gentle ascending semi-parabolic, an

gentle ascending semi-parabolic, and a1 is the value of ignition
timing that was not postponed after preignition happens, b1 is
limit value that can be postponed to inhibit pre-ignition, C1 is
the limit value of inhibition degree of preignition corresponding
to b1.
If preignition happens on medium or small load conditions,
preignition can be inhibited by postponing ignition
timing. Ignition timing x1 corresponds to inhibition degree of
preignition 41 (x1).
Assumpt that the evaluation function is on economy m1
(x)， so relation between the evaluation function of economy
m1 (x)and inhibition degree of preignition 41 (x)can be established
as follows:
m1

x

¼ gejð41
ðxÞÞ (4)
Because preignition strength expression is j1 ( y) on current
conditions, formula（4）reachesminimumonly on the condition
of j1 ( y) < 41 (x)  C1 to not only inhibit pre-ignition, but
also take consideration to economy. So j1 ( y) < 41 (x)  C1 is
regarded as constraint condition for evaluation function on
economy， the final evaluation function on economy is

Min m1ðxÞ
S:t: j1
ðyÞh41
ðxÞ  c1
(5)
4.3. The condition for elimination of backfire on large or
full load condition
In general, backfire degree is more serious while preignition
occurs on large or full load conditions. elimination of backfire
has been described above on large or full load conditions by
postponing ignition timing combined with water injection of
intake manifold. To clearly express the relation between
backfire and ignition timing or between backfire and water
injection, in this paper, the concept of backfire strength,
elimination degree of backfire was introduced. Backfire
strength is defined as backfire size. If backfire happens, the
pressure in intake manifold will increase so rapidly that
pressure fluctuation is caused. The backfire size can be got by
pressure sensor and PC which are used to measure pressure
and pressure fluctuation. The expression of backfire strength
is j2 ( y). The elimination degree of backfire is defined as
capability of eliminating backfire, and the expression of the
elimination degree of backfire is f (x, z), and f (x, z) ¼ k2,j2 ( y),
k2 ¼ 1.1e1.2. The water injection rate is defined as the ratio of
Fig. 3 e Functional relationship between inhibition degree