A Novel Quotient Gradient System for Power Line Inspection Model

Deep neural networks have become a key technology in Power Line Inspection Models. Traditional methods for training deep neural networks mostly use gradient descent optimization algorithms. This paper develops a novel optimization method based on trajectories of a class of nonlinear dynamical system, quotient gradient system (QGS) for training deep neural network. This method overcomes the problems of slow convergence speed and low accuracy of GDs algorithms. In theory, the robustness of the QGS-based method is supported by Theorem presented in the paper. The idea of mini-batch mode is integrated into the QGS based method resulting a fast convergence and high accuracy training method, which can reduce the computational cost of quotient gradient system by an order of magnitude. Furthermore, to enhance the scalability of the proposed mini-batch QGS-based system, the limited memory method is integrated into the method to adjust the search direction. We apply the proposed method to training and testing the deep neural network on the CIFAR-10 dataset. The error rate was reduced by $0.45 \%$ and the training speed was increased by $58 \%$. We also apply the proposed method to classify an imbalance set of homemade power line inspection dataset (PLID) with promising results, with a classification error rate of $3.2 \%$, and the problem of dataset imbalance has been solved to the greatest extent from the perspective of algorithms.