Seismic fragility of controlled structures: On the effects of signal loss

The use of wireless sensors in structural control brings attractive benefits, such as cost effectiveness and flexibility. However, the inherent limitations of wireless communication, particularly signal loss, can result in a significant drop in system performance. The objective of this work is to address how this performance degradation affects the reliability of controlled structures under seismic loading. In this case, the seismic fragility curve is used for the evaluation of system performance. Fragility curves relate the earthquake intensity measurement (IM) to the probability of failure (probability that the response measurement (RM) is above the limit state). The work presents a method for developing fragility curves of a controlled structural system with feedback loss and applies it to a benchmark structure. The structural control is assumed to be an active control system, which implements a linear quadratic regulator. The controller uses the full-state feedback from the sensors, and the whole feedback packet may be lost with a known probability. The proposed method is a combination of a statistical analysis and a mathematical analysis. The statistical analysis gathers data from simulations and creates the function relating IM and RM of the no-feedback-loss system. The mathematical analysis deals with a Markovian jump linear system (MJLS), the linear algebraic representation of the system with feedback loss, and predicts the degradation in performance as a function of the probability of data loss. Based on the predicted degradation, the IM-RM relationship is updated to include the effect of the feedback loss, and the final fragility curve is derived based on the updated IM-RM function. The method reduces the simulation cost for the fragility analysis. To validate the method, several fragility analyses are done on a three-story example structure with different probabilities of signal loss. Results also show the close relationship between the change in system H2-norm and the change in maximum inter-story drift during earthquakes. The accuracy of the analysis promotes the use of mathematical system analysis in seismic damage prediction.