Active cluster replacement algorithm as a tool to assess bifurcation early-warning signs for von Karman equations

Abstract

The paper deals with a novel algorithm used to improve identification quality of clusters generated by predictive clustering algorithm as a tool to identify states preceding to bifurcations for a system governed by von Karman equations. To construct bifurcation precursors, solutions (of the equations) observed on bifurcation paths are clustered; centers of the clusters constitute a set of bifurcation precursors. To decrease identification error rate, quality of each precursor is assessed with the employment of an additional, validation set. The paper concerns with two approaches to this procedure; the first one employs a single number to assess identification value of a cluster in order to delete those with low identification values. The second approach uses proposed knowledge extraction procedure to ascertain rules of replacement of the precursors chosen by the algorithm (active) by more efficient one. A wide-ranging simulation reveals that the best variant (provided that the Wishart clustering algorithm is utilized) is the replacement of the active cluster in conjunction local normalization of data. The optimal parameters values for both algorithms, arriving at essentially decreased identification errors.