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This article presents a discrete mathematical model for fan blades and theoretically analyses the mathematical relationship between the location and depth of crack and fan blade natural frequency. On the basis of the blade mathematical model, using the theoretical computed natural frequency as the fault feature, this article proposes a fast and efficient fan blade crack fault diagnosis method. Transfer matrix method is used to calculate the first three-order blade natural frequencies under different crack cases and then to build the database in MATLAB. Subsequently, the damaged blade can be detected using changes in natural frequencies by solving the reverse problem. The experimental result shows that this discrete mathematical model can get the exact solution of natural frequency, and the method has certain application value.