Tobacco manufacturing is an important industry. With the development of productivity, people have raised higher requirements for product quality and production safety. Among them, tracing and analyzing faults in the tobacco production process are crucial for ensuring safety and providing maintenance recommendations. To tackle this problem, we propose a novel approach that combines non-linear Granger causality with a type of sparse multilayer perceptron (MLP). Specifically, we use sparse MLP to establish non-linear regression between variables, and promote sparsity of their dependency relationships through hierarchical group lasso penalty. Finally, the causal relationships between variables can be extracted utilizing Granger causality inference. To demonstrate the effectiveness of our proposed method, we apply it to the heat transfer oil drum type tobacco drying system as a case study. A detailed introduction and analysis are provided in this paper, the results show that it can accurately diagnose the causal dependence between variables during flow interruption. Through causal reasoning and mechanism analysis, the root cause and propagation path of flow interruption in tobacco production line can be accurately determined.