This paper proposes tools from bifurcation theory, specifically numerical continuation, as a complementary method for efficiently mapping the state-parameter space of an internal combustion engine model. Numerical continuation allows a steady-state engine response to be traced directly through the state-parameter space, under the simultaneous variation of one or more model parameters. By applying this approach to two nonlinear engine models (a physics-based model and a data-driven model), this work determines how input parameters ‘throttle position’ and ‘desired load torque’ affect the engine’s dynamics. Performing a bifurcation analysis allows the model’s parameter space to be divided into regions of different qualitative types of the dynamic behaviour, with the identified bifurcations shown to correspond to key physical properties of the system in the physics-based model: minimum throttle angles required for steady-state operation of the engine are indicated by fold bifurcations; regions containing self-sustaining oscillations are bounded by supercritical Hopf bifurcations. The bifurcation analysis of a data-driven engine model shows how numerical continuation could be used to evaluate the efficacy of data-driven models.

中文翻译：

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数值延拓应用于内燃机模型

本文提出了来自分叉理论的工具，特别是数值延拓，作为一种有效映射内燃机模型状态参数空间的补充方法。在一个或多个模型参数同时变化的情况下，数值连续允许通过状态参数空间直接跟踪稳态发动机响应。通过将这种方法应用于两个非线性发动机模型（基于物理的模型和数据驱动的模型），这项工作确定了输入参数“节气门位置”和“所需负载扭矩”如何影响发动机的动力学。执行分岔分析允许将模型的参数空间划分为动态行为的不同定性类型的区域，在基于物理的模型中，识别出的分岔对应于系统的关键物理特性：发动机稳态运行所需的最小节气门角度由折叠分岔表示；包含自持振荡的区域以超临界 Hopf 分岔为界。数据驱动发动机模型的分岔分析显示了如何使用数值连续性来评估数据驱动模型的功效。