Page 58 - Numerical Analysis and Modelling in Geomechanics

COMPRESSED AIR TUNNELLING 39
Therefore, the material parameter identification technique has three main
elements:

• Measurement of some responses of the system,
• Numerical modelling of the same response of the system, and
• A technique to adapt the material parameters in the numerical model by
comparing the measured and calculated responses.

In the parameter identification approach used in this study, the error function is
defined using the least squares method.

Problem formulation
The material parameters to be identified can be considered as elements of a
N
vector x≥ R . Then the optimisation problem can be formulated as finding vector
x that minimises the objective function:

(2.9)

where
M is the total number of individual measured responses which have also been
obtained as a result of the numerical simulation, N is the number of parameters to
α
be identified, F (x) is a dimensionless function defined as:

(2.10)

which measures the deviation of the computed α-th individual response, from the
α
measured response, , S is the total number of the discrete set of data points, θ is
α
the weight coefficient which determines the relative contribution of information
yielded by the α-th set of experimental data, A , B are the lower and upper limits
i
i
of the values of material parameters stipulated by physical considerations.
Genetic algorithm
Genetic algorithms (GAs) are a group of randomised methods used in function
optimisation. They offer a high probability of locating the global optimum in the
optimisation variable space for complex optimisation problems. Early
14
developments in the field of GAs are generally credited to Holland and since
then they have been successfully applied to various optimisation problems. 15
To implement a GA, the procedure starts by creating a set of binary strings (or
chromosomes) of 0s and 1s of a fixed length (the so-called initial population). In