In the process industry, fault monitoring related to output is an important step to ensure product quality and improve economic benefits. In order to distinguish the influence of input variables on the output more accurately, this paper introduces a subalgorithm of fault-unrelated block partition into the prototype knockoff filter (PKF) algorithm for its improvement. The improved PKF algorithm can divide the input data into three blocks: fault-unrelated block, output-related block, and output-unrelated block. Removing the data of fault-unrelated blocks can greatly reduce the difficulty of fault monitoring. This paper proposes a feature selection based on the Laplacian Eigen maps and sparse regression algorithm for output-unrelated blocks. The algorithm has the ability to detect faults caused by variables with small contribution to variance and proves the descent of the algorithm from a theoretical point of view. The output relation block is monitored by the Broyden–Fletcher–Goldfarb–Shanno method. Finally, the effectiveness of the proposed fault detection method is verified by the recognized Eastman process data in Tennessee.

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In the process industry, fault prediction and product-related fault monitoring are important links to ensure product quality and improve economic benefits. In this paper, under the framework of the BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm, a new and more accurate data-driven method, the ABFGS algorithm, is proposed. Compared with the BFGS algorithm, the ABFGS algorithm adds output-related fault monitoring capabilities and has strong robustness, which can eliminate the influence of outliers on measurement data. The effectiveness of this method has been verified by the Eastman benchmark program in Tennessee. The simulation results show that this method can eliminate the influence of outliers and effectively predict the process. Compared with the other three algorithms, the ABFGS algorithm can not only clearly and accurately indicate whether the detected fault is related to the output but also provide a higher fault monitoring rate.