基于相对误差平方和的BP算法

The BP Algorithm Based on the Square Sum of the Relative Error

考虑到在很多情况下 ,人们更关心预报模型的预报值与实际值的相对误差情况 ,从而该文采用实际输出与希望输出的相对误差的平方和作为目标函数 ,给出了一种基于相对误差平方和为最小的BP算法。考虑到网络的实际输出值介于 0到 1之间 ,该文对实际问题的理想输出值给出了一种规范化处理方法。通过大量算例检验证实 ,在基于相对误差平方和为检验标准前提下 ,利用该文所给算法求得的拟合值或预报结果要优于传统的基于绝对误差平方和作为目标函数的BP算法所得结果。

As in many cases, people pay more attention to the relative error between actual output values and the idea output values, in this paper, an improved BP algorithm based on the smallest square sum of the relative error is proposed in this paper, which looks on the square sum of relative error between the idea output and the actual output as the object function. Because the network's actual output values are between 0 and 1, a method of standardization management is given to the idea output of actual problem in this paper. It has been proved in many examples that the BP algorithm based in the square sum of the relative error is better than the conventional BP method.