Process identification using a new component analysis model and particle swarm optimization

A novel component analysis model is proposed to identify the mixed process signals which are frequently encountered in the statistical process control (SPC) and engineering process control (EPC) practice. Based upon one of existing state-of-the-art evolutionary algorithms, called particle swarm optimization (PSO), the proposed model provides a solution (i.e., demixing matrix) by maximizing the determinant of the corresponding second-order moment (variance-covariance) matrix of the reconstructed signals. Then, the estimated demixing matrix is used to separate mixed signals arising from several original process signals. The process signals considered in this paper include inconsistent variance series, autoregressive (AR) series, step change, and Gaussian noises in the process data. In practice, most of industrial manufacturing processes can be well characterized by a mixture of these four types of data. By following the proposed model, the blind signal separation framework can be cast into a nonlinear constrained optimization problem, where only the demixing matrix appears as unknown. Several illustrative examples involving linear mixtures of the process signals with different statistical characteristics are demonstrated to justify the new component analysis model.