N-dimensional extension of unfold-PCA for granular systems monitoring

This work is focused on the data based modelling and monitoring of a family of modular systems that have
multiple replicated structures with the same nominal variables and show temporal behaviour with certain
periodicity. These characteristics are present in many systems in numerous fields such as the construction or
energy sector or in industry. The challenge for these systems is to be able to exploit the redundancy in both time
and the physical structure.
In this paper the authors present a method for representing such granular systems using N-dimensional
data arrays which are then transformed into the suitable 2-dimensional matrices required to perform statistical
processing. Here, the focus is on pre-processing data using a non-unique folding–unfolding algorithm in a way
that allows for different statistical models to be built in accordance with the monitoring requirements selected.
Principal Component Analysis (PCA) is assumed as the underlying principle to carry out the monitoring. Thus,
the method extends the Unfold Principal Component Analysis (Unfold-PCA or Multiway PCA), applied to 3D
arrays, to deal with N-dimensional matrices. However, this method is general enough to be applied in other
multivariate monitoring strategies.
Two of examples in the area of energy efficiency illustrate the application of the method for modelling. Both
examples illustrate how when a unique data-set folded and unfolded in different ways, it offers different modelling
capabilities. Moreover, one of the examples is extended to exploit real data. In this case, real data collected over
a two-year period from a multi-housing social-building located in down town Barcelona (Catalonia) has been
used.