System modeling oriented time-delay estimation

Training models to approximate target systems is the dominant method applied to unknown-structure delay system modeling. Due to limited learning ability of the models, the time-delay estimation (TDE) process should be executed prior to the training. The TDE for unknown-structure multi-input multi-output (MIMO) delay systems remains a challenge due to the physical interaction within the system the correlations among the system inputs and outputs. This paper addresses the TDE problem of unknown-structure MIMO delay systems. A dependence measure employed from copula theory, which is named C-dependence, is introduced to measure the dependence among the system inputs and outputs. The relationship between the C-dependence and the time-delays is studied, and the time-delays are estimated by maximizing the C-dependence. The highlight of the proposed method is that no prior decoupling process and system structure are required during the TDE process. Simulation and real data experiments are provided to demonstrate the effectiveness of the proposed method. [Display omitted] •The impact of time-delays in system modeling is firstly discussed from a geometric perspective.•C-dependence is introduced to measure the dependence among system inputs and outputs.•No prior decoupling process are required during the time-delay estimation process.•Modeling framework for delay systems is improved by adding a time-delay estimation process.