Performance study of multi-fidelity gradient enhanced kriging

Multi-fidelity surrogate modelling offers an efficient way to approximate computationally expensive simulations. In particular, Kriging-based surrogate models are popular for approximating deterministic data. In this work, the performance of Kriging is investigated when multi-fidelity gradient data is introduced along with multi-fidelity function data to approximate computationally expensive black-box simulations. To achieve this, the recursive CoKriging formulation is extended by incorporating multi-fidelity gradient information. This approach, denoted by Gradient-Enhanced recursive CoKriging (GECoK), is initially applied to two analytical problems. As expected, results from the analytical benchmark problems show that additional gradient information of different fidelities can significantly improve the accuracy of the Kriging model. Moreover, GECoK provides a better approximation even when the gradient information is only partially available. Further comparison between CoKriging, Gradient Enhanced Kriging, denoted by GEK, and GECoK highlights various advantages of employing single and multi-fidelity gradient data. Finally, GECoK is further applied to two real-life examples

Benchmarking of localization solutions : guidelines for the selection of evaluation points

Indoor localization solutions are key enablers for next-generation indoor navigation and track and tracing solutions. As a result, an increasing number of different localization algorithms have been proposed and evaluated in scientific literature. However, many of these publications do not accurately substantiate the used evaluation methods. In particular, many authors utilize a different number of evaluation points, but they do not (i) analyze if the number of used evaluation points is sufficient to accurately evaluate the performance of their solutions and (ii) report on the uncertainty of the published results. To remedy this, this paper evaluates the influence of the selection of evaluation points. Based on statistical parameters such as the standard error of the mean value, an estimator is defined that can be used to quantitatively analyze the impact of the number of used evaluation points on the confidence interval of the mean value of the obtained results. This estimator is used to estimate the uncertainty of the presented accuracy results, and can be used to identify if more evaluations are required. To validate the proposed estimator, two different localization algorithms are evaluated in different testbeds and using different types of technology, showing that the number of required evaluation points does indeed vary significantly depending on the evaluated solution. (C) 2017 Elsevier B.V. All rights reserved

Variable-fidelity surrogate modelling with kriging

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A linear regression based cost function for WSN localization

Localization with Wireless Sensor Networks (WSN) creates new opportunities for location-based consumer communication applications. There is a great need for cost functions of maximum likelihood localization algorithms that are not only accurate but also lack local minima. In this paper we present Linear Regression based Cost Function for Localization (LiReCoFuL), a new cost function based on regression tools that fulfills these requirements. With empirical test results on a real-life test bed, we show that our cost function outperforms the accuracy of a minimum mean square error cost function. Furthermore we show that LiReCoFuL is as accurate as relative location estimation error cost functions and has very few local extremes

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

Multiobjective global surrogate modeling, dealing with the 5-percent problem

When dealing with computationally expensive simulation codes or process measurement data, surrogate modeling methods are firmly established as facilitators for design space exploration, sensitivity analysis, visualization, prototyping and optimization. Typically the model parameter (=hyperparameter) optimization problem as part of global surrogate modeling is formulated in a single objective way. Models are generated according to a single objective (accuracy). However, this requires an engineer to determine a single accuracy target and measure upfront, which is hard to do if the behavior of the response is unknown. Likewise, the different outputs of a multi-output system are typically modeled separately by independent models. Again, a multiobjective approach would benefit the domain expert by giving information about output correlation and enabling automatic model type selection for each output dynamically. With this paper the authors attempt to increase awareness of the subtleties involved and discuss a number of solutions and applications. In particular, we present a multiobjective framework for global surrogate model generation to help tackle both problems and that is applicable in both the static and sequential design (adaptive sampling) case