The monitoring of mechanical systems aims at detecting damages at an early stage, in general by using output-only vibration measurements under ambient excitation. In this paper, a method is proposed for the detection and isolation of small changes in the physical parameters of a linear mechanical system. Based on a recent work where the multiplicative change detection problem is transformed to an additive one by means of perturbation analysis, changes in the eigenvalues and eigenvectors of the mechanical system are considered in the first step. In a second step, these changes are related to physical parameters of the mechanical system. Finally, another transformation further simplifies the detection and isolation problem into the framework of a linear regression subject to additive white Gaussian noises, leading to a numerically efficient solution of the considered problems. A numerical example of a simulated mechanical structure is reported for damage detection and localization.