Abstract A physically-based thermal error model of the servo axis was established, aiming at the time-varying nonlinear thermal error of the screw. However, the thermal characteristic parameters of the model may differ from the working state of the machine tool. In order to analyze the influence of the variation of the thermal characteristic parameters on the prediction results of the model, and considering that the performance functions of the physically-based servo axis thermal error model are implicit and have no explicit analytical expression, a new method for calculating model reliability using deep belief network (DBN) and the Monte Carlo method was presented, and DBN was used to substitute the implicit functions. The reliability and residual prediction of the model with single parameter and multi-parameter fluctuations was determined. Finally, the robustness of the model and the accuracy of the proposed reliability calculation method were experimentally verified.

中文翻译：

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基于DBN和Monte Carlo方法的热误差模型可靠性分析

摘要 针对螺杆随时间变化的非线性热误差，建立了基于物理的伺服轴热误差模型。但是，模型的热特性参数可能与机床的工作状态不同。为了分析热特性参数的变化对模型预测结果的影响，并考虑到基于物理的伺服轴热误差模型的性能函数是隐式的，没有明确的解析表达式，一种新的方法提出了使用深度置信网络（DBN）和蒙特卡罗方法计算模型可靠性，并使用DBN替代隐函数。确定了具有单参数和多参数波动的模型的可靠性和残差预测。