Sensor placement for model identification of multi-story buildings under unknown earthquake ground motion

The number of sensors and their position is very important for the acquisition of high-quality measurement data in structural health monitoring (SHM), where the detection and evaluation of structural health status under unknown seismic ground motion have been an important research area. It is undoubtedly that the identification of structural model parameters under unknown seismic ground motion or joint identification of model parameters and seismic time-history input depends on the effective placement of sensors on structures. At present, the investigation of sensor configuration is mainly intended for structural model or modal parameter identification without taking into account the seismic effect, which cannot guarantee the effective contribution of the dynamic measurement data to the joint identification of ground motion and model parameters. To the best of authors knowledge, the optimal sensor configuration for the purpose of model parameter identification under unknown seismic ground motion has not yet been reported in the current literature. In the framework of Bayes' theorem and information theory, this paper proposes an optimal sensor placement methodology targeting at model parameter identification under unknown seismic ground motion. Based on the joint identification of ground motion and structural model parameters, the optimal configuration scheme for a given number of sensors is determined by maximizing a proposed expected entropy measure formed by utilizing the marginal distribution of model parameters prior to the availability of the measurement data. In addition, to solve the combinatorial optimization problem arising from the optimal sensor configuration, this paper also proposes a simple yet efficient strategy for revising the fitness function of genetic algorithm, which converts the continuous variable representation of the sensor configuration vector into a binary string representation. This completely avoids the common approaches relying on modifying various genetic operators to ensure the mandatory constraint of always configuring a fixed number of sensors. The validity of the proposed methodology is fully validated by numerical and experimental case studies conducted respectively for a 20-story shear-building model and a laboratory 6-story shear-building model under shaking table test.