To define more clearly vibration-related problems of ship propulsion systems, a procedure incorporating operating state recognition into conventional vibration analysis is proposed in this paper. Emphasis is placed on identifying operating modes and decay levels through a multi-layer perceptron (MLP) with a hierarchical prior. First, a variant of stochastic gradient descent (SGD) with momentum is presented for integrating a hierarchical prior into the parameter learning of an MLP network. Then, the MLP network, governing information representation through multiple levels of abstraction is designed, and the hierarchical prior, representing a clear explanation in physics of system operating for an operator or maintainer, is also constructed. Finally, the operating data from a combined diesel or gas turbine (CODOG) system validate that the accuracy improvement of operating state recognition can be achieved by MLP with a hierarchical prior when the sample size is relatively small. Meanwhile, the vibration signals from the CODOG system verify the effectiveness of the vibration analysis procedure coupled with operating state recognition.