基于半参数回归模型的制造过程加工误差流建模与分析

Stream of Variation Modeling and Analysis for Manufacturing Processes Based on a Semi-parametric Regression Model

针对多工序制造过程中加工误差流的传递和累积问题,研究工序输入尺寸误差、系统误差和随机误差与工序输出尺寸误差间的关系,构建数学模型并给出了模型解算方法。基于泰勒公式展开和实际加工经验假设,建立工序输出尺寸误差与工序输入尺寸误差间的参数化表达式,并将与工序输出尺寸误差关系未知的工序系统误差非参数化表达,建立制造过程加工误差流的半参数回归模型;采用广义交叉核实函数计算平滑因子,以实际机械加工经验确定正规化矩阵,由补偿最小二乘法求解了所建立半参数回归模型的参数和非参数估计。以二工序磨削加工实例证明,采用半参数回归模型描述加工误差流,不仅能够反映工序间误差传递关系,分离工序系统误差和随机误差,而且比完全参数建模方法和非参数建模方法具有更好的解释性和适用性。

To model the stream ofvariation＇s propagation and accumulation in multi- station manufacturing processes, the relationships among the input errors, system errors, random errors and output errors at a station are investigated and a corresponding model and its solution method are presented. Based on Taylor formula and the practical experiences assumptions, a semi-paramea-ic regression model is proposed to denote the relationship between station input errors and output errors by the parametedzed method and the relationship between station output errors and system errors by the non-parametric method. By calculation of the smoothing parameter using a generalized cross validation method and the regularize matrix on the practical experiences, a penalized least squares method is used to offer the parametric and non-parametric estimation of the proposed model. A two-station grinding example is taken to illustrate that the proposed model is able to not only model correctly the variation propagation and accumulation in multi-station manufacturing processes with the separation of system errors and random errors, but also show a good interpretability and applicability.