MONITORING OF SIGNALS FROM MANUFACTURING PROCESSES USING THE KARHUNEN–LOÈVE TRANSFORM

Abstract

Monitoring the condition of signals during manufacturing can provide valuable information about the status of the parts being produced, as well as that of the components of the manufacturing machine. To this end, we introduce a monitoring technique based on the Karhunen–Loève transform, which decomposes measured manufacturing signals into decorrelated components in the form of fundamental eigenfunctions. The isolated eigenfunctions are monitored by means of the corresponding coefficient vectors, which indicate stationary and non-stationary changes in the deterministic and stochastic fundamental patterns. In this paper, the mathematical foundations of the technique are explored to form a good understanding of the mechanics of the transformation. This understanding is achieved with simple illustrative examples in the discrete and continuous domains, followed by an example of multicomponent signal decomposition by means of numerical simulations. The monitoring potential of the technique is illustrated with an example from a milling process, where the main modes are extracted by means of the eigenvectors and coefficient vectors.