The Rayleigh-Ritz Autoencoder (RRAE) is an architecture for unsupervised scientific machine learning. The RRAE combines a machine learning tool, the autoencoder, with a classical engineering tool, the Rayleigh-Ritz method. The RRAE consists of an encoder, which is a trainable neural network, and a decoder, which can be considered as a pre-trained neural network, that implements the values of the synthesised admissible functions. This architecture, combined with the automatic synthesis of admissible functions, provides a machine learning framework that allows the exact fulfilment of generalised constraints.

The extremely high cost of lost production time with heavy plant and machinery makes incident analysis a major issue in claims management. The digital twin maintains a historical data base for the real-time machine data over long periods with high temporal resolution. In this project a rule execution engine was developed to automatically search the historical data for specific conditions. In this manner hypotheses can be formulated and tested to see if there is a causal relationship to the incident.

This project is focused on developing and applying mathematical methods to analyze measurement data. One method is used to detect discontinuities in the n-th derivative, which can be later used as break points for spline modeling of the data. Another method focuses on separating periodic signals having an aperiodic trend, using the method of variable projection. The periodic portion of the data is modeled by trigonometric functions, whereas the aperiodic portion is modeled by B-splines. Both of these methods make heavy usage of B-splines when modeling data, since they perform much better when compared to other basis functions.

This project explored new ways to fuse knowledge-based modelling and machine learning for condition monitoring. Instead of integrating process-specific knowledge, generic analytic methods developed at the chair are combined with learning algorithms. In detail, the potential of polynomial discontinuity measures and discrete orthogonal basis functions to enhance autoencoders is demonstrated. This results in models with reduced training data requirement and higher physical consistency that work in an unsupervised manner.

Industrial vibrating screens are used in the field of secondary raw material processing. The efficiency of such a screen depends heavily on the movement that the screen makes while material is being processed. In this project the motion of a sieve was monitored with a new developed sensor system including a 3-axis accelerometer. Since the orbital data is composed by a sine and Gaussian noise, the probability density function of both components were used to model the data. The separation of the two components enables the acceleration amplitude to be determined and further the displacement to be derived.

Railway rails are exposed to cyclical stress in the contact zone between rail and wheel causing so called rolling contact fatigue (RCF). In this project inductive thermography was used to detect Squats and Head Checks – two common types of surface  defects caused by RCF. Phase images where used to characterize Head Checks and estimate the depth as well as the penetration angle of Head Checks.

Delamination during production and impact defects caused during the live cycle of CFRP plates are two types of defects which can be hardly detected by visual inspection. Flash thermography is a method for non destructive testing which can be used to detect these defects. With this method it is possible to locate the defects and estimate the depth in which the delamination occurs.