Causal Discovery for Rolling Bearing Fault Under Missing Data: From the Perspective of Causal Effect and Information Flow

Missing data phenomenon is ubiquitous in many domains which imposes difficulties on the reconstruction of causal relationships due to incomplete datasets. Currently, although causal discovery techniques tackling data missing complete at random (MCAR) and missing at random (MAR) are known to the public, attaining causal structure from data missing not at random (MNAR) is still beyond our reach. In this article, a causal effect and information flow Peter Clark (CEIFPC) algorithm is proposed, which uses a missingness graph to represent the missing mechanism and combines causal effect correction criteria (CECC) with information flow to recover the potential causal structure. First, in the sketchy stage, a test-wise deletion Peter Clark (TD-PC) algorithm for causal skeleton learning is introduced. Second, in the refining stage, by employing CECC, one can identify erroneous edges within the causal skeleton and subsequently eliminate them. Finally, in the orientation stage, the directional strategies from the Peter Clark (PC) algorithm and information flow are incorporated to accurately determine the directions of causal edges. Our proposed CEIFPC algorithm not only theoretically yields asymptotically correct results but also demonstrates superior performance in recovering the potential causal structure under nonrandom missing data. As shown by experimental results, our proposed method, CEIFPC, exhibits good performance on both synthetic and real bearing failure datasets.