, Volume 54, Issue 1–2, pp 33–46 | Cite as

Identification of the tension force in cables with insulators

  • Bruno J. RangoEmail author
  • Fernando J. Serralunga
  • Marcelo T. Piovan
  • Jorge S. Ballaben
  • Marta B. Rosales


The present paper explores two approaches which, based on the measurement of the two first natural frequencies, allow the identification of the tension force in cables with insulators. For this purpose, the nonlinear mathematical model of the mechanical system and its Finite Element discretization are firstly stated. Besides, free-vibrations experiments on both a laboratory and a real-scale simulated configuration of cables with insulators are performed in order to derive their frequency response. During the laboratory experiments, a vision-based methodology is implemented for the register of the time series displacements of the cable. On this basis, a Bayesian approach is first addressed. In this framework, the cable tension is regarded as a random variable and the Bayes rule is applied to combine the experimental natural frequencies with the prior information about the random variable to derive the posterior distribution of the tension force. The Markov Chain Monte Carlo-Metropolis Hastings algorithm is implemented for the evaluation of the posterior distribution. On the other hand, a heuristic approach is proposed through the implementation of an Artificial Neural Network (ANN) as an inverse model between the parameters of the cable—including the natural frequencies—and its tension force. The training patterns are obtained from computational simulations of different cable configurations. The experimental natural frequencies are then applied to the trained ANNs to infer the tension force of the laboratory and real-scale configurations. Both approaches provide estimates of the tension force within admissible error margins.


Guy cable Insulators Force identification Bayesian inference Artificial Neural Network 



The authors acknowledge the reviewers for the valuable criticism and suggestions which helped to improve the manuscript.


This study was funded by Secretaría General de Ciencia y Tecnología, Universidad Nacional del Sur (Grant No. 24/J075); FONCyT, Agencia Nacional de Promoción Científica y Tecnológica (Grant No. PICT-2015-0220); CONICET (Grant No. 112 201301 00007 CO).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of EngineeringUniversidad Nacional del SurBahía BlancaArgentina
  2. 2.IFISUR-CONICETBahía BlancaArgentina
  3. 3.Group of Mechanical Systems AnalysisUniversidad Tecnológica Nacional - Facultad Regional Bahía BlancaBahía BlancaArgentina
  4. 4.CONICETBahía BlancaArgentina

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