Mechanical MNIST: A benchmark dataset for mechanical metamodels

Metamodels, or models of models, map defined model inputs to defined model outputs. Typically, metamodels are constructed by generating a dataset through sampling a direct model and training a machine learning algorithm to predict a limited number of model outputs from varying model inputs. When metamodels are constructed to be computationally cheap, they are an invaluable tool for applications ranging from topology optimization, to uncertainty quantification, to multi-scale simulation. By nature, a given metamodel will be tailored to a specific dataset. However, the most pragmatic metamodel type and structure will often be general to larger classes of problems. At present, the most pragmatic metamodel selection for dealing with mechanical data has not been thoroughly explored. Drawing inspiration from the benchmark datasets available to the computer vision research community, we introduce a benchmark data set (Mechanical MNIST) for constructing metamodels of heterogeneous material undergoing large deformation. We then show examples of how our benchmark dataset can be used, and establish baseline metamodel performance. Because our dataset is readily available, it will enable the direct quantitative comparison between different metamodeling approaches in a pragmatic manner. We anticipate that it will enable the broader community of researchers to develop improved metamodeling techniques for mechanical data that will surpass the baseline performance that we show here.Accepted manuscrip

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

Automatic surrogate model type selection during the optimization of expensive black-box problems

The use of Surrogate Based Optimization (SBO) has become commonplace for optimizing expensive black-box simulation codes. A popular SBO method is the Efficient Global Optimization (EGO) approach. However, the performance of SBO methods critically depends on the quality of the guiding surrogate. In EGO the surrogate type is usually fixed to Kriging even though this may not be optimal for all problems. In this paper the authors propose to extend the well-known EGO method with an automatic surrogate model type selection framework that is able to dynamically select the best model type (including hybrid ensembles) depending on the data available so far. Hence, the expected improvement criterion will always be based on the best approximation available at each step of the optimization process. The approach is demonstrated on a structural optimization problem, i.e., reducing the stress on a truss-like structure. Results show that the proposed algorithm consequently finds better optimums than traditional kriging-based infill optimization

Computational Intelligence and Its Applications in Uncertainty-Based Design Optimization

The large computational cost, the curse of dimensionality and the multidisciplinary nature are known as the main challenges in dealing with real-world engineering optimization problems. The consideration of inevitable uncertainties in such problems will exacerbate mentioned difficulties as much as possible. Therefore, the computational intelligence methods (also known as surrogate-models or metamodels, which are computationally cheaper approximations of the true expensive function) have been considered as powerful paradigms to overcome or at least to alleviate the mentioned issues over the last three decades. This chapter presents an extensive survey on surrogate-assisted optimization (SAO) methods. The main focus areas are the working styles of surrogate-models and the management of the metamodels during the optimization process. In addition, challenges and future trends of this field of study are introduced. Then, a comparison study will be carried out by employing a novel evolution control strategies (ECS) and recently developed efficient global optimization (EGO) method in the framework of uncertainty-based design optimization (UDO). To conclude, some open research questions in this area are discussed

Adaptive active subspace-based metamodeling for high-dimensional reliability analysis

To address the challenges of reliability analysis in high-dimensional probability spaces, this paper proposes a new metamodeling method that couples active subspace, heteroscedastic Gaussian process, and active learning. The active subspace is leveraged to identify low-dimensional salient features of a high-dimensional computational model. A surrogate computational model is built in the low-dimensional feature space by a heteroscedastic Gaussian process. Active learning adaptively guides the surrogate model training toward the critical region that significantly contributes to the failure probability. A critical trait of the proposed method is that the three main ingredients-active subspace, heteroscedastic Gaussian process, and active learning-are coupled to adaptively optimize the feature space mapping in conjunction with the surrogate modeling. This coupling empowers the proposed method to accurately solve nontrivial high-dimensional reliability problems via low-dimensional surrogate modeling. Finally, numerical examples of a high-dimensional nonlinear function and structural engineering applications are investigated to verify the performance of the proposed method

MULTI-DIMENSIONAL SURROGATE BASED AFT FORM OPTIMIZATION OF SHIPS USING HIGH FIDELITY SOLVERS

Surrogate (metamodel) based optimization has numerous potential applications in the field of naval architecture. It is aimed here to establish a methodology for the aft form optimization for minimum viscous resistance, thus the present study is focused on the aft form where the viscous effects become dominant. It is necessary to solve this problem within acceptable time span from practical naval architectural point of view which requires metamodeling techniques currently under investigation. Accordingly, the present paper investigates the metamodeling ability of the Kriging interpolation and attempts to explore its capabilities and limitations in the aft form optimization from viscous resistance point of view. As metamodeling techniques become more widely used, their constraints are more apparent. Especially in highly nonlinear design spaces, the effect of dimensionality should be taken into consideration. Taking all those factors into account, the present paper is to examine the capabilities of Kriging and to establish the learning performance in terms of RMS error, correlation coefficient and required number of training points according to selected optimization algorithm for multidimensional ship design problem. The results show that, at least 5% reduction in viscous pressure drag can be attained by the present optimization methodology

MODEL-BASED PREDICTIVE ANALYTICS FOR ADDITIVE AND SMART MANUFACTURING

Qualification and certification for additive and smart manufacturing systems can be uncertain and very costly. Using available historical data can mitigate some costs of producing and testing sample parts. However, use of such data lacks the flexibility to represent specific new problems which decreases predictive accuracy and efficiency. To address these compelling needs, in this dissertation modeling techniques are introduced that can proactively estimate results expected from additive and smart manufacturing processes swiftly and with practical levels of accuracy and reliability. More specifically, this research addresses the current challenges and limitations posed by use of available data and the high costs of new data by tailoring statistics-based metamodeling techniques to enable affordable prediction of these systems. The result is an integrated approach to customize and build predictive metamodels for the unique features of additive and smart manufacturing systems. This integrated approach is composed of five main parts that cover the broad spectrum of requirements. A domain-driven metamodeling approach uses physics-based knowledge to optimally select the most appropriate metamodeling algorithm without reliance upon statistical data. A maximum predictive error updating method iteratively improves predictability from a given dataset. A grey-box metamodeling approach combines statistics-based black-box and physics-based white-box models to significantly increase predictive accuracy with less expensive data overall. To improve computational efficiency for large datasets, a dynamic metamodeling method modifies the traditional Kriging technique to improve its efficiency and predictability for smart manufacturing systems. Finally, a super-metamodeling method optimizes results regardless of problem conditions by avoiding the challenge with selecting the most appropriate metamodeling algorithm. To realize the benefits of all five approaches, an integrated metamodeling process was developed and implemented into a tool package to systematically select the suitable algorithm, sampling method, and combination of models. All the functions of this tool package were validated and demonstrated by the use of two empirical datasets from additive manufacturing processes