Variation trends of dimensionless power density (PD) with a compression ratio and thermal efficiency (TE) are discussed according to the irreversible Atkinson cycle (AC) model established in previous literature. Then, for the fixed cycle temperature ratio, the maximum specific volume ratios, the maximum pressure ratios, and the TEs corresponding to the maximum power output (PO) and the maximum PD are compared. Finally, multi-objective optimization (MOO) of cycle performance with dimensionless PO, TE, dimensionless PD, and dimensionless ecological function (EF) as the optimization objectives and compression ratio as the optimization variable are performed by applying the non-dominated sorting genetic algorithm-II (NSGA-II). The results show that there is an optimal compression ratio which will maximize the dimensionless PD. The relation curve of the dimensionless PD and compression ratio is a parabolic-like one, and the dimensionless PD and TE is a loop-shaped one. The AC engine has smaller size and higher TE under the maximum PD condition than those of under the maximum PO condition. With the increase of TE, the dimensionless PO will decrease, the dimensionless PD will increase, and the dimensionless EF will first increase and then decrease. There is no positive ideal point in Pareto frontier. The optimal solutions by using three decision-making methods are compared. This paper analyzes the performance of the PD of the AC with three losses, and performs MOO of dimensionless PO, TE, dimensionless PD, and dimensionless EF. The new conclusions obtained have theoretical guideline value for the optimal design of actual Atkinson heat engine.

中文翻译：

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基于NSGA-II的不可逆阿特金森循环四目标优化


根据文献中建立的不可逆阿特金森循环（AC）模型，讨论了无量纲功率密度（PD）随压缩比和热效率（TE）的变化趋势。然后，对于固定循环温度比，比较最大比容比、最大压力比以及与最大功率输出(PO)和最大PD对应的TE。最后，应用非支配排序遗传算法，以无量纲PO、TE、无量纲PD、无量纲生态函数（EF）为优化目标，压缩比为优化变量进行循环性能多目标优化（MOO） -II (NSGA-II)。结果表明，存在一个最佳压缩比，可以使无量纲 PD 最大化。无量纲PD与压缩比的关系曲线为抛物线状，无量纲PD与TE的关系曲线为环状。交流发动机在最大PD工况下比在最大PO工况下具有更小的尺寸和更高的TE。随着TE的增大，无因次PO减小，无因次PD增大，无因次EF先增大后减小。帕累托边界不存在正理想点。比较了三种决策方法的最优解。本文分析了AC在三种损耗下的PD性能，并对无量纲PO、TE、无量纲PD、无量纲EF进行了MOO。获得的新结论对于实际阿特金森热机的优化设计具有理论指导价值。