用于解决非线性受电弓系统的启发式神经网络计算（英文）

发布时间：2018-08-26 16:52

【摘要】：本文提出了一种启发式神经网络计算平台,用于解决基于不同阶数泛函微分方程的非线性受电弓系统(Pantograph systems based on functional differential equations,P-FDEs)中的初值问题(Initial value problems,IVPs)。该方案利用了前馈人工神经网络(Artificial neural networks,ANNs)、基于遗传算法(Genetic algorithms,GAs)的进化计算技术,以及内点技术(Interior-point technique,IPT)。通过设定一个无监督学习误差,针对完全和不完全满足初始条件两种情况,利用ANNs创建了系统的两种数学模型。采用GA IPT混合算法,对ANN模型的设计参数进行了优化。在GA IPT中,GA是有效的全局搜索工具,IPT则用于快速的局部收敛。针对三种不同类型的1 3阶P-FDEs的IVPs对该方案进行了测试。通过对比现有的精确解,确认了该方案的正确性。通过采用不同数量神经元的ANN模型进行了大量的数值实验,进一步验证了该方案的准确性和收敛性。
[Abstract]:In this paper, a heuristic neural network computing platform is proposed to solve the initial value problem (Initial value problems,IVPs) in a nonlinear pantograph system based on different order functional differential equations (Pantograph systems based on functional differential equations,P-FDEs). The scheme uses feedforward artificial neural network (Artificial neural networks,ANNs), evolutionary computing based on genetic algorithm (Genetic algorithms,GAs) and interior point technique (Interior-point technique,IPT). By setting up an unsupervised learning error, two mathematical models of the system are created by using ANNs for the two cases of complete and incomplete initial conditions. The design parameters of ANN model are optimized by using GA / IPT hybrid algorithm. In GA IPT, GA is an effective global search tool for fast local convergence. The scheme is tested for three different types of IVPs of order 1 and 3 P-FDEs. The correctness of the scheme is confirmed by comparing the existing exact solutions. The accuracy and convergence of the proposed scheme are further verified by a large number of numerical experiments using the ANN model with different number of neurons.
【作者单位】： Department
【分类号】：TP183;O175

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