Chaos theory-based time series analysis of in-cylinder pressure and its application in combustion control of SI engines

Huanyu DI, Yahui ZHANG, Tielong SHEN
2020 Journal of Thermal Science and Technology  
Combustion control is a significant topic for achieving high efficiency and low emissions of internal combustion engines. Recently, in-cylinder pressure sensor-based closed-loop control strategies have become the preferred solution. However, their practical applications in automotive industries are limited due to the intensive acquisition of pressure series for a whole cycle and subsequent calculation of combustion indicators. This paper proposes a method for in-cylinder pressure information
more » ... raction and combustion phase estimation of spark ignition (SI) engines based on pressure measurements at several points coordinated by the crank angle. First, nonlinear dynamics analysis is introduced to analyze the system of in-cylinder pressure evolution, which is proved to be a deterministic nonlinear dynamic system with chaotic characteristics. Then, a 3-dimensional system state variable is determined to replace the pressure series during combustion. Second, with the determined system state variable, the in-cylinder pressure series during combustion and the combustion phase are learned and estimated by a machine learning method, namely, extreme learning machine (ELM). As a result, only pressure measurements at 3 points and ELM estimation models are required, instead of intensive data acquisition and calculation. The experimental validations carried out on a gasoline engine test bench have proved that the reconstruction and estimation results are accurate and that the method can perform well in real-time combustion control. Nonlinear dynamics analysis, especially chaos theory can be used to analyze data series with internal relationships. For example, a wind power time series has been analyzed by chaos theory, and a kernel function prediction model based on the chaos analysis is introduced (Ouyang et al., 2016). Chaos theory is also applied to traffic flow information analysis, and short-term traffic speed forecasting is completed by the support vector machine model (Wang et al., 2013) . Chaos theory was introduced to engine research in the 2000s. Period doubling bifurcations, one of the typical chaos phenomena, are observed in homogeneous charge compression ignition (HCCI) engine combustion. Then based on a near chaos dynamic model, combustion timing has been predicted successfully (Lee et al., 2009) . Li apply Poincaré section and return map to show the chaos dynamics of the in-cylinder pressure of a lean-burn natural gas engine (Li et al., 2008) . And Matsumoto use Pyragas' method, which is an effective method to control chaos dynamic systems, to reduce the low-frequency oscillations of power output in a motor engine (Matsumoto et al., 2008) . However, experimental evidence has shown that both random and chaotic features spark can affect ignition engines. This ambiguity therefore leads to a continuing debate on the truth of state evolution in the cylinders of SI engines (Daw et al., 1998) . In this paper, the evolution of in-cylinder pressure series is reconstructed by the mutual information (MI) method and Grassberger-Procaccia (G-P) approach. A 3-dimensional vector consisting of three moments of pressure data is applied to describe the system state. The nonlinear dynamic analysis indicates that each reconstructed data point contains the nearby evolution information. It is reasonable to predict the transformation of system state based on the evolution information. Using a proper reconstructed system state point, the in-cylinder pressure during combustion is estimated by an extreme learning machine (ELM). This approach indicates that one proper state point contains the information of in-cylinder pressure during combustion, making it possible to use one reconstructed system state point of one cycle to estimate the combustion phase (CA50). The estimation of CA50 is achieved by ELM. This estimation is verified under different operating conditions. The cycle-to-cycle varied CA50 is precisely estimated according to three moments of pressure data by learning results of the ELM method. In addition, a control experiment is undertaken as an application example. The estimated CA50 is applied to the extremum seeking (ES) method to control SA to a high efficiency point. The control result is contrasted with the situation when calculated CA50 is applied. This contrasting result shows that this estimation of CA50 can replace the complex calculations (Appendix A) in real time control. The rest of this paper is organized as follows. In section two, the engine test bench and design of experiments are introduced. The in-cylinder pressure is reconstructed and analyzed in section three. The Lyapunov exponent of in-cylinder pressure is calculated, and surrogate test is introduced. In section four, ELM model is introduced and then utilized for estimation of in-cylinder pressure during combustion and combustion phase. Section five shows experimental validations of the proposed reconstruction and estimation method in SA ES control. Final conclusions are drawn in section six.
doi:10.1299/jtst.2020jtst0001 fatcat:6qosbxvgavcebda6lksd4eezsq