Active control of earthquake-excited structures with the use of hedge-algebras-based controllers

In this paper, we introduce a hedge-algebras-based methodology in vibration control of structural systems to design fuzzy controllers, referred to as hedge-algebras-based controllers (HACs). In this methodology, vague linguistic terms are not expressed by fuzzy sets, but by inherent order relationships between vague terms existing in a term-domain. Semantically quantifying mappings (SQMs), which preserve semantics-based order relationships in termdomains, are defined in a close relationship with the fuzziness measure and the fuzziness intervals of vague terms. Utilizing these SQMs, fuzzy reasoning methods can be transformed into numeric interpolation methods with respect to the points in a multi-dimensional Euclid space defined relying on the if-then rules of the given control knowledge. This provides sound mathematical fundamentals supporting the construction of the control algorithm. The proposed methodology is simple, transparent and effective. As a case study, HACs and optimal HACs have been designed based on this methodology to control high-rise civil structures. They are shown to be more successful in reducing maximum displacement responses of the structure than fuzzy counterparts under three different earthquake scenarios: El Centro, Northridge and Kobe. This demonstrates the effectiveness of the proposed methodology.