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In this paper, a new sequential learning algorithm is constructed by combining the Online Sequential Extreme Learning Machine (OS-ELM) and Kalman filter regression. The Kalman Online Sequential Extreme Learning Machine (KOSELM) handles the problem of multicollinearity of the OS-ELM, which can generate poor predictions and unstable models. The KOSELM learns the training data one-by-one or chunk-by-chunk by adjusting the variance of the output weights through the Kalman filter. The performance of the proposed algorithm has been validated on benchmark regression datasets, and the results show that KOSELM can achieve a higher learning accuracy than OS-ELM and its related extensions. A statistical validation for the differences of the accuracy for all algorithms is performed, and the results confirm that KOSELM has better stability than ReOS-ELM, TOSELM and LS-IELM. [ABSTRACT FROM AUTHOR]

Abstract: Look-up tables are commonly used in the automotive field for handling operating point variations. However, constant maps cannot cope with systems variations and ageing. Methods, such as Kalman filter or Extended Kalman filter for non-linear cases, can be used for table adaptation providing an optimal solution to the problem. But these methods are computationally intensive, making difficult to implement them on commercial engine control units. The current paper proposes a learning method for online updating of look-up tables or maps. This algorithm uses precalculated membership functions based on a standard Kalman filter observer for weighting the adaptation. The main contribution of the method is the derivation of a steady-state Kalman filter observer that lowers the calculation burden and simplifies the implementation against the standard Kalman filter implementation that requires higher computational cost. As far as table is updated online while engine runs, this allows correcting drift errors and the unit-to-unit dispersion. The method is illustrated for mapping engine variables such as and in a Diesel engine by using an adaptive look-up table, and its characteristics make it suitable for implementing in commercial engine electronic control units for online purposes. [Copyright &y& Elsevier]