Abstract The S-transform is a special type of Fourier transform with the time localization and frequency dependent window. It is viewed as a hybrid of continuous wavelet transform and short-time Fourier transform. In the present study, we propose an S-transform-based random vibration theory to evaluate the response of the linear elastic single-degree-of-freedom (SDOF) system subjected to nonstationary stochastic excitation. We show that within the established framework, the time–frequency power spectral density (TFPSD) function of the structural response could be represented as the multiplication of the square of the mechanical admittance function and the TFPSD function of the nonstationary stochastic excitation. This simple relation facilitates the computation and statistical characterization of the structural responses subjected to nonstationary stochastic excitation that is modelled based on the S-transform, which implicitly includes the time-varying amplitude and frequency characteristics. We illustrate the use of the TFPSD function to estimate the statistics of the responses and first passage probability of SDOF systems subjected to stochastic earthquake or wind excitations, where the stochastic excitations are represented using the TFPSD functions obtained from the S-transform.

中文翻译：

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非平稳随机激励下线弹性单自由度系统的响应和首次通过概率通过 S 变换建模

摘要 S变换是一种特殊类型的傅里叶变换，具有时间定位和频率相关的窗口。它被视为连续小波变换和短时傅立叶变换的混合。在本研究中，我们提出了一种基于 S 变换的随机振动理论来评估线弹性单自由度 (SDOF) 系统在非平稳随机激励下的响应。我们表明，在已建立的框架内，结构响应的时频功率谱密度 (TFPSD) 函数可以表示为机械导纳函数的平方与非平稳随机激励的 TFPSD 函数的乘积。这种简单的关系有助于对基于 S 变换建模的非平稳随机激励下的结构响应进行计算和统计表征，其中隐含地包括随时间变化的幅度和频率特性。我们说明了使用 TFPSD 函数来估计受到随机地震或风激励的 SDOF 系统的响应和首次通过概率的统计数据，其中使用从 S 变换获得的 TFPSD 函数表示随机激励。