Modelling of diesel engine performance using advanced machine learning methods under scarce and exponential data set |
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| Authors: | Ka In Wong Pak Kin Wong Chun Shun Cheung Chi Man Vong |
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| Affiliation: | 1. Department of Electromechanical Engineering, University of Macau, Macau;2. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong;3. Department of Computer and Information Science, University of Macau, Macau |
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| Abstract: | Traditional methods on creating diesel engine models include the analytical methods like multi-zone models and the intelligent based models like artificial neural network (ANN) based models. However, those analytical models require excessive assumptions while those ANN models have many drawbacks such as the tendency to overfitting and the difficulties to determine the optimal network structure. In this paper, several emerging advanced machine learning techniques, including least squares support vector machine (LS-SVM), relevance vector machine (RVM), basic extreme learning machine (ELM) and kernel based ELM, are newly applied to the modelling of diesel engine performance. Experiments were carried out to collect sample data for model training and verification. Limited by the experiment conditions, only 24 sample data sets were acquired, resulting in data scarcity. Six-fold cross-validation is therefore adopted to address this issue. Some of the sample data are also found to suffer from the problem of data exponentiality, where the engine performance output grows up exponentially along the engine speed and engine torque. This seriously deteriorates the prediction accuracy. Thus, logarithmic transformation of dependent variables is utilized to pre-process the data. Besides, a hybrid of leave-one-out cross-validation and Bayesian inference is, for the first time, proposed for the selection of hyperparameters of kernel based ELM. A comparison among the advanced machine learning techniques, along with two traditional types of ANN models, namely back propagation neural network (BPNN) and radial basis function neural network (RBFNN), is conducted. The model evaluation is made based on the time complexity, space complexity, and prediction accuracy. The evaluation results show that kernel based ELM with the logarithmic transformation and hybrid inference is far better than basic ELM, LS-SVM, RVM, BPNN and RBFNN, in terms of prediction accuracy and training time. |
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| Keywords: | AFR, air&ndash fuel ratio ANN, artificial neural network ATDC, after top dead centre BPNN, back-propagation neural network BSCO, brake-specific carbon monoxide BSNOx, brake-specific nitrogen oxides BTDC, before top dead centre BTE, brake thermal efficiency CO, carbon monoxide CO2, carbon dioxide ELM, extreme learning machine ELMbasic, basic extreme learning machine ELMkernel, kernel based extreme learning machine HRRpeak, peak heat release rate KKT, Karush&ndash Kuhn&ndash Tucker LOOCV, leave-one-out cross-validation LS-SVM, least square support vector machine NOx, nitrogen oxides Ppeak, peak pressure PM, particulate mass RBF, radial basis function RBFNN, radial basis function neural network RMSE, root mean square error RMSEtrain, root mean square error for training data sets RMSEtest, root mean square error for test data sets rpm, revolution per minute RVM, relevance vector machine SLFN, single-hidden-layer feedforward neural network SVM, support vector machine |
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