The problem of fault diagnosis for dimensional integrity in multistation assembly systems is addressed in this paper. Fault diagnosis under this context is to identify the process errors which significantly contribute to the large product dimensional variation based on sensor data. The main challenges to be resolved in this paper include (1) the number of measurements is less than the process errors, which is typical in practice, but results in an ill-posed estimation problem, and (2) there exists spatial correlation among the dimensional variation of process errors, which has not been addressed yet by existing literature. A spatially correlated Bayesian learning (SCBL) algorithm to address these challenges is developed. The SCBL algorithm is based on the relevance vector machine (RVM) by exploiting the spatial correlation of dimensional variation from various process errors, which occurs in some circumstances of assembled parts and is well defined in GD&T standards. The proposed algorithm relies on a parametrized prior including the spatial correlation, and eventually leads sparsity in fault diagnosis; hence, the issues with ill-posedness and structured process errors will be addressed. A number of simulation studies are performed to illustrate the superiority of SCBL algorithm over state-of-the-art algorithms in sparse estimation problems when spatial correlation exists among the nonzero elements. A real autobody assembly process is also used to demonstrate the effectiveness of proposed SCBL algorithm.

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