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Research Papers

Estimating Recoverable Performance Degradation Rates and Optimizing Maintenance Scheduling

[+] Author and Article Information
Cody W. Allen

Solar Turbines Incorporated,
San Diego, CA
e-mail: allen_cody_w@solarturbines.com

Chad M. Holcomb

Solar Turbines Incorporated,
San Diego, CA
e-mail: holcomb_chad_m@solarturbines.com

Maurício de Oliveira

Department of Mechanical and
Aeronautical Engineering,
University of California,
9500 Gilman Drive,
San Diego, CA 92093-0411
e-mail: mauricio@ucsd.edu

1Corresponding author.

Manuscript received June 23, 2018; final manuscript received July 6, 2018; published online November 14, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(1), 011032 (Nov 14, 2018) (10 pages) Paper No: GTP-18-1322; doi: 10.1115/1.4041004 History: Received June 23, 2018; Revised July 06, 2018

Many of the components on a gas turbine are subject to fouling and degradation over time due to debris buildup. For example, axial compressors are susceptible to degradation as a result of debris buildup on compressor blades. Similarly, air-cooled lube oil heat exchangers incur degradation as a result of debris buildup in the cooling air passageways. In this paper, we develop a method for estimating the degradation rate of a given gas turbine component that experiences recoverable degradation due to normal operation over time. We then establish an economic maintenance scheduling model, which utilizes the derived rate and user input economic factors to provide a locally optimal maintenance schedule with minimized operator costs. The rate estimation method makes use of statistical methods combined with historical data to give an algorithm with which a performance loss rate can be extracted from noisy data measurements. The economic maintenance schedule is then derived by minimizing the cost model in user specified intervals and the final schedule results as a combination of the locally optimized schedules. The goal of the combination of algorithms is to maximize component output and efficiency, while minimizing maintenance costs. The rate estimation method is validated by simulation where the underlying noisy data measurements come from a known probability distribution. Then, an example schedule optimization is provided to validate the economic optimization model and show the efficacy of the combined methods.

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References

EIA, 2017, “ Annual Energy Outlook 2017 With Projections to 2050,” U.S. Energy Information Administration, Washington, DC.
Kurz, R. , and Brun, K. , 2001, “ Degradation in Gas Turbine Systems,” ASME J. Eng. Gas Turbines Power, 123(1), pp. 70–77. [CrossRef]
Sánchez, D. , Chacartegui, R. , Becerra, J. , and Sánchez, T. , 2009, “ Determining Compressor Wash Programmes for Fouled Gas Turbines,” Proc. Inst. Mech. Eng., Part A, 223(4), pp. 467–476.
Mitsui, J. , Hori, Y. , and Tanaka, M. , 1983, “ Thermohydrodynamic Analysis of Cooling Effect of Supply Oil in Circular Journal Bearing,” ASME J. Lubr. Technol., 105(3), pp. 414–420. [CrossRef]
Wang, F.-L. , He, Y.-L. , Tang, S.-Z. , and Tong, Z.-X. , 2017, “ Parameter Study on the Fouling Characteristics of the H-Type Finned Tube Heat Exchangers,” Int. J. Heat Mass Transfer, 112, pp. 367–378. [CrossRef]
Brun, K. , Grimley, T. A. , Foiles, W. C. , and Kurz, R. , 2015, “ Experimental Evaluation of the Effectiveness of Online Water-Washing in Gas Turbine Compressors,” ASME J. Eng. Gas Turbines Power, 137(4), p. 042605. [CrossRef]
Boyce, M. P. , 2012, Gas Turbine Engineering Handbook, 4th ed., Elsevier, Waltham, MA.
Boyce, M. P. , and Gonzalez, F. , 2007, “ A Study of On-Line and Off-Line Turbine Washing to Optimize the Operation of a Gas Turbine,” ASME J. Eng. Gas Turbines Power, 129(1), pp. 114–122. [CrossRef]
Allen, C. , Holcomb, C. , and de Oliveira, M. , 2016, “ Fault Detection Using Reduced Rank Linear Engine Models,” ASME Paper No. GT2016-57916.
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Ljung, L. , 1999, System Identification: Theory for the User (Prentice Hall Information and System Science Series), Prentice Hall, Upper Saddle River, NJ.
Arfken, G. B. , and Weber, H. J. , 2005, Mathematical Methods for Physicists, 6th ed., Elsevier Academic Press, Waltham, MA.
Mattingly, J. D. , 1996, Elements of Gas Turbine Propulsion, McGraw-Hill, New York.
Aretakis, N. , Roumeliotis, I. , Doumouras, G. , and Mathioudakis, K. , 2012, “ Compressor Washing Economic Analysis and Optimization for Power Generation,” Appl. Energy, 95, pp. 77–86. [CrossRef]
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Boyd, S. , and Vandenberghe, L. , 2004, Convex Optimization, Cambridge University Press, Cambridge, UK.

Figures

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Fig. 1

Depicts different degradation rates of compressor isentropic efficiency with various cleaning methods applied: Credit: Aretakis et al. [14]

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Fig. 2

Depicts degradation of compressor isentropic efficiency for two engines (side by side at site) over 6 month period where no compressor washing occurs (bottom curve) and where regular online washing occurred (top curve). The rate of degradation when no washing occurs can be approximated by a line, giving a linear rate of degradation. Credit: Boyce[8].

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Fig. 3

Top: example sawtooth function and observations. The function was generated with T=(0,392,619), N = 2, α=0.004, β0=4.732, β1=4.4967 and β2=3.4919. The observations are generated by adding zero-mean Gaussian white noise with 0.5625 variance to the function. Bottom: Difference values. Threshold value set to 3σD, where σD=2.961 is the standard deviation of the set of difference values.

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Fig. 4

Example sawtooth function, observations, and estimated sawtooth function. From the method outlined, we find α̂=0.00395, β̂0=4.732, β̂1=4.15, and β̂2=3.528.

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Fig. 5

Once the triangle areas are specified, congruency allows sliding within an interval without changing the overall area in the interval. The length scales in the bottom right section of the image sum to the length scale in the upper right section of the image, showing how we can slice the final triangle and slide a portion to the beginning of the interval. This permits flexibility in choosing when the first maintenance session is performed for a new interval. Note that the number of washes is unchanged and that the maximum postponement length is ti+1,p=(Δtj+1)i+1.

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Fig. 6

Using data from Table 1 we produce Q(t) and Qi,i+1. Here, there are four intervals we have chosen where we approximate Q with the constant model. Interval selection is a user choice.

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Fig. 7

LPi+1,w models given over each interval for i > 1. The optimal number of washes per interval comes from the minimum integer of each of these curves. Note that each curve is convex, a key characteristic necessary for optimality.

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Fig. 8

Depiction of overall wash schedule. Vertical lines indicate washes or maintenance sessions. Within each sub-interval, time between washes varies, based on the solution of the optimization problem.

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Fig. 9

Comparison of percentage of LP functions. Shown is the value (LPpreset/LPopt−1)·100. Top is full view, bottom is zoomed into area of interest.

Tables

Errata

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