An Incremental Modeling Approach with a Hierarchical Structure and Progressive Accuracy using Dyadic Wavelet-Based Neural Networks

Abstract

The wavelet neural network (WNN) is a recently developed mathematical tool that can be used in nonlinear system modeling. Motivated by the multi-resolution definition in multi-resolution approximation theory, this paper proposes a novel WNN-based modeling approach possessing two unique characteristics. Firstly, a multi-resolution system model, having an output corresponding to each resolution, is developed from a coarser approximation to a finer representation by adding more details progressively. Secondly, the model at a low resolution is compatible with the model at a high resolution, which means that the well trained WNNs used in a low resolution can be directly incorporated into a high resolution without any modification. The theoretical verification of this approach shows that the incremental characteristic and the compatibility feature of the system modeling at different resolutions is guaranteed by the definition of the modeling subspace division and by the utilization of the dyadic activation functions in WNNs. As a result, by applying this technology into electric ship design and simulation, different users can activate different resolutions according to their requirements during model utilization. At the same time, the compatible modeling structure avoids a large amount of modeling repetition for model developers and thus lightens the computational burden