Precursor for bifurcation of axial compression system via deterministic learning

In this paper, a precursor for Pitchfork bifurcation in axial compression system was proposed. Firstly, the bifurcation behavior of Moore-Greitzer model was analyzed; Secondly, based on the bifurcation behavior of Moore-Greitzer model, a precursor for Pitchfork bifurcation was proposed via deterministic learning, which was recently presented to learn unknown nonlinear system dynamics from uncertain dynamic environments. Specifically: (i) several typical patterns in Moore-Greitzer model were identified by deterministic learning, the obtained knowledge of the approximated system dynamics is stored in constant RBF networks; (ii) A bank of estimators are constructed using the constant RBF networks to represent the training patterns and previously learned system dynamics is embedded in the estimators; (iii) By comparing the set of estimators with the test pattern, a set of recognition errors are generated, and the average L1 norms of the errors are taken as the similarity measure between the dynamics of the training patterns and the dynamics of the test pattern. Therefore, the test pattern (Pitchfork bifurcation) similar to one of the training patterns can be rapidly recognized according to the smallest error principle.