A novel approach to determine very accurately multiple parametric variations by analyzing sensitivity vector fields is proposed. These sensitivity vector fields describe changes in the state space attractor of the dynamics and system behavior when parametric variations occur. The parametric changes are reconstructed by analyzing the deformation of the attractor in state space (characterized by means of the sensitivity vector fields). An optimal set of basis functions in the vector space formed by the sensitivity fields is obtained and used to successfully identify test cases involving multiple simultaneous parametric variations. The method presented is shown to be robust over a wide range of parametric variations and to perform well in the presence of noise. The main application and the emphasis of the proposed technique is on detecting multiple simultaneous damages in vibration-based structural health monitoring.