This paper deals with the identification of the fractional order Hammerstein model by using proposed adaptive differential evolution with the Local search strategy (ADELS) algorithm with the steepest descent method and the overparameterization based auxiliary model recursive least squares (OAMRLS) algorithm. The parameters of the static nonlinear block and the dynamic linear block of the model are all unknown, including the fractional order. The initial value of the parameter is obtained by the proposed ADELS algorithm. The main innovation of ADELS is to adaptively generate the next generation based on the fitness function value within the population through scoring rules and introduce Chebyshev mapping into the newly generated population for local search. Based on the steepest descent method, the fractional order identification using initial values is derived. The remaining parameters are derived through the OAMRLS algorithm. With the initial value obtained by ADELS, the identification result of the algorithm is more accurate. The simulation results illustrate the significance of the proposed algorithm.

Summary In this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.

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The problems of inconsistent data sampling frequency, outliers, and coloured noise often exist in system identification, resulting in unsatisfactory identification results. In this study, a novel identification method of input non‐uniform sampling Wiener model with a coloured heavy‐tailed noise is proposed. The lifted Wiener model with coloured noise and outlier value disturbed is constructed. Under the expectation‐maximisation (EM) algorithm framework, the student's t‐distribution is introduced to model the contaminated output data. The variance scale is regarded as a unique latent variable, and the iterative parameter estimation formula of the non‐uniform sampling Wiener model is derived. The idea of the auxiliary model is applied to acquire the unmeasured middle variable and handle the coloured noise variable in the non‐uniformly sampled Wiener model. The Differential Evolution algorithm is used to calculate the intractable part of the Q‐function. The convergence analysis of the proposed algorithm is given. Two numerical examples and one water tank simulation are employed to indicate the effectiveness of the proposed method.