Abstract
In the field of engineering, surrogate models are commonly used for approximating the behavior of a physical phenomenon in order to reduce the computational costs. Generally, a surrogate model is created based on a set of training data, where a typical method for the statistical design is the Latin hypercube sampling (LHS). Even though a space-filling distribution of the training data is reached, the sampling process takes no information on the underlying behavior of the physical phenomenon into account and new data cannot be sampled in the same distribution if the approximation quality is not sufficient. Therefore, in this study we present a novel adaptive sampling method based on a specific surrogate model, the least-squares support vector regression. The adaptive sampling method generates training data based on the uncertainty in local prognosis capabilities of the surrogate model - areas of higher uncertainty require more sample data. The approach offers a cost efficient calculation due to the properties of the least-squares support vector regression. The opportunities of the adaptive sampling method are proven in comparison with the LHS on different analytical examples. Furthermore, the adaptive sampling method is applied to the calculation of global sensitivity values according to Sobol, where it shows faster convergence than the LHS method. With the applications in this paper it is shown that the presented adaptive sampling method improves the estimation of global sensitivity values, hence reducing the overall computational costs visibly.
Highlights
In numerous fields in civil engineering, numerical models and physical experiments representing the reality are applied for observing physical phenomenona
After a brief review of the main surrogate modeling techniques, we address issues of adaptive sampling strategies; we present the least-squares support vector regression, which is the applied surrogate model, and introduce the novel adaptive sampling method
In the approach presented in this paper, we focus on the least-squares support vector regression (LSSVR) because it provides the basis for the investigated method with a favorable calculation of the leave-one-out cross-validation error
Summary
In numerous fields in civil engineering, numerical models and physical experiments representing the reality are applied for observing physical phenomenona. A commonly applied technique to reduce computational cost is to use data-based models, socalled surrogate models. An influence on the accuracy of the approximation has on the one hand the choice of the surrogate model and the corresponding model parameters and on the other hand the structure of the training data. This contribution deals with the second issue and especially with the challenge of adding new points to an existing sampling set. We present a novel adaptive sampling method with the aim to accelerate and improve surrogate-based sensitivity analysis. We analyze the functionality and applicability of this method and observe the impact on global sensitivity analysis
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