A comprehensive expectation identification framework for multirate time-delayed systems

Chen, Jing; Gao, Jie; Liu, Yanjun; Wang, Cheng; Zhu, Quanmin

Abstract

The expectation maximization (EM) algorithm has been extensively used to solve system identification problems with hidden variables. It needs to calculate a derivative equation and perform a matrix inversion in the EM-M step. The equations related to the EM algorithm may be unsolvable for some complex nonlinear systems, and the matrix inversion has heavy computational costs for large-scale systems. This paper provides two expectation based algorithms with the aim of constructing a comprehensive expectation framework concerning different kinds of time-delayed systems: (1) for a small-scale linear system, the classical EM algorithm can quickly obtain the parameter and time-delay estimates; (2) for a complex nonlinear system with low order, the proposed expectation gradient descent (EGD) algorithm can avoid derivative function calculation; (3) for a large-scale system, the proposed expectation multi-direction (EMD) algorithm does not require eigenvalue calculation and has less computational costs. These two algorithms are developed based on the gradient descent and multi-direction methods. Under such an expectation framework, different kinds of models are identified on a case-by-case basis. The convergence analysis and simulation examples show effectiveness of the algorithms.

• Journal Article Type: Article
• Acceptance Date: Jul 25, 2022
• Online Publication Date: Jul 28, 2022
• Publication Date: May 1, 2023
• Deposit Date: May 23, 2023
• Publicly Available Date: May 24, 2023
• Journal: IEEE Transactions on Industrial Informatics
• Print ISSN: 1551-3203
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 19
• Issue: 5
• Pages: 7011-7021
• DOI: https://doi.org/10.1109/TII.2022.3194656
• Keywords: Comprehensive expectation framework, gradient descent (GD) method, maximization method, multidirection (MD) method, time-delayed system
• Public URL: https://uwe-repository.worktribe.com/output/10800871
• Publisher URL: https://ieeexplore.ieee.org/document/9844294