The accurate and reliable identification of damage in modern engineered structures is essential for timely corrective measures. Vibration-based damage prediction has been studied extensively by virtue of its global damage detection ability and simplicity in practical implementation. However, due to noise and damping influences, the accuracy of this method is inhibited when direct peak detection (DPD) is utilized to determine resonant frequency shifts. This research investigates an alternative method to detect frequency shifts caused by structural damage based on the utilization of strongly nonlinear bifurcation phenomena in bistable electrical circuits coupled with piezoelectric transducers integrated with the structure. It is shown that frequency shift predictions by the proposed approach are significantly less susceptible to error than DPD when realistic noise and damping levels distort the shifting resonance peaks. As implemented alongside adaptive piezoelectric circuitry with tunable inductance, the new method yields damage location and severity identification that is significantly more robust and accurate than results obtained following the DPD approach.