Online time-sequence incremental and decremental least squares support vector machines for engine air-ratio prediction

Fuel efficiency and pollution reduction relate closely to air-ratio (i.e. lambda) control among all the engine control variables. Lambda indicates the amount that the actual available air-fuel ratio mixture differs from the stoichiometric air-fuel ratio of the fuel being used. Accurate lambda prediction is essential for effective lambda control. This paper employs an emerging online time-sequence incremental algorithm and proposes one novel online time-sequence decremental algorithm based on least squares support vector machines (LS-SVMs) to continually update the built LS-SVM lambda function whenever a sample is added to, or removed from, the training dataset. Moreover, the online time-sequence algorithm can also significantly shorten the function updating time as compared with function retraining from scratch. In order to evaluate the effectiveness of this pair of online time-sequence algorithms, three lambda time series obtained from experiments under different operating conditions are employed. The prediction results of the online time-sequence algorithms over unseen cases are compared with those under classical LS-SVMs, typical decremental LS-SVMs, and neural networks. Experimental results show that the online time-sequence incremental and decremental LS-SVMs are superior to the other three typical methods.