Wiener-Hammerstein System Identification: A Fast Approach Through Spearman Correlation

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21 Citations (Scopus)


The Wiener-Hammerstein (W-H) system is a popular and easy to understand class of Volterra nonlinear dynamical system. It consists of a static nonlinearity positioned between two dynamical subsystems. The main identification challenge resides in separating two linear filters as a rational form of poles and zeros. According to previous studies, an initial guess of the separated dynamics is made by browsing through all possible combinations of pole-zero. Then, based on the root-mean-square error (RMSE), good partitions are selected and later all parameters are optimized mutually to determine the best model. As the RMSE before and after optimization behaves erratically, this paper proposes the use of the Spearman correlation to select good models for optimizing. The proposed technique avoids the estimation of the local nonlinearity for each partition and optimizes only few good models. Thus, a massive speedup in processing time is achieved without any prior knowledge about the system. The theoretical verification complies with the simulation study and the measurement analysis.
Original languageEnglish
Pages (from-to)1628-1636
Number of pages9
JournalIEEE Transactions on Instrumentation and measurement
Issue number5
Early online date5 Mar 2019
Publication statusPublished - 1 May 2019


  • Dynamical system
  • Spearman correlation
  • Winer-Hammerstein (W-H) system
  • nonlinear identification
  • nonlinear optimization


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