Regularized online sequential extreme learning machine with adaptive regulation factor for time-varying nonlinear system

In order to more accurately model time-varying nonlinear systems, we propose a regularized online sequential extreme learning machine with adaptive regulation factor (ROSELM-ARF). The construction of a new objective function allows for the online updating of both the model coefficient as well as the regulation factor, while negating the influence of the cumulate error. This differs from the traditional regularized online sequential extreme learning machine (ReOS-ELM) which only updates the model coefficient. The development and application of a two-step solving method is used to determine the optimal parameters, where the optimal regulation factor is derived using the proposed fast and online leave-one-out cross validation (FOLOO) method. The computational performance could be drastically improved by using the proposed FOLOO method as compared to using the existing leave-one-out cross validation (LOO) method. The application of the proposed method in the modeling of two practical cases is done in order to demonstrate its effectiveness. The experimental results indicate that the proposed method provides a more accurate model than several conventional modeling methods, while also improving the computational performance.