Selvakumar Ulaganathan

Performance study of gradient-enhanced Kriging

Abstract The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Kriging-based surrogate models are popular for approximating deterministic computer models. In this work, the performance of Kriging is investigated when gradient information is introduced for the approximation of computationally expensive black-box simulations. This approach, known as gradient-enhanced Kriging, is applied to various benchmark functions of varying dimensionality (2D-20D). As expected, results from the benchmark problems show that additional gradient information can significantly enhance the accuracy of Kriging. Gradient-enhanced Kriging provides a better approximation even when gradient information is only partially available. Further comparison between gradient-enhanced Kriging and an alternative formulation of gradient-enhanced Kriging, called indirect gradient-enhanced Kriging, highlights various advantages of directly employing gradient information, such as improved surrogate model accuracy, better conditioning of the correlation matrix, etc. Finally, gradient-enhanced Kriging is used to model 6- and 10-variable fluid–structure interaction problems from bio-mechanics to identify the arterial wall’s stiffness.

A matlab toolbox for kriging metamodelling

Metamodelling offers an efficient way to imitate the behaviour of computationally expensive simulators. Kriging based metamodels are popular in approximating computation-intensive simulations of deterministic nature. Irrespective of the existence of various variants of Kriging in the literature, only a handful of Kriging implementations are publicly available and most, if not all, free libraries only provide the standard Kriging metamodel. ooDACE toolbox offers a robust, flexible and easily extendable framework where various Kriging variants are implemented in an object-oriented fashion under a single platform. This paper presents an incremental update of the ooDACE toolbox introducing an implementation of Gradient Enhanced Kriging which has been tested and validated on several engineering problems.

On the use of gradients in kriging surrogate models

The use of Kriging surrogate models has become popular in approximating computation-intensive deterministic computer models. In this work, the effect of enhancing Kriging surrogate models with a (partial) set of gradients is investigated. While, intuitively, gradient information is useful to enhance prediction accuracy, another motivation behind this work is to see whether it is worth including the gradients versus their computation time. Test results of two analytical functions and a fluid-structure interaction (FSI) problem from bio-mechanics show that this approach, known as Gradient Enhanced Kriging (GEK), can significantly enhance the accuracy of Kriging models even when the gradient data is only partially available.

Building accurate radio environment maps from multi-fidelity spectrum sensing data

In cognitive wireless networks, active monitoring of the wireless environment is often performed through advanced spectrum sensing and network sniffing. This leads to a set of spatially distributed measurements which are collected from different sensing devices. Nowadays, several interpolation methods (e.g., Kriging) are available and can be used to combine these measurements into a single globally accurate radio environment map that covers a certain geographical area. However, the calibration of multi-fidelity measurements from heterogeneous sensing devices, and the integration into a map is a challenging problem. In this paper, the auto-regressive co-Kriging model is proposed as a novel solution. The algorithm is applied to model measurements which are collected in a heterogeneous wireless testbed environment, and the effectiveness of the new methodology is validated.

Cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging

Reliable yet fast surrogate models are indispensable in the design of contemporary antenna structures. Data-driven models, e.g., based on Gaussian Processes or support-vector regression, offer sufficient flexibility and speed, however, their setup cost is large and grows very quickly with the dimensionality of the design space. In this paper, we propose cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging. In our approach, the training data set contains, apart from the EM-simulation responses of the structure at hand, also derivative data at the respective training locations obtained at little extra cost using adjoint sensitivity techniques. We demonstrate that introduction of the derivative information into the model allows for considerable reduction of the model setup cost (in terms of the number of training points required) without compromising its predictive power. The Gradient-Enhanced Kriging technique is illustrated using a dielectric resonator antenna structure. Comparison with conventional Kriging interpolation is also provided.

Surrogate modeling based cognitive decision engine for optimization of WLAN performance

Due to the rapid growth of wireless networks and the dearth of the electromagnetic spectrum, more interference is imposed to the wireless terminals which constrains their performance. In order to mitigate such performance degradation, this paper proposes a novel experimentally verified surrogate model based cognitive decision engine which aims at performance optimization of IEEE 802.11 links. The surrogate model takes the current state and configuration of the network as input and makes a prediction of the QoS parameter that would assist the decision engine to steer the network towards the optimal configuration. The decision engine was applied in two realistic interference scenarios where in both cases, utilization of the cognitive decision engine significantly outperformed the case where the decision engine was not deployed.

A hybrid sequential sampling based metamodelling approach for high dimensional problems

High Dimensional Model Representation (HDMR) offers efficient ways to approximate computation-intensive high- dimensional black-box functions. The distinctive nature of HDMR allows a high-dimensional problem to be decomposed into a low-dimensional function or a combination of various low-dimensional functions, thus making it more attractive than other popular metamodelling approaches such as Kriging, Radial basis function, etc. However, the computational cost of HDMR is still a bottleneck for high-dimensional problems. In this work, a hybrid sequential sampling based Kriging metamodelling technique is integrated with HDMR to improve the computational efficiency of HDMR for high-dimensional problems. The performance of the proposed metamodelling approach for high-dimensional problems is validated with various benchmark mathematical problems of a wide scope of dimensionalities.

Fast design optimization of UWB antenna with WLAN band-notch

In this paper, a methodology for rapid design optimization of an ultra-wideband (UWB) monopole antenna with a lower WLAN band-notch is presented. The band-notch is realized using an open loop resonator implemented in the radiation patch of the antenna. Design optimization is a two stage process, with the first stage focused on the design of the antenna itself, and the second stage aiming at identification of the appropriate dimensions of the resonator with the purpose of allocating the band-notch in the desired frequency range. Both optimization stages are realized using surrogate-based optimization involving variable-fidelity electromagnetic (EM) simulation models as well as an additive response correction (first stage), and sequential approximate optimization (second stage). The final antenna design is obtained at the CPU cost corresponding to only 23 high-fidelity EM antenna simulations.

Surrogate Models for Aerodynamic Shape Optimisation

The main challenges in full-scale aerospace systems development are related to the level of our understanding with respect to the systems behaviour. Computational modelling, through high-fidelity simulations, provides a viable approach towards efficient implementation of the design specifications and enhancing our understanding of the system’s response. Although high-fidelity modelling provides valuable information the associated computational cost restricts its applicability to full-scaled systems. This chapter presents a Computational Fluid Dynamics optimisation strategy based on surrogate modelling for obtaining high-fidelity predictions of aerodynamic forces and aerodynamic efficiency. An Aerodynamic Shape Optimisation problem is formulated and solved using Genetic Algorithm with surrogate models in the place of actual computational fluid dynamics algorithms. Ordinary Kriging approach and Hammersley Sequence Sampling plan are used to construct the surrogate models.