<p>Mining information from the thermodynamic process of the internal combustion engine (ICE), which is the most commonly used mobile power source, is of great importance for emission reduction and energy saving. In this paper, a crank-angle sensitivity analysis of the thermodynamic process was conducted for underlying feature recognition of the in-cylinder pressure trace. First, a pressure–volume-phase-difference governing apparent heat transfer model (PPDH) was established via nonlinear analysis of the in-cylinder pressure trace. Second, a pressure–volume-phase-difference constrained by zero-net-heat-transfer (PPDZ) model was derived through nonlinear analysis of the in-cylinder pressure and the definite integral of the PPDH. Third, an extended pressure–volume-phase-difference constrained by zero-net-heat- transfer (EPPDZ) model was proposed using perturbation analysis and simplified with odd/even decomposition of the in-cylinder pressure and order of magnitude analysis. Finally, based on the EPPDZ and the maximum-pressure crank angle (MPCA), an implicit thermodynamic feature insensitive to phase error was derived, and a method for estimating the heat-loss-angle (HLA) of the ICE was obtained. The results indicate that: (1) the PPDH can be modeled by the first-order approximations of the pressure- volume-phase-difference (PPD); (2) the PPDZ is approximately equal to the sum of the EPPDZ and the crank angle positioning error; (3) the difference between the EPPDZ and the MPCA, denoted as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Delta \theta \left(\mathcal{A}, \varphi \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>θ</mi> <mfenced close=")" open="("> <mi mathvariant="script">A</mi> <mo>,</mo> <mi>φ</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, is analytically derived to be insensitive to the crank angle positioning error; (4) <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\Delta \theta \left(\mathcal{A}, \varphi \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>θ</mi> <mfenced close=")" open="("> <mi mathvariant="script">A</mi> <mo>,</mo> <mi>φ</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> is effective for estimating the HLA of ICE. The research provides a novel way for information mining of the in-cylinder thermodynamic process based on nonlinear analysis. Preliminary application indicates that the derived implicit thermodynamic quantity <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Delta \theta \left(\mathcal{A}, \varphi \right)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <mi>θ</mi> <mfenced close=")" open="("> <mi mathvariant="script">A</mi> <mo>,</mo> <mi>φ</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> can be applied to estimate the HLA immune to the inherent positioning error between the measured in-cylinder pressure trace and the volume trace.</p>

An underlying feature recognition of the in-cylinder pressure trace based on the crank-angle sensitivity analysis of the thermodynamic process and its application

期刊论文
发表日期：

2026年6月22日

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Xi-Bo Wang,
Yan-Fei Gao,
Chang-Feng Zhou,
Xin-Lei Liu,
Ai-Juan Li,
Qing-Gao Hou,
Xin Huang

摘要

Mining information from the thermodynamic process of the internal combustion engine (ICE), which is the most commonly used mobile power source, is of great importance for emission reduction and energy saving. In this paper, a crank-angle sensitivity analysis of the thermodynamic process was conducted for underlying feature recognition of the in-cylinder pressure trace. First, a pressure–volume-phase-difference governing apparent heat transfer model (PPDH) was established via nonlinear analysis of the in-cylinder pressure trace. Second, a pressure–volume-phase-difference constrained by zero-net-heat-transfer (PPDZ) model was derived through nonlinear analysis of the in-cylinder pressure and the definite integral of the PPDH. Third, an extended pressure–volume-phase-difference constrained by zero-net-heat- transfer (EPPDZ) model was proposed using perturbation analysis and simplified with odd/even decomposition of the in-cylinder pressure and order of magnitude analysis. Finally, based on the EPPDZ and the maximum-pressure crank angle (MPCA), an implicit thermodynamic feature insensitive to phase error was derived, and a method for estimating the heat-loss-angle (HLA) of the ICE was obtained. The results indicate that: (1) the PPDH can be modeled by the first-order approximations of the pressure- volume-phase-difference (PPD); (2) the PPDZ is approximately equal to the sum of the EPPDZ and the crank angle positioning error; (3) the difference between the EPPDZ and the MPCA, denoted as $\Delta \theta \left(\mathcal{A}, \varphi \right)$ $Δ θ (A, φ)$ , is analytically derived to be insensitive to the crank angle positioning error; (4) $\Delta \theta \left(\mathcal{A}, \varphi \right)$ $Δ θ (A, φ)$ is effective for estimating the HLA of ICE. The research provides a novel way for information mining of the in-cylinder thermodynamic process based on nonlinear analysis. Preliminary application indicates that the derived implicit thermodynamic quantity $\Delta \theta \left(\mathcal{A}, \varphi \right)$ $Δ θ (A, φ)$ can be applied to estimate the HLA immune to the inherent positioning error between the measured in-cylinder pressure trace and the volume trace.