Prediction of Fold Bifurcations through Neural Network
Témavezető
Habib Giuseppe
Email
habib@mm.bme.hu
Típus
BSc MSc TDK
Nyelv
magyar angol
Bevezető:
Many dynamical systems of engineering relevance are affected by the problem of limited global stability. In other words, although the system is stable, a large enough perturbation might lead the system to converge towards another solution, potentially causing accidents. This problem is experienced, for example, in wheel shimmy, machine tool vibrations, and robot dynamics, to name a few.Fold bifurcations usually delimit the region where systems present this problem. However, they are often overlooked during a system analysis, and identifying them is not trivial.
In a recent study, we demonstrated that convolutional neural networks can accurately identify a trajectory close to a fold bifurcation.
This thesis work builds up on that study with two objectives. On the one hand, we aim to extend the previous study to an experimental apparatus, particularly a towed wheel undergoing shimmy vibrations, already available in the department laboratory. On the other hand, we aim to enable the neural network to predict the approximate position of a fold bifurcation and not only identify a trajectory close to one.
Depending on the applicant's inclination, one of these two objectives should be targeted.
Feladatok:
- Perform a literature review about methods for identifying fold bifurcations- Study the most relevant machine learning architectures available for analyzing time series
In the case of implementation of the method on an experimental apparatus:
- Study the basics of wheel shimmy vibrations
- Perform numerous experiments to provide data for neural network training and testing
- Define a neural network architecture based on the results obtained in our previous study
- Evaluate the results obtained by the network
In case of extension of the method for fold bifurcation position estimation
- Define several possible neural network architectures for studying and comparing time series for the estimation of the fold position
- Generate numerical data from systems already known in the literature
- Test the various architectures developed and provide conclusions about their performance
Example of a fold bifurcation limiting the bistable region of a pitch-and-plunge wing profile
