Surrogate Modeling
Surrogate Modeling
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Surrogate models are computationally cheap approximations that mimic the behavior of complex numerical models. Surrogate models can also be used to replicate the behavior of a real engineering systems, this can be done by collecting experimental data from the system.
Such models can be used for different purposes such as:
Uncertainty propagation in mechanical systems
Computationally cheap optimization
Simulation of real life data
Some of the examples that I worked on are shown below. The polynomial chaos expansion (PCE) method was used to develop the surrogate models.
Computationally cheap optimization of a tmd system
Computationally cheap optimization of a tmd system
A 10 floors shear building is considered. The building is to be fitted with a tuned mass damper (TMD) to minimize the effects of earthquake vibrations. Both the mass and the stiffness of the floors can vary between pre specified ranges. The TMD properties can vary too (stiffness and damping).
A dual PCE is fitted to estimate the response of the structure to El Centro earthquake. The response is the displacement of the top floor over the duration of the earthquake. 1000 simulations are used to train the system. The response obtained by the surrogate and from the finite elements analysis fit very well when evaluating a new simulation not belonging to the training set.
The objective function corresponds to the maximum displacement value. A genetic algorithm was used to optimize it. In the table below the values of the optimal properties of the damper and the objective function value are compared between the one obtained using the surrogate models and the ones obtained using a finite element analysis.
Surrogate Modeling: Shear walls performance preditction using experimental data
Surrogate Modeling: Shear walls performance preditction using experimental data
In this example, data coming from a database of shear walls is used. The data contains information about the dimensions of the walls, steel reinforcements properties and the strength of the wall, measured experimentally. Hence the output in this set of data is the wall strength and the other variables form the inputs.
The PCE is used over two stages:
Clustering: the set of walls is partitioned using the PCE into different clusters based on their properties
Surrogate modelling: for each set a PCE function is obtained
150 walls are used and they were separated into 3 classes. The obtained PCE model had an error of 10%.
The PCE function can then be used to predict the strength of a new wall that is not originally in the training database.
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