Quantitative Comparison of Optimization Approaches for the Design of Supplemental Damping in Earthquake Engineering Practice

One approach to the optimal design of passive controllers in linear structures for earthquake engineering applications makes use of active control tools. Usually, when this approach is adopted, the actual objective function is a time integral of a functional of given mathematical structure of response quantities and control forces. This approach has been used for the design of added dampers and is appealing due to its simplicity and the minor computational effort it requires. In adapting the active control approach to passive control, it has often been assumed that an objective function of this kind is suitable. It has been a widespread opinion in the passive control community, however, that minimization of such a smeared quantity that has a predetermined mathematical structure cannot lead to truly optimal added damper schemes. This paper formally addresses this issue and shows that what has been suspected for some time is indeed the case. The optimal location and size of each of the added dampers and, thus, the total added damping for given structures are attained here by directly solving the practical optimization problem as a reference. For the same total added damping, an active control approach is then used to find its own optimal location and size of each of the added dampers. A time history analysis is finally carried out for an a priori chosen ensemble of earthquakes to yield the envelope of maximal interstory drifts. It is shown that the active control approach is not satisfactory, in the practical sense, since it leads to much larger maximal interstory drifts.