Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method

Wang, Linpeng; Dai, Yuting; Yang, Chao

doi:10.1155/2017/2571253

Cited by 3 publications

(3 citation statements)

References 31 publications

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“…ρðw, x 1 ðkÞÞ and zðw, x 1 ðkÞÞ correspond to the two aspects, respectively. In addition, when the pitching motion with a high angle of attack is carried out at a low Mach number, the separation and reattachment between the flow and wing surface will be delayed, which will bring additional aerodynamic force called "overshoot" [25,53]. Here, the influence of "overshoot" is represented by z lma ðw, x 1 ðkÞÞ.…”

Section: Nonlinear Correction Model Based On Flow Separationmentioning

confidence: 99%

Nonlinear Unsteady Aerodynamics Reduced Order Model of Airfoils Based on Algorithm Fusion and Multifidelity Framework

Shi

Wan

et al. 2021

International Journal of Aerospace Engineering

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A reduced order modeling method based on algorithm fusion and multifidelity framework for nonlinear unsteady aerodynamics is proposed to obtain a low-cost and high-precision unsteady aerodynamic model. This method integrates the traditional algorithm, intelligent algorithm, and multifidelity data fusion algorithm. In this method, the traditional algorithm is based on separated flow theory, the intelligent algorithm refers to the nonlinear autoregressive (NARX) method, and the multifidelity data fusion algorithm uses different fidelity data for aerodynamic modeling, which can shorten the time cost of data acquisition. In the process of modeling, firstly, a multifidelity model with NARX description provides a general intelligent algorithm framework for unsteady aerodynamics. Then, based on the separated flow theory, the correction equation from low-fidelity model to high-fidelity result is constructed, and the cuckoo algorithm based on chaos optimization is used to identify the parameters. In order to verify the effectiveness of the method, an unsteady aerodynamic model of NACA0012 airfoil is established. Three kinds of data with low, medium, and high fidelity are used for modeling. The low-fidelity and medium-fidelity data is obtained from the CFD-Euler solver and CFD-RANS solver, respectively, while the high-fidelity data comes from the experimental results. Then, the model is established, and its prediction of unsteady aerodynamic coefficients is in good agreement with the CFD results and the experimental data. After that, the model is applied to a two-dimensional aeroelastic system, and the bifurcation and limit cycle response analysis are compared with the experimental results, which further shows that the model can accurately capture the main flow characteristics in the flow range of low speed and high angle of attack. In addition, the convergence of the model is studied; the accuracy and generalization ability as well as applicability scope of the model are compared with other aerodynamic models and finally discussed.

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Section: Nonlinear Correction Model Based On Flow Separationmentioning

confidence: 99%

Nonlinear Unsteady Aerodynamics Reduced Order Model of Airfoils Based on Algorithm Fusion and Multifidelity Framework

Shi

Wan

et al. 2021

International Journal of Aerospace Engineering

Self Cite

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“…Hence, a TP might be much closer to the current system state than expected from the 'best estimate' model parameters [24]. Only recently, this link between parametric uncertainty and bifurcations has emerged as a sub-area within the theory of nonlinear dynamics [25][26][27][28], with methods being developed for applications in fields including aerospace engineering [29,30] and biomedical science [31]. Studies in the climate domain have been limited; however [16,21,22] show the possibility of AMOC collapse in certain parameter regimes of simple and intermediate-complexity climate models.…”

Section: Introductionmentioning

confidence: 99%

Assessing the impact of parametric uncertainty on tipping points of the Atlantic meridional overturning circulation

Lux

Ashwin²,

Wood³

et al. 2022

Environ. Res. Lett.

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Various elements of the Earth system have the potential to undergo critical transitions to a radically different state, under sustained changes to climate forcing. The Atlantic meridional overturning circulation (AMOC) is of particular importance for North Atlantic heat transport and is thought to be potentially at risk of passing such a tipping point (TP). In climate models, the location and likelihood of such TPs depends on model parameters that may be poorly known. Reducing this parametric uncertainty is important to understand the likelihood of tipping behaviour. In this letter, we develop estimates for parametric uncertainty in a simple model of AMOC tipping, using a Bayesian inversion technique. When applied using synthetic (‘perfect model’) salinity timeseries data, the technique drastically reduces the uncertainty in model parameters, compared to prior estimates derived from previous literature, resulting in tighter constraints on the AMOC TPs. To visualise the impact of parametric uncertainty on TPs, we extend classical tipping diagrams by showing probabilistic bifurcation curves according to the inferred distribution of the model parameter, allowing the uncertain locations of TPs along the probabilistic bifurcation curves to be highlighted. Our results show that suitable palaeo-proxy timeseries may contain enough information to assess the likely position of AMOC (and potentially other Earth system) TPs, even in cases where no tipping occurred during the period of the proxy data.

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“…In [23], polynomial chaos based approaches have been developed to generate probabilistic fixed point stability diagrams in the context of heart rhythm dynamics for given probability distributions. In [31], the authors analyse how uncertainty in aerodynamic and structure parameters affects the bifurcation position.…”

Section: Introductionmentioning

confidence: 99%

Uniting Parametric Uncertainty and Tipping Diagrams

Lux¹,

Ashwin²,

Wood³

et al. 2021

Preprint

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Various subsystems of the Earth system may undergo critical transitions by passing a socalled tipping point, under sustained changes to forcing. For example, the Atlantic Meridional Overturning Circulation (AMOC) is of particular importance for North Atlantic heat transport and is thought to be potentially at risk of tipping. Given a model of such a subsystem that accurately includes the relevant physical processes, whether tipping occurs or not, will depend on model parameters that typically are uncertain. Reducing this parametric uncertainty is important to understand the likelihood of tipping behavior being present in the system and possible tipping locations. In this letter, we develop improved estimates for the parametric uncertainty by inferring probability distributions for the model parameters based on physical constraints and by using a Bayesian inversion technique. To visualize the impact of parametric uncertainty, we extend classical tipping diagrams by visualizing probabilistic bifurcation curves according to the inferred distribution of the model parameter. Furthermore, we highlight the uncertain locations of tipping points along the probabilistic bifurcation curves. We showcase our probabilistic visualizations of the tipping behavior using a simple box-model of the AMOC, the Stommel-Cessi model [5].

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Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method

Cited by 3 publications

References 31 publications

Nonlinear Unsteady Aerodynamics Reduced Order Model of Airfoils Based on Algorithm Fusion and Multifidelity Framework

Nonlinear Unsteady Aerodynamics Reduced Order Model of Airfoils Based on Algorithm Fusion and Multifidelity Framework

Assessing the impact of parametric uncertainty on tipping points of the Atlantic meridional overturning circulation

Uniting Parametric Uncertainty and Tipping Diagrams

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