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

Measurement Selection for Engine Transients by Parameter Signatures

[+] Author and Article Information
James R. McCusker

Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst, Amherst, MA 01003

Kourosh Danai1

Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst, Amherst, MA 01003danai@ecs.umass.edu

1

Corresponding author.

J. Eng. Gas Turbines Power 132(12), 121601 (Aug 24, 2010) (10 pages) doi:10.1115/1.4001808 History: Received December 22, 2009; Revised March 26, 2010; Published August 24, 2010; Online August 24, 2010

A method of measurement selection is introduced that relies on parameter signatures to assess the identifiability of dynamic model parameters by different outputs. A parameter signature is a region in the time-scale plane wherein the sensitivity of the output with respect to one model parameter is much larger than the rest of the output sensitivities. Since a parameter signature can be extracted when the corresponding output sensitivity is independent of the others, the ability to extract parameter signatures is indicative of parameter identifiability by the output and used here for output/measurement selection. The purpose of this paper is to introduce a strategy for measurement selection by parameter signatures and to demonstrate its applicability to the transient decks of turbojet engines. The validity of the selected outputs in providing observability to all the engine model parameters is independently verified by successful estimation of parameters by nonlinear least-squares estimation.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the high-bypass-ratio turbofan engine represented by the FANJETPW simulation model, shown with the station and primary component locations

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Figure 2

The PLA input used to generate the transient outputs of the engine model together with four of the seven simulated outputs

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Figure 3

Parameter signatures of an engine parameter extracted at the three different dominance factors of 2, 2.5, and 3

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Figure 4

Estimated value of the parameter error at individual pixels of the parameter signatures in Fig. 3

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Figure 5

Two highly correlated output sensitivities and the difference between the absolute normalized values of their Gauss wavelet coefficients

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Figure 6

Two uncorrelated output sensitivities and the difference between the absolute normalized values of their Gauss wavelet coefficients

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Figure 7

The parameter signatures of hypothetical parameters corresponding to the output sensitivities ζ1 and ζ2 in Fig. 5 and ζ3 and ζ4 in Fig. 6, as shown, respectively, in the top and bottom subfigures. As expected, there are very few pixels included in the top parameter signatures due to the high correlation of ζ1 and ζ2. In contrast, the extracted parameter signatures associated with the uncorrelated signals ζ3 and ζ4 comprise many pixels.

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Figure 8

Illustration of the added resolution provided by wavelet coefficients in delineating the local dissimilarities between output sensitivities (between the dotted lines)

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Figure 9

The output sensitivities of output N2 with respect to the model parameters

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Figure 10

The parameter signatures for the output N2 extracted at a dominance factor of 2

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Figure 11

The parameter identifiability provided by engine outputs at the dominance factors of 2, 2.5, and 3. Parameters are numbered according to the following order: HPCNc, HPCeff, HPTNc, HPTeff, LPCNc, LPCeff, LPTNc, LPTeff, fanNc, and faneff; the outputs are ordered as N2, N1, T25, T50, P25, T30, and P30. The dark blocks indicate the presence of parameter signatures.

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Figure 12

Several sets of parameter estimation results by NLS using the suite of four outputs: N2, N1, T30, and P30 with the starting parameter values within ±4% of the true parameter values, shown by the dashed lines.

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Figure 13

Parameter estimation results by NLS using output suites of three outputs, each missing one of the outputs N2, N1, T30, and P30 that were deemed necessary for parameter estimation. The x at the end of runs denotes a failed simulation due to a drastically erroneous parameter estimate. The initial parameter values are the same as those in Fig. 1.

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