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Stochastic model updating with novel quantification approaches for multi-source uncertainties in aerospace engineering

   Department of Mechanical and Aerospace Engineering

About the Project

The department of Mechanical and Aerospace Engineering at the University of Strathclyde is inviting applications for the following fully funded PhD project, expected to commence in October 2022.




Computational models of large-scale structural systems with acceptable precision, robustness, and efficiency are critical, especially for applications where a large amount of experimental data is hard to obtain, such as aerospace engineering. Model updating [1] has been developed as a typical technique to reduce the discrepancy between the numerical simulations and the experimental measurements. The typical deterministic updating is performed under the single-test-single-simulation strategy, where the emphasis is placed on pursuing the maximum fidelity regarding the single measurement. Recently, it tends to consider the inevitable uncertainties involved in both simulations and experiments. A better understanding of the discrepancy between them, in the background of uncertainty, would achieve a better outcome of model updating. The involvement of uncertainty motivates the development of the so-called Stochastic Model Updating, which possesses the most interests of the current research in model updating.

In stochastic model updating, uncertainties are regarded as the reason of the discrepancy between the numerical simulations and the experimental measurements. The deterministic updating approaches assume the model parameters as unknown scalars, and calibrate them such that the model predictions are tuned towards the measurement. These approaches take an arbitrary treatment of the parameter and modelling uncertainties together while neglecting experimental uncertainty.

The stochastic model updating is hence required to provide model predictions with considerable robustness according to multi-source uncertainties; to integrate novel Uncertainty Quantification (UQ) approaches, e.g. the imprecise probability, interval, and fuzzy, capable of capturing uncertainty information from limited experimental data; and finally, to develop efficient algorithms to inversely calibrate the input parameters with the aid of advanced sampling and optimisation algorithms and the AI technologies.

Overall aim:


This project is focusing on the further development of stochastic model updating with robustness quantification regarding multi-source uncertainties, under the aid of novel UQ approaches based on interval and fuzzy representations. The overall approach is expected to generate better solutions compared with the current published works on the two editions of the NASA UQ Challenge proposed in 2014 [2] and 2019 [3], respectively. This project will also develop a benchmark dataset measured from a series of lab-scale aeroplane models, to represent the experimental uncertainties.

Student experience and training

Scientific training through research: Scientific independence; Programming skills; On-site experimental skills.

Transferrable skills training: Scientific writing; Knowledge exchange; International collaboration.

Desirable features of the candidates:

Mathematic background (especially probabilistic and statistical approaches)

Engineering mechanics and structural dynamics

Finite element analysis and software skills

Familiar with MATLAB and other programming tools such as C++ or Python. 


model updating, uncertainty quantification, mechanical engineering, aerospace engineering

Subject areas include: Aeronautical, Maritime and Transport Engineering, Mechanical Engineering, Civil & Structural Engineering

Funding Notes

The successful candidate will be fully funded for 3 years with home fee and stipend at the UKRI Doctoral Stipend rate (approx. £16,000 annually)


[1] S. Bi, M. Beer, Overview of Stochastic Model Updating in Aerospace Application Under Uncertainty Treatment, in: L.J.M. Aslett, F.P.A. Coolen, J. De Bock (Eds.), Uncertain. Eng. Introd. to Methods Appl., Springer International Publishing, Cham, 2022: pp. 115–129. https://doi.org/10.1007/978-3-030-83640-5_8.
[2] L.G. Crespo, S.P. Kennyy, D.P. Giesyz, The NASA langley multidisciplinary uncertainty quantification challenge, in: 16th AIAA Non-Deterministic Approaches Conf., 2014: pp. 1–9. https://doi.org/10.2514/6.2014-1347.
[3] L.G. Crespo, S.P. Kenny, The NASA Langley Challenge on Optimization Under Uncertainty, Mech. Syst. Signal Process. 152 (2021) 107405. https://doi.org/10.1016/j.ymssp.2020.107405.

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