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Research Papers: Internal Combustion Engines

Fast Computation of Combustion Phasing and Its Influence on Classifying Random or Deterministic Patterns

[+] Author and Article Information
Huan Lian

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: hlian@umich.edu

Jason Martz, Niket Prakash, Anna Stefanopoulou

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

1Corresponding author.

Contributed by the IC Engine Division of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 4, 2016; final manuscript received April 8, 2016; published online May 17, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(11), 112802 (May 17, 2016) (8 pages) Paper No: GTP-16-1004; doi: 10.1115/1.4033469 History: Received January 04, 2016; Revised April 08, 2016

The classification between a sequence of highly variable combustion events that have an underlying deterministic pattern and a sequence of combustion events with similar level of variability but random characteristics is important for control of combustion phasing. In the case of high cyclic variation (CV) with underlying deterministic patterns, it is possible to apply closed-loop combustion control on a cyclic-basis with a fixed mean value, such as injection timing in homogeneous charge compression ignition (HCCI) or spark timing in spark ignition (SI) applications, to contract the CV. In the case of a random distribution, the high CV can be avoided by shifting operating conditions away from the unstable region via advancing or retarding the injection timing or the spark timing in the mean-sense. Therefore, the focus of this paper is on the various methods of computing CA50 for analyzing and classifying cycle-to-cycle variability. The assumptions made to establish fast and possibly online methods can alter the distribution of the calculated parameters from cycle-to-cycle, possibly leading to incorrect pattern interpretation and improper control action. Finally, we apply a statistical technique named “permutation entropy” for the first time on classifying combustion patterns in HCCI and SI engine for varying operating conditions. Then, the various fast methods for computing CA50 feed the two statistical methods, permutation and the Shannon entropy, and their differences and similarities are highlighted.

Copyright © 2016 by ASME
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References

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Figures

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Fig. 1

Scope of the current work (engine map from Ref. [5])

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Fig. 2

Marvin's graphical method for estimating combustion phasing of SI combustion, with 42% internal EGR fraction, spark timing 38 deg bTDC, 298 cycles

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Fig. 3

CA50 calculation of SI combustion with 42% internal EGR fraction, spark timing 38 deg bTDC: (a) scatter plot and (b) relationship with the baseline CA50 from dHR. Detailed heat release is noted as dHR and fast heat release is noted as fHR. Marvin's method is noted as Marvin, and Rasseweiler and Withrow's method is noted as R&W.

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Fig. 4

CA50 calculation of HCCI combustion: (a) scatter plot and (b) relationship with the baseline CA50 from dHR

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Fig. 5

Return map of CA50 of high CV HCCI combustion: (a) detailed heat release (noted as dHR in gray dots) versus fast heat release (noted as fHR, in black dots), (b) detailed heat release (noted as dHR in gray dots) versus Marvin's method (noted as Marvin, in black dots), and (c) detailed heat release (noted as dHR in gray dots) versus Rasseweiler and Withrow's method (noted as R&W, in black dots)

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Fig. 6

The modified Shannon entropy of CA50 of high CV HCCI combustion: (a) dHR, (b) fHR, (c) Marvin's method, and (d) R&W method

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Fig. 7

Symbol statistics of CA50 of high CV HCCI combustion: (a) dHR versus fHR, (b) dHR versus Marvin's method, and (c) dHR versus R&W method

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Fig. 8

Quantification of CV in SI combustion with 42% internal EGR fraction, spark timing 38 deg bTDC: (a) return map, (b) the modified Shannon entropy, and (c) symbol statistics

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Fig. 9

Example of discretization of the calculation of permutation entropy: (a) time series example and (b) rank order

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Fig. 10

Diagnostic of determinism in HCCI and SI combustion: (a) scatter plot of CA50 of HCCI and SI combustion, (b) COV of IMEP and standard deviation of CA50 for 100 cycles with step of 1, and (c) the modified Shannon entropy and the permutation entropy for 100 cycles with step of 1 cycle, the permutation order is 4

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Fig. 11

Schematic of the sliding window used to enable entropy calculations with varying operating conditions

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Fig. 12

Diagnostic of determinism in HCCI and SI combustion: (a) permutation entropy and (b) Shannon entropy. Note that 2999 cycles of HCCI combustion and 1192 cycles of SI combustion are artificially joined together for this analysis, which is intended to demonstrate the entropy's response to a change in operating conditions with no real experiment with combustion mode switch.

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Fig. 13

Diagnostic of determinism in HCCI and SI combustion between HCCI and SI transition: (a) permutation entropy and (b) Shannon entropy. Note that 2999 cycles of HCCI combustion and 1192 cycles of SI combustion are artificially joined together for this analysis, which is intended to demonstrate the entropy's response to a change in operating conditions with no real experiment with combustion mode switch.

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Fig. 14

The first derivative of permutation entropy and Shannon entropy with combustion phasing calculated from dHR analysis. Note that 2999 cycles of HCCI combustion and 1192 cycles of SI combustion are artificially joined together for this analysis, which is intended to demonstrate the entropy's response to a change in operating conditions with no real experiment with combustion mode switch.

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Fig. 15

Block diagram of selection of control strategy

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