In the last few years, researchers have paid close attention to developing smart structures that simultaneously combine structural health monitoring and vibration control. In this regard, real-time system identification is one of the major challenges due to various time delay factors in smart structures. This study presents a new model-based online damage detection method using an adaptive control approach (MODAC) under indeterminate conditions (limitations on the number of sensors). Here, it is assumed that the input and output data of the system during the vibration under environmental excitations can be measured, and, in addition, the information about the mechanical parameters of the intact system is available. In the proposed MODAC method, unlike the common methods, which mainly use optimization algorithms and are time consuming, the variations in the structural parameters of the system are mathematically formulated and directly calculated in real time. In addition, this paper introduces a new scheme that combines the MODAC method with the semiactive control strategy to create a smart structure that compensates for possible damages to the structure. The MODAC method’s accuracy, as well as the presented scheme’s performance and efficiency, is assessed through numerical examples when various excitation records are considered. The obtained results indicate that damage can be identified instantaneously with acceptable accuracy even under indeterminate conditions and in the presence of noise. Furthermore, the proposed scheme can effectively decrease dynamic responses and compensate for the permanent damage in the smart structure during strong ground motions.
