Cluster Analysis for Multivariable Process Control

be profitable to industry in the long term, but also creates an academic interest in the field of multivariable control. a search window is placed, whose lower and upper limits [lower, upper] are [C(x j)-a(x j) , C(x j) + a(x j)] for j = 1 ... N (1) where C(x j) is the centre of the search window on the x j axis a(x j) is the predefined length interval on the x j axis. The centre of gravity (c.o.g) of the search window is then determined by calculating the mean value of all the vectors which lie within the boundary given in (1). The window is then recentred at this value and the procedure is repeated until the c.o.g converges to some constant. Once all the clusters have been found, a grouping procedure is carried out on each individual cluster centre. This is done by grouping each data point to its nearest cluster, given that the distance between them is close enough, thus a data point D is said to be closest to cluster S and is valid to be grouped to it iff M k = max {C k,j-d j -λ j : j = 1. λ j : predefined interval length of the Manhattan grouping boundary on the x j axis, and noc: number of clusters. If M = min {∅ } where ∅ indicates a null vector, then D is classified as an outlier and is left ungrouped. The implementation of the Mean-Tracking algorithm on real data acquired from high-speed machinery has been carried out. As confidentiality has been imposed upon discussion of the nature of the application, the freedom to convey some aspects in detail is limited. Parameter settings for the application are given as follows; n = 10373; N = 7; a(x j) = 1.036σ(x j) / 2; λ = 1.08σ(x j) / 2 where σ(x j) is the standard deviation of x j : this is found to be a reasonable size for the search window through the experience acquired from applying the algorithm to various data sets. Multiple clusters are located by placing a number of search windows , some of which may locate clusters already found (duplicate clusters) whilst others may locate spurious ones (further discussion to be published). A 2-dimensional cluster search is shown in figure 1 for explanation purposes, and as it is difficult to visualise searches in …