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

Abstract

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  term-domains,  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.