One embodiment can provide a system for estimating useful life of a load-bearing structure. During operation, the system can perform a degradation measurement on the structure to obtain degradation data for a predetermined time interval, apply a constraint convex regression model to the degradation data, estimate a total useful life (TUL) of the structure based on outputs of the constraint convex regression model, and predicting a remaining useful life (RUL) based on the TUL and a current time.