On a Grey Box Modelling Framework for Nonlinear System Identification

  • T. J. RogersEmail author
  • G. R. Holmes
  • E. J. Cross
  • K. Worden
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


In machine learning, black box models are often used to make excellent predictions of system behaviour. They are especially useful where the physics of a system is unknown or hard to model. This paper examines whether prior knowledge of certain physical properties of a system, encoded in a white box model, can be incorporated into black box methods to improve predictive performance. A combination of genetic algorithm optimisation of the white box model and Gaussian process regression on the residual error is presented as an improved method for system identification. This approach retains physical insight into the behaviour of the system while also reducing the error. Comparisons are made between pure white and black box models and the combined grey box model for several test applications. It is found that the combined model has significant advantages in predictive accuracy. This is especially seen in the case of nonlinear models. Here the full physics of the system is often too complicated or inaccessible to be modelled accurately with a white box method, but also the state space relationships are sufficiently complicated to make black box modelling equally challenging. The use of the proposed grey box method can reduce the complexity of the relationship that the black box is attempting to represent, leading to gains in accuracy. As a bonus, training time is reduced, as less complicated techniques are required to identify the process accurately.


Nonlinear system identification White box Black box Grey box Gaussian processes 



The authors wish to thank Ramboll for providing funding for this work and in particular Ulf Tyge Tygesen whom they are working with directly.


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Copyright information

© The Society for Experimental Mechanics, Inc. 2017

Authors and Affiliations

  • T. J. Rogers
    • 1
    Email author
  • G. R. Holmes
    • 1
  • E. J. Cross
    • 1
  • K. Worden
    • 1
  1. 1.Dynamics Research Group, Department of Mechanical EngineeringUniversity of SheffieldSheffieldUK

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