Machine learning for dynamic systems

The importance of nonlinear vibrations continues to increase in industrial applications. These vibrations always occur when the material properties, the geometry under consideration or the kinematics lead to nonlinear behavior. Components that are subjected to external excitation and thus exhibit (nonlinear) oscillations play an important role. Prominent examples are components in the automotive industry, which are excited by the road surface or by vibrations from an electric motor/combustion engine. In order to describe the dynamics of these systems, either a complex FEM model including material models that are sometimes difficult to determine or a complex derivation of minimal models is necessary.

Modern machine learning and deep learning methods open up a different approach here: These offer the possibility of extracting the system behavior from existing measurement data and predicting it for future measurements. The best known representative of machine learning are so-called neural networks, which are inspired by the neural structure in biological brains. These can be viewed as a universal function approximator and therefore might be able to extract system properties in a data-driven manner and subsequently predict future behavior.

The goal of this research is to apply neural networks to the prediction of dynamic system behavior with a focus on forced nonlinear oscillations and to develop a soft sensor that describes the transfer behavior between excitation and behavior.

The focus is on the use of neural networks to describe transfer behavior. In a first step, the method is investigated using simple academic examples (see below). Here, the system response x is to be inferred from a known excitation f(t). Neural networks are adapted to given data via a gradient-based training algorithm.

The animation shows the training progress of an Autoregressive Neural Network (ARNN) over the individual epochs. The system behavior under white noise excitation was used as training data. In many simulations a very good approximation by means of the ARNN can be shown, as well as a good extrapolation ability to structurally different excitations.

In addition to the academic example shown, the practical application is also considered. Components in automobiles are constantly exposed to external influences from the road and engine. The transfer behavior between the loads at vehicle level (excitation) and the individual component (system response) is measured in elaborate tests. In addition to the complex transfer path through complex geometries with different component properties, the multidimensional excitation and system response is a major challenge.

The use of a neural network to describe the transfer behavior shows promising results in first experiments and approximates the system response for many maneuvers better than classical linear methods for transfer path modeling.