Analysis of Numerical Integration in RNN-Based Residuals for Fault
  Diagnosis of Dynamic Systems
Arman Mohammadi Theodor Westny Daniel Jung Mattias Krysander
Data-driven modeling and machine learning are widely used to model the
behavior of dynamic systems. One application is the residual evaluation of
technical systems where model predictions are compared with measurement data to
create residuals for fault diagnosis applications. While recurrent neural
network models have been shown capable of modeling complex non-linear dynamic
systems, they are limited to fixed steps discrete-time simulation. Modeling
using neural ordinary differential equations, however, make it possible to
evaluate the state variables at specific times, compute gradients when training
the model and use standard numerical solvers to explicitly model the underlying
dynamic of the time-series data. Here, the effect of solver selection on the
performance of neural ordinary differential equation residuals during training
and evaluation is investigated. The paper includes a case study of a heavy-duty
truck's after-treatment system to highlight the potential of these techniques
for improving fault diagnosis performance.