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The systems containing both continuous dynamics described by differential equations and discrete events such as ON/OFF switches are referred to as hybrid system. Recently, the system identification of hybrid systems have received more attention not only in academia but also in industry. In this study, an identification method of a hybrid mechanical system switched by the absolute value of velocity or displacement as shown in Fig.1 is considered. On the identification of the hybrid systems, parameters and region of each submodel on the regression vector space are estimated. A support vector machine (SVM) is usually applied to separate the regression vector space by a hyperplane. However, we have shown that the regression vector space of the system shown in Fig.1 can not be separated by a linear discriminant function in the following cases: • The spring constant k or the damping coefficient c is switched by the velocity of the mass m. • The damping coefficient c is switched by the position of the mass m. For these cases, we propose an identification method based on SVM with polynomial kernel, and the effectiveness is shown by simulations.

An Identification Method of a Mechanical Hybrid System Switched by the Absolute Value of Velocity or Displacement