The robustness of combination of sigmoid function wavelet neural network

The disturbing sensitivity and robustness of combination of sigmoid function wavelet neural network are discussed by making use of probability statistics and symbolic logic. If the faint perturbation appears, the robust invariability condition of wavelet neural network is obtained, and if the sensitive disturbance appears, the sensitivity formula and robustness formula are given. It is proved theoretically that to a certain extent, the more hidden wavelet nerve cells, the less robustness of wavelet neural network. Consequently, it validates analytically the intuitionistic hypothesis of the relationship between hidden layer wavelet nerve cells number and the robustness of wavelet neural network.