Pressure prediction of a spark ignition single cylinder engine using optimized extreme learning machine models

In this study, the cyclic of a spark ignition engine using octane fuel is modeled using extreme learning machine, an emergent technology related to single-hidden layer feedforward neural networks (SLFNs). The experimental engine case study was operated with five different engine speeds from 1000 to 3000 rpm, and crankshaft angle from 360 to 360 without exhaust gas recirculation. The mean effective pressure was used to indicate the cyclic variability for the mean of 100 consecutive cycles. In this study the extreme learning machine (ELM), the regularized extreme learning machine and the outlier robust extreme learning machine were applied to predict the conditions of a combustion parameter used to reflect pressure information for entire cycle in a single-cylinder compression ignition naturally aspirated engine. Prediction by ELM models is normally faster than mathematical models employed to solve a set of differential equations by iterative numerical methods. The essence of ELM is that the hidden layer of SLFNs need not be tuned. Nevertheless, the selection of an appropriate ELM topology is crucial in terms of simplicity, velocity and accuracy. The suitable determination of the number of hidden layer nodes (neurons), type of activation function, and sparse connection structure of weights and biases were obtained using a modified biogeography-based optimization approach (BBO), a population-based metaheuristic algorithm inspired on the mathematical model of organism distribution in biological systems. The experimental dataset were used to train ELM models, and the reliability of these models was assessed and compared for two case studies based on performance criteria related to accuracy, sparsity and complexity using a cross-validation procedure. After training, experimental results show that the pressure can be modeled with reasonable accuracy. The results analysis indicated that the proposed optimized ELM and its variants optimized by BBO approaches have potential for prediction the mean effective pressure showed reasonable consistency with the experimental results.