Keywords: stationary Gaussian processes, power spectral density functions, analog filters, fluctuating wind speed, track irregularity, fractional-order derivatives.

Environmental excitations acting on engineering structures, such as wind, ocean waves, and track irregularities, are often modelled as stationary Gaussian stochastic processes, with their statistical characteristics quantitatively described by the power spectral density functions. These excitations can be reproduced through stochastic simulation by filtering white noise using a constructed filter. A linear analog filter system is proposed in this study for simulating excitation power spectral density functions with non-rational characteristics. By introducing a fractional-order derivative operator, the proposed model can be applied to the simulation of turbulent wind speed with fractional-order asymptotic spectral properties. For track irregularity spectra with multiple segments, a corresponding piecewise form can be adopted in the model and efficient simulation can be achieved using a frequency-domain approach. The effectiveness and efficiency of the proposed method are validated through applications in the simulation of various commonly used fluctuating wind speed spectra and railway track irregularity spectra. To enhance adaptability, filter parameter conversion formulae are provided, allowing the benchmark model to be conveniently extended to scenarios with varied spectral parameters. The proposed method offers an efficient approach for the simulation of Gaussian stationary excitations with complex spectral properties. Further, it provides a foundation for stochastic response analysis and reliability analysis on the probability density level, say, by the method based on the dimension-reduced probability density evolution equation.

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