Aiming at the complexity, nonlinearity and difficulty in modeling of nonlinear system. In this paper, an improved back-propagation(BP) neural network based on restricted boltzmann machine(RBM-IBPNN) is proposed for nonlinear systems modeling. First, the structure of BP neural network(BPNN) is optimized by using sensitivity analysis(SA) and mutual information(MI) of the hidden neurons. Namely when the SA value and the MI value of the hidden neurons satisfy the set standard, the corresponding neurons will be pruned, split or merged. second, the restricted boltzmann machine(RBM) is employed to perform parameters initialization of training on the IBPNN. Finally, the proposed RBM-IBPNN is evaluated on nonlinear system identification, lorenz chaotic time series prediction and the total phosphorus prediction problems. The experimental results demonstrate that the proposed RBM-IBPNN not only has faster convergence speed and higher prediction accuracy, but also realizes a more compact network structure.

针对非线性系统建模的复杂性，非线性和难点。针对非线性系统建模问题，提出了一种基于受限boltzmann机（RBM-IBPNN）的改进BP神经网络。首先，利用隐含神经元的敏感性分析和互信息，优化了BP神经网络的结构。即，当隐藏神经元的SA值和MI值满足设定标准时，将修剪，拆分或合并相应的神经元。其次，采用受限的博茨曼机器（RBM）对IBPNN进行训练参数的初始化。最后，对提出的RBM-IBPNN进行非线性系统辨识，洛伦兹混沌时间序列预测和总磷预测问题进行了评估。