Model identification in engineering dynamics

A model is a virtual representation of a system used to understand and predict the behaviour and performance of the physical counterpart. Models are used in engineering throughout the product’s lifetime to simulate, predict, and optimise the design of a single component and support the integration of multiple components before investing in physical prototypes and test activities. For example, a model can support the design of a new product by predicting its performance from the early design stages reducing the development cost and time. In addition, it can capture and analyse the system’s behaviour to take decisions in-service (e.g. maintenance scheduling or substitution of a part).

To ensure that a model is a reliable representation of the physical system, a model identification based on a combination of physics simulation, data from sensors installed on physical objects, and machine learning capabilities needs to be performed.

Traditionally, model identification in engineering dynamics has been addressed using linear deterministic system theory. The main limitations of the linear approaches are that they do not adequately address nonlinearity and uncertainty.

In terms of nonlinearity, much work has been carried out in the past, and many different approaches to nonlinear system identification have been developed, each with its optimal domain of applicability. In terms of uncertainties, it has been recognised since the beginning of system identification that noise is always present in any measured data and must be considered to identify parameters of the model, which will allow to represent the underlying physical behaviour of the system.

Machine learning advances

Recent advances in machine learning have offered more general approaches for nonlinear system identifications and uncertainty modelling.

This paper aims to demonstrate the applicability of a machine learning method to identify a nonlinear model of a physical component of interest in the helicopter industry.

The component considered is a helicopter lead-lag damper. Lead-lag dampers are used in articulated rotors as their function is to guarantee the stability of aircraft by damping the blade lead-lag motion. Due to their significant contribution to the overall aircraft behaviour, an accurate model of their dynamics is essential to predict complex phenomena such as instabilities, limit cycles, rotor loads, etc. during the design. Moreover, an accurate damper model can be used for performance monitoring on in-service aircraft.

Lead-lag dampers have been widely studied, and different architectures, such as hydraulic and elastomeric, to cite the most common ones, have been used in articulated rotors. The presence of the fluid and elastomeric materials has shown that the dynamics of these devices are inherently nonlinear and generally dependent on displacement, deformation rate, and temperature.

The grey-box model

The model identification approach used is the so-called grey-box model, which combines the insight of a physics-based (white-box) model with the explanatory power of machine learners (black-box), which have general representation properties.

The white-box is a set of nonlinear differential equations of motion derived from the underlying physics of the component whose parameters have direct physical meanings. The model has to be complex enough (i.e. the number of equations and parameters used) to capture the core dynamics of the damper without modelling more complex secondary phenomena.

A particle swarm optimisation algorithm is used to optimise the white box parameters based on the available experimental test data. The black box, consisting of a general machine learning approximation approach, is then used to improve the overall model accuracy capturing the complex dynamics not described in the white box. In this case, two regression methods to fit the black box to the data are compared: Gaussian Process (also able to model the uncertainties) and Neural Network. The two methods give similar model accuracy however, the neural network is the preferred option due to its lower computational effort.

The paper shows that the grey-box model offers the advantage of using a relatively simple physical model, which can be integrated with limited computational effort, and delegate the more complex dynamic to a general regression model improving the overall accuracy.

Damper model identification using mixed physical and machine-learning-based approach. Zilletti, M. and Fosco, E. (2023).
This open access paper appears in Volume 127 – Issue 1314 of The Aeronautical Journal.

The Royal Aeronautical Society is the world’s only professional body dedicated to the entire aerospace community. Established in 1866 to further the art, science and engineering of aeronautics, the Society has been at the forefront of developments ever since.

www.aerosociety.com | National Aerospace Library catalogue & e-books

Book reviews covering academic, scientific and technical books covering aeronautical engineering and topics relating to it can be found here: www.aerosociety.com/news-expertise/national-aerospace-library/book-reviews

The Aeronautical Journal has, for over a century, been the UK’s leading scientific and technical aeronautics Journal and is the world’s oldest Aerospace Journal that remains in production. Published monthly, The Aeronautical Journal draws upon the expertise and resources of The Royal Aeronautical Society providing a world-wide forum for authors from the UK and overseas.