Improved Incremental RVFL With Compact Structure and Its Application in Quality Prediction of Blast Furnace

This article proposes an improved incremental random vector functional-link network (RVFL) with a compact structure and presents its application to quality prediction of blast furnace (BF) ironmaking processes. Different from the original RVFL, the improved incremental RVFL has no input-output direct links and no output bias (NLNB) and approaches the desired network output by sequentially updating the output weights of fixed hidden neurons. Moreover, it is proved that this improved incremental RVFL with NLNB (I-I-RVFL-NLNB) is able to approximate a given continuous function with arbitrary small errors with fewer hidden neurons. As a result, the developed network has more compact requiring less execution time, while retaining the conventional incremental RVFL's advantage of monotonically decreasing errors and avoiding the overfitting issue of the basic RVFL-NLNB. Since the zero approximation error is not needed in practical applications, the terminal condition of the existing incremental RVFL is improved by using the difference of root mean squared error (RMSE) between two consecutive iterations as one of the indices to characterize the imperceptible descending trend of RMSE. A series of comparisons are made by both benchmark simulations and a real quality modeling problem for a large BF ironmaking plant in South China, which show that the proposed algorithm has better performance in terms of modeling accuracy and efficiency.