  This paper proposes a statistical simulator for the engine knock based on the
Mixture Density Network (MDN) and the accept-reject method. The proposed
simulator can generate the random knock intensity signal corresponding to the
input signal. The generated knock intensity has a consistent probability
distribution with the real engine. Firstly, the statistical analysis is
conducted with the experimental data. From the analysis results, some important
assumptions on the statistical properties of the knock intensity are made.
Regarding the knock intensity as a random variable on the discrete-time index,
it is independent and identically distributed if the input of the engine is
identical. The probability distribution of the knock intensity under identical
input can be approximated by the Gaussian Mixture Model(GMM). The parameter of
the GMM is a function of the input. Based on these assumptions, two
sub-problems for establishing the statistical simulator are formulated: One is
to approximate the function from input to the parameters of the knock intensity
distribution with an absolutely continuous function; The other one is to design
a random number generator that outputs the random data consistent with the
given distribution. The MDN is applied to approximate the probability density
of the knock intensity and the accept-reject algorithm is used for the random
number generator design. The proposed method is evaluated in experimental
data-based validation.
