Dependence Measure and Wolfe-Powell Criterion Based Two-stage Algorithm for Identification of Time Delay FIR Models

Time delay dynamic systems are widely existed due to sensors, actuators or other reasons. In this paper, a time delay FIR system is considered to model linear dynamic systems. The reason why the FIR model is selected is to highlight the proposed time-delay estimation method and parameter identification algorithm, and avoid the impact of a complex model on readers' understanding of the proposed technologies. Firstly, to obtain an estimate of the time delay, a dependence measure based method is proposed. Unlike the optimization method that requires the parameter estimate and needs to round the estimated delay, the delay estimation method based on the 2-copula dependence measure can give accurate delay estimates independently of the parameters and without rounding. Secondly, to estimate the parameters, a variable stacking length multi-gradient identification algorithm is studied. The multi-gradient technique takes recent several gradients to accelerate the stochastic gradient algorithm. The stacking length, i.e., the number of gradients used in each iteration, is determined by the Wolfe-Powell criterion. The effectiveness is tested by numerical simulations and case study.