A fast U-D factorization-based learning algorithm with applications to nonlinear system modeling and identification

A fast learning algorithm for training multilayer feedforward neural networks (FNN) by using a fading memory extended Kalman filter (FMEKF) is presented first, along with a technique using a self-adjusting time-varying forgetting factor. Then a U-D factorization-based FMEKF is proposed to further improve the learning rate and accuracy of the FNN. In comparison with the backpropagation (BP) and existing EKF-based learning algorithms, the proposed U-D factorization-based FMEKF algorithm provides much more accurate learning results, using fewer hidden nodes. It has improved convergence rate and numerical stability (robustness). In addition, it is less sensitive to start-up parameters (e.g., initial weights and covariance matrix) and the randomness in the observed data. It also has good generalization ability and needs less training time to achieve a specified learning accuracy. Simulation results in modeling and identification of nonlinear dynamic systems are given to show the effectiveness and efficiency of the proposed algorithm.