Uncertainty Quantification of a Jet Engine Performance Model Under Scarce Data Availability

2021 ◽  
Author(s):  
Norbert Ludwig ◽  
Giulia Antinori ◽  
Marco Daub ◽  
Fabian Duddeck
Keyword(s):  
Uncertainty Quantification ◽  
Probabilistic Approach ◽  
Engine Performance ◽  
Theoretical Background ◽  
Performance Model ◽  
Data Availability ◽  
Data Set ◽  
Jet Engine ◽  
Probabilistic Uncertainty ◽  
Flow Capacity

Abstract The development of jet engine components requires a detailed quantification of different uncertainty sources to improve the quality and robustness of the design. In order to get a better understanding of the entire interdisciplinary jet engine design process, the detailed uncertainty quantification of the performance parameters is of vital importance. This paper demonstrates a new approach how to represent the uncertainties in a jet engine performance model caused by the manufacturing and assembly process. In earlier research studies, the manufacturing process was modeled with a probabilistic approach, i.e. by assuming a multivariate normal distribution for the corresponding parameters. Within the scope of this paper, the uncertainty of the components’ flow capacity and efficiency is quantified based on a limited set of data. Due to the extreme scarcity of the data set, it is proposed to use methods from the field of non-probabilistic uncertainty quantification. In this paper, three different approaches to derive the variation of the components’ flow capacity and efficiency are compared with each other. In contrast to probabilistic methodologies, all approaches are able to represent the lack of data without making any additional assumptions regarding the underlying type of distribution. As a result, each of the methodologies describes the uncertain parameters by probability-boxes. After clarifying the theoretical background, the results obtained from the different approaches are discussed in detail. It figured out that the propagation method for probability-boxes plays a crucial role for the uncertainty quantification.

A Hyper-Ellipsoid Approach for Inverse Lack-of-Knowledge Uncertainty Quantification

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Norbert Ludwig ◽  
Fabian Duddeck ◽  
Marco Daub
Keyword(s):  
Uncertainty Quantification ◽  
Engine Performance ◽  
Computation Time ◽  
Solution Procedure ◽  
Performance Model ◽  
High Dimensional ◽  
System Response ◽  
Test Case ◽  
Jet Engine ◽  
Output Space

Abstract This paper presents a novel methodology to solve an inverse uncertainty quantification problem where only the variation of the system response is provided by a small set of experimental data. Furthermore, the method is extended for cases where the uncertainty of the response quantities is given by an incomplete set of statistical moments. For both cases, the uncertainty on the output space is represented by a minimum volume enclosing ellipsoid (MVEE). The actual inverse uncertainty quantification is conducted by identifying also a hyper-ellipsoid for the input parameters, which has an image on the output space that matches the MVEE as close as possible. Hence, the newly introduced approach is a contribution to the field of nonprobabilistic uncertainty quantification methods. Compared to literature, the new approach has often superior accuracy and especially an improved efficiency for high-dimensional problems. The method is validated first by an analytical test case and subsequently applied to a jet engine performance model, where this type of inverse uncertainty quantification has to be solved to allow for a consistent and integrated solution procedure. In both cases, the results are compared with an inverse method where the variability on the input side is quantified by a multidimensional interval. It can be shown that the hyper-ellipsoid approach is superior with respect to the computation time in high-dimensional problems encountered not only in jet engine design.

Bayesian Network Approach for Gas Path Fault Diagnosis

2004 ◽  
Vol 128 (1) ◽  
pp. 64-72 ◽  
Author(s):  
C. Romessis ◽  
K. Mathioudakis
Keyword(s):  
Fault Diagnosis ◽  
Diagnostic Procedure ◽  
Deterministic Model ◽  
Probabilistic Approach ◽  
Engine Performance ◽  
Performance Model ◽  
Jet Engine ◽  
Turbine Performance ◽  
Gas Path Fault ◽  
Set Up

A method for solving the gas path analysis problem of jet engine diagnostics based on a probabilistic approach is presented. The method is materialized through the use of a Bayesian Belief Network (BBN). Building a BBN for gas turbine performance fault diagnosis requires information of a stochastic nature expressing the probability of whether a series of events occurred or not. This information can be extracted by a deterministic model and does not depend on hard to find flight data of different faulty operations of the engine. The diagnostic problem and the overall diagnostic procedure are first described. A detailed description of the way the diagnostic procedure is set-up, with focus on building the BBN from an engine performance model, follows. The case of a turbofan engine is used to evaluate the effectiveness of the method. Several simulated and benchmark fault case scenarios have been considered for this reason. The examined cases demonstrate that the proposed BBN-based diagnostic method composes a powerful tool. This work also shows that building a diagnostic tool, based on information provided by an engine performance model, is feasible and can be efficient as well.

Bayesian Network Approach for Gas Path Fault Diagnosis

2004 ◽  
Author(s):  
C. Romessis ◽  
K. Mathioudakis
Keyword(s):  
Fault Diagnosis ◽  
Diagnostic Procedure ◽  
Deterministic Model ◽  
Probabilistic Approach ◽  
Engine Performance ◽  
Performance Model ◽  
Jet Engine ◽  
Turbine Performance ◽  
Gas Path Fault ◽  
Set Up

A method for solving the gas path analysis problem of jet engine diagnostics based on a probabilistic approach is presented. The method is materialized through the use of a Bayesian Belief Network (BBN). Building a BBN for gas turbine performance fault diagnosis requires information of a stochastic nature expressing the probability of whether a series of events occurred or not. This information can be extracted by a deterministic model and does not depend on hard to find flight data of different faulty operations of the engine. The diagnostic problem and the overall diagnostic procedure are first described. A detailed description of the way the diagnostic procedure is set-up, with focus on building the BBN from an engine performance model, follows. The case of a turbofan engine is used to evaluate the effectiveness of the method. Several simulated and benchmark fault case scenarios have been considered for this reason. The examined cases demonstrate that the proposed BBN-based diagnostic method composes a powerful tool. This work also shows that building a diagnostic tool, based on information provided by an engine performance model, is feasible and can be efficient as well.

Irradiation and PV array energy output, cost, and optimal positioning estimation for South Africa

2007 ◽  
Vol 18 (2) ◽  
pp. 16-25 ◽  
Author(s):  
B. Bekker
Keyword(s):  
South Africa ◽  
Performance Model ◽  
Data Availability ◽  
Energy Output ◽  
Measurement Interval ◽  
Data Set ◽  
Pv Array ◽  
Pv Panel ◽  
Simulation Results ◽  
The Cost

Simulation results of an irradiation and PV array performance software package (SunSim) are pre-sented. South African irradiation data availability is discussed, an irradiation data classification system proposed, and the estimation of diffuse irradiation on tilted surfaces analysed. Estimation of PV array energy output using King’s performance model is explained, and the influence of the irradiation and temperature data set measurement interval on PV energy output estimation investigated. Simulation results are presented, aimed at identifying optimal fixed PV panel tilt angles and solar-tracking config-urations for different locations in South Africa. Lastly, the cost of PV-based generation in South Africa is investigated.

Financial distress determinants among SMEs: empirical evidence from Sweden

2020 ◽  
Vol 47 (3) ◽  
pp. 547-560 ◽  
Author(s):  
Darush Yazdanfar ◽  
Peter Öhman
Keyword(s):  
Financial Crisis ◽  
Financial Distress ◽  
Large Scale ◽  
Global Financial Crisis ◽  
Binary Logistic Regression ◽  
Data Availability ◽  
Cross Sectional ◽  
Data Set ◽  
Content Type ◽  
The Global Financial Crisis

PurposeThe purpose of this study is to empirically investigate determinants of financial distress among small and medium-sized enterprises (SMEs) during the global financial crisis and post-crisis periods.Design/methodology/approachSeveral statistical methods, including multiple binary logistic regression, were used to analyse a longitudinal cross-sectional panel data set of 3,865 Swedish SMEs operating in five industries over the 2008–2015 period.FindingsThe results suggest that financial distress is influenced by macroeconomic conditions (i.e. the global financial crisis) and, in particular, by various firm-specific characteristics (i.e. performance, financial leverage and financial distress in previous year). However, firm size and industry affiliation have no significant relationship with financial distress.Research limitationsDue to data availability, this study is limited to a sample of Swedish SMEs in five industries covering eight years. Further research could examine the generalizability of these findings by investigating other firms operating in other industries and other countries.Originality/valueThis study is the first to examine determinants of financial distress among SMEs operating in Sweden using data from a large-scale longitudinal cross-sectional database.

Effect of Manufacturing Variability on Turbine Engine Performance: A Probabilistic Study

2013 ◽  
Author(s):  
Michael Gorelik ◽  
Jacob Obayomi ◽  
Jack Slovisky ◽  
Dan Frias ◽  
Howie Swanson ◽  
...  
Keyword(s):  
Performance Metrics ◽  
Model Development ◽  
Engine Performance ◽  
Performance Model ◽  
Probabilistic Methods ◽  
System Level ◽  
Turbine Engine ◽  
Probabilistic Study ◽  
Blade Geometry

While turbine engine Original Equipment Manufacturers (OEMs) accumulated significant experience in the application of probabilistic methods (PM) and uncertainty quantification (UQ) methods to specific technical disciplines and engine components, experience with system-level PM applications has been limited. To demonstrate the feasibility and benefits of an integrated PM-based system, a numerical case study has been developed around the Honeywell turbine engine application. The case study uses experimental observations of engine performance such as horsepower and fuel flow from a population of engines. Due to manufacturing variability, there are unit-to-unit and supplier-to-supplier variations in compressor blade geometry. Blade inspection data are available for the characterization of these geometric variations, and CFD analysis can be linked to the engine performance model, so that the effect of blade geometry variation on system-level performance characteristics can be quantified. Other elements of the case study included the use of engine performance and blade geometry data to perform Bayesian updating of the model inputs, such as efficiency adders and turbine tip clearances. A probabilistic engine performance model was developed, system-level sensitivity analysis performed, and the predicted distribution of engine performance metrics was calibrated against the observed distributions. This paper describes the model development approach and key simulation results. The benefits of using PM and UQ methods in the system-level framework are discussed. This case study was developed under Defense Advanced Research Projects Agency (DARPA) funding which is gratefully acknowledged.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

Adaptation Application to Engine Modelling

2007 ◽  
Author(s):  
Jude Iyinbor
Keyword(s):  
Measurement Data ◽  
Engine Performance ◽  
Performance Model ◽  
Operating Conditions ◽  
Adaptation Process ◽  
Design Point ◽  
Component Map ◽  
Important Measurement ◽  
Unknown Component ◽  
Selection Of

The optimisation of engine performance by predictive means can help save cost and reduce environmental pollution. This can be achieved by developing a performance model which depicts the operating conditions of a given engine. Such models can also be used for diagnostic and prognostic purposes. Creating such models requires a method that can cope with the lack of component parameters and some important measurement data. This kind of method is said to be adaptive since it predicts unknown component parameters that match available target measurement data. In this paper an industrial aeroderivative gas turbine has been modelled at design and off-design points using an adaptation approach. At design point, a sensitivity analysis has been used to evaluate the relationships between the available target performance parameters and the unknown component parameters. This ensured the proper selection of parameters for the adaptation process which led to a minimisation of the adaptation error and a comprehensive prediction of the unknown component and available target parameters. At off-design point, the adaptation process predicted component map scaling factors necessary to match available off-design point performance data.

Development and Integration of Rain Ingestion Effects in Engine Performance Simulations

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
I. Roumeliotis ◽  
A. Alexiou ◽  
N. Aretakis ◽  
G. Sieros ◽  
K. Mathioudakis
Keyword(s):  
Engine Performance ◽  
Velocity Slip ◽  
Droplet Surface ◽  
Performance Model ◽  
Droplet Breakup ◽  
Test Case ◽  
Case Scenario ◽  
Worst Case ◽  
Engine Model ◽  
Component Models

Rain ingestion can significantly affect the performance and operability of gas turbine aero-engines. In order to study and understand rain ingestion phenomena at engine level, a performance model is required that integrates component models capable of simulating the physics of rain ingestion. The current work provides, for the first time in the open literature, information about the setup of a mixed-fidelity engine model suitable for rain ingestion simulation and corresponding overall engine performance results. Such a model can initially support an analysis of rain ingestion during the predesign phase of engine development. Once components and engine models are validated and calibrated versus experimental data, they can then be used to support certification tests, the extrapolation of ground test results to altitude conditions, the evaluation of control or engine hardware improvements and eventually the investigation of in-flight events. In the present paper, component models of various levels of fidelity are first described. These models account for the scoop effect at engine inlet, the fan effect and the effects of water presence in the operation and performance of the compressors and the combustor. Phenomena such as velocity slip between the liquid and gaseous phases, droplet breakup, droplet–surface interaction, droplet and film evaporation as well as compressor stages rematching due to evaporation are included in the calculations. Water ingestion influences the operation of the components and their matching, so in order to simulate rain ingestion at engine level, a suitable multifidelity engine model has been developed in the Proosis simulation platform. The engine model's architecture is discussed, and a generic high bypass turbofan is selected as a demonstration test case engine. The analysis of rain ingestion effects on engine performance and operability is performed for the worst case scenario, with respect to the water quantity entering the engine. The results indicate that rain ingestion has a strong negative effect on high-pressure compressor surge margin, fuel consumption, and combustor efficiency, while more than half of the water entering the core is expected to remain unevaporated and reach the combustor in the form of film.

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