Program of optimization of engine parameters

d42gs_an.gif (7195 bytes)
prevgray.gif (1301 bytes) home.gif (1299 bytes) russian.gif (1294 bytes) nextgray.gif (1360 bytes)

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
Zj = Zj (Xk). The finding of an extremum of a goal function is a problem of optimization.

Vector of explanatory variables:

    The vector of explanatory variables Xk 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 Yi = Yi (Xk).

     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 Zj (Xk) at presence of limitations: Yi min < Yi (Xk) < Y i max

   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.

push.gif (233 bytes)

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

 

SCANNING

   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).


opt_3d.gif (7320 bytes)

 

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.

 

prevgray.gif (1301 bytes) home.gif (1299 bytes) e-mail.gif (1629 bytes) nextgray.gif (1360 bytes)