Modeling and optimization of biodiesel engine performance using kernel-based extreme learning machine and cuckoo search

• A new modeling framework with optimization of biodiesel ratio for diesel engines.
• A new application of kernel-based extreme learning machine to biodiesel engine modelling.
• A first application of cuckoo search to biodiesel engine optimization problem.
• A flexible objective function for multi-objective optimization of biodiesel ratio.
• A comparison of various techniques for biodiesel engine modeling and optimization problem.

This study presents the optimization of biodiesel engine performance that can achieve the goal of fewer emissions, low fuel cost and wide engine operating range. A new biodiesel engine modeling and optimization framework based on extreme learning machine (ELM) is proposed. As an accurate model is required for effective optimization result, kernel-based ELM (K-ELM) is used instead of basic ELM because K-ELM can provide better generalization performance, and the randomness of basic ELM does not occur in K-ELM. By using K-ELM, a biodiesel engine model is first created based on experimental data. Logarithmic transformation of dependent variables is used to alleviate the problems of data scarcity and data exponentiality simultaneously. With the K-ELM engine model, cuckoo search (CS) is then employed to determine the optimal biodiesel ratio. A flexible objective function is designed so that various user-defined constraints can be applied. As an illustrative study, the fuel price in Macau is used to perform the optimization. To verify the modeling and optimization framework, the K-ELM model is compared with a least-squares support vector machine (LS-SVM) model, and the CS optimization result is compared with particle swarm optimization and experimental results. The evaluation result shows that K-ELM can achieve comparable performance to LS-SVM, resulting in a reliable prediction result for optimization. It also shows that the optimization results based on CS is effective.