Characterization of knock intensity distributions: Part 1: statistical independence and scalar measures

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.