Abstract
This paper proposes a statistical confidence interval based nonlinear model parameter refinement approach for the health monitoring of structural systems subjected to seismic excitations. The developed model refinement approach uses the 95% confidence interval of the estimated structural parameters to determine their statistical significance in a least-squares regression setting. When the parameters' confidence interval covers the zero value, it is statistically sustainable to truncate such parameters. The remaining parameters will repetitively undergo such parameter sifting process for model refinement until all the parameters' statistical significance cannot be further improved. This newly developed model refinement approach is implemented for the series models of multivariable polynomial expansions: the linear, the Taylor series, and the power series model, leading to a more accurate identification as well as a more controllable design for system vibration control. Because the statistical regression based model refinement approach is intrinsically used to process a “batch” of data and obtain an ensemble average estimation such as the structural stiffness, the Kalman filter and one of its extended versions is introduced to the refined power series model for structural health monitoring.
Highlights
System identification for structural health monitoring and damage detection in civil structures is moving to the forefront of worldwide research activities
According to the definition of stiffness, the reciprocal of these relative displacements results in the stiffness estimation of the first, second, and third floor as 1652892.562 N/m, 1524390.244 N/m, and 1582278.481 N/m, respectively. Other structural properties such as the damping coefficient cannot be evaluated in the same way, because of the relative velocities not being able to be directly obtained using the static analysis method. It is for this reason that we propose an alternative – a statistical model parameter refinement approach for the non-destructive evaluation of structural systems in the multiple regression setting
The Kalman filter can be considered equivalent to the multiple least-squares regression algorithm, provided that the covariance of the state estimation error in the Kalman filter is equal to the adaptation gain matrix in the multiple regression, along with other entailed adjustments [7]
Summary
System identification for structural health monitoring and damage detection in civil structures is moving to the forefront of worldwide research activities. Other structural properties such as the damping coefficient cannot be evaluated in the same way, because of the relative velocities not being able to be directly obtained using the static analysis method It is for this reason that we propose an alternative – a statistical model parameter refinement approach for the non-destructive evaluation of structural systems in the multiple regression setting. This newly developed model refinement approach is able to account for model uncertainties and is applicable to a wide variety of series models for model simplification, enabling an economic design for structural vibration control
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