The statistical characteristics of knock signal waveforms

Abstract

Individual instances of the knock resonant response are easy to acquire but these are subject to noise and vary considerably from cycle to cycle due to random variations in the knock process. This work provides a new way to quantify and model the stochastic properties of knock signals, capturing both the time domain resonant characteristics within a cycle as well as the random variations from cycle to cycle. A new phase alignment method enables the ensemble mean knock waveform to be identified from the data which also removes noise components without the need for narrowband filtering. This ensemble waveform shows the empirical characteristics of knock onset, decay, and frequency slurring within the cycle as the gas expands and cools. The phase-aligned cyclic variations of the knock waveform are also shown to approximate a (time-varying) dual-Gaussian distribution, and fitting such a model to the data enables the statistical properties of the dataset as a whole to be decomposed into separate knocking and non-knocking populations providing further insight into the knock process. The technique is applied both to filtered cylinder pressure signals and to accelerometer-based knock signals, and the results are compared and contrasted.