Post-nonlinear blind source separation with kurtosis constraints using augmented Lagrangian particle swarm optimization and its application to mechanical systems

Abstract

To accurately estimate source signals from their post-nonlinear mixtures, a post-nonlinear blind source separation (PNLBSS) method with kurtosis constraints is proposed based on augmented Lagrangian particle swarm optimization (PSO). First, an improved contrast function is presented by combining mutual information of the separated signals and kurtosis ranges of source signals. Second, an augmented Lagrangian multiplier method is used to convert PNLBSS into an unconstrained pseudo-objective optimization problem. Then, improved PSO is applied to update the parameters in complex nonlinear spaces. Finally, numerical case studies and experimental case studies are provided to evaluate the performance of the proposed method. By adding the kurtosis ranges constraints, the estimation accuracy of source signals could be improved, which would benefit vibration and acoustic monitoring and control.

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“…Blind source separation (BSS) can estimate source signals with little prior knowledge of the signal source and transmission channel, which is widely used in signal separation and extraction [7][8][9]. According to the different mixing methods, the signal mixing model of the BSS problem can be divided into the linear instantaneous mixing model [10], the convolution mixing model [11], and the nonlinear mixing model [12].…”

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“…Jutten et al proposed the PNL mixed model and proved that the solution of post-nonlinear BSS (PNLBSS) is unique without considering the indeterminacies of scaling and permutation [8]. In the past few decades, PNLBSS has been applied in mechanical systems [9], intelligent sensor array design [10], biomedical signal processing [11] and image processing [12]. The above methods jointly optimize the nonlinear compensation parameters and unmixing parameters under the guidance of the objective function, which can be called joint approaches, and are all for the instantaneous mixing model.…”