STOCHASTIC OPTIMIZATION OF PARAMETERS AND CONTROL
LAWS OF THE AIRCRAFT GAS-TURBINE ENGINES – A STEP TO A ROBUST DESIGN
ISIP 2001, Nagana, Japan, 2001.
This paper is devoted to the problem of complex engineering systems robust
designing. As applied to the aircraft gas-turbine engines it presents
the main theses of stochastic approach to the multimeasure optimization
of parameters and control laws. This approach allows us to optimize the
engines taking into account the technological deflections which occur
in the process of manufacturing of engine’s components as well as engine’s
control deflections.
In the paper an aircraft gas-turbine engine is being analyzed as a stochastic
system, which has a great number of uncertainties. It is shown that the
optimum criterion value and therefore the design quality, being obtained
with the deterministic approach, are nothing but the maximum achievable
effect, one ought to seek. The question needs to be discussed concerning
the possibility of implementation of this maximum effect. First there
is the problem of assurance of the stability of the obtained solution
under possible deflections of optimized parameters. Such deflections inevitably
take place in practice while implementing any engineering project, even
if there are used the most perfect technology levels. Secondly it is hard
to predict if one can influence either the property or the extent of solution
stability, optimizing parameters and control laws of an object being researched.
In the real-life conditions the numerical values of these uncertainties
are unknown, therefore the classic deterministic approach is not applicable
for the search of the robust solution. However there is just enough practical
experience of GTE production, which allows us to estimate the law of distribution
of these uncertainties with acceptable accuracy. Within the presented
approach we use the assumption that the distribution law is normal and
its standard deviation is known.
In the paper there are considered several types of stochastic optimization
criteria. They are the probability of assurance of the criterion value
which is not worse than a pre-defined value; the mathematical expectation
of the goal parameter value; the dispersion of the optimized parameter,
and the complex probabilistic criterion, taking into account both dispersion
and mathematical expectation. The comparative analysis of these criteria
is presented.
This paper presents some results dealing with the search of optimum control
laws of mixed flow turbofan engine for throttle operating modes. These
optimization problems have been aimed at the minimization of the specific
fuel consumption over the range of engine throttle thrust under pre-defined
flight conditions. The researches have been carried out using the mathematical
model of the engine with 2-D axial symmetrical simulation of the low pressure
compressor. The dispersions in the control laws implementation have been
taken into account, i.e. we have treated the probabilistic character of
obtained control laws.
These optimization problems have been successfully solved, and according
to their result it has been proved that it is hard to implement in practice
the deterministic solution. However the results which have been obtained
using the stochastic criteria have much better robustness than that of
the deterministic problems. The physical nature of the solution robust
features improvement is discussed in the paper.
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