Diesel engine modelling using extreme learning machine under scarce and exponential data sets

To predict the performance of a diesel engine, current practice relies on the use of black-box identification where numerous experiments must be carried out in order to obtain numerical values for model training. Although many diesel engine models based on artificial neural networks (ANNs) have already been developed, they have many drawbacks such as local minima, user burden on selection of optimal network structure, large training data size and poor generalization performance, making themselves difficult to be put into practice. This paper proposes to use extreme learning machine (ELM), which can overcome most of the aforementioned drawbacks, to model the emission characteristics and the brake-specific fuel consumption of the diesel engine under scarce and exponential sample data sets. The resulting ELM model is compared with those developed using popular ANNs such as radial basis function neural network (RBFNN) and advanced techniques such as support vector machine (SVM) and its variants, namely least squares support vector machine (LS-SVM) and relevance vector machine (RVM). Furthermore, some emission outputs of diesel engines suffer from the problem of exponentiality (i.e., the output y grows up exponentially along input x) that will deteriorate the prediction accuracy. A logarithmic transformation is therefore applied to preprocess and post-process the sample data sets in order to improve the prediction accuracy of the model. Evaluation results show that ELM with the logarithmic transformation is better than SVM, LS-SVM, RVM and RBFNN with/without the logarithmic transformation, regardless the model accuracy and training time.