A state diagnostic system for equipment is disclosed. The system is constructed of a neural network model for learning in advance one or more samples of information on vibrations, which are produced in a specific operation state of the equipment, in association with the corresponding operation state and obtaining an output signal corresponding to results of the learning when information on vibrations produced upon operation of the equipment is inputted; an input unit for inputting to the neural network model the information on the vibrations produced upon operation of the equipment; and an output unit for outputting the output signal from the neural network model as diagnostic results to a user. State diagnostic methods, learning system, preview/predict system, diagnosis training system, service life estimation assisting system, service life estimation assisting system, and maintenance assisting system are also disclosed.