Best practice in metamodeling for data derived from civil engineering application
Maria Steiner, Tom Lahmer
Bauhaus-Universitaet Weimar, Germany
Frequent civil engineering problems exist that lead to a high computation time for
determining the optimal deployment of construction materials. Application of mathematical
models is useful in reducing the costs and thus in keeping the computation time low without
incurring a loss in model quality. With response surface methods, also called metamodels, calculations
and forecasts can be completed faster because of a reduced amount of numerical or
experimental data required. The aim of this contribution is at first to analyze the applicability of
metamodels to civil engineering problems where the data come either from mathematical models
or experimental tests, in particular in the field of structural health monitoring. Furthermore,
it seeks to illustrate which metamodel is the best for various specific application fields.
In the literature two different types of metamodels can be found, which differ significantly
in their properties and thus in their applicability. At first, deterministic methods are mentioned.
In this area Polynomial Regression [1, 2], Radial Basis Function Interpolation , and
Moving Least Squares  are specific examples. On the other hand, the Stochastic Process
Model (Kriging) and its variations [5, 6] are part of the second group of models, the stochastic
methods. Furthermore, it should be noted that there is a distinction between interpolation and
regression possible. For noisy measurement data regressive methods can be more advantageous
because of a possible smoothing. With respect to the decision which metamodel is to be used,
the different computational effort, flexibility, predictive ability, and robustness of all available
models should be observed.
To infer to a general applicability for response surface methods used in civil engineering, the
models are analyzed with several examples. As one of them a variance based sensitivity analysis
 of a model representing a triaxial soil test is considered. In order to receive the data, various
finite element methods are used. A large amount of data is required to determine sufficiently
accurate and robust values; therefore, the computation time magnifies with increasing number
of input parameters. Even for a comparatively simple material model, Mohr Coulomb, with
five parameters a computation time of often more then 20 hours is necessary for a normal
computation power. With application of metamodels, for example linear regression, the cost
can be extremely reduced and it leads to a similar solution. However, there are some open
points that need to be discussed: The necessary amount of the data to produce the various metamodels, the trade-off between model complexity and accuracy, and the criteria for optimal
model selection. The decision of which method is used is coupled to these criteria and may vary
depending on the situation.
In order to provide a general overview, it is necessary to classify the engineering models
based on their underlying partial differential equations. There is a separation in elliptic,
parabolic and hyperbolic equations possible, which is related to the different engineering fields
of the problems. It is obvious that for example static systems and problems related to the heat
equation differ visibly. Thus it is probable that also different metamodels are optimal for each
application field. For testing purposes, fundamental solutions, which exist in each equation
field, can be used. Particularly in the simplified one dimensional case they provide explicit and
simple to evaluate functions.
Furthermore, it may happen that no single model emerges as the optimal method for some
engineering tasks. In this case it is necessary to discuss a combination of several response
surface methods. In conclusion, it is possible to increase the use of metamodels by providing
an overview of the relation between these models and the corresponding classes of civil
engineering problems and thereby improve the construction of engineering models.
ISSN 1611 - 4086 | © IKM 2015