Uncertainty Quantification of Aeroelastic Stability

2014 ◽  
pp. 329-356 ◽  
Author(s):  
Georgia Georgiou ◽  
Hamed Haddad Khodaparast ◽  
Jonathan E. Cooper
Keyword(s):  
Uncertainty Quantification ◽  
Random Sampling ◽  
Expansion Method ◽  
Probability Density Functions ◽  
Fuel Load ◽  
Aeroelastic Stability ◽  
Aeroelastic System ◽  
Tunnel Model ◽  
Structural Mass ◽  
Kriging Predictor

The application of uncertainty analysis for the prediction of aeroelastic stability, using probabilistic and non-probabilistic methodologies, is considered in this chapter. Initially, a background to aeroelasticity and possible instabilities, in particular “flutter,” that can occur in aircraft is given along with the consideration of why Uncertainty Quantification (UQ) is becoming an important issue to the aerospace industry. The Polynomial Chaos Expansion method and the Fuzzy Analysis for UQ are then introduced and a range of different random and quasi-random sampling techniques as well as methods for surrogate modeling are discussed. The implementation of these methods is demonstrated for the prediction of the effects that variations in the structural mass, resembling variations in the fuel load, have on the aeroelastic behavior of the Semi-Span Super-Sonic Transport wind-tunnel model (S4T). A numerical model of the aircraft is investigated using an eigenvalue analysis and a series of linear flutter analyses for a range of subsonic and supersonic speeds. It is shown how the Probability Density Functions (PDF) of the resulting critical flutter speeds can be determined efficiently using both UQ approaches and how the membership functions of the aeroelastic system outputs can be obtained accurately using a Kriging predictor.

scholarly journals Generating a Baseline Map of Surface Fuel Loading Using Stratified Random Sampling Inventory Data through Cokriging and Multiple Linear Regression Methods

2021 ◽  
Vol 13 (8) ◽  
pp. 1561
Author(s):  
Chinsu Lin ◽  
Siao-En Ma ◽  
Li-Ping Huang ◽  
Chung-I Chen ◽  
Pei-Ting Lin ◽  
...  
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Random Sampling ◽  
Fuel Load ◽  
Estimation Accuracy ◽  
Slope Aspect ◽  
Stratified Random Sampling ◽  
Inventory Data ◽  
Fuel Loading ◽  
Regression Methods

Surface fuel loading is a key factor in controlling wildfires and planning sustainable forest management. Spatially explicit maps of surface fuel loading can highlight the risks of a forest fire. Geospatial information is critical in enabling careful use of deliberate fire setting and also helps to minimize the possibility of heat conduction over forest lands. In contrast to lidar sensing and/or optical sensing based methods, an approach of integrating in-situ fuel inventory data, geospatial interpolation techniques, and multiple linear regression methods provides an alternative approach to surface fuel load estimation and mapping over mountainous forests. Using a stratified random sampling based inventory and cokriging analysis, surface fuel loading data of 120 plots distributed over four kinds of fuel types were collected in order to develop a total surface fuel loading model (lntSFL-BioTopo model) and a fine surface fuel model (lnfSFL-BioTopo model) for generating tSFL and fSFL maps. Results showed that the combination of topographic parameters such as slope, aspect, and their cross products and the fuel types such as pine stand, non-pine conifer stand, broadleaf stand, and conifer–broadleaf mixed stand was able to appropriately describe the changes in surface fuel loads over a forest with diverse terrain morphology. Based on a cross-validation method, the estimation of tSFL and fSFL of the study site had an RMSE of 3.476 tons/ha and 3.384 tons/ha, respectively. In contrast to the average loading of all inventory plots, the estimation for tSFL and fSFL had a relative error of 38% (PRMSE). The reciprocal of estimation bias of both SFL-BioTopo models tended to be an exponential growth function of the amount of surface fuel load, indicating that the estimation accuracy of the proposed method is likely to be improved with further study. In the regression modeling, a natural logarithm transformation of the surface fuel loading prevented the outcome of negative estimates and thus improved the estimation. Based on the results, this paper defined a minimum sampling unit (MSU) as the area for collecting surface fuels for interpolation using a cokriging model. Allocating the MSUs at the boundary and center of a plot improved surface fuel load prediction and mapping.

Assessing uncertainties in velocity models and images with a fast nonlinear uncertainty quantification method

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R63-R75 ◽  
Author(s):  
Gregory Ely ◽  
Alison Malcolm ◽  
Oleg V. Poliannikov
Keyword(s):  
Uncertainty Quantification ◽  
Seismic Imaging ◽  
Low Frequency ◽  
Expansion Method ◽  
Velocity Model ◽  
Image Features ◽  
Visible Image ◽  
Waveform Data ◽  
Velocity Models ◽  
Seismic Reflections

Seismic imaging is conventionally performed using noisy data and a presumably inexact velocity model. Uncertainties in the input parameters propagate directly into the final image and therefore into any quantity of interest, or qualitative interpretation, obtained from the image. We considered the problem of uncertainty quantification in velocity building and seismic imaging using Bayesian inference. Using a reduced velocity model, a fast field expansion method for simulating recorded wavefields, and the adaptive Metropolis-Hastings algorithm, we efficiently quantify velocity model uncertainty by generating multiple models consistent with low-frequency full-waveform data. A second application of Bayesian inversion to any seismic reflections present in the recorded data reconstructs the corresponding structures’ position along with its associated uncertainty. Our analysis complements rather than replaces traditional imaging because it allows us to assess the reliability of visible image features and to take that into account in subsequent interpretations.

Aeroelastic Stability and Response of Composite Swept Wings in Subsonic Flow Using Indicial Aerodynamics

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
S. A. Sina ◽  
T. Farsadi ◽  
H. Haddadpour
Keyword(s):  
Compressible Flow ◽  
Structural Model ◽  
Equations Of Motion ◽  
Aeroelastic Stability ◽  
Aeroelastic System ◽  
Aeroelastic Instability ◽  
Eigen Analysis ◽  
Strip Theory ◽  
The Time Domain ◽  
Composite Wing

In this study, the aeroelastic stability and response of an aircraft swept composite wing in subsonic compressible flow are investigated. The composite wing was modeled as an anisotropic thin-walled composite beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. Also, the structural model consists of a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsional model, and rotary inertia. The finite state form of the unsteady aerodynamic loads have been modeled based on the indicial aerodynamic theory and strip theory in the subsonic compressible flow. Novel Mach dependent exponential approximations of the indicial aerodynamic functions have been developed. The extended Galerkin’s method was used to construct the mass, stiffness, and damping matrices of the nonconservative aeroelastic system. Eigen analysis of the system was performed to obtain the aeroelastic instability (divergence and flutter) boundaries. Also, solving the equations of motion in the time domain leads to the aeroelastic response of wing in different flight speeds. The obtained results are compared with the available results in the literature, which reveals an excellent agreement. The numerical results obtained in this article seek to clarify the effects of geometrical and material couplings and flight Mach number on the aeroelastic instability and response of composite wings in subsonic compressible flow.

scholarly journals Uncertainty Quantification Methodologies Applied to the Rotor Tip Clearance Effect in a Twin Scroll Radial Turbine

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 114
Author(s):  
Carlo Cravero ◽  
Andrea Ottonello
Keyword(s):  
Uncertainty Quantification ◽  
Leading Edge ◽  
Expansion Method ◽  
Quantitative Information ◽  
Tip Clearance ◽  
Simulation Tools ◽  
Numerical Predictions ◽  
Physical Experiments ◽  
Comparison Of The Results ◽  
Radial Turbines

In the last three decades computer simulation tools have achieved wide spread use in the design and analysis of engineering devices. This has shortened the overall product design cycle (physical experiments may be impossible during early design stages) and it has also provided better understanding of the operating behavior of the systems under investigation. As a consequence numerical simulation have led to a reduction of physical prototyping and to lower costs for manufacturing production chains. Despite this success, it remains difficult to provide objective confidence levels in quantitative information derived from numerical predictions. The complexity arises from the amount of uncertainties related to the inputs of any computation attempting to represent a physical system. This paper focuses on geometrical sources of uncertainty in the field of CFD applied to twin scroll radial turbines. In particular it has been investigated the effect of uncertainties on tip clearance values at rotor blade leading edge and trailing edge on selected turbine performance parameters. The analysis shows the use of the Surrogate-based uncertainty quantification technique that has been setup by the authors in the Dakota® environment. The polynomial chaos expansion method has been applied to the same case. The comparison of the results coming from the different approaches and the discussion of the pros and cons related to each technique lead to interesting conclusions, which are proposed as guidelines for future UQ applications on the theme of CFD applied to radial turbines.

scholarly journals On Stochastic Investigation of Flow Problems Using the Viscous Burgers’ Equation as an Example

2019 ◽  
Vol 81 (2) ◽  
pp. 1111-1117 ◽  
Author(s):  
Markus Wahlsten ◽  
Jan Nordström
Keyword(s):  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Burgers Equation ◽  
Probability Density Functions ◽  
Galerkin Projection ◽  
Density Functions ◽  
Flow Problems ◽  
Stochastic Space ◽  
Stochastic Galerkin ◽  
Insight Into

Abstract We consider a stochastic analysis of non-linear viscous fluid flow problems with smooth and sharp gradients in stochastic space. As a representative example we consider the viscous Burgers’ equation and compare two typical intrusive and non-intrusive uncertainty quantification methods. The specific intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The specific non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are compared in terms of error in the estimated variance, computational efficiency and accuracy. This comparison, although not general, provide insight into uncertainty quantification of problems with a combination of sharp and smooth variations in stochastic space. It suggests that combining intrusive and non-intrusive methods could be advantageous.

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