Modelling of Davenport and Kaimal Wind Spectra with a Stochastic Differential Operator in Multiple Frequency Domains

Accurate probabilistic analysis of wind-induced structural vibration is essential for accurately analyzing structural safety and serviceability. Though the FPK equation offers a tool for analysis, its application is challenged by the noise characteristics of wind spectra, such as the Davenport and Kaimal spectra. Using the conventional second-order linear filter model to fit Davenport and Kaimal spectra tends to underestimate their spectral energy in the mid-to-high-frequency range. To address this limitation, this paper proposes an improved second-order filter model that enhances fidelity without increasing filter dimensionality. This model is complemented by an optimization strategy based on the idea that the frequency range is partitioned, which generates three models specifically for low-, mid-, and high-frequency ranges. These models can better fit Davenport and Kaimal spectra in a much larger frequency range compared to the conventional model. The effectiveness of the proposed models is validated through numerically analyzing a linear SDOF stochastic oscillator and a nonlinear stochastic SDOF oscillator in various cases. The results demonstrate that the proposed models maintain exceptional accuracy across a wide range of structural natural frequencies.