The fused magnesia smelting process is a very complex industrial process, and the fault probability is quite high. Current process monitoring and fault detection methods have difficulty accurately capturing the small fault signals in the smelting process, resulting in serious irreversible consequences. Under the background of big data, the performance of the fused magnesia smelting process fault detection method has also gradually improved from the use of physical variable data modeling to the use of video data modeling and has achieved the purpose of monitoring the smelting process. However, it is difficult to achieve the expected monitoring effect by modeling with only physical or video data. Therefore, in this paper, a novel fault detection approach for nonlinear industrial processes is proposed. First, we propose a bidirectional sparse orthogonal discriminant analysis method for feature selection. Second, dimension reduction of the eigenmatrix is carried out by the manifold learning bilinear regression method. Finally, a collaborative optimization process monitoring model is established to realize online monitoring and fault detection of early and minor faults in the fused magnesia smelting process. The simulation results show the effectiveness of the proposed method.