Academic literature on the topic 'UQ forward analyses'

Abstract. Assessing the impact of uncertainties in ice-sheet models is a major and challenging issue that needs to be faced by the ice-sheet community to provide more robust and reliable model-based projections of ice-sheet mass balance. In recent years, uncertainty quantification (UQ) has been increasingly used to characterize and explore uncertainty in ice-sheet models and improve the robustness of their projections. A typical UQ analysis first involves the (probabilistic) characterization of the sources of uncertainty, followed by the propagation and sensitivity analysis of these sources of uncertainty. Previous studies concerned with UQ in ice-sheet models have generally focused on the last two steps but have paid relatively little attention to the preliminary and critical step of the characterization of uncertainty. Sources of uncertainty in ice-sheet models, like uncertainties in ice-sheet geometry or surface mass balance, typically vary in space and potentially in time. For that reason, they are more adequately described as spatio-(temporal) random fields, which account naturally for spatial (and temporal) correlation. As a means of improving the characterization of the sources of uncertainties for forward UQ analysis within the Ice-sheet and Sea-level System Model (ISSM), we present in this paper a stochastic sampler for Gaussian random fields with Matérn covariance function. The class of Matérn covariance functions provides a flexible model able to capture statistical dependence between locations with different degrees of spatial correlation or smoothness properties. The implementation of this stochastic sampler is based on a notable explicit link between Gaussian random fields with Matérn covariance function and a certain stochastic partial differential equation. Discretization of this stochastic partial differential equation by the finite-element method results in a sparse, scalable and computationally efficient representation known as a Gaussian Markov random field. In addition, spatio-temporal samples can be generated by combining an autoregressive temporal model and the Matérn field. The implementation is tested on a set of synthetic experiments to verify that it captures the desired spatial and temporal correlations well. Finally, we illustrate the interest of this stochastic sampler for forward UQ analysis in an application concerned with assessing the impact of various sources of uncertainties on the Pine Island Glacier, West Antarctica. We find that larger spatial and temporal correlations lengths will both likely result in increased uncertainty in the projections.

The tiltrotor has unique flight dynamics due to the aerodynamic interference characteristics. Multiple aerodynamics calculation approaches, such as the CFD method, are utilised to characterise this feature. The calculation process is usually time-consuming, and the obtained results are generally varied from each other. Thus, the uncertainty quantification (UQ) method will be utilised in this research to identify the aerodynamic inaccuracy effect on the handling qualities of the tiltrotor aircraft. The study aims to quantify the influence of the aerodynamic interference on the tiltrotor flight dynamics in different flight states, such as forward speeds and nacelle tilting angles, which can guide the flight dynamics modelling simplification to improve the simulation efficiency. Therefore, uncertainty identification and full factorial numerical integration (FFNI) methods are introduced to scale these aerodynamic uncertainties. The eigenvalue and bandwidth and phase delay requirements are presented as the failure criteria. The UQ calculation indicates that the uncertainties of the aerodynamic calculation significantly affect the handling quality ratings in two flight ranges: the helicopter mode and the conversion and aeroplane modes with higher forward speed (close to the conversion envelope). Furthermore, a sensitivity analysis is performed to identify the mechanism behind these influences. The results demonstrate that aerodynamics affect the pitching attitude, the pitching damping, and the velocity and incidence stability derivatives. However, the effects of the velocity stability and the incidence stability are the reason causing the handling qualities’ degradation in the helicopter mode and high-speed mode, respectively.

AbstractPersonalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

Many sources of uncertainty exist when emissions are modeled for a gas turbine combustion system. They originate from uncertain inputs, boundary conditions, calibration, or lack of sufficient fidelity in a model. In this paper, a nonintrusive polynomial chaos expansion (NIPCE) method is coupled with a chemical reactor network (CRN) model using Python to quantify uncertainties of NOx emission in a premixed burner. The first objective of uncertainty quantification (UQ) in this study is development of a global sensitivity analysis method based on the NIPCE method to capture aleatory uncertainty on NOx emission due to variation of operating conditions. The second objective is uncertainty analysis (UA) of NOx emission due to uncertain Arrhenius parameters in a chemical kinetic mechanism to study epistemic uncertainty in emission modeling. A two-reactor CRN consisting of a perfectly stirred reactor (PSR) and a plug flow reactor (PFR) is constructed in this study using Cantera to model NOx emission in a benchmark premixed burner under gas turbine operating conditions. The results of uncertainty and sensitivity analysis (SA) using NIPCE based on point collocation method (PCM) are then compared with the results of advanced Monte Carlo simulation (MCS). A set of surrogate models is also developed based on the NIPCE approach and compared with the forward model in Cantera to predict NOx emissions. The results show the capability of NIPCE approach for UQ using a limited number of evaluations to develop a UQ-enabled emission prediction tool for gas turbine combustion systems.

Abstract With increasing aerodynamic and thermal loads, film cooling has been a popular technology integrated into the design of the modern gas turbine vane endwall, especially for the first-stage vane endwall. A staggering amount of research has been completed to quantify the effect of operating conditions and cooling hole geometrical properties. However, most of these investigations did not address the influence of the manufacturing tolerances, assembly errors and operation degradations on the endwall misalignment. In this paper, uncertainty quantification (UQ) analysis was performed to quantify the impacts of upstream endwall misalignment uncertainties on the endwall film cooling performance and vane surface phantom cooling performance. The upstream endwall misalignment, step geometry with various step heights, commonly exists between the combustor exit and the first-stage vane endwall. Based on the non-intrusive polynomial chaos expansion (NIPC) and the uniform probability distribution assumption, the deviation (step height) uncertainties of the upstream endwall misalignment were quantified. To predict the endwall secondary flow and film cooling effectiveness in the transonic linear vane passage, the commercial CFD solver ANSYS FLUENT was used to numerically solve the three dimensional steady-state Reynolds-Averaged Navier-Stokes (RANS) equations. The robustness analysis of endwall film cooling performance and phantom cooling performance to the upstream endwall misalignment was conducted for three design upstream step heights (ΔH): a baseline configuration (ΔH = 0 mm), two misaligned configurations with forward step (ΔH = −5 mm) and backward step (ΔH = 5 mm), respectively.

Nowadays, earthquakes are one of the most catastrophic natural events that have a significant human, socio-economic and environmental impact. Besides, based on both observations of damage following recent major/moderate seismic events and numerical/experimental studies, it clearly emerges that critical non-structural components (NSCs) that are ubiquitous to most industrial facilities are particularly and even disproportionately vulnerable to those events. Nonetheless and despite their great importance, seismic provisions for industrial facilities and their process equipment are still based on the classical load-and-resistance factor design (LRFD) approach; a performance-based earthquake engineering (PBEE) approach should, instead, be preferred. Along this vein, in recent years, much research has been devoted to setting computational fragility frameworks for special-risk industrial components and structures. However, within a PBEE perspective, studies have clearly remarked: i) a lack of definition of performance objectives for NSCs; ii) the need for fully comprehensive testing campaigns data on coupling effects between main structures and NSCs. In this respect, this doctorate thesis introduces a computational framework for an efficient and accurate seismic state-dependent fragility analysis; it is based on a combination of data acquired from an extensive experimental shake table test campaign on a full-scale prototype industrial steel frame structure and the most recent surrogate-based UQ forward analysis advancements. Specifically, the framework is applied to a real-world application consisting of seismic shake table tests of a representative industrial multi-storey frame structure equipped with complex process components, carried out at the EUCENTRE facility in Italy, within the European SPIF project: Seismic Performance of Multi-Component Systems in Special Risk Industrial Facilities. The results of this experimental research campaign also aspire to improve the understanding of these complex systems and improve the knowledge of FE modelling techniques. The main goals aim to reduce the huge computational burden and to assess, as well, when the importance of coupling effects between NSCs and the main structure comes into play. Insights provided by innovative monitoring systems were then deployed to develop and validate numerical and analytical models. At the same time, the adoption of Der Kiureghian's stochastic site-based ground motion model (GMM) was deemed necessary to severely excite the process equipment and supplement the scarcity of real records with a specific frequency content capable of enhancing coupling effects. Finally, to assess the seismic risk of NSCs of those special facilities, this thesis introduces state-dependent fragility curves that consider the accumulation of damage effects due to sequential seismic events. To this end, the computational burden was alleviated by adopting polynomial chaos expansion (PCE) surrogate models. More precisely, the dimensionality of a seismic input random vector has been reduced by performing the principal component analysis (PCA) on the experimental realizations. Successively, by bootstrapping on the experimental design, separate PCE coefficients have been determined, yielding a full response sample at each point. Eventually, empirical state-dependent fragility curves were derived.

Many sources of uncertainty exist when emissions are modelled for a gas turbine combustion system. They originate from uncertain inputs, boundary conditions, calibration, or lack of sufficient fidelity in the model. In this paper, a non-intrusive polynomial chaos expansion (NIPCE) method is coupled with a chemical reactor network (CRN) model using Python to rigorously quantify uncertainties of NOx emission in a premixed burner. The first objective of the uncertainty quantification (UQ) in this study is development of a global sensitivity analysis method based on NIPCE to capture aleatory uncertainty due to the variation of operating conditions and input parameters. The second objective is uncertainty analysis of Arrhenius parameters in the chemical kinetic mechanism to study the epistemic uncertainty in the modelling of NOx emission. A two-reactor CRN consisting of a perfectly stirred reactor (PSR) and a plug flow reactor (PFR) is constructed in this study using Cantera to model NOx for natural gas at the relevant operating conditions for a benchmark premixed burner. UQ is performed through the use of a number of packages in Python. The results of uncertainty and sensitivity analysis using NIPCE based on point collocation method (PCM) are then compared with the results of advanced Monte Carlo simulation (MCS). Surrogate models are also developed based on the NIPCE approach and compared with the forward model in Cantera to predict NOx emissions. The results show the capability of NIPCE approach for UQ using a limited number of evaluations to develop a UQ-enabled emission prediction tool for gas turbine combustion systems.

Abstract With increasing aerodynamic and thermal loads, film cooling has been a popular technology integrated into the design of the modern gas turbine vane endwall, especially for the first-stage vane endwall. A staggering amount of research has been completed to quantify the effect of operating conditions and cooling hole geometrical properties. However, most of these investigations did not address the influence of the manufacturing tolerances, assembly errors and operation degradations on the endwall misalignment. In this paper, therefore, uncertainty quantification (UQ) analysis was performed to quantify the impacts of upstream endwall misalignment uncertainties on the film cooling performance of endwalls as well as the phantom cooling performance of the vane pressure side surface. The upstream endwall misalignment represents the step geometry between the combustor exit and the first-stage vane endwall. Based on the non-intrusive polynomial chaos expansion (NIPC) and the Uniform probability distribution assumption, the deviation (step height) uncertainties of the upstream endwall misalignment were quantified. To predict the endwall secondary flow and film cooling effectiveness in the transonic linear vane passage, the commercial CFD solver ANSYS FLUENT is used to numerically solve the three dimensional steady-state Reynolds-Averaged Navier-Stokes (RANS) equations. The robustness analysis of endwall film cooling performance and phantom cooling to the upstream endwall misalignment was conducted for three design upstream step heights (ΔH): a baseline configuration (ΔH = 0 mm), two misaligned configurations with forward step (ΔH = −5 mm) and backward step (ΔH = 5 mm) respectively. Results show that the actual cooling performance has a high probability of deviating from the nominal value for the baseline configuration. The critical regions that are most sensitive to the upstream step misalignment are also identified by variances. The UQ results also show that the design geometry with a forward step has a more robust film cooling performance on endwall and phantom cooling performance on the vane pressure side surface which means a smaller variance and a better expectation than the no step configuration. In contrast, the design geometry with a backward step induces the reductions of the expectation of the film cooling effectiveness and coolant coverage and the amplification of performance fluctuations. This work provides a certain guiding direction for the optimization design for the upstream step geometry.

Combustion instabilities can develop in modern gas-turbines as large amplitude pressure oscillations coupled with heat release fluctuations. In extreme cases, they lead to irreversible damage which can destroy the combustor. Prediction and control of all acoustic modes of the configuration at the design stage are therefore required to avoid these instabilities. This is a challenging task because of the large number of parameters involved. This situation becomes even more complex when considering uncertainties of the underlying models and input parameters. The forward uncertainty quantification problem is addressed in the case of a single swirled burner combustor. First, a Helmholtz solver is used to analyze the thermoacoustic modes of the combustion chamber. The Flame Transfer Function measured experimentally is used as a flame model for the Helmholtz solver. Then, the frequency of oscillation and the growth rate of the first thermoacoustic mode are computed in 24 different operating points. Comparisons between experimental and numerical results show good agreements except for modes which are marginally stable/unstable. The main reason is that the uncertainties can arbitrary change the nature of these modes (stable vs unstable); in other words, the usual mode classification stable/unstable must be replaced by a more continuous description such as the risk factor, i.e. the probability for a mode to be unstable given the uncertainties on the input parameters. To do so, a Monte Carlo analysis is performed using 4000 Helmholtz simulations of a single experimental operating point but with random perturbations on the FTF parameters. This allows the computation of the risk factor associated to this acoustic mode. Finally, the analysis of the Monte Carlo database suggests that a reduced two-step UQ strategy may be efficient to deal with thermoacoustics in such a system. First, two bilinear surrogate models are tuned from a moderate number of Helmholtz solutions (a few tens). Then, these algebraic models are used to perform a Monte Carlo analysis at reduced cost and approximate the risk factor of the mode. The accuracy and efficiency of this reduced UQ strategy are assessed by comparing the reference risk factor given by the full Monte Carlo database and the approximate risk factor obtained by the surrogate models. It shows a good agreement which proves that reduced efficient methods can be used to predict unstable modes.