中文摘要：

通过一维杆的一维传热的分组显式数值求解,分析热弹性效应的存在及规律,得出随着时间的增长,温升—热变形之间的关系会逐渐趋近稳态,但不可能获得绝对的稳态;在传热过程中,随着距离增加,温度衰减很快,离热源越远的点的热弹性效环应越窄。提出用非线性时序模型与前向神经网络相结合的模型（Nonlinear auto-regressive moving average neural network with exogenousinputs,NARMAX-NN）来辨识热弹性效应。用NARMAX-NN模型对高速进给系统试验台的热动态特性进行建模,获得良好的效果。此方法比多变量回归模型、反馈神经网络模型及广义最小二乘输出误差模型有更好的精度和鲁棒性,能精确地对复杂结构、多热源的时变非线性热误差特性进行建模和预测。

英文摘要：

Through group explicit numerical solution approach of unidimensional heat transferring, the existence and law of thermoelastic effect are analyzed. With the increase of time, the relationship between temperature rise and thermal deformation tends to steady state gradually, but absolute steady state cannot be reached. In the process of heat transfer, with the increase of distance, the temperature decreases rapidly, and the more distant a point from the heat source is, the narrower the thermoelastic effect loop of the point will be. A model which combines nonlinear time series models with neural network models （NARMAX-NN） is put forward to identify the thermoelastic effect. By using the model, the thermal dynamic model of high-speed feed system is built. Compared with multi-variable regression model, feedback neural network model and generalized least squares-output error model, this model has better accuracy and robustness and can accurately carry out modeling and prediction for time-varying and nonlinear thermal error characteristics under machining condition of complex structure and multi-heat sources.