In practical process industries, a variety of online and offline sensors and measuring instruments have been used for process control and monitoring purposes, which indicates that the measurements coming from different sources are collected at different sampling rates. To build a complete process monitoring strategy, all these multi-rate measurements should be considered for data-based modeling and monitoring. In this paper, a novel kernel multi-rate probabilistic principal component analysis(KMPPCA) model is proposed to extract the nonlinear correlations among different sampling rates. In the proposed model, the model parameters are calibrated using the kernel trick and the expectation-maximum(EM) algorithm. Also, the corresponding fault detection methods based on the nonlinear features are developed. Finally, a simulated nonlinear case and an actual predecarburization unit in the ammonia synthesis process are tested to demonstrate the efficiency of the proposed method.