Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 237–252 | Cite as

Piezoelectric sensor location by the observability Gramian maximization using topology optimization

  • Odair Menuzzi
  • Jun S. O. Fonseca
  • Eduardo A. Perondi
  • Juliano F. Gonçalves
  • Eduardo Padoin
  • Otávio A. A. Silveira


This work presents an optimal design methodology for piezoelectric material positioning in structures aiming at vibration measurements. The main objective is to find the optimal location of piezoelectric sensors using a suitable topology optimization strategy. The sensors location is determined by an optimization formulation that defines where the material should have piezoelectric properties. The objective of the optimization is maximizing observability, measured by means of the trace of the Gramian matrix. The control strategy development is based on a truncated modal system model. A case study and its results are presented and discussed, showing that the optimal placement of the piezoelectric sensors in a cantilever beam can be suitably achieved through the proposed approach.


Sensor placement Observability Gramian Topology optimization Piezoelectric material 

Mathematics Subject Classification

65K10 Optimization and variational techniques 93Bxx Controllability, observability, and system structure 



The authors acknowledge the financial support of the Brazilian agencies CAPES and CNPq.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Farroupilha Federal Institute of EducationScience and TechnologySão BorjaBrazil
  2. 2.Department of Mechanical EngineeringFederal University of Rio Grande do SulPorto AlegreBrazil
  3. 3.Farroupilha Federal Institute of EducationScience and TechnologyAlegreteBrazil
  4. 4.Department of Civil EngineeringFederal University of Santa CatarinaFlorianópolisBrazil

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