局部连接神经网络简化了网络结构,提升了网络收敛速度和减少了网络训练复杂度,可用于函数逼近和系统建模.为了采用直观的建模方式对实际系统网络拓扑逼近,对此文章提出一种新型的局部连接BP网络模型 (local BP neural network, LBPNN).该模型的网络结构可以模拟任意前馈型网络拓扑结构, 其网络模型中的连接权和神经元与被模拟的网络拓扑中的边和节点一一对应. 传统带约束的非线性规划和智能优化算法,其参数辨识受限条件多和算法代价较大, 同时提出了与LBPNN模型相应的一种新型的带约束的随机梯度下降法(constrained stochastic gradient descent, CSGD)对其权值参数进行训练.通过算例仿真验证了CSGD训练算法的有效性,稳定性和鲁棒性.

The traditional mathematical modeling is nonrepresentational and it is hard for understanding. In order to model the real system in an intuitive method, a novel local BP neural network (LBPNN) model has been proposed to imitate arbitrary feed-forward topologies of networks and the weights’ training algorithm–constrained stochastic gradient descent (CSGD) is also introduced in this paper. The network model could be used to approach functions which could improve the training speed and model complex system. With the LBPNN model and the CSGD training algo- rithm, network’s parameter of weight could be identified within constrains. The train- ing algorithm’s effectiveness, stability and robustness are verified in a test LBPNN model.