An adaptive diagonal recurrent wavelet neural network based on compact wavelet frame and its application

A multidimensional adaptive diagonal recurrent wavelet neural network based on a compact wavelet frame is proposed. The network consists of an initial network and sub-networks that will be incorporated during training according to the precision. Suitable dilation and translation was chosen to construct a single dilation compact wavelet frame to form every sub-network that can solve the "dimension disaster" in the multidimensional wavelet neural network. The hidden layer of every network is constructed by a compact wavelet frame under increasing single dilation. Every sub-network has the same input and output as the initial network. The expected output of the sub-network is the error of the last sub-network. The structure of hidden layer neurons is diagonal recurrent. A dynamic recurrent least squares algorithm with a forgetting factor was constructed to train network parameters which can avoid a local minimum in the training. Training of the parameters of the sub-network that has just been incorporated has no influence on the parameters that have already been trained. This network is used in the fault diagnosis of pumping jacks in an oilfield.