面向Hughes效应改善的EM-BP模型--以运载火箭研制经费估算为例

EM-BP Model for Hughes Effect Improvement:An Exampleof Launch Vichle Cost Forecasting

小样本、特征维度高,特征数多于样本数会导致大部分模型分析结果误差较大,这种现象称为Hughes效应。其中运载火箭经费估算就是典型案例.而通过EM算法改进BP神经网络得到EM-BP模型,可有效改善Hughes效应。该模型首先将高维样本输入至输入层,其后EM算法基于输入神经元提取出低维神经元,并激活传送至隐藏层后,再判断是否需继续使用EM算法,直至最终多次迭代至输出层得出分析结果。该模型使用TcnsorFlow实现,并以长征系列运载火箭经费估算为例验证效果。结果表明:EM-BP模型较其他常用模型的预测精度有所提高,预测结果平均相对误差绝对值为3.93%,模型的训练误差波动小更稳定,且只需4000次迭代即收敛,表明该模型不仅有效改善Hughes效应,同时提高模型分析效率。

Small samples, high feature dimensions and more features than samples will lead to large errors in most model analytical results, which is called the Hughes effect.Carrier rocket fund estimation is a typical case.Hughes effect can be effectively reduced by EM-BP model,which is obtained by improving BP neural network by EM algorithm.The model first inputs high-dimensional samples to the input layer.Then EM algorithm extracts low-dimensional neurons based on input neurons and transfers to the hidden layer, then determine whether to continue to use EM algorithm.Finally, it iterates several times to the output layer to get the analysis results.The EM-BP model is implemented using TensorFlow and is verified by taking the long march series carrier rocket fund estimation.The results show that the prediction accuracy of EM-BP model is higher than other common models.The absolute mean relative error of the predicted results is 3.93%.The training error fluctuation of the model is smaller and more stable and only takes 4000 iterations to converge.It shows that the Hughes effect is not only effectively reduced by this model.At the same time,EM-BP model can improve the efficiency of model analysis.