Adaptive multi-fidelity sparse polynomial chaos-Kriging metamodeling for global approximation of aerodynamic data

A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System

“…This is beyond the scope of the present study. Yet, research is envisaged to combine the FMMs-and Kriging-based iterative exploration framework here proposed with state-of-the-art stochastic simulation techniques for the accurate and precise evaluation of the PSSs functional failure probability (e.g., Importance sampling-IS, Markov Chain Monte Carlo-MCMC, Subset Simulation-SS, Line Sampling-LS), with emphasis on: i) abrupt, multi-modal, possibly disconnected system state-spaces to be probed (like the one of interest in the present article) and ii) those challenging cases where the size of the critical region is quite small and its location is far from the nominal design [16,77,[93][94][95][96]98].…”

“…[94] and [95] develop an active learning method combining Kriging metamodels (ALK) and Importance Sampling (IS) to analyze systems with very small failure probabilities and multiple failure regions: in particular, evolutionary algorithms from the field of multimodal optimization are used to find all the local and global most probable points on the (surrogate) failure boundaries at each iteration of the metamodel training process. [96] presents an Adaptive Multi-Fidelity sparse Polynomial Chaos-Kriging (AMF-PCK) metamodeling for the global approximation of aerodynamic data, which proves useful for the efficient uncertainty analysis and optimization of expensive multimodal engineering problems. In this approach, low-fidelity computations are used to build the PCK model as a trend for the high-fidelity function and to capture the relative importance of sparse polynomial bases selected by Least Angle Regression (LAR).…”

“…A large amount of works has been devoted, in the last few years, to the intelligent, iterative improvement of the AK-MCS algorithm. Only few of the most relevant techniques are listed hereafter: the Adaptive Kriging-Importance Sampling (AK-IS) [25]; the Meta Adaptive Kriging-Importance Sampling 2 (MetaAK-IS 2 ) [14], which combines AK-IS and Meta-IS [22]; the Active learning and Kriging-based SYStem reliability method (AK-SYS) [27]; the Adaptive Kriging-Line Sampling (AK-LS) [53]; the AK-Subset Simulation (AK-SS) [39] and the AK-Subset Simulation-Importance Sampling (AK-SS-IS) [82]; the Polynomial Chaos Kriging (PCK) [77]; the AK-MCSi algorithm, employing sequential MCS and multipoint enrichment techniques to allow parallelization [50]; the Active Learning Kriging-Kernel Density Estimation-Importance Sampling (ALK-KDE-IS) [93]; the ALK-Evolutionary Multimodal Optimization-Importance Sampling (ALK-EMO-IS) [94] and the ALK-Multimodal Adaptive Importance Sampling-Truncated Candidate Region (ALK-MAIS-TCR) [95]; the Multifidelity Efficient Global Reliability Analysis (MfEGRA) method [16]; the Adaptive Multi-Fidelity sparse Polynomial Chaos Kriging (AMF-PCK) technique [96] and the Adaptive Kriging-based Directional Sampling (AK-DS) [98]. The objective of all the methods listed above is the efficient propagation of uncertainties, physically described by different probability distributions, through the (expensive) system models, for the accurate and precise estimation of (small) failure probabilities.…”

High-Accuracy and Fast Calculation Framework for Berthing Collision Force of Docks Based on Surrogate Models

“…The PCK method combines the merits of Kriging and polynomial chaotic expansion, enabling the capture of both global behavior and local changes in computational models. The surrogate model established by Zhao et al [27] using PCK exhibits the high flexibility and the strong nonlinear modeling ability, making it an optimal choice. Specifically, PCK consists of a general-purpose Kriging model whose trend part is a sparse set of orthogonal polynomials:…”

Assessment of Multi-fidelity Surrogate Models for High-Altitude Propeller Optimization

“…The use of multi-fidelity methods has gained significant interest in the last years, also in the field of aeronautics. Different methods have been proposed and demonstrated in engineering applications ranging from aerodynamic optimization of airfoils [13,14], to optimization of an axial flow compressor [15], wing optimization [16] and also optimization of a high-altitude propeller [17].…”