This paper investigates one eigenvalue decomposition-based source number estimation method, and three information-based source number estimation methods, namely the Akaike Information Criterion (AIC), Minimum Description Length (MDL) and Bayesian Information Criterion (BIC), and improves BIC as Improved BIC (IBIC) to make it more efficient and easier for calculation. The performances of the abovementioned source number estimation methods are studied comparatively with numerical case studies, which contain a linear superposition case and a both linear superposition and nonlinear modulation mixing case. A test bed with three sound sources is constructed to test the performances of these methods on mechanical systems, and source separation is carried out to validate the effectiveness of the experimental studies. This work can benefit model order selection, complexity analysis of a system, and applications of source separation to mechanical systems for condition monitoring and fault diagnosis purposes.