Previous works have shown that only relying on measurement data is generally insufficient to identify root causes of the dimensional variation for the complex manufacturing system. It is also well known that for underdetermined multistage assembly processes (MAPs), the number of measurements is less than that of process errors so that the traditional methods are not available for the variation source identification. Therefore, there exists a substantial challenge for fault diagnosis of underdetermined MAPs, especially for the case with multiple fault patterns. To tackle this problem, a novel approach that integrates statistical analysis with domain knowledge is proposed in this paper. First, the variation propagation model is employed to reveal the inherent relationship between key control characteristics and key product characteristics, and then the corresponding variance model is constructed to interpret process faults by means of the abnormal variance of process errors. Considering that the probability of less process faults is far higher than that of more process faults in MAPs, the problem of fault diagnosis is further transformed into searching the sparse solution of abnormal variance changes for process faults. Afterwards, based on the non-negative property of the covariance matrix, an enhanced Bayesian hierarchical model is developed to favor sparse estimation of the variance for the underdetermined system in MAPs. Finally, experimental results of both the numeric simulation and practical case study demonstrate the proposed diagnosis methodology can effectively identify the process faults for different patterns with system noise.

先前的工作表明，仅依靠测量数据通常不足以识别复杂制造系统尺寸变化的根本原因。众所周知，对于不确定的多级组装过程（MAP），测量数量少于过程错误的数量，因此传统方法无法用于变化源识别。因此，对于不确定的MAP的故障诊断，尤其是对于具有多个故障模式的情况，存在很大的挑战。为了解决这个问题，本文提出了一种将统计分析与领域知识相结合的新方法。首先，采用变异传播模型揭示关键控制特征与关键产品特征之间的内在联系，然后构造相应的方差模型，利用过程误差的异常方差来解释过程故障。考虑到MAP中较少的过程故障概率远大于较多的过程故障概率，因此将故障诊断问题进一步转化为寻找过程异常的异常方差变化的稀疏解。然后，基于协方差矩阵的非负性质，开发了增强的贝叶斯层次模型，以支持对MAPs中欠定系统的方差的稀疏估计。最后，数值模拟和实际案例研究的实验结果表明，所提出的诊断方法可以有效地识别具有系统噪声的不同模式的过程故障。