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Research Papers: Gas Turbines: Controls, Diagnostics, and Instrumentation

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

[+] Author and Article Information
Holger Lipowsky

Institute of Aircraft Propulsion Systems (ILA), University of Stuttgart, Pfaffenwaldring 6, 70569 Stuttgart, Germanylipowsky@ila.uni-stuttgart.de

Stephan Staudacher

Institute of Aircraft Propulsion Systems (ILA), University of Stuttgart, Pfaffenwaldring 6, 70569 Stuttgart, Germanystaudacher@ila.uni-stuttgart.de

Michael Bauer

Department of Performance, TEAP, MTU Aero Engines GmbH, Dachauer Strasse 665, 80995 München, Germanymichael.bauer@mtu.de

Klaus-Juergen Schmidt

Department of Performance, TEAP, MTU Aero Engines GmbH, Dachauer Strasse 665, 80995 München, Germanyklaus-juergen.schmidt@mtu.de

J. Eng. Gas Turbines Power 132(3), 031602 (Dec 03, 2009) (8 pages) doi:10.1115/1.3159367 History: Received March 22, 2009; Revised March 23, 2009; Published December 03, 2009; Online December 03, 2009

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.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Health monitoring process (15)

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Figure 2

Second order DLM process modeling

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Figure 3

Decision tree explanation of Bayes’ theorem

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Figure 4

Application to residuals with an implanted change height of Δμ=−3σ at cycle t=51

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Figure 5

Derivation of the Bayes factor and the ucl from the parameter h

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Figure 6

Uncertainty limit as a function of h

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Figure 7

Application of outlier detection to sample data (outliers are marked with a square ◻)

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Figure 8

Bayes factor H, maximum cumulative Bayes factor L, and run length lr of the sample data

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Figure 9

Flow chart of the detection algorithm

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Figure 10

Application of the method to a change with a change height of Δμ=−3σ(retrospectivity=1)

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Figure 11

Application of the method to a change with a change height of Δμ=−1.5σ(retrospectivity=5)

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Figure 12

Prognosis example with constant gradient

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Figure 13

Derivation of the limit PDF and the limit CDF

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Figure 14

Definition of the different detection rates

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Figure 15

Definition of a correct detection using the detection limit parameter

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Figure 16

Detection rate as functions of change height and uncertainty limit (detection limit=3)

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Figure 17

False detection rate as functions of change height and uncertainty limit (detection limit=3)

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