Multi-objective optimum design of an alpha type Stirling engine using meta-models and co-simulation approach

Abstract

An alpha type Stirling engine was optimized using meta-models considering uninterrupted electric power supply concurrently with natural gas combi boilers at homes during electricity interruptions. To predict and optimize the power and efficiency of the designed Stirling engine, an artificial neural network (ANN) model was trained as a meta-model. The ANN modeling method was used in solving a multi-objective Pareto optimization problem under some constraints to determine the optimum engine parameters. The design parameters were swept volume, hot and cold cylinder temperatures, gas constant, charge pressure and engine operation speed. Feed forward and Levenberg-Marquardt back propagation algorithms were evaluated to determine the best resulting network architecture that was found as 6-12-8-1. Subsequently, the fraction of variance (R-f) value was calculated close to 1 and the absolute mean error percentage (AMEP) was calculated as 6.07%. Trained ANN model was used in solving the multi-objective optimization problem. Using the optimum design parameters, the meta model predicted the power as 73.3 W and efficiency as 32.2%. Co-simulation approach was followed to verify the optimization results, and the nominal power output and corresponding efficiency were calculated using the Schmidt theory and the calibrated 1-D model created by the GT-Suite software that yield respectively, 144.6 W and 85.8 W for the power and 35% and 35.1% for the cycle efficiency. Consequently, the use of an ANN model in solving the associated optimization problem proved itself as a fast, accurate enough and powerful method to find the optimum design parameters and predict the engine performance.