Real-Time Subspace Tracking for Condition Monitoring Using Karhunen–Loève–Transform

In order to monitor the dynamics of a distributed or high-dimensional dynamical system, an infinite- or high-dimensional Hilbert space is required as this class of systems may show various and complex dynamics. For example, different operational regimes can be observed depending on the current external loads. However, very often, the relevant dynamics of each of the observed operational regimes take place in a low-dimensional active subspace which is spanned by a low number of active modes. For changes in operational conditions, the active modes and therefore the low-dimensional subspace will be subjected to change as well. As Karhunen–Loève–Transform (KLT) is always applied to a history of measurements, good convergence and fast detection of changes in system dynamics conflict when choosing the length of the time interval. We present an algorithm based on KLT which uses an adaptive sliding time window. It can be employed for real-time tracking of the active subspace. The data from the real-time subspace tracking can be used to categorize different operational conditions and thus monitor the system in real time. We show that with currently available technology, an efficient implementation of the subspace tracking with sampling frequencies of 1,000 Hz is possible.