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An optimizationless stochastic volterra series approach for nonlinear model identification

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Abstract

Volterra series is a widely used tool for identifying physical systems with polynomial nonlinearities. In this approach, the Volterra kernels expanded using Kautz functions can be identified using several techniques to optimize the filters’ poles. This methodology is very efficient when the system observations are not subject to high noise-induced variabilities (uncertainties). However, this optimization procedure may not be effective when the uncertainty level is increased since the optimal value might be susceptible to small perturbations. Seeking to overcome this weakness, the present work proposes a new stochastic method of identification based on the Volterra series, which does not solve an optimization problem. In this new approach, the Volterra kernels are described as stochastic processes. The parameters of Kautz filters are considered independent random variables so that their probability distribution captures the variabilities. The effectiveness of the new technique is tested experimentally in a nonlinear mechanical system. The results show that the identified stochastic Volterra kernels can reproduce the nonlinear dynamics characteristics and the data variability.

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Funding

The authors are thankful for the financial support provided by São Paulo Research Foundation (FAPESP), Grant Numbers 2012/09135-3 and 2015/25676-2; Carlos Chagas Filho Research Foundation of Rio de Janeiro State (FAPERJ), Grant Numbers 211.304/2015, 210.021/2018, 210.167/2019, 211.037/2019, and 201.294/2021; Brazilian National Council for Scientific and Technological Development (CNPq), Grant Numbers 303403/2013-6 and 306526/2019-0; and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES), Finance Code 001.

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Authors and Affiliations

  1. Departamento de Engenharia Mecânica, Centro Tecnológico, Universidade Federal do Espírito Santo – UFES, Av. Fernando Ferrari, 514, Vitoria, Espírito Santo, Brazil

    Luis Gustavo Giacon Villani

  2. Faculdade de Engenharia de Ilha Solteira, Universidade Estadual Paulista – UNESP, Av. Brasil, 56, Ilha Solteira, São Paulo, Brazil

    Samuel da Silva

  3. Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro – UERJ, R. São Francisco Xavier, 524, Rio de Janeiro, Rio de Janeiro, Brazil

    Americo Cunha Jr

Authors
  1. Luis Gustavo Giacon Villani
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  2. Samuel da Silva
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  3. Americo Cunha Jr
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Correspondence to Luis Gustavo Giacon Villani.

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Technical Editor: Andre T. Beck.

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Villani, L.G.G., da Silva, S. & Cunha, A. An optimizationless stochastic volterra series approach for nonlinear model identification. J Braz. Soc. Mech. Sci. Eng. 44, 260 (2022). https://doi.org/10.1007/s40430-022-03558-z

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