Model Order Reduction Based on Agglomerative Hierarchical Clustering

This paper presents an improved method for reducing high-order dynamical system models via clustering. Agglomerative hierarchical clustering based on performance evaluation (HC-PE) is introduced for model order reduction. This method computes the reduced order denominator of the transfer function model by clustering system poles in a hierarchical dendrogram. The base layer represents an nth order system, which is used to calculate each successive layer to reduce the model order until finally reaching a second-order system. HC-PE uses a mean-squared error (MSE) in every reduced order, which modifies the pole placement process. The coefficients for the numerator of the reduced model are calculated by using the Pade approximation (PA) or alternatively a genetic algorithm (GA). Several numerical examples of reducing techniques are taken from the literature to compare with HC-PE. Two classes of results are shown in this paper. The first sets are single-input single-output models that range from simple models to 48th order systems. The second sets of experiments are with a multi-input multi-output model. We demonstrate the best performance for HC-PE through minimum MSEs compared with other methods. Furthermore, the robustness of HC-PE combined with PA or GA is confirmed by evaluating the third-order reduced model for the triple-link inverted pendulum model by adding a disturbance impulse signal and by changing model parameters. The relevant stability proofs are provided in Appendixes A and B in the supplementary material. HC-PE with PA slightly outperforms its performance with GA, but both approaches are attractive alternatives to other published methods.