The characterization of knock intensity distributions can provide useful insights into the process and help to improve knock control system designs. In this paper, an extensive statistical analysis is performed on knock intensity data recorded under a broad range of operating conditions. First, the critical issue of whether the data exhibit any cycle-to-cycle correlations is investigated, and it is shown that knock intensity closely approximates a cyclically independent random process. The study then focuses on the variation of knock intensity distributions with operating condition, and on the quantification of these distributions using simple scalar measures. The relationship between knock event distributions and knock intensity distributions is also investigated, and it is shown that knock event data are binomially distributed regardless of the underlying knock intensity distribution. This supports ongoing efforts to exploit binomial probability theory in knock event simulation and controller design.

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Knock intensity behaves as a random process which may be characterized using simple scalar metrics such as the mean and variance, or (more commonly) by the probability of knock events. However, such measures discard much of the information present in the signal. Several researchers have therefore sought to obtain a more complete characterization of the process by fitting parametric log-normal or gamma distribution models to knock intensity distributions. The present study extends this work both in terms of the range of engine operating conditions considered and in terms of the evaluation of the goodness of fit between two different models and the experimental data. In particular, new and arguably more application-appropriate measures of the goodness of fit provide a clearer assessment of the performance of the models, and a like-for-like comparison of log-normal and gamma distribution model forms demonstrates that the log-normal model better characterizes the experimental data used in this study.

Knock control remains a critical issue in modern engine powertrains, and a renewed emphasis on knock as a stochastic process has proved beneficial in the development of new controller designs. However, the random nature of knock also makes it hard to evaluate the closed-loop performance of a knock controller in a rigorous, repeatable way. This work therefore focuses particularly on the statistical properties of knock intensities and knock events, and a new Markovbased analysis is used to compute the corresponding statistical properties and distribution of the closed-loop response. The method is applied to a conventional knock controller, revealing new aspects of its behavior. In particular, the closedloop spark advance distribution is found to be periodic initially, only collapsing to an invariant steady-state distribution as a result of limits applied to the spark advance actuation. The stochastic response of the controller to different initial conditions is also investigated, providing a more rigorous insight into its performance. The results of the Markov-based analysis are confirmed using Monte Carlo simulations.

A new method for optimizing the knock threshold is presented and shown to significantly improve the closed loop performance of a standard knock controller. Traditional approaches assume that in order to control potentially damaging knock events, it is necessary to use thresholds set to detect such events. The proposed new method takes a more stochastic view and sets the threshold such that it maximizes the sensitivity to changes in the knock intensity distribution. The behavior of a standard knock controller in response to different threshold and gain values is investigated and illustrated using experimental and simulation data. In particular, it is shown that optimizing the threshold and controller parameters in the manner proposed results in a controller with fast transient response, improved mean spark advance, and reduced cyclic dispersion. With no modifications other than optimizing the parameters of a standard controller, it is therefore possible to operate closer to the knock limit, thereby improving fuel efficiency, emissions, and output torque.