine has an input signal for varying the geometry, a rotational flange connector and an outlet gas connector.…”

“…4.3 Parameter optimization in JModelica.org JModelica.org [11] has been used for optimization of model parameters for heat transfer and thermal dynamics in the exhaust gas path. The method used is the derivative free Nelder-Mead simplex method [12,13]. for optimization of more complex models, and model modifications for optimization purposes are not necessary.…”

Relative Consistency and Robust Stability Measures for Sequential Co-simulation

“…With quality measures defined the optimization becomes a feasible method for the choice of a co-simulation master. The optimization in co-simulation has been introduced as a means to improve the parameters of the simulated system in order to get a better signal response (Gedda et al, 2012). This paper introduces a problem of improvement of a co-simulation master as a multi-objective optimization problem (Kalyanmoy, 2001).…”