Environmental Engineering Reference
In-Depth Information
7
Optimisation of non-destructive testing
7.1 General
Optimisation is the selection of the best solution. Optimisation theory
includes fundamental results and numerical methods which can be used to
find the best option among many possible alternatives without exhaustive
search and comparison.
In order to use the results and computational procedures of optimisation
theory in practice, it is first necessary to formulate the considered problem
in mathematical language, i.e. construct a mathematical model of the
object to be optimised. The mathematical model is a more or less complete
mathematical description of the process or phenomenon.
In most real situations, an exhaustive mathematical representation of the
optimised system with all interactions of all its parts, interactions with the
outside world and all the goals of functioning of the system is difficult or
impossible. Therefore, in constructing a mathematical model it is necessary
to separate and consider further only the most important aspects of the
object to enable its mathematical description as well as the subsequent
solution of the given mathematical problem. In this case, the factors ignored
in the mathematical model should not significantly affect the final result
of optimisation. Thus, the optimisation is a complex and demanding task,
requiring from the researcher in-depth knowledge in the relevant region,
expertise, intuition and critical analysis of the results.
Despite the fact that there is no general recipe for constructing
mathematical models of optimisation, the process of mathematical modelling
can be divided into the following main stages.
Definition of the boundaries of the optimisation object
The necessity of this stage is dictated by the fact that it is not possible
to take into account and describe in detail all sides of most real
systems. Highlighting the main variables, parameters and limitations, the
system should be regarded approximately as some isolated part of the real
world and to its internal structure should be simplified..
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