An evolutionary algorithm-based approach for efficient design of Wiener spline non-linear adaptive filter and its experimental validation

Wiener spline adaptive filters (WSAFs) are newly proposed non-linear adaptive filters consisting of a linear filter that is succeeded by the non-linear spline network. Recently, the WSAFs have efficiently been modelled for non-linear practical systems with computational complexity using advanced versions of least mean square algorithms. However, the existing WSAFs fail to mitigate the noise effectively when the systems are highly non-linear. Moreover, they furnish poor estimates with slow convergence, and the exactness of results relies on the decent setting of some initial state parameters such as bounds of learning rates, filter selection, nonlinearity selection, etc. In this work, an evolutionary algorithm (EA) is employed to design WSAF while conquering the above issues successfully. In this technique, the EA simultaneously updates linear filter coefficients and the control points of the spline function by using the well-formulated cost function. As a result, further enhancement is guaranteed in estimation accuracy, convergence quality, steady-state accuracy and filter stability compared to other reported works. This work simulates several benchmark WSAFs using an efficient newly developed EA called reptile search algorithm (RSA). As compared with other employed state-of-the-art algorithms, the mean squared deviation (MSD) between the real and estimated parameters and the output mean squared error (MSE) metric results of the proposed RSA-based WSAF are as low as 1.01E−07 and 2.07E−08, respectively, and also the quality of fitness (QF) is 99.79%. Moreover, the significant MSE results of −52.47 dB and −47.77 dB, respectively, are achieved through the proposed RSA-based WSAF design for practical plants such as liquid-saturated heat exchangers (LSHE) and cascade tanks. Further, the corresponding proposed model is also implemented on the TMS320C6713 digital signal processor hardware to verify the feasibility of the proposed scheme in the real-time scenario.