Calibration and Uncertainty Quantification of Gas Turbine Performance Models

2015 ◽  
Author(s):  
Manuel Arias Chao ◽  
Darrel S. Lilley ◽  
Peter Mathé ◽  
Volker Schloßhauer
Keyword(s):  
Uncertainty Quantification ◽  
Gas Turbine ◽  
Bayesian Approach ◽  
Least Squares Method ◽  
Measurement Data ◽  
Operating Conditions ◽  
Performance Models ◽  
Regression Problem ◽  
Calibration Problem ◽  
Calibration Parameters

Calibration and uncertainty quantification for gas turbine (GT) performance models is a key activity for GT manufacturers. The adjustment between the numerical model and measured GT data is obtained with a calibration technique. Since both, the calibration parameters and the measurement data are uncertain the calibration process is intrinsically stochastic. Traditional approaches for calibration of a numerical GT model are deterministic. Therefore, quantification of the remaining uncertainty of the calibrated GT model is not clearly derived. However, there is the business need to provide the probability of the GT performance predictions at tested or untested conditions. Furthermore, a GT performance prediction might be required for a new GT model when no test data for this model are available yet. In this case, quantification of the uncertainty of the baseline GT, upon which the new development is based on, and propagation of the design uncertainty for the new GT is required for risk assessment and decision making reasons. By using as a benchmark a GT model, the calibration problem is discussed and several possible model calibration methodologies are presented. Uncertainty quantification based on both a conventional least squares method and a Bayesian approach will be presented and discussed. For the general nonlinear model a fully Bayesian approach is conducted, and the posterior of the calibration problem is computed based on a Markov Chain Monte Carlo simulation using a Metropolis-Hastings sampling scheme. When considering the calibration parameters dependent on operating conditions, a novel formulation of the GT calibration problem is presented in terms of a Gaussian process regression problem.

Uncertainty Quantification of NOx Emission Due to Operating Conditions and Chemical Kinetic Parameters in a Premixed Burner

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Sajjad Yousefian ◽  
Gilles Bourque ◽  
Rory F. D. Monaghan
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Gas Turbine ◽  
Flow Reactor ◽  
Epistemic Uncertainty ◽  
Plug Flow ◽  
Chemical Kinetic ◽  
Operating Conditions ◽  
Nox Emission ◽  
Gas Turbine Combustion

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.

Nonlinear Multiple Points Gas Turbine Off-Design Performance Adaptation Using a Genetic Algorithm

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Y. G. Li ◽  
M. F. Abdul Ghafir ◽  
L. Wang ◽  
R. Singh ◽  
K. Huang ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Gas Turbine ◽  
Scaling Factor ◽  
Performance Model ◽  
Operating Conditions ◽  
Performance Models ◽  
Design Performance ◽  
Turbine Performance ◽  
Thermodynamic Performance ◽  
Performance Adaptation

Accurate gas turbine performance models are crucial in many gas turbine performance analysis and gas path diagnostic applications. With current thermodynamic performance modeling techniques, the accuracy of gas turbine performance models at off-design conditions is determined by engine component characteristic maps obtained in rig tests and these maps may not be available to gas turbine users or may not be accurate for individual engines. In this paper, a nonlinear multiple point performance adaptation approach using a genetic algorithm is introduced with the aim to improve the performance prediction accuracy of gas turbine engines at different off-design conditions by calibrating the engine performance models against available test data. Such calibration is carried out with introduced nonlinear map scaling factor functions by “modifying” initially implemented component characteristic maps in the gas turbine thermodynamic performance models. A genetic algorithm is used to search for an optimal set of nonlinear scaling factor functions for the maps via an objective function that measures the difference between the simulated and actual gas path measurements. The developed off-design performance adaptation approach has been applied to a model single spool turbo-shaft aero gas turbine engine and has demonstrated a significant improvement in the performance model accuracy at off-design operating conditions.

Computer Models for Education on Performance Monitoring and Diagnostics of Gas Turbines

2002 ◽  
Vol 30 (3) ◽  
pp. 204-218 ◽  
Author(s):  
K. Mathioudakis ◽  
A. Stamatis ◽  
A. Tsalavoutas ◽  
N. Aretakis
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Performance Monitoring ◽  
Measurement Data ◽  
Performance Model ◽  
Operating Conditions ◽  
Engine Operation ◽  
Monitoring And Diagnostics ◽  
Engine Components ◽  
The Way

The paper discusses how performance models can be incorporated in education on the subject of gas turbine performance monitoring and diagnostics. A particular performance model, built for educational purposes, is employed to demonstrate the different aspects of this process. The way of building a model is discussed, in order to ensure the connection between the physical principles used for diagnostics and the structure of the software. The first aspect discussed is model usage for understanding gas turbine behaviour under different operating conditions. Understanding this behaviour is essential, in order to have the possibility to distinguish between operation in ‘healthy’ and ‘faulty’ engine condition. A graphics interface is used to present information in different ways such as operating line, operating points on component maps, interrelation between performance variables and parameters. The way of studying faulty engine operation is then presented, featuring a novel comparison to existing simulation programs. Faults can be implanted into different engine components and their impact on engine performance studied. The notion of fault signatures on measured quantities is explained. The model has also a diagnostic capability, allowing the introduction of measurement data from faulty engines and providing a diagnosis, namely a picture of how the performance of engine components has deviated from a ‘healthy’ condition

Instructing the Principles of Gas Turbine Performance Monitoring and Diagnostics by Means of Interactive Computer Models

2000 ◽  
Author(s):  
K. Mathioudakis ◽  
A. Stamatis ◽  
A. Tsalavoutas ◽  
N. Aretakis
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Performance Monitoring ◽  
Measurement Data ◽  
Engine Performance ◽  
Performance Model ◽  
Operating Conditions ◽  
Engine Operation ◽  
Turbine Performance ◽  
Engine Components

The paper discusses how the principles employed for monitoring the performance of gas turbines in industrial duty can be explained by using suitable Gas Turbine performance models. A particular performance model that can be used for educational purposes is presented. The model allows the presentation of basic rules of gas turbine engine behavior and helps understanding different aspects of its operation. It is equipped with a graphics interface, so it can present engine operating point data in a number of different ways: operating line, operating points of the components, variation of particular quantities with operating conditions etc. Its novel feature, compared to existing simulation programs, is that it can be used for studying cases of faulty engine operation. Faults can be implanted into different engine components and their impact on engine performance studied. The notion of fault signatures on measured quantities is clearly demonstrated. On the other hand, the model has a diagnostic capability, allowing the introduction of measurement data from faulty engines and providing a diagnosis, namely a picture of how the performance of engine components has deviated from nominal condition, and how this information gives the possibility for fault identification.

Application of Gas Path Analysis to Compressor Diagnosis of an Industrial Gas Turbine Using Field Data

2014 ◽  
Author(s):  
J. Blinstrub ◽  
Y. G. Li ◽  
M. Newby ◽  
Q. Zhou ◽  
G. Stigant ◽  
...  
Keyword(s):  
Path Analysis ◽  
Gas Turbine ◽  
Field Data ◽  
Measurement Data ◽  
Diagnostic Technique ◽  
Operating Conditions ◽  
Maintenance Cost ◽  
Diagnostic Analysis ◽  
Major Life ◽  
Monitoring And Diagnostics

Maintenance cost is one of the major life cycle costs of gas turbine engines. To reduce the maintenance costs, the maintenance should be changed from preventive (or scheduled) maintenance to predictive (or condition-based) maintenance where condition monitoring and diagnostics become crucially important. This paper represents the application of a gas path diagnostic technique, Gas Path Analysis, to the diagnostic analysis of an aero-derivative gas turbine (GE LM2500+) operated by Manx Electricity Authority in the Isle of Man, UK. In the application, an engine thermodynamic model is created and adapted to the performance of the engine using field data obtained at different operating conditions. Different data pre-processing methods are presented and compared in the diagnostic analysis. The uncertainty of measurement data is analysed and the most suitable measurements are identified in the prediction of key gas path component degradation. A non-linear GPA diagnostic analysis provides promising results for the prediction of compressor degradation and the performance improvement due to a compressor water washing. Such diagnostic information would be very useful for maintenance engineers to optimise their maintenance activities including overhauls and compressor washing.

Non-Linear Multiple Points Gas Turbine Off-Design Performance Adaptation Using a Genetic Algorithm

2010 ◽  
Author(s):  
Y. G. Li ◽  
M. F. Abdul Ghafir ◽  
L. Wang ◽  
R. Singh ◽  
K. Huang ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Gas Turbine ◽  
Scaling Factor ◽  
Operating Conditions ◽  
Performance Models ◽  
Design Performance ◽  
Turbine Performance ◽  
Thermodynamic Performance ◽  
Non Linear ◽  
Performance Adaptation

Accurate gas turbine performance models are crucial in many gas turbine performance analysis and gas path diagnostic applications. With current thermodynamic performance modelling techniques, the accuracy of gas turbine performance models at off-design conditions is determined by engine component characteristic maps obtained in rig tests and these maps may not be available to gas turbine users or may not be accurate for individual engines. In this paper, a non-linear multiple point performance adaptation approach using a Genetic Algorithm is introduced with the aim to improve the performance prediction accuracy of gas turbine engines at different off-design conditions by calibrating the engine performance models against available test data. Such calibration is carried out with introduced non-linear map scaling factor functions by ‘modifying’ initially implemented component characteristic maps in the gas turbine thermodynamic performance models. A Genetic Algorithm is used to search for an optimal set of non-linear scaling factor functions for the maps via an objective function that measures the difference between the simulated and actual gas path measurements. The developed off-design performance adaptation approach has been applied to a model single spool turboshaft aero gas turbine engine and demonstrated a significant improvement in the performance model accuracy at off-design operating conditions.

The Implementation of the Data Validation Process in a Gas Turbine Performance Monitoring System

2005 ◽  
Author(s):  
Pen-Chung Chen ◽  
Helmer Andersen
Keyword(s):  
Energy Balance ◽  
Performance Measurement ◽  
Gas Turbine ◽  
Mass Flow ◽  
Measurement Data ◽  
Measured Data ◽  
Operating Conditions ◽  
Data Validation ◽  
Balance Equations ◽  
Validation Process

It is an important issue for the power generation industry to minimize maintenance cost; increase plant reliability and availability and enhance equipment performance. Knowing the operating conditions of a gas turbine, engineers can analyze and optimize the process throughout the operation. The accuracy of the performance measurement data is very critical in the gas turbine operation, because it is the foundation of the analysis. To verify the accuracy of measurement data, this paper will present a mathematical approach based on the data validation process. The data validation process is a method for correcting and verifying the measurement data and associated uncertainties by satisfying the different conservation laws like mass balance, energy balance and other related balances. The data validation process will increase the overall accuracy of the measurement data. The procedure of data validation will be illustrated by determining the inlet mass flow of a compressor. For the practical purpose, the measurement data presented in this paper is acquired from a commercial gas turbine plant. The inlet mass flow of compressor can be calculated using multiple mass- and energy balance equations. The result of the comparison of the initial measured data and the validated data will be discussed. This paper will also show that the data validation process can identify serious measurement errors and eliminate the common contradictions among the balance equations. After applying the data validation method on the performance measurement data, plant users will have more confidence to optimize the daily operation. The data validation is an auxiliary method to evaluate the quality of measured data and uncertainties. However, it still cannot replace the accurate and calibrated measurement equipments during the performance test. The data validation approach is used as an auxiliary tool for Alstom’s Plant Monitoring and Diagnostic System (AMODIS) [1], which can optimize plant operation and enhance turbine monitoring in critical areas for early warning.

Uncertainty Quantification of NOx Emission due to Operating Conditions and Chemical Kinetic Parameters in a Premixed Burner

2018 ◽  
Author(s):  
Sajjad Yousefian ◽  
Gilles Bourque ◽  
Rory F. D. Monaghan
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Gas Turbine ◽  
Flow Reactor ◽  
Epistemic Uncertainty ◽  
Plug Flow ◽  
Chemical Kinetic ◽  
Operating Conditions ◽  
Nox Emission ◽  
Gas Turbine Combustion

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.

Training Future Engineers on Gas Turbine Gas Path Diagnostics Using PYTHIA

2014 ◽  
Author(s):  
Y. G. Li
Keyword(s):  
Gas Turbine ◽  
Condition Monitoring ◽  
Measurement Data ◽  
Engine Performance ◽  
Training Model ◽  
Industrial Applications ◽  
Performance Models ◽  
Training And Education ◽  
Thermodynamic Performance ◽  
User Friendly

Technology on gas turbine gas path diagnostics has become more and more mature over the years and the demand of the technology in industrial applications, training and education is increasing. To make the technology more accessible to gas turbine users in different areas, including gas turbine design, operation, condition monitoring, maintenance, education, training, etc., comprehensive software to support an easy, fast and user friendly application of the technology has become highly desirable. In this paper, gas turbine thermodynamic performance and diagnostics software, PYTHIA, and a training model on gas turbine gas path diagnostics have been introduced. The objective of the training is to provide trainees the knowledge and an opportunity to effectively learn how to set up gas turbine thermodynamic performance models, understand degradation effects on engine performance, improve the accuracy of engine performance models, pre-process measurement data, detect sensor faults and carry out engine diagnostic analysis. Four tutorial exercises are provided to demonstrate how to use the PYTHIA software to support the training and education. As the gas path diagnostic technology and the software have been developed for industrial applications, particular for gas turbine condition monitoring and diagnostics, it is user friendly and has a high level of flexibility to be used for different gas turbine engines and can be accessed remotely via internet. Therefore it provides a useful tool and a virtual environment to enhance the effectiveness of the training and education of the technology. Such technology and training model is suitable for professional engineers and postgraduate students.

Impacts of Engine Secondary Air System Uncertainties on Gas Turbine Compressor Heat Transfer

2010 ◽  
Author(s):  
Sohail Alizadeh ◽  
Naveen Gopinathrao
Keyword(s):  
Heat Transfer ◽  
Uncertainty Quantification ◽  
Gas Turbine ◽  
Operating Conditions ◽  
Design Parameters ◽  
Influence Coefficient ◽  
Resource Requirement ◽  
Uncertainty Sources ◽  
Air System ◽  
Secondary Air

The compressor is a particularly sensitive component in a gas turbine engine. Variations from design geometry or operating conditions can have detrimental effects on performance, efficiency and compressor life. In this work the propagation of secondary air system operational uncertainty sources on a rotor-stator cavity at the front of a large turbofan IPC are assessed. The calculations are carried through from appropriate Computational Fluid Dynamics (CFD) analyses, characterising the flow and heat transfer in the cavity adjacent to an IP1 disc, to the FE Thermo-mechanical calculations. The application provides an example demonstration how uncertainty quantification may be undertaken for compressor analysis involving intensive CFD computations. The non-deterministic solution provides probabilistic definitions for disc temperatures and blade tip clearances, as key parameters in the design of the component. Whilst CFD has found increasing use in gas turbine air system R&D and design applications, resource requirement has almost always limited its use to deterministic single-input single-output cases. Here, by employing efficient uncertainty quantification based on Polynomial Chaos Methodologies to CFD, the air mass flow and temperature feed to the cavity are treated as operational uncertainty sources. Both single variable and multi-variable sources are considered. The CFD-FE link is established through a Temperature Influence Coefficient methodology and in propagating and managing the uncertainties through both analyses, means and standard deviations in the key design parameters are derived. The value of such a methodology in contrast to deterministic calculations is discussed from the view point of the designer with reference to component temperatures and thermal growths.

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