Engineering with Computers

, Volume 35, Issue 2, pp 519–535 | Cite as

A multiobjective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation

  • Guilherme Ferreira GomesEmail author
  • Fabricio Alves de Almeida
  • Patricia da Silva Lopes Alexandrino
  • Sebastiao Simões da CunhaJr.
  • Bruno Silva de Sousa
  • Antonio Carlos AncelottiJr.
Original Article


Sensor placement optimization plays a key role in structural health monitoring (SHM) of large mechanical structures. Given the existence of an effective damage identification procedure, the problem arises as to how the acquisition points should be placed for optimal efficiency of the detection system. The global multiobjective optimization of sensor locations for structural health monitoring systems is studied in this paper. First, a laminated composite plate is modelled using Finite Element Method (FEM) and put into modal analysis. Then, multiobjective genetic algorithms (GAs) are adopted to search for the optimal locations of sensors. Numerical issues arising in the selection of the optimal sensor configuration in structural dynamics are addressed. A method of multiobjective sensor locations optimization using the collected information by Fisher Information Matrix (FIM) and mode shape interpolation is presented in this paper. The sensor locations are prioritized according to their ability to localize structural damage based on the eigenvector sensitivity method. The proposed method presented in this paper allows to distribute the points of acquisition on a structure in the best possible way so as to obtain both data of greater modal information and data for better modal reconstruction from a minimum point interpolation. Numerical example and test results show that the proposed method is effective to distribute a reduced number of sensors on a structure and at the same time guarantee the quality of information obtained. The results still indicate that the modal configuration obtained by multiobjective optimization does not become trivial when a set of modes is used in the construction of the objective function. This strategy is an advantage in experimental modal analysis tests, since it is only necessary to acquire signals in a limited number of points, saving time and operational costs.


Sensor placement optimization Structural health monitoring Multiobjective optimization Genetic algorithm Mode shape interpolation 



The authors would like to acknowledge the financial support from the Brazilian agency CNPq—Conselho Nacional de Desenvolvimento Científico e Tecnológico and CAPES— Coordenaco de AperfeiÇoamento de Pessoal de Nível Superior.


  1. 1.
    Abdullah MM, Richardson A, Hanif J (2001) Placement of sensors/actuators on civil structures using genetic algorithms. Earthq Eng Struct Dyn 30(8):1167–1184CrossRefGoogle Scholar
  2. 2.
    Angeles J, Park FC (2008) Performance evaluation and design criteria. In: Springer handbook of robotics. Springer, pp 229–244Google Scholar
  3. 3.
    Argyris C, Papadimitriou C, Panetsos P (2017) Bayesian optimal sensor placement for modal identification of civil infrastructures. J Smart Cities 2(2):69–86CrossRefGoogle Scholar
  4. 4.
    Barthorpe RJ, Worden K (2009) Sensor placement optimization. Encyclopedia of structural health monitoringGoogle Scholar
  5. 5.
    Benner P, Herzog R, Lang N, Riedel I, Saak J (2017) Comparison of model order reduction methods for optimal sensor placement for thermo-elastic modelsGoogle Scholar
  6. 6.
    Blanloeuil P, Nurhazli NA, Veidt M (2016) Particle swarm optimization for optimal sensor placement in ultrasonic shm systems. In: Nondestructive characterization and monitoring of advanced materials, aerospace, and civil infrastructure 2016, vol 9804. International Society for Optics and Photonics, p 98040EGoogle Scholar
  7. 7.
    Bookstein FL (1989) Principal warps: thin-plate splines and the decomposition of deformations. IEEE Trans Pattern Anal Mach Intell 11(6):567–585CrossRefzbMATHGoogle Scholar
  8. 8.
    Christodoulou SE, Gagatsis A, Xanthos S, Kranioti S, Agathokleous A, Fragiadakis M (2013) Entropy-based sensor placement optimization for waterloss detection in water distribution networks. Water Resour Manage 27(13):4443–4468CrossRefGoogle Scholar
  9. 9.
    Coote J, Lieven N, Skingle G (2005) Sensor placement optimisation for modal testing of a helicopter fuselage. In: Proceedings of the 24th International Modal Analysis Conference (IMAC-XXIII), Orlando, Fl’, CiteseerGoogle Scholar
  10. 10.
    De Stefano M, Gherlone M, Mattone M, Di Sciuva M, Worden K (2015) Optimum sensor placement for impact location using trilateration. Strain 51(2):89–100CrossRefGoogle Scholar
  11. 11.
    Deb K (2008) Introduction to evolutionary multiobjective optimization. In: Multiobjective Optimization, Springer, pp 59–96Google Scholar
  12. 12.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  13. 13.
    Downey A, Hu C, Laflamme S (2017) Optimal sensor placement within a hybrid dense sensor network using an adaptive genetic algorithm with learning gene pool. Struct Health Monit, p 1475921717702537Google Scholar
  14. 14.
    Feng S, Jia J-Q, Zhang J-C (2017) Sensor configuration optimizing in modal identification by siege ant colony algorithm. Journal of Mechanics 33(2):269–277CrossRefGoogle Scholar
  15. 15.
    Guo H, Zhang L, Zhang L, Zhou J (2004) Optimal placement of sensors for structural health monitoring using improved genetic algorithms. Smart Mater Struct 13(3):528CrossRefGoogle Scholar
  16. 16.
    He C, Xing J, Li J, Yang Q, Wang R, Zhang X (2015) A new optimal sensor placement strategy based on modified modal assurance criterion and improved adaptive genetic algorithm for structural health monitoring. Math Probl EngGoogle Scholar
  17. 17.
    Hemez FM, Farhat C (1994) An energy based optimum sensor placement criterion and its application to structural damage detection. In: Proceedings-SPIE The International Society for Optical Engineering. SPIE international society for optical, pp 1568–1568Google Scholar
  18. 18.
    Huang Y, Ludwig SA, Deng F (2016) Sensor optimization using a genetic algorithm for structural health monitoring in harsh environments. J Civ Struct Health Monit 6(3):509–519CrossRefGoogle Scholar
  19. 19.
    Hutchinson MF (1995) Interpolating mean rainfall using thin plate smoothing splines. Int J Geogr Inf Syst 9(4):385–403CrossRefGoogle Scholar
  20. 20.
    Jaimes AL, Martınez SZ, Coello CAC (2009) An introduction to multiobjective optimization techniques. Optimization in Polymer Processing, pp 29–57Google Scholar
  21. 21.
    Jiang Y, Li D, Song G (2017) On the physical significance of the effective independence method for sensor placement. J Phys Conf Ser 842:012030. IOP PublishingGoogle Scholar
  22. 22.
    Jung B, Cho J, Jeong W (2015) Sensor placement optimization for structural modal identification of flexible structures using genetic algorithm. J Mech Sci Technol 29(7):2775–2783CrossRefGoogle Scholar
  23. 23.
    Kammer DC (1991) Sensor placement for on-orbit modal identification and correlation of large space structures. J Guid Control Dyn 14(2):251–259CrossRefGoogle Scholar
  24. 24.
    Kammer DC, Tinker ML (2004) Optimal placement of triaxial accelerometers for modal vibration tests. Mech Syst Signal Process 18(1):29–41CrossRefGoogle Scholar
  25. 25.
    Kirkegaard PH, Brincker R (1994) On the optimal location of sensors for parametric identification of linear structural systems. Mech Syst Signal Process 8(6):639–647CrossRefGoogle Scholar
  26. 26.
    Li D, Li H, Fritzen C (2007) The connection between effective independence and modal kinetic energy methods for sensor placement. J Sound Vib 305(4–5):945–955CrossRefGoogle Scholar
  27. 27.
    Lim T (1991) Sensor placement for on-orbit modal identification. In: Proc. 32nd Conf. AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and MaterialsGoogle Scholar
  28. 28.
    Liu W, Gao W-C, Sun Y, Xu M-J (2008) Optimal sensor placement for spatial lattice structure based on genetic algorithms. J Sound Vib 317(1):175–189CrossRefGoogle Scholar
  29. 29.
    MartíNez S, Bullo F (2006) Optimal sensor placement and motion coordination for target tracking. Automatica 42(4):661–668MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Naimimohasses R, Barnett D, Green D, Smith P (1995) Sensor optimization using neural network sensitivity measures. Meas Sci Technol 6(9):1291CrossRefGoogle Scholar
  31. 31.
    Nor KA, Muthalif AG, Wahid AN (2013) Ant colony optimization for controller and sensor-actuator location in active vibration control. J Low Freq Noise Vib Act Control 32(4):293–308CrossRefGoogle Scholar
  32. 32.
    Papadimitriou C (2004) Optimal sensor placement methodology for parametric identification of structural systems. J Sound Vib 278(4):923–947Google Scholar
  33. 33.
    Papadimitriou C, Beck JL, Au S-K (2000) Entropy-based optimal sensor location for structural model updating. J Vib Control 6(5):781–800CrossRefGoogle Scholar
  34. 34.
    Qin BY, Lin XK (2011) Optimal sensor placement based on particle swarm optimization. In: Advanced Materials Research, vol 271. Trans Tech Publ, pp 1108–1113Google Scholar
  35. 35.
    Rao ARM, Anandakumar G (2007) Optimal placement of sensors for structural system identification and health monitoring using a hybrid swarm intelligence technique. Smart Mater Struct 16(6):2658CrossRefGoogle Scholar
  36. 36.
    Rao ARM, Lakshmi K, Kumar SK (2015) Detection of delamination in laminated composites with limited measurements combining pca and dynamic qpso. Adv Eng Softw 86:85–106CrossRefGoogle Scholar
  37. 37.
    Reynier M, Abou-Kandil H (1999) Sensors location for updating problems. Mech Syst Signal Process 13(2):297–314CrossRefGoogle Scholar
  38. 38.
    Shah P, Udwadia F (1978) A methodology for optimal sensor locations for identification of dynamic systems. J Appl Mech 45(1):188–196CrossRefGoogle Scholar
  39. 39.
    Shi Z, Law S, Zhang L (2000) Optimum sensor placement for structural damage detection. J Eng Mech 126(11):1173–1179CrossRefGoogle Scholar
  40. 40.
    Tongpadungrod P, Rhys T, Brett P (2003) An approach to optimise the critical sensor locations in one-dimensional novel distributive tactile surface to maximise performance. Sens Actuators A 105(1):47–54CrossRefGoogle Scholar
  41. 41.
    Udwadia FE (1994) Methodology for optimum sensor locations for parameter identification in dynamic systems. J Eng Mech 120(2):368–390MathSciNetCrossRefGoogle Scholar
  42. 42.
    Udwadia F, Garba J (1985) Optimal sensor locations for structural identificationGoogle Scholar
  43. 43.
    Vincenzi L, Simonini L (2017) Influence of model errors in optimal sensor placement. J Sound Vib 389:119–133CrossRefGoogle Scholar
  44. 44.
    Wang H, He C, Liu Y (2010) Pareto optimization of power system reconstruction using nsga-ii algorithm. In: Power and Energy Engineering Conference (APPEEC), 2010 Asia-Pacific. IEEE, pp 1–5Google Scholar
  45. 45.
    Wang H, Yao K, Pottie G, Estrin D (2004) Entropy-based sensor selection heuristic for target localization. In: Proceedings of the 3rd international symposium on Information processing in sensor networks. ACM, pp 36–45Google Scholar
  46. 46.
    Worden K, Burrows A (2001) Optimal sensor placement for fault detection. Eng Struct 23(8):885–901CrossRefGoogle Scholar
  47. 47.
    Wouwer AV, Point N, Porteman S, Remy M (2000) An approach to the selection of optimal sensor locations in distributed parameter systems. J Process Control 10(4):291–300CrossRefGoogle Scholar
  48. 48.
    Yang C, Lu Z (2017) An interval effective independence method for optimal sensor placement based on non-probabilistic approach. Sci China Technol Sci 60(2):186–198MathSciNetCrossRefGoogle Scholar
  49. 49.
    Yang C, Lu Z, Yang Z (2018) Robust optimal sensor placement for uncertain structures with interval parameters. IEEE Sens JGoogle Scholar
  50. 50.
    Yao L, Sethares WA, Kammer DC (1993) Sensor placement for on-orbit modal identification via a genetic algorithm. AIAA J 31(10):1922–1928CrossRefGoogle Scholar
  51. 51.
    Yi T-H, Li H-N, Gu M (2011) Optimal sensor placement for structural health monitoring based on multiple optimization strategies. Struct Des Tall Spec Build 20(7):881–900CrossRefGoogle Scholar
  52. 52.
    Yin T, Yuen K-V, Lam H-F, Zhu H-P (2017) Entropy-based optimal sensor placement for model identification of periodic structures endowed with bolted joints. Comput Aid Civ Infrastruct Eng 32(12):1007–1024CrossRefGoogle Scholar
  53. 53.
    Yuen K-V, Kuok S-C (2015) Efficient bayesian sensor placement algorithm for structural identification: a general approach for multi-type sensory systems. Earthq Eng Struct Dyn 44(5):757–774CrossRefGoogle Scholar
  54. 54.
    Zhang X, Li J, Xing J, Wang P, Yang Q, Wang R, He C (2014) Optimal sensor placement for latticed shell structure based on an improved particle swarm optimization algorithm. Math Probl EngGoogle Scholar
  55. 55.
    Zhu L, Dai J, Bai G (2015) Sensor placement optimization of vibration test on medium-speed mill. Shock VibGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Guilherme Ferreira Gomes
    • 1
    Email author
  • Fabricio Alves de Almeida
    • 2
  • Patricia da Silva Lopes Alexandrino
    • 1
  • Sebastiao Simões da CunhaJr.
    • 1
  • Bruno Silva de Sousa
    • 1
  • Antonio Carlos AncelottiJr.
    • 1
  1. 1.Mechanical Engineering InstituteFederal University of ItajubáItajubáBrazil
  2. 2.Institute of Industrial Engineering and ManagementFederal University of ItajubáItajubáBrazil

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