Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations

2015 ◽  
Vol 520 ◽  
pp. 101-122 ◽  
Author(s):  
Mohammad Mahdi Rajabi ◽  
Behzad Ataie-Ashtiani ◽  
Craig T. Simmons
Keyword(s):  
Sensitivity Analysis ◽  
Seawater Intrusion ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Polynomial Chaos Expansions

Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging

2019 ◽  
Vol 37 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Xiaosong Du ◽  
Leifur Leifsson
Keyword(s):  
Polynomial Chaos ◽  
State Of The Art ◽  
Uncertainty Propagation ◽  
Kriging Model ◽  
Probability Of Detection ◽  
Kriging Interpolation ◽  
Benchmark Problems ◽  
Content Type ◽  
Order Of Magnitude ◽  
Polynomial Chaos Expansions

Purpose Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models. Design/methodology/approach In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels. Findings To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent. Originality/value The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

scholarly journals Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Gustavo Tapia ◽  
Wayne King ◽  
Luke Johnson ◽  
Raymundo Arroyave ◽  
Ibrahim Karaman ◽  
...  
Keyword(s):  
Additive Manufacturing ◽  
Computational Models ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Model Parameters ◽  
Powder Bed Fusion ◽  
Multiple Sources ◽  
Powder Bed ◽  
Model Code ◽  
Polynomial Chaos Expansions

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

System Uncertainty Effects on the Wave Frequency Response Of Floating Vessels Based on Polynomial Chaos Expansion

2021 ◽  
Author(s):  
Gowtham Radhakrishnan ◽  
Xu Han ◽  
Svein Sævik ◽  
Zhen Gao ◽  
Bernt Johan Leira
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Polynomial Chaos ◽  
Response Spectrum ◽  
Uncertainty Propagation ◽  
Wave Spectrum ◽  
Frequency Domain Analysis ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Polynomial Coefficients

Abstract From a mathematical viewpoint, the frequency domain analysis of vessel motion responses due to wave actions incorporates the integration of system dynamics idealized in terms of response amplitude operators (RAOs) for 6 DOF rigid body motions and an input wave spectrum to yield the response spectrum. Various quantities of interest can be deduced from the response spectrum and further used for decision support in marine operations, extreme value and fatigue analysis. The variation of such quantities, owing to the uncertainties associated with the vessel system parameters, can be quantified by performing uncertainty propagation (UP) and consequent sensitivity analysis (SA). This study, emphasizes and proposes a computational-efficient way of assessing the sensitivity of the system model output with respect to the uncertainties residing in the input parameters by operating on a surrogate model representation. In this respect, the global sensitivity analysis is effectively carried out by deploying an efficient non-intrusive polynomial chaos expansion (PCE) surrogate model built using a point collocation strategy. Successively, the coherent and effective Sobol’ indices are obtained from the analytical decomposition of the polynomial coefficients. The indices, eventually, are employed to quantitatively gauge the effects of input uncertainties on the output 6 DOF vessel responses.

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