This paper discusses nonlinear system identification issue for a Hammerstein–Wiener time-delay model. The presented Hammerstein–Wiener model consists of two static nonlinear blocks sandwiching a dynamic linear block, and the nonlinear blocks are established using neuro-fuzzy networks, the dynamic linear block is constructed by a time-delay transfer function. To estimate the unknown parameters of the Hammerstein–Wiener time-delay model, we introduce the theory of separable signals. Initially, the output nonlinear block parameters are estimated through correlation analysis and cluster techniques based on available input-output of separable signals. Then, estimation of time-delay transfer function is facilitated by iteration method, so that time-delay parameter and transfer function parameters are alternately estimated. Finally, the input nonlinear block estimation is facilitated by integrating improved particle swarm optimization with cuckoo search techniques, which resulted in an improvement in the global search ability and convergence speed of neuro-fuzzy network. The simulation comparison results are finally verified via numerical case and state of charge estimation of lithium battery in terms of the feasibility and advantage of the developed Hammerstein–Wiener time-delay model identification.
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