Abstract
Substructurability theory is proposed to analyze the feasibility and suitability of dynamically substructured system (DSS) testing methods, and substructurability index quantifies the implementation efficiency of DSS tests. DSS is one of the hybrid testing techniques, which decompose an engineering system into numerical and physical substructures. Successful tests require a robust controller to compensate for unwanted dynamics introduced by actuator systems within the physical substructure and to achieve synchronized responses of the numerical and physical outputs in real-time. However, it is noted that the dynamic properties of the substructures sometimes influence the synchronization stability and accuracy. For example, low damping coefficient might cause system unstable or testing inefficiency. Therefore, this study introduces the concept of substructurability via a theory of system analysis in order to suggest the efficiency and robustness of DSS. This study analyze the robustness of DSS via state space representations, Lyapunov functions, Riccati-like inequalities and linear matrix inequalities (LMI) to propose 7 different indices to evaluate the testing efficacy in advance. When the index has a larger value, this means the corresponding real-time dynamic test is not robust and inefficient. When the index has a smaller value, the dynamic test is relatively robust and efficient. Analytical and experimental results based on a two-variable mass-spring-damper DSS are presented to verify this theory. The substructurability theory is contributive to interpret the dynamic limits of DSS and is helpful to search for reasonable solutions.