This paper deals with the parameter estimation of Hammerstein–Wiener (H–W) nonlinear systems which have unknown time delay. The linear variable weight particle swarm method is formulated for such time delay systems. This algorithm transforms the nonlinear system identification issue into a function optimization issue in the parameter space, then utilizes the parallel searching ability of the particle swarm optimization and the iterative identification technique to realize the simultaneous estimation of all parameters and the unknown time delay. Finally, parameters in the linear submodule, nonlinear submodule and the time delay are separated from the optimum parameter. Moreover, two illustrative examples are exhibited to evaluate the effectiveness of the proposed method. The simulation results demonstrate that the derived method has fast convergence speed and high estimation accuracy for estimating H–W systems with unknown time delay, and it is applied to the identification of the bed temperature systems.

本文讨论了具有未知时延的 Hammerstein-Wiener (H-W) 非线性系统的参数估计。线性变权粒子群方法是为这种时延系统制定的。该算法将非线性系统辨识问题转化为参数空间中的函数优化问题，然后利用粒子群优化的并行搜索能力和迭代辨识技术，实现所有参数的同时估计和未知时延。最后，将线性子模块、非线性子模块中的参数和时延从最优参数中分离出来。此外，展示了两个说明性示例来评估所提出方法的有效性。