Twelve-story Shear Building

In this simulated-data example, a twelve-story shear building is considered. It is assumed that this building has uniformly distributed floor mass and uniform stiffness across the height. The mass per floor is taken to be 100 metric tons, while the interstory stiffness is chosen to be k = 202.767 MN/m so that the first five modal frequencies are 0.900,2.686,4.429,6.103 and 7.680 Hz. The covariance matrix is diagonal with the variances corresponding to a 1.0% coefficient of variation of the measurement error of the squared modal frequencies and mode shapes for all modes, a reasonable value based on typical modal test results. For the simulated modal data, a sample of zero-mean Gaussian noise with covariance matrix was added to the exact modal frequencies and mode shapes. 

The nominal value of each story stiffness parameter is selected Ifom a uniform distribution over 2K to ik, where k is the actual interstory stiffness, so the nominal values O are significantly overestimated and the variation between the different interstory stiffness values is very substantial. Recall that the nominal stiffness values are taken as the initial values in the optimization to find the most probable values based on the modal data and it affects the prior distribution of the stiffness parameters. The subsystem stiffness matrices are given by Ko = 0i2x 12 since the problem is linear  

Parameter Initial values 2 modes 3 modes 4 modes 5 modes 

Bayesian Methods for Structural Dynamics and Civil Engineering 

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