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Fluid catalytic cracking (FCC) is an important process in petroleum processing. Effective monitoring of the status and quality of FCC is vital. Accurate description of the relationship between process and quality variables is the basis of quality-driven monitoring. Many process variables affect the quality of FCC; some of these effects are linear, and others are nonlinear. We propose a combination method from the perspective of linearity and nonlinearity to improve the monitoring performance of FCC quality. Partial least squares (PLS) is initially used to extract linear features, and its residual space is saved as the input of the deep feedforward neural network (DFNN). DFNN is then used to extract nonlinear features for the further decomposition of subspaces. The PLS-DFNN method accurately describes processes involving linearity and nonlinearity. We construct three monitoring statistics to characterize the types of faults. The proposed method proves its excellent effect on a numerical simulation data set. It effectively distinguishes the types of faults on the Tennessee Eastman process data set, and the fault detection rate is superior to other related methods. Finally, we apply this method to the actual FCC and verify the superiority of this combination. [ABSTRACT FROM AUTHOR]