## Program of optimization of engine parameters |

**MULTIPARAMETRIC OPTIMIZATION**

__ At the solution of
exploratory problems connected with searching of rational combination at once of several
parameters of an engine, such as: a compression ratio; injection lead; diameter, number
and directivity of injector nozzles; shape of a piston bowl; swirl intensity; phases of a
valve timing, parameters of a turbocharging etc.; often it happens difficulty to create
the schedule of numerical experiment with a great many of the varied factors and to
process the results of this experiment. In this case the multiparametric optimization is a
very effective means. The searching of rational combination of the varied factors is
entrusted to a formal procedure of non-linear programming. The engineer should only
formulate correctly a problem of optimum searching and analyze the obtained solution. __

__Goal function:__

Parameters
of efficiency of an engine or its separate processes can be included in a goal function

*Z _{j }= Z_{j} (X_{k})*. The finding of an extremum of a goal function is a problem of optimization.

__Vector of explanatory variables:__

The vector of
explanatory variables *X _{k }*is a set of design data
of an engine. At the expense of selection of value of these data is planned to achieve an
extremum of a goal function.

__Restrictions:__

As
a rule at a searching of optimum combination of engine design data it is necessary to
monitor its thermal and mechanical tensions, emission level of harmful materials and other
monitoring factors which limit area of optimum searching and are the restrictions. The
restraining parameters, as well as a goal function depend on explanatory variables *Y _{i}
= Y_{i }(X_{k})*.

The analytical relation between a goal function both restrictions on the one hand and vector of explanatory variables on the other hand does not exist, therefore for their calculation the mathematical model of a combine engine is used.

Thus, the problem of optimization of
an engine is reduced to a problem of non-linear programming, i.e. to a problem of
searching of an optimum of a function *Z _{j}
(X_{k})* at presence of limitations:

The presence of restrictions essentially complicates a solution of optimization problems, therefore it is expedient to reduce a problem of conditional optimization to a problem of non-conditional optimization, the algorithms for which much better designed. Method of penal functions is an effective mode to take into account of restrictions. The essence of a method is, that at violation of restriction to a minimized goal function the penalty is added. The penalty will increase in accordance with magnification of violation of restriction.

*Library of algorithms of software DIESEL-2/4t.*

For searching an extremum of
function of many variables the well known algorithms of nonlinear programming are used.
There are 14 methods included in the library of the program:

- "on-coordinates descent" method;

- "deformable polyhedron" method by Nelder and Mead;

- Rosenbrok method;

- Powell method;

- "quickest descent" method;

- "heavy ball" method;

- Flatcher - Reeves method;

- Flatcher - Powell method;

- Pearson method;

- "Monte-Carlo" method; etc.

The great many of methods is necessary for checkout of the obtained solutions. If the solutions obtained by different methods are similar, there is greater reliance that the obtained solution is really optimal.

The program of optimization allows to user to formulate problems of optimization: to choose the goal function, to specify a set of restrictions and their limiting values, to nominate the explanatory variables and their fields of acceptable values.

Usage of the optimization program is especially effective at solving the problems of engine boosting, at development of new constructions, and also at modernization directed on decrease of fuel consumption and emission of harmful materials.

The example of usage of the optimization is represented in
site: Multiparametric optimization of a medium-speed marine diesel at increase its capacity. |

If the problem of optimization any of process can be formulated as bivariate (number of explanatory variables equally to two), for a solution of such problem it is expedient to use a means of scanning. The possibility of visual pictorial map of a goal function and restrictions at once as function of two arguments helps better to interpret quantitative regularities of happening processes and to accept an optimum solution.

**Example:** Display of scanning results
in the 3-D diagram:

Two-stroke diesel engine capacity "Ne" as a function of compression ratio
(horizontal) and angle of a lead of injection (perpendicular).

**Example:** Display of scanning
results in the families of isolines:

Curves of diesel capacity "Ne" and maximum cylinder pressure
"Pz"

in co-ordinates of compression ratio (horizontal) and injection lead
(vertical).

Notations:

*b* is Ne=390 kW; *d *is Ne=395 kW;
*e* is Ne=400 kW; *f* is
Ne=405 kW;

*g* is Pz=100 bar; *i* is
Pz=140 bar; *h* is Pz=120 bar;
*j* is Pz=160 bar.

Use of the apparatus of scanning allows to find quickly the effective decisions at operational development of working process of engines.