Investigations on In-Cylinder Pressure Cycle-to-Cycle Variations in a Diesel Engine by Recurrence Analysis

Ding, Shun-Liang; Yang, Liping; Song, Enzhe

doi:10.4271/2015-01-0875

Cited by 14 publications

(6 citation statements)

References 33 publications

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“…The dynamics associated with the engine speed (2) is the scaled difference between torque generation (7) and load torque (3) (7) The terms , are Willans parameters, which are simplifications of the engine's characteristics, while represents Enthalpy.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Recurrence plots have been used to provide insight into the deterministic nature of engine parameters injection impulse width and engine angular speed [1]. Recurrence plot and recurrence quantification analysis were used to investigate the dynamics associated with cycle-to-cycle variations in a diesel engine [2]. Multi-level sub structuring procedures were applied to study the periodic steady-state response of large engine models in a computationally-efficient way [3].…”

Section: Introductionmentioning

confidence: 99%

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A Bifurcation Analysis of an Open Loop Internal Combustion Engine

Smith

Knowles

Mason

2019

SAE Technical Paper Series

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The process of engine mapping in the automotive industry identifies steady-state engine responses by running an engine at a given operating point (speed and load) until its output has settled. While the time simulating this process with a computational model for one set of parameters is relatively short, the cumulative time to map all possible combinations becomes computationally inefficient. This work presents an alternative method for mapping out the steady-state response of an engine in simulation by applying bifurcation theory. The bifurcation approach used in this work allows the engine's steady-state response to be traced through the model's stateparameter space under the simultaneous variation of one or more model parameters. To demonstrate this approach, a bifurcation analysis of a simplified nonlinear engine model is presented. Using "throttle demand" and "desired load torque signal", the engine's dynamic response is classified into distinct regions bounded by bifurcation points. These bifurcations are shown to correspond to key physical properties of the open-loop system: fold bifurcations correspond to the minimum throttle angle required for a steady-state engine response; Hopf bifurcations bound a region where selfsustaining oscillations occur. The techniques used in this case study demonstrate the efficiency a bifurcation approach has at highlighting different regions of dynamic behavior in the engine's state-parameter space. Such an approach could speed up the mapping process and enhance the automotive engineer's understanding of an engine's underlying dynamic behavior. The information obtained from the bifurcation analysis could also be used to inform the design of future engine control strategies.

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Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Bifurcation Analysis of an Open Loop Internal Combustion Engine

Smith

Knowles

Mason

2019

SAE Technical Paper Series

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“…Earlier, RPs have been used for investigating the effect of operating parameters on discrete combustion dynamics of SI [28][29][30] and CI engines, 31,32 and recently of RCCI 33 and HCCI engines. 27 Ding et al 31 observed chaotic like characteristic of IMEP fluctuations of a diesel engine at lower load and speed which transformed into more stable and deterministic type at higher engine speed and load. RP-based analysis of diesel engine combustion indicated a more periodic nature of fluctuations at the engine speed of 1200 and 2000 rpm while an intermittent nature at the intermediate speeds.…”

Section: Introductionmentioning

confidence: 99%

Effects of intake charge temperature and relative air-fuel ratio on the deterministic characteristics of cyclic combustion dynamics of a HCCI engine

Singh

Maurya

2022

International Journal of Engine Research

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Homogenous charge compression ignition (HCCI) combustion can significantly reduce automotive pollution and increase the thermal efficiency of the engine. However, combustion phasing control is a major challenge in HCCI engines due to severe cyclic combustion variations. This study investigates the cyclic combustion dynamics of the HCCI engine using nonlinear dynamic methods such as return maps, recurrence plots (RPs), and recurrence quantitative analysis (RQA). Combustion stability and cyclic variations of HCCI combustion parameters were investigated on a modified four-stroke diesel engine. The experiments were conducted by varying relative air-fuel ratios ([Formula: see text]) and intake air temperatures ([Formula: see text]) at two engine speeds. In-cylinder pressure data of 2000 consecutive engine combustion cycles is logged for each test condition. In this study, deterministic characteristics of combustion phasing (CA50) and crank angle position of maximum cylinder pressure ([Formula: see text]) are investigated and compared by employing nonlinear dynamical methods. Return maps revealed that [Formula: see text] is having distinct and more frequently observed deterministic characteristics in comparison to CA50. Patterns in RPs showed a more persistent and sudden change in the combustion dynamics at higher engine speeds. Recurrence plot-based analysis found the existence of deterministic features in the combustion dynamics irrespective of the operating conditions. It was found using RQA parameters that the deterministic nature becomes stronger with a decrease in [Formula: see text] and any deviation in intermediate values of [Formula: see text]. Additionally, RQA measures advocate that CA50 has more deterministic characteristics at higher engine speed while [Formula: see text] at lower engine speed. Strong coupling and synchronization between [Formula: see text] and CA50 is indicated by cross-recurrence plots and CPR index when engine operated with a comparatively richer mixture.

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“…A variety of approaches to complement conventional time history simulations of nonlinear dynamic models have been presented in engine literature: recurrence plots and recurrence quantification analysis have been used to investigate the relation between injection impulse with engine speed 1 and the dynamics associated with cycle-to-cycle variations in a diesel engine 2 ; multi-level substructuring procedures were used to study periodic responses of large engine models in Theodosiou et al 3 ; 0-1 testing was applied to classify chaotic behaviour within the combustion process. 4 Understanding the steady-state response of engine models is also highlighted as a challenge in the literature: in Beno et al, 5 the authors studied the calibration of a turbocharged diesel engine by representing the highly nonlinear system as a mean value model.…”

Section: Introductionmentioning

confidence: 99%

Numerical continuation applied to internal combustion engine models

Smith

Knowles

Mason

2020

Proceedings of the Institution of Mechanical Engineers, Part D:

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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.

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Investigations on In-Cylinder Pressure Cycle-to-Cycle Variations in a Diesel Engine by Recurrence Analysis

Cited by 14 publications

References 33 publications

A Bifurcation Analysis of an Open Loop Internal Combustion Engine

A Bifurcation Analysis of an Open Loop Internal Combustion Engine

Effects of intake charge temperature and relative air-fuel ratio on the deterministic characteristics of cyclic combustion dynamics of a HCCI engine

Numerical continuation applied to internal combustion engine models

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