Subspace identification of dynamic processes with consideration of time delays: A Bayesian optimization scheme

For decades, subspace identification method (SIM) has been widely adopted for modeling multiple-input multiple-output processes. However, conventional SIMs yield unsatisfactory performance in modeling processes with evident dead time characteristics. To tackle this challenge, we develop in this work an efficient SIM scheme with consideration of time delays along with a tailored Bayesian optimization (BO) solution algorithm, aiming at simultaneously identifying the state-space matrices, time delays and model order of a time-delayed state-space model from input–output data. The identification problem is formulated as a black-box optimization problem over time delays and model order. In the proposed tailored BO algorithm, a decomposition strategy is developed to address the existence of multiple identical solutions. Besides, a prior-weighted acquisition function is proposed to improve the algorithm efficiency. Numerical examples and an experiment on industrial dataset showcase that the proposed method achieves significant improvement in identification accuracy over conventional SIMs owing to the explicit consideration of time delays. In addition, the proposed BO algorithm outperforms the naive random search and the naive BO algorithm in terms of computational efficiency.