The Pearson test is used to confirm that knock intensity data closely approximate a cyclically independent random process which is therefore fully characterized by its probability density function or cumulative distribution function. Although these distributions are often assumed to be log-normal, other results have shown that the data do not conform to a log-normal distribution at the 5% significance level. A new dual log-normal model is therefore proposed based on the assumption that the data comprise a mixture of two distributions, one knocking and one non-knocking. Methods for estimating the parameters of this model, and for assessing the quality of fit, are presented. The results show a significantly improved model fit.
EckertPKongS-CReitzRD.Modeling autoignition and engine knock under spark ignition conditions (2003-01-0011). SAE Trans J Engines2003; 112(3).
2.
TerajiATsudaTNodaTKuboMItohT.Development of a three-dimensional knock simulation method incorporating a high-accuracy flame propagation model. Int J Engine Res2005; 6(1): 73–83.
3.
LafossasFACastagneMDumasJPHenriotS.Development and validation of a knock model in spark ignition engines using a CFD code (2002-01-2701). Transit J Fuels Lubr2002; 111(4).
4.
CortiEForteC.Combination of in-cylinder pressure signal analysis and CFD simulation for knock detection purposes. SAE Int J Engines2009; 2(2): 368–380.
5.
LinseDKleemannAHasseC.Probability density function approach coupled with detailed chemical kinetics for the prediction of knock in turbocharged direct injection spark ignition engines. Combust Flame2014; 161(4): 997–1014.
6.
D’AdamoABredaSIaccarinoSBerniFFontanesiSZardinB, et al. Development of a RANS-based knock model to infer the knock probability in a research spark-ignition engine. SAE Int J Engines2017; 10(3): 722–739.
7.
SpelinaJMPeyton JonesJCFreyJ.Characterization of knock intensity distributions: part 1: statistical independence and scalar measuresProc IMechE, Part D: J Automobile Engineering2014; 228(2): 117–128.
8.
Peyton JonesJCSpelinaJMFreyJ.Likelihood-based control of engine knock. IEEE T Contr Syst T2013; 21(6): 2169–2180.
9.
LeppardWR.Individual-cylinder knock occurrence and intensity in multicylinder engines. SAE technical paper 820074, 1982.
10.
MilloFFerraroC, Knock in S.I. engines: a comparison between different techniques for detection and control, (982477). SAE Trans J Fuels and Lubricants1998; 107(4).
11.
SinnerstadK.Knock intensity and torque control on an SVC engine. Master’s Thesis, Linköping University, Linköping, 2003.
12.
NaberJDBloughJRFrankowskiDGobleMSzpytmanJE.Analysis of combustion knock metrics in spark-ignition engines (2006-01-0400). SAE Trans J Engines2006; 115(3): 23.
13.
WuG. A real time statistical method for engine knock detection. SAE technical paper 2007-01-1507, 2007.
14.
AbhijitANaberJD.Ionization signal response during combustion knock and comparison to cylinder pressure for SI engines. SAE Int J Passeng Cars: Electron Electr Syst2008; 1(1): 349–364.
15.
SpelinaJMPeyton JonesJCFreyJ.Characterization of knock intensity distributions: part 2: parametric models. Proc IMechE, Part D: J Automobile Engineering2013; 227(12): 1650–1660.
PlackettRL.Karl Pearson and the chi-squared test. Int Stat Rev1983; 51(1): 59–72.
18.
SpelinaJMPeyton JonesJCFreyJ.Recent advances in knock analysis, simulation, and control. SAE Int J Engines2014; 7(2): 947–955.
19.
KassaM.Analysis and control of compression-ignition and spark-ignited engines operating with dual-fuel combustion strategy. PhD Thesis, Illinois Institute of Technology, Chicago, IL, 2017.
20.
LivengoodJCWuPC.Correlation of autoignition phenomenon in internal combustion engines and rapid compression machines. Int Symp Combust1955; 5: 347–356.
21.
MoonTK.The expectation-maximization algorithm. IEEE Signal Proc Mag1996; 13(6): 47–60.
22.
BarberD (ed.). Mixture models. In: BarberD (ed.) Bayesian reasoning and machine learning. Cambridge: Cambridge University Press, 2012, pp.432–461.
23.
ArthurDVassilvitskiiS. k-means++: the advantages of careful seeding. In: Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms, New Orleans, LA, 7–9 January 2007, pp.1027-1035. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2007.
24.
StuteWManteigaWGQuindimilMP.Bootstrap based goodness-of-fit-tests. Metrika1993; 40(1): 243–256.
