An Improved Bayesian Structural Identification Using the First Two Derivatives of Log-Likelihood Measure

Abstract

The posterior density of structural parameters conditioned by the measurement is obtained by a differential evolution adaptive Metropolis algorithm (DREAM). The surface of the formal log-likelihood measure is studied considering the uncertainty of measurement error to illustrate the problem of equifinality. To overcome the problem of equifinality, the first two derivatives of the log-likelihood measure are proposed to formulate a new informal likelihood measure for the sake of improving the accuracy of the estimator. Moreover, the proposed measure also reduces the standard deviation (uncertain range) of the posterior samples. The benefit of the proposed approach is demonstrated by simulations on identifying the structural parameters with limit output data and noise polluted measurements.

Parameter and State Estimation of Shear Buildings Using Spline Interpolation and Linear Integral Filters

“…Remark 5. The methods described in [1,3,[6][7][8][9][10][11][12][13][14][15] report good results in the parameter estimation of buildings with ratios / up to 0.5, 0.33, 0.5, 0.43, 0.5, 0.33, 0.25, 0.5, 0.18, 0.5, 0.5, and 0.5, respectively. Note that the ratio / = 0.5 is the most common among them.…”

“…Note that the ratio / = 0.5 is the most common among them. Moreover, all of these methods operate offline with exception of the techniques presented in [3,6], and most of them require transforming the building model from continuous one to its discrete time counterpart. Although the ratio / = 0.4, corresponding to the proposed method, is larger than the ratios / obtained with the offline techniques described in [9,10,12], the proposed technique can be implemented online and can detect parameter changes produced by an anomaly in the structure due to a weak component or failure of elements.…”

“…In order to compute the coefficients 0 and 1 of the Rayleigh damping, we decided to fix both damping ratios 1 and 2 to 1%, since this value is between 0.7% and 1.6%. These natural frequencies and damping factors allow obtaining parameters 1 = 0.1642 and 2 = 0.0005 using (6), which are employed for computing the variableŝand̂of parameterization (33).…”

“…Parameter and state estimation of civil structures using recorded responses has attracted the attention of a large number of researchers around the world during the last four decades. Some relevant references for not fully instrumented structures [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] are revised here. Amini and Hedayati [1] propose a Sparse Component Analysis approach for modal identification of structures, where the number of sensors is smaller than the number of active modes.…”

“…Nevertheless, some poles of the linearized model may lie on the imaginary axis and, as a consequence, some parameter and/or states may be unbounded. On the other hand, Zhou et al [6] recursively estimate the stiffness and damping ratios of a structure using the first two derivatives of Log-Likelihood Measure and the knowledge of the building mass. Mukhopadhyay et al [7] develop mode shape normalization and expansion approaches that utilize the topology of the structural matrices for estimating the mass and stiffness parameters of a building under base excitation; authors obtain the global identifiability requirements for their methodology and show that, for estimating the structural parameters, the number of instrumented floors should satisfy ≥ √ and ≥ (1 + √ 4 − 3)/2 if the floor masses at sensor locations are known and if the total mass of the structure is known, respectively, where is the number of floors of the building.…”