Uncertainty quantification of combustion noise by generalized polynomial chaos and state-space models

2020 ◽  
Vol 217 ◽  
pp. 113-130
Author(s):  
C.F. Silva ◽  
P. Pettersson ◽  
G. Iaccarino ◽  
M. Ihme
Keyword(s):  
Uncertainty Quantification ◽  
State Space ◽  
Polynomial Chaos ◽  
State Space Models ◽  
Combustion Noise ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial

Generalized Polynomial Chaos-Based Extended Kalman Filter: Improvement and Expansion

2013 ◽  
Author(s):  
Jeremy Kolansky ◽  
Corina Sandu
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
Polynomial Chaos ◽  
Computationally Efficient ◽  
Generalized Polynomial Chaos ◽  
Parameter Estimations ◽  
Generalized Polynomial ◽  
State Estimations ◽  
Polynomial Chaos Expansions

The generalized polynomial chaos (gPC) method for propagating uncertain parameters through dynamical systems (previously developed at Virginia Tech) has been shown to be very computationally efficient. This method seems also to be ideal for real-time parameter estimation when merged with the Extended Kalman Filter (EKF). The resulting technique is shown in the present paper for systems in state-space representations, and then expanded to systems in regressions formulations. Due to the way the filter interacts with the polynomial chaos expansions, the covariance matrix is forced to zero in finite time. This problem shows itself as an inability to perform state estimations and causes the parameters to converge to incorrect values for state space systems. In order to address this issue, improvements to the method are implemented and the updated method is applied to both state space and regression systems. The resultant technique shows high accuracy of both state and parameter estimations.

A Metamodeling Approach for Instant Severity Assessment and Uncertainty Quantification of Iliac Artery Stenoses

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
S. G. H. Heinen ◽  
K. Gashi ◽  
D. A. F van den Heuvel ◽  
J. P. P. M. de Vries ◽  
F. N. van de Vosse ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Iliac Artery ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Pressure Drops ◽  
Output Uncertainty ◽  
Generalized Polynomial ◽  
2D Model

Abstract Two-dimensional (2D) or three-dimensional (3D) models of blood flow in stenosed arteries can be used to patient-specifically predict outcome metrics, thereby supporting the physicians in decision making processes. However, these models are time consuming which limits the feasibility of output uncertainty quantification (UQ). Accurate surrogates (metamodels) might be the solution. In this study, we aim to demonstrate the feasibility of a generalized polynomial chaos expansion-based metamodel to predict a clinically relevant output metric and to quantify the output uncertainty. As an example, a metamodel was constructed from a recently developed 2D model that was shown to be able to estimate translesional pressure drops in iliac artery stenoses (−0.9 ± 12.7 mmHg, R2 = 0.81). The metamodel was constructed from a virtual database using the adaptive generalized polynomial chaos expansion (agPCE) method. The constructed metamodel was then applied to 25 stenosed iliac arteries to predict the patient-specific pressure drop and to perform UQ. Comparing predicted pressure drops of the metamodel and in vivo measured pressure drops, the mean bias (−0.2 ± 13.7 mmHg) and the coefficient of determination (R2 = 0.80) were as good as of the original 2D computational fluid dynamics (CFD) model. UQ results of the 2D and metamodel were comparable. Estimation of the uncertainty interval using the original 2D model took 14 days, whereas the result of the metamodel was instantly available. In conclusion, it is feasible to quantify the uncertainty of the output metric and perform sensitivity analysis (SA) instantly using a metamodel. Future studies should investigate the possibility to construct a metamodel of more complex problems.

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