Robust Online Sequential RVFLNs for Data Modeling of Dynamic Time-Varying Systems With Application of an Ironmaking Blast Furnace

By dealing with robust modeling and online learning together in a unified random vector functional-link networks (RVFLNs) framework, this paper presents a novel robust online sequential RVFLNs for data modeling of dynamic time-varying systems together with its application for a blast furnace (BF) ironmaking process. First, to overcome the difficulties caused by the nonlinear time-varying dynamics of process and to enable the RVFLNs to learn online and to avoid data saturation, an improved online sequential version of RVFLNs (OS-RVFLNs) is presented by sequential learning with forgetting factor. It has been shown that the improved OS-RVFLNs with forgetting factor is not only suitable for the large-scale and real-time data transfer situation but also can adjust the sensitivity of the algorithm to different samples. Second, in order to solve the issue of modeling robustness when the dataset is contaminated with various outliers, a Cauchy distribution function weighted M-estimator is introduced to strengthen the robustness of the improved OS-RVFLNs. The non-Gaussian Cauchy distribution function is used to estimate the weights of different data and thus the corresponding contribution on modeling can be properly distinguished. Experiments using actual industrial data of a large BF ironmaking process have demonstrated that the proposed algorithm produces a much stronger robustness and better estimation accuracy than other algorithms.