Identifying a class of output error models using a multi-gradient algorithm with optimal stacking length

The output error model is widely used in industrial modeling. This work introduces an innovative gradient algorithm tailored for output error models. It is widely recognized that while traditional stochastic gradient algorithms offer low computational complexity, they are often criticized for their sluggish convergence rates. In response to this challenge, multi-gradient algorithms have been developed; however, current multi-gradient algorithms lack a straightforward approach for determining the appropriate stacking length. This paper presents a user-friendly variable stacking length multi-gradient algorithm grounded in the principle of cost function minimization. Simulation experiments demonstrate that the proposed method retains the benefits of traditional gradient algorithms while achieving rapid convergence with only a minor increase in computational complexity.