Estimation of the sintering state has importance for clinker quality improvements and the safe operation of the rotary kiln. Class imbalanced thermal signals usually pose challenges in feature extraction and abnormal state recognition. In this article, a novel framework that integrates prior knowledge and hidden information is developed for sintering state recognition in the class imbalance condition. For discriminative feature extraction of imbalanced data, a cascaded stack autoencoder (SAE) model is proposed to fuse our prior knowledge and hidden information. The model includes a feature extraction SAE and a deep fusion SAE: the former extracts hidden information from thermal signals, and the latter deeply fuses and compresses our prior knowledge and hidden information. For the class imbalance of sintering samples, we propose a data-dependent kernel modification optimal margin distribution machine (ddKMODM) as a sintering state recognition model. Modifying the original kernel function by a conformal function depending on the data distribution in kernel space, ddKMODM can change the local volume expansion coefficient of the feature space to eliminate the negative effects caused by imbalanced samples. Experiments on real data show that the proposed framework can balance the detection rate of each state in the class imbalanced condition, and its overall sintering state recognition accuracy exceeds 92%.