Firefly approach optimized wavenets applied to multivariable identification of a thermal process

The combination of wavelet theory and feedforward artificial neural networks has resulted in wavelet neural networks or wavenets (WNNs). In these networks, the activation functions are described by discrete wavelet functions. Due to the promising properties of time-frequency localization and multi-resolution signal processing of the wavelet transform combined with the approximation capability of artificial neural networks, WNNs have found applications in dynamic system identification field during the past years. The paper aims at the development of the WNN based on traditional firefly algorithm (FA). The proposed FA is based on Tinkerbell map to tune the spread of wavelets and number of selected wavelet bases. The FA is a stochastic metaheuristic approach based on the idealized behaviour of the flashing characteristics of fireflies. In FA, the flashing light can be formulated in such a way that it is associated with the objective function to be optimized, which makes it possible to formulate the firefly algorithm. The efficacy of WNN with FA tuning is tested on the identification of a multivariable thermal process.