Parameter Estimation Incorporating Modal Data and Boundary Conditions

A new error function is introduced to use natural frequencies and associated mode shapes measured at a selected subset of degrees of freedom for stiffness and mass parameter estimation at the element level. The incomplete mode shapes are used to form the “modal stiffness-based error function” by condensing out the mode shapes at the unmeasured degrees of freedom. Structural modeling errors cannot be completely avoided in any analytical procedure that relies on finite-element models; however, some errors may be controlled. Two elements are used for the first time in parameter estimation to more accurately capture the structural behavior at complex interfaces, thus reducing error. First, the soil-substructure superelement is introduced into the parameter estimation and is intended to capture stiffness and mass properties of the foundation. Second, the partially restrained frame element enables connections to be modeled as partially restrained, in addition to the more traditional fixed or pinned assumptions. To examine the capability of the proposed parameter estimation algorithm, these two new elements are incorporated in a parameter estimation example using simulated modal data. In this example, stiffness and mass parameter estimates successfully converged to the “true” parameter values with no bias within the desired tolerance level. Such parameter estimates can be used for model updating and to establish a baseline for structural condition assessment.