受環境影響的隨機訊號，在不知道外力大小的情況下能夠確定系統參數。在土木工程中，建築物的系統參數，如勁度、阻尼，經由記錄的訊號能夠近似的被評估出來。同樣的想法能應用在熱燥動的情況下測量奈米尺度的物件。在本研究中，自然頻率與阻尼比來當作結構體的力學指標。運用有限元模擬軟體COMSOL，模擬一受高斯白噪音下的懸臂樑來展現計算方法，例如隨機遞減法。接著在一兩個自由度系統受白噪作用進行驗證分析，然後運用高屏溪斜張橋的位移訊號和隨機遞減法和Ibrahim時域法 (ITD) 來進行分析，在自回歸向量 (ARV) 的解析下，這兩種方法都能夠有相似的自然頻率和阻尼比。

Random signals, from environmental vibrations, enable determination of system parameters without knowing input force. In civil engineering, system parameters, such as stiffness and damping ratio, of structures can hence be approximately estimated through output-only recordings. The same idea can be applied to measure mechanical properties of nano-scale objects under thermal fluctuations. In this study, natural frequencies and damping ratios are used as the mechanical indicators of the structures. Finite element software COMSOL was adopted to simulate a cantilever beam under Gaussian white noise, to demonstrate the methodologies, such as the random decrement (Randomdec) method. Furthermore, oscillators with one and two degrees of freedom were analyzed for validation. In addition, the displacement responses of the Kao-Ping-Hsi cable-stayed bridge from field tests were analyzed with the random decrement technique and Ibrahim time domain (ITD). Both methods are able to produce similar natural frequencies and damping ratios with the assistance of autoregressive vector (ARV) analysis.

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