Abstract: We first introduce a new approach for optimising a cascaded spline adaptive filter (CSAF) to identify unknown nonlinear systems by using a meta-heuristic optimisation algorithm (MOA). The CSAF architecture combines Hammerstein and Wiener systems, where the nonlinear blocks are implemented with the spline network. The algorithms used optimise the weights of the spline interpolation function and linear filter by using an adequately weighted cost function, leading to improved filter stability, steady state performance, and guaranteed convergence to globally optimal solutions. We investigate two CSAF architectures: Hammerstein‍–‍Wiener SAF (HW-SAF) and Wiener‍–‍Hammerstein SAF (WH-SAF) structures. These architectures have been designed using gradient-based approaches which are inefficient due to poor convergence speed, and produce suboptimal solutions in a Gaussian noise environment. To avert these difficulties, we estimate the design parameters of the CSAF architecture using four independent MOAs: differential evolution (DE), brainstorm optimisation (BSO), multi-verse optimiser (MVO), and a recently proposed remora optimisation algorithm (ROA). In ROA, the remora factor’s control parameters produce near-global optimal parameters with a higher convergence speed. ROA also ensures the most balanced exploration and exploitation phases compared to DE-, BSO-, and MVO-based design approaches. Finally, the identification results of three numerical and industry-specific benchmark systems, including coupled electric drives, a thermic wall, and a continuous stirred tank reactor, are presented to emphasise the effectiveness of the ROA-based CSAF design.

Key words: Cascaded spline adaptive filter; Nonlinear system identification; Remora optimisation algorithm

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