PhD Studentship: Identification of reduced models of mechanical systems from vibration data

University of Bristol - Engineering Mathematics

The project:

In order to gain understanding of the dynamics of a mechanical system it is useful to have a reduced order model. The best reduced models are exact: they describe the motion exactly for a specific set of initial conditions. For other initial conditions the dynamics will exponentially tend to the solution described by the reduced model. Finding such reduced models is equivalent to finding invariant manifolds with certain properties. In a recent paper [1] we have shown that it is possible to find such unique reduced models from experimental data. We have used the most general model that was constructed using a least squares method. This model then was analysed using analytical techniques. It is however desirable that the model being identified has low number of parameters, which is possible to achieve if the fitting and analysis of the model is carried out in one step. The task in the PhD project is to develop this method with the minimum number of parameters required to obtain a reduced model. To test the method, we will use various experimental data and data from finite element simulations to test the method.

[1] R. Szalai, D Ehrhardt, G. Haller. Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations. Proc. R. Soc. A 2017 473 20160759

If you are interested in this potential PhD project, please visit for more details on funding and eligibility criteria.

How to apply:

Candidates should get in touch prior to applying, as a letter of support from the intended supervisor is required (Dr Robert Szalai,

Please make an online application for this project at Please select > on the Programme Choice page. You will be prompted to enter details of the studentship in the Funding and Research Details sections of the form.

Candidate requirements: 

A minimum of 2.1 honours degree in Applied Mathematics, Physics, Mechanical, and Aerospace Engineering or similar is required.

Basic skills and knowledge required

Experience with programming in MATLAB or other similar scientific programming language (Julia, SciPy) is essential.


If awarded, the successful candidate will be offered one or both of the following: 
• full UK/EU/Overseas PhD tuition fees 
• a tax-free bursary at the current RCUK rate (£14,553 p.a. in 2017/18)


Please contact Dr Robert Szalai,

For general enquiries, please email

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South West England