|ijphm_16_030.pdf||1.05 MB||October 25, 2016 - 5:46am|
The article aims to illustrate some results of a research project developed jointly by the Polytechnic University of Turin and Tetra Pak.
The packaging machines produced by Tetra Pak are installed in many countries and in extremely various contexts of industrial productive plants. For many issues as maintenance, efficiency, safety, and supply, the industrial plant is the relevant level of organization in this complex system of customers. An accurate characterization (feature extraction and classification) of the specific behavior of a plant is an important task.
A packaging line monitoring system is installed on huge part of the machines produced by Tetra Pak. It provides detailed information on both the health and the mechanical efficiency of the productive lines. The amount of in-service data collected world-wide from all the monitored machines is very big. In particular a set of indicators is computed in order to monitor the mechanical performances of each machine.
Typically the values of the efficiency parameters measured on machines installed in a single industrial plant spread over huge portions of the physical space of the indicators and completely overlap with data from many other plants. For this reason standard clustering techniques and multivariate statistical tools revealed as completely inefficient for classification purposes on plant level.
The highly non-local nature of this behavior suggested the application of modern manifold learning methods which provide relevant global degrees of freedom. In the paper is provided a short introduction based on a naturally unified geometric viewpoint, to some manifold leaning methods which involve spectral analysis of discretized differential operators, kernel procedures etc.
As a result a compact and homogeneous fingerprint of the behavior of each industrial plant emerges neatly in a nonphysical space generated by selected eigenfunctions of the analogue of the Laplace-Beltrami operator defined over a discrete manifold obtained from the data cluster. The evidence of such a spontaneous grouping made possible the construction of a data-driven classification of the types of emergent behavior. The classification done by analogous spectral clustering techniques is characterized by very high predictive power. The validation of the implemented classifier showed more that 93% correctly classified plants. In particular an interesting “at risk” behavioral class has been detected by the spectral clustering procedure.
The highly non local characteristics of efficiency behavior of an industrial plant from the viewpoint of its efficiency is investigated and mathematically interpreted as an emergent phenomenon in a complex system.