A modified gaussian neural network and growth/training algorithm for on-line identification of nonlinear dynamic systems
Abstract
This investigation focuses on neural networks for on-line identification of nonlinear systems whose dynamics are not well-understood. A gaussian-type network is developed that utilizes direction as well as magnitude of the network input vector to approximate a function. The directional information allows more flexible mappings with a single node than otherwise possible. As such, fewer nodes for this paradigm are required than similar paradigms to achieve the same approximation capability. Therefore, a major benefit of this new network paradigm is a reduction in training time if the network is implemented on a serial machine or a reduction of processing hardware if implemented on a parallel machine. Initial off-line training studies establish the benefits of the new paradigm through comparisons with conventional gaussian paradigms. To achieve reliable on-line training behavior, an integrated network growth/training procedure is constructed. The algorithm automates the node selection process and adjusts the learning rate as training progresses while promoting network mapping convergence by preventing inappropriate weight adjustments. The training portion of the algorithm, different from recursive prediction error methods, is essentially a modified Levenberg-Marquardt technique applied to both current local information and summarized global information. The growth portion of the algorithm adds nodes when approximation errors are large or when multiple consecutive training failures occur. Nodes are deleted if their mapping contributions decrease below a prespecified threshold or when they no longer contribute to the Levenberg-Marquardt procedure. Success of the algorithm is largely independent of the classical notion of persistence of excitation. The algorithm is intended for networks using localized basis functions and is specifically applied to a gaussian-type network in this work. Results from on-line tests dealing with static and dynamic systems are presented, and the lessened importance of persistence of excitation during training is demonstrated.
Degree
Ph.D.
Advisors
Meckl, Purdue University.
Subject Area
Mechanical engineering
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