Fault detection is considered a significant and urgent issue in industrial processes. However, faults rarely occur, resulting in an imbalance between normal data and fault data. This paper presents a novel fault-detection model based on wavelet packet decomposition and a bilayer convolutional neural network (WPD-biCNN) within imbalanced data conditions. WPD helps eliminate the adverse impact of data scarcity by mining information in multiple frequency domains rather than generating new data. More rich information in various time and frequency scales is obtained from collected fault samples, which increases the fault information and can help address the imbalance. The improved bilayer convolutional neural network combining local and full convolution stages is employed to extract features and detect fault. The experimental results of an actual polyethylene production process reveal that the proposed method achieves effective performance in the fault detection of agglomeration. In particular, the proposed method exhibits an excellent classification ability for imbalanced data sets with less fault data and more normal data.