基于遗传算法及BP网络的主轴热误差建模

High-speed spindle thermal error modeling based on genetic algorithm and BP neural network

针对基于多输入多输出(MIMO)反向传播(BP)神经网络的热误差建模方法过度依赖于训练样本、通用性与收敛性较差的问题,利用灰色聚类分组与相关分析法对温度变量进行分组并提取热敏感点,利用遗传算法(GA)将预测输出与期望输出的误差绝对值和的倒数作为判断隐含层节点数的准则,对MIMO-BP网络的拓扑结构进行优化,设定输出层残差误差限,实现了网络阈值与权值的有效优化。建立了基于MIMOM-BP与GA-BP的主轴轴向热伸长与径向热倾角的热误差模型。以精密坐标镗床主轴为研究对象,采用五点法对热误差进行测量,验证了测量及建模方法的有效性,表明GA-BP模型可实现不同工况下主轴空间位姿状态的高精度预测,更适合作为热误差补偿模型。

To avoid the disadvantages of thermal error modeling method based on Multiple Input Multiple Output- Back Propagation neural network （MIMO-BP） such as excessive dependence on training samples and poor conver- gence and worse generality, the gray cluster grouping and correlation analysis were used to group temperature varia- bles and optimize thermal senstive points. Subsequently, a Genetic Algorithm （GA） which regarded the absolute value sum＇s reciprocal of differences between predictive and desired outputs as the number of nodes in hidden layer was used to optimize the topology of MIMO-BP network. The thresholds and weights of network were optimized by setting the residual error limits of output layer. The elongation and thermal tilt angle models were established based on MIMO-BP and GA-BP modeling. The five-point method was utilized to measure the spindle thermal errors of jig- boring, and the effectiveness of the measurement and modeling was validated by the experiment results. The GA-BP model could predict thermal errors under different cutting conditions, and it was more suitable as the thermal error compensation model.