Application of Bayesian Forecasting to Change Detection and Prognosis of Gas Turbine Performance

2009 ◽  
Author(s):  
Holger Lipowsky ◽  
Stephan Staudacher ◽  
Michael Bauer ◽  
Klaus-Juergen Schmidt
Keyword(s):  
Change Detection ◽  
Probability Density ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Alternative Model ◽  
Linear Models ◽  
Current Model ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Bayesian Forecasting

This paper presents a novel technique for automatic change detection of the performance of gas turbines. In addition to change detection the proposed technique has the ability to perform a prognosis of measurement values. The proposed technique is deemed to be new in the field of gas turbine monitoring and forms the basic building block of a patent pending filed by the authors [1]. The technique used is called Bayesian Forecasting and is applied to Dynamic Linear Models (DLMs). The idea of Bayesian Forecasting is based on Bayes’ Theorem, which enables the calculation of conditional probabilities. In combination with DLMs (which break down the chronological sequence of the observed parameter into mathematical components like value, gradient, etc.) Bayesian Forecasting can be used to calculate probability density functions prior to the next observation, so called forecast distributions. The change detection is carried out by comparing the current model with an alternative model which mean value is shifted by a prescribed offset. If the forecast distribution of the alternative model better fits the actual observation, a potential change is detected. To determine whether the respective observation is a single outlier or the first observation of a significant change, a special logic is developed. Studies have shown that a confident change detection is possible for a change height of only 1.5 times the standard deviation of the observed signal. In terms of prognostic abilities the proposed technique not only estimates the point of time of a potential limit exceedance of respective parameters, but also calculates confidence bounds as well as probability density and cumulative distribution functions for the prognosis.

Application of Bayesian Forecasting to Change Detection and Prognosis of Gas Turbine Performance

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
Holger Lipowsky ◽  
Stephan Staudacher ◽  
Michael Bauer ◽  
Klaus-Juergen Schmidt
Keyword(s):  
Change Detection ◽  
Probability Density ◽  
Alternative Model ◽  
Detection Rate ◽  
Bayesian Forecasting ◽  
False Detection Rate ◽  
False Detection ◽  
High Detection Rate ◽  
Detection Rates ◽  
High Detection

The performance of gas turbines degrades over time due to deterioration mechanisms and single fault events. While deterioration mechanisms occur gradually, single fault events are characterized by occurring accidentally. In the case of single events, abrupt changes in the engine parameters are expected. Identifying these changes as soon as possible is referred to as detection. State-of-the-art detection algorithms are based on expert systems, neural networks, special filters, or fuzzy logic. This paper presents a novel detection technique, which is based on Bayesian forecasting and dynamic linear models (DLMs). Bayesian forecasting enables the calculation of conditional probabilities, whereas DLMs are a mathematical tool for time series analysis. The combination of the two methods can be used to calculate probability density functions prior to the next observation, or the so called forecast distributions. The change detection is carried out by comparing the current model with an alternative model, where the mean value is shifted by a prescribed offset. If the forecast distribution of the alternative model better fits the actual observation, a potential change is detected. To determine whether the respective observation is a single outlier or the first observation of a significant change, a special logic is developed. In addition to change detection, the proposed technique has the ability to perform a prognosis of measurement values. The developed method was run through an extensive test program. Detection rates >92% have been achieved for changed heights, as small as 1.5 times the standard deviation of the observed signal (sigma). For changed heights greater than 2 sigma, the detection rates have proven to be 100%. It could also be shown that a high detection rate is gained by a high false detection rate (∼2%). An optimum must be chosen between a high detection rate and a low false detection rate, by choosing an appropriate uncertainty limit for the detection. Increasing the uncertainty limit decreases both detection rate and false detection rate. In terms of prognostic abilities, the proposed technique not only estimates the point of time of a potential limit exceedance of respective parameters, but also calculates confidence bounds, as well as probability density and cumulative distribution functions for the prognosis. The conflictive requirements of a high degree of smoothing and a quick reaction to changes are fulfilled in parallel by combining two different detection conditions.

Effects of Variational Particle Restitution Characteristics on Turbomachinery Erosion

1993 ◽  
Author(s):  
Awatef Hamed ◽  
Timothy P. Kuhn
Keyword(s):  
Gas Turbines ◽  
Laser Doppler Velocimetry ◽  
Particle Trajectory ◽  
Particle Dynamics ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Sampling Techniques ◽  
Flow Conditions ◽  
Mean Values ◽  
Particle Velocities

This paper presents the results of an investigation to determine the effects of variational particle rebounding models on surface impacts and blade erosion patterns in gas turbines. The variance in the particle velocities after the surface impacts are modeled based on the experimental measurements using Laser Doppler Velocimetry (LDV) under varying flow conditions. The probabilistic particle trajectory computations simulate the experimental variance in the particle restitution characteristics using cumulative distribution functions and random sampling techniques. The results are presented for the particle dynamics through a gas turbine flow field and are compared to those obtained with deterministic rebound models based on experimental mean values.

Effects of Variational Particle Restitution Characteristics on Turbomachinery Erosion

1995 ◽  
Vol 117 (3) ◽  
pp. 432-440 ◽  
Author(s):  
A. Hamed ◽  
T. P. Kuhn
Keyword(s):  
Gas Turbines ◽  
Laser Doppler Velocimetry ◽  
Particle Trajectory ◽  
Particle Dynamics ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Sampling Techniques ◽  
Flow Conditions ◽  
Mean Values ◽  
Particle Velocities

This paper presents the results of an investigation to determine the effects of variational particle rebounding models on surface impacts and blade erosion patterns in gas turbines. The variance in the particle velocities after the surface impacts are modeled based on the experimental measurements using Laser-Doppler Velocimetry (LDV) under varying flow conditions. The probabilistic particle trajectory computations simulate the experimental variance in the particle restitution characteristics using cumulative distribution functions and random sampling techniques. The results are presented for the particle dynamics through a gas turbine flow field and are compared to those obtained with deterministic rebound models based on experimental mean values.

A new stochastic analysis method for mechanical components

2012 ◽  
Vol 227 (8) ◽  
pp. 1818-1829 ◽  
Author(s):  
YL Zhang ◽  
YM Zhang
Keyword(s):  
Finite Element ◽  
Dimension Reduction ◽  
Probability Density ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Entropy Principle ◽  
Input Variables ◽  
First Four Moments

Univariate dimension-reduction integration, maximum entropy principle, and finite element method are employed to present a computational procedure for estimating probability densities and distributions of stochastic responses of structures. The proposed procedure can be described as follows: 1. Choose input variables and corresponding distributions. 2. Calculate the integration points and perform finite element analysis. 3. Calculate the first four moments of structural responses by univariate dimension-reduction integration. 4. Estimate probability density function and cumulative distribution function of responses by maximum entropy principle. Numerical integration formulas are obtained for non-normal distributions. The non-normal input variables need not to be transformed into equivalent normal ones. Three numerical examples involving explicit performance functions and solid mechanic problems without explicit performance functions are used to illustrate the proposed procedure. Accuracy and efficiency of the proposed procedure are demonstrated by comparisons of the estimated probability density functions and cumulative distribution functions obtained by maximum entropy principle and Monte Carlo simulation.

scholarly journals Fault Detection for Gas Turbine Sensors Using I/O Dynamic Linear Models: Methodology of Fault Code Generation

1996 ◽  
Author(s):  
R. Bettocchi ◽  
P. R. Spina ◽  
P. M. Azzoni
Keyword(s):  
Gas Turbine ◽  
Code Generation ◽  
Gas Turbines ◽  
Dynamic Models ◽  
Linear Models ◽  
Time Series Data ◽  
External Input ◽  
Series Data ◽  
Single Output ◽  
Industrial Gas Turbines

This paper presents a methodology of sensor diagnosis which appears to be particularly suitable also for application in the field of small/medium power size industrial gas turbines. The methodology is based on the Analytical Redundancy technique and uses ARX (Auto Regressive with eXternal input) MISO (Multi-Input/Single-Output) linear dynamic models obtained from time series data of the gas turbine operating condition. The linear models allow the on-line calculation of some measurable parameter starting from the values of other measured parameters. The comparison between computed and measured values of the same parameters allows setting-up a vector of residuals which, if compared with the columns of the fault matrix, permits the identification of a possible sensor fault. The initial applications of the methodology to a single-shaft industrial gas turbine show an unambiguous and certain detection and isolation of fault in sensors used both in the measurement only and in feedback by the machine control system.

scholarly journals Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Maximiano Pinheiro
Keyword(s):  
Probability Density ◽  
Distribution Functions ◽  
Joint Density ◽  
Cumulative Distribution ◽  
Marginal Probability ◽  
Affine Transformations ◽  
Skewed Distributions ◽  
Random Vectors ◽  
Marginal Distributions ◽  
Cumulative Distribution Functions

Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by nonsingular affine transformations of vectors of independent two-piece normal variables, the most important subclass of Ferreira and Steel's general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of Arellano-Valle and Azzalini's unified skew-normal densities and then using the property of closure under marginalization of the latter class.

Application of Forecasting Methodologies to Predict Gas Turbine Behavior Over Time

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Andrea Cavarzere ◽  
Mauro Venturini
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Current Trend ◽  
Threshold Value ◽  
Bayesian Forecasting ◽  
Industrial Systems ◽  
Forecasting Method ◽  
The Future ◽  
Double Exponential Smoothing ◽  
Over Time

The growing need to increase the competitiveness of industrial systems continuously requires a reduction of maintenance costs, without compromising safe plant operation. Therefore, forecasting the future behavior of a system allows planning maintenance actions and saving costs, because unexpected stops can be avoided. In this paper, four different methodologies are applied to predict gas turbine behavior over time: Linear and Nonlinear Regression, One Parameter Double Exponential Smoothing, Kalman Filter and Bayesian Forecasting Method. The four methodologies are used to provide a prediction of the time when a threshold value will be exceeded in the future, as a function of the current trend of the considered parameter. The application considers different scenarios which may be representative of the trend over time of some significant parameters for gas turbines. Moreover, the Bayesian Forecasting Method, which allows the detection of discontinuities in time series, is also tested for predicting system behavior after two consecutive trends. The results presented in this paper aim to select the most suitable methodology that allows both trending and forecasting as a function of data trend over time, in order to predict time evolution of gas turbine characteristic parameters and to provide an estimate of the occurrence of a failure.

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