Statistical Modeling of the Surface Fluctuation

a simple linear single-degree-of-freedom system is used to characterize the surface fluctuation dynamics  

Discrete data with a time step Af are collected in the experiment. Let y be the measured surface fluctuation at time t = nAt. There is a difference between the measured response y and the actual response x nAt) due to measurement noise and this is modeled here by a discrete white noise process e with zero mean and variance 

By using the measurements yo, yi, - , yjv-i, the spectral density estimator can be computed  

Let = [S2, f, 5/0, 5eo] denote the vector of the uncertain model parameters to be identified. The most probable values of the parameters and their associated uncertainty are updated by the Bayesian spectral density approach. 

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