Conference article

Hybrid Mechanistic + Neural Model of Laboratory Helicopter

Christopher Rackauckas
Massachusetts Institute of Technology, USA

Roshan Sharma
University of South-Eastern Norway, Norway

Bernt Lie
2University of South-Eastern Norway, Norway

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Published in: Proceedings of The 61st SIMS Conference on Simulation and Modelling SIMS 2020, September 22-24, Virtual Conference, Finland

Linköping Electronic Conference Proceedings 176:37, s. 264-271

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Published: 2021-03-03

ISBN: 978-91-7929-731-2

ISSN: 1650-3686 (print), 1650-3740 (online)


There is a growing interest in data-driven models of dynamic systems developed from “Big Data”. Data-driven models have some limitations, e.g., without data, there is no model. Hybrid models consisting of relatively simple mechanistic models in tandem with data-driven models offer a compromise: physics understanding and design/synthesis of control structure prior to building the system, and improved model as data becomes available. Here, we studied a strategy to develop hybrid models based on a laboratory helicopter case study. We presented the system, with a model based on Lagrangian mechanics. Torques were assumed linear: actuator torque in voltages, and friction torque in angular velocities. Nominal model parameters were taken from a laboratory set-up. Experimental data from a laboratory process was presented; the model gave poor model fit with nominal parameters. Optimal model parameters were found based on a ballistic fit measure, and gave acceptable fit for pitch angle measurements, but poor fit for yaw angle measurements. Next, the assumption of linear controller torque was relaxed by adding a feed forward neural network block within the continuous time dynamic model. Upon training, this still gave imperfect, but considerably better prediction of the yaw angle. In a final, “model discovery” step, physically relevant alternatives to the neural network were explored. The key idea of the paper was to illustrate a strategy for hybrid models. The current model still has some structural imperfections which should be resolved before model validation becomes meaningful.


neural differential equations, mechanistic model, hybrid data-driven and mechanistic model, helicopter model, control relevant model


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