Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method

Jie Liu, Xingsheng Sun, Xu Han, Chao Jiang, Dejie Yu

Research output: Contribution to journalArticlepeer-review

146 Scopus citations


Based on the Gegenbauer polynomial expansion theory and regularization method, an analytical method is proposed to identify dynamic loads acting on stochastic structures. Dynamic loads are expressed as functions of time and random parameters in time domain and the forward model of dynamic load identification is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions of system. Random parameters are approximated through the random variables with λ-probability density function (PDFs) or their derivative PDFs. For this kind of random variables, Gegenbauer polynomial expansion is the unique correct choice to transform the problem of load identification for a stochastic structure into its equivalent deterministic system. Just via its equivalent deterministic system, the load identification problem of a stochastic structure can be solved by any available deterministic methods. With measured responses containing noise, the improved regularization operator is adopted to overcome the ill-posedness of load reconstruction and to obtain the stable and approximate solutions of certain inverse problems and the valid assessments of the statistics of identified loads. Numerical simulations demonstrate that with regard to stochastic structures, the identification and assessment of dynamic loads are achieved steadily and effectively by the presented method.

Original languageEnglish
Pages (from-to)35-54
Number of pages20
JournalMechanical Systems and Signal Processing
StatePublished - May 1 2015

Bibliographical note

Funding Information:
This work is supported by the National Natural Science Foundation of China ( 11202076 , 11232004 ), the Key Project of Chinese National Programs for Fundamental Research and Development ( 2010CB832705 ) and the Doctoral Fund of Ministry of Education of China ( 20120161120003 ).

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.


  • Gegenbauer polynomials
  • Load identification
  • Orthogonal polynomial expansion
  • Regularization
  • Stochastic structures
  • λ-PDF

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications


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