A rapid estimation method for the probability of wind-induced first plastic displacement of SDOF systems based on the Slepian model

The conventional method based on the Slepian model for estimating the probability distribution of the first plastic displacement of an ideal elastic-plastic oscillator (EPO) is only applicable for zero-mean white noise loads. This study proposes an improved method applicable to wind loads with non-zero mean and non-white noise characteristics for structures whose resonant response dominates the fluctuating wind-induced response. The original EPO's symmetric constitutive model under non-zero mean loads is modified to be equivalent to an asymmetric constitutive model under zero mean loads; thus, a SDOF system subjected to non-zero mean loads is transformed into a SDOF system under zero mean loads. When the resonant response dominates the fluctuating wind-induced response, the fluctuating wind-induced response can be approximated as a narrow-band stochastic process, the extreme values following a Rayleigh distribution, and the probability distribution of the local maximum displacement of the associated linear oscillator (ALO) can be directly obtained, making the Slepian model-based method applicable for non-white noise loads. A case study is performed to validate the accuracy of the proposed improved method, and the results demonstrate that the improved method proposed in this study can significantly enhance computational efficiency. The accuracy of the improved method is independent of the load characteristics but rather depends on the narrowband characteristics of the structural response. When the narrowband characteristics of the structural response are prominent, the improved method exhibits high accuracy.