Stochastic Gradient Based Extreme Learning Machines For Online Learning of Advanced Combustion Engines

In this article, a stochastic gradient based online learning algorithm for Extreme Learning Machines (ELM) is developed (SG-ELM). A stability criterion based on Lyapunov approach is used to prove both asymptotic stability of estimation error and stability in the estimated parameters suitable for identification of nonlinear dynamic systems. The developed algorithm not only guarantees stability, but also reduces the computational demand compared to the OS-ELM approach based on recursive least squares. In order to demonstrate the effectiveness of the algorithm on a real-world scenario, an advanced combustion engine identification problem is considered. The algorithm is applied to two case studies: An online regression learning for system identification of a Homogeneous Charge Compression Ignition (HCCI) Engine and an online classification learning (with class imbalance) for identifying the dynamic operating envelope of the HCCI Engine. The results indicate that the accuracy of the proposed SG-ELM is comparable to that of the state-of-the-art but adds stability and a reduction in computational effort.