In view of the demand for accurate modal identification, and based on the characteristics of free vibration response, this paper introduces a new window function for Fourier Transform called the Power–Exponential window. The Power–Exponential window addresses the characteristics of free vibration response. It significantly enhances the accuracy of modal identification by improving the spectral properties of structural response. The proposed window function consists of exponential and power terms. This study focuses on the additional damping and frequency-domain differentiation introduced by the Power–Exponential window function. The exponential term weakens the boundary effect related to the time-domain truncation and suppresses the spectral leakage. Moreover, it can be interpreted in clear physical terms as providing additional damping to the signal. The power term in the window function corresponds to frequency domain differentiation, and it alleviates the spectral broadening that arises due to the additional damping. Furthermore, the analytical expression for the response spectrum confirms that the Power–Exponential window not only aligns the peak response frequency with the damped natural frequency but also establishes an explicit linear relationship between the actual structural damping ratio and the identification result from the half power bandwidth method. Both contribute to an improved accuracy and usability of certain frequency-domain modal identification methods. The influence of the Power–Exponential window parameters on modal parameter identification is analyzed, and the optimal selection principle and suggested parameter values are proposed. Finally, numerical simulations and an experimental frame model test are conducted to verify the accuracy and validity of modal parameter identification based on the Power–Exponential window.

中文翻译：

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使用幂指数窗函数识别结构模态参数


针对精确模态识别的需求，基于自由振动响应的特点，本文提出了一种新的傅里叶变换窗函数，称为幂指数窗。幂指数窗口解决了自由振动响应的特征。它通过改善结构响应的光谱特性显着提高模态识别的准确性。所提出的窗函数由指数项和幂项组成。本研究重点关注幂指数窗函数引入的附加阻尼和频域微分。指数项减弱了与时域截断相关的边界效应并抑制了频谱泄漏。此外，它可以用清晰的物理术语解释为为信号提供额外的阻尼。窗函数中的幂项对应于频域微分，它减轻了由于附加阻尼而产生的频谱展宽。此外，响应谱的解析表达式证实了功率指数窗不仅将峰值响应频率与阻尼固有频率对齐，而且在实际结构阻尼比与半功率带宽识别结果之间建立了明确的线性关系方法。两者都有助于提高某些频域模态识别方法的准确性和可用性。分析了幂指数窗参数对模态参数识别的影响，提出了最优选择原则和建议参数值。 最后，进行数值模拟和实验框架模型测试，验证基于幂指数窗模态参数识别的准确性和有效性。