An algorithm for diagnosing nonlinear characteristics of dynamic systems with the integrated periodicity ratio and lyapunov exponent methods

Abstract The present research aims to develop a novel approach for diagnosing the nonlinear behavior of dynamic systems with an algorithm integrating the Periodicity Ratio (P-R) and Lyapunov exponent methods. The advantages and disadvantages of the nonlinear behavior diagnostic methodologies with separate employment of the two methods are studied and compared. Although the two methods generally show effectiveness in diagnosing the characteristics of nonlinear dynamic systems, in some cases both methods may miss or misinterpret some of the characteristics of the nonlinear systems. In fact, the two methods can be complementary as identified in this research. With a specified integration of the two methods, the proposed algorithm maintains the advantages and overcomes the shortcomings of the two methods. The proposed algorithm therefore provides higher completeness, efficiency and accuracy to diagnose the nonlinear characteristics in dynamic systems compared with the existing methods such as the Lyapunov exponent method and the P-R method. The algorithm of the proposed approach is presented in detail with a case study to demonstrate its application.