Measurement 139 (2019) 355–360
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Multispectral pyrometer for high temperature measurements inside combustion chamber of gas turbine engines M.V. Mekhrengin a,⇑, I.K. Meshkovskii a, V.A. Tashkinov b, V.I. Guryev a, A.V. Sukhinets a, D.S. Smirnov a a b
ITMO University, St. Petersburg 197101, Russia PJSC «UEC-Saturn», Rybinsk 152903, Russia
a r t i c l e
i n f o
Article history: Received 14 December 2018 Received in revised form 27 February 2019 Accepted 28 February 2019 Available online 1 March 2019 Keywords: Pyrometry Multispectral sensor Blackbody radiation Temperature measurement Combustion chamber Gas turbine engine
a b s t r a c t Currently, the solution for the problem of temperature measurement of the gas phase of combustion products inside the combustion chambers of gas turbine engines is still in progress. Conventional thermocouples, which are the industry standard, are intrusive and provide spatially and temporally averaged data. In this work, a spectral system for the temperature measurement of gas flow inside the combustion chamber has been developed. The system is based on the method of multi-wave pyrometry of soot in the visible optical range and comprises a multispectral sensor-on-chip solution. Field tests on the gas turbine engine confirmed that the presented system allows measuring temperature in the range from 810 to 1120 °C with a measurement error of 3%. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The precise and timeous control of the gas temperature in the combustion chamber of gas turbine engine (GTE) is important due to maximum possible temperature limit of the combustors’ walls, thus, the combustion temperature must not exceed the temperature that is suitable for the materials of hot parts of a turbine assembly. Moreover, the control of the temperature of the burning process in GTE might help to control the level of pollutant emissions at the combustor exhaust [1]. Non-contact temperature measurement methods are more suitable over contact methods because of faster response, wider dynamic range and higher heat resistance [2]. Contact temperature measurement methods, such as thermocouples, have rather a low temperature limit that constraints their application in the combustion chamber of GTE. They also physically change the gas flow field of GTE [3]. The most suitable methods for temperature measurement of hot gases inside GTE are the optical spectral methods because the emission spectrum from combustion chamber contains information which allows estimating temperature, flame fluctuations and chemical composition of gas flow. There are methods for the measuring of the temperature or the fuel-to-air ratio of flame by observation of particular spectral bands such as Swan bands (C*2 ⇑ Corresponding author at: ITMO University, Kronverksky Pr. 49, St. Petersburg 197101, Russia. E-mail address:
[email protected] (M.V. Mekhrengin). https://doi.org/10.1016/j.measurement.2019.02.084 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.
radical), CH* and OH* radicals, which are located in visible wave range [4–6]. Other methods provide temperature measurement using the emission of H2 O and CO2 in the infrared (IR) region [7,8]. Various spectral approaches of the temperature measurement of gas flow inside the combustion chamber such as brightness [9], two-color [10,11], multi-wave and spectral pyrometry [12,13] are used. In the light of recent spectral measurement studies of the flame temperature, the most promising techniques are multi-wave and spectral pyrometry that provide accuracy within 1% depending on measuring environments [14] and the application of these techniques [12]. Khan et al. developed a multi-wave technique which allowed estimating the maximum error of temperature measurement and proved this method to be feasible using a spectrometer. Furthermore, multi-wave techniques are more successful than brightness or two-color approaches, because multi-wave techniques assume a wavelength dependent emissivity function and have been reported to be accurate to within 1%. [14]. Backstrom et al. developed a methodology that provides information about in-flame particle radiation in the industrial scale flames. They measured basic parameters of flame such as total radiative intensity, gas temperature, and gas composition [15]. Liang et al. described the development of a novel multi-target multispectral pyrometer purposed for remote measuring the true temperature of the flame of a solid fuel rocket engine in a harsh environment [13]. Ruzicka et al. demonstrated that a single-crystal sapphire tube could be used as a temperature indicator in tight thermal contact with the environment
356
M.V. Mekhrengin et al. / Measurement 139 (2019) 355–360
Nomenclature I, IðkÞ k T w
e
b
spectral radiance of gas flow, W m2 nm1 radiation wavelength, nm gas flow temperature, K weight coefficient of linear regression gas flow emissivity bias of linear regression
m
number of wavelength
Constants C1 ¼ 3:7418 1020 W nm4 m2 first radiation constant C2 ¼ 14:388 106 nm K second radiation constant
up to 1700 °C [16]. As for the spectral pyrometry, it uses the grey body radiation to evaluate the temperature of gas flow by the shape of the spectrum. The main advantage of spectral pyrometry is that the temperature of gas flame can be determined without knowledge of emissivity constant [17,18]. The main objective of the present study is the development of a system based on a multispectral sensor-on-chip solution, which utilizes the method of multi-wave pyrometry for measuring the temperature of the flame inside the dilution zone of the combustion chamber of GTE. In this work, we also propose the solution of obtaining the optical access to the internal volume of a combustion chamber using a heatproof sapphire rod. The article provides the measurement results in the dilution zone of GTE.
wave range. Linear regression technique is used to estimate the temperature by data received from the multispectral sensor:
2. Measurement methods
3.1. Sensor design
2.1. Spectral pyrometry
The sensor consists of a sapphire rod, a metallic rig (special fixture for installing the sapphire rod into the wall of the combustion chamber), a fiber bundle, a control board. Previously it has been shown, that an assembly consisting of the fiber bundle and the sapphire rod could serve as a reliable instrument for screening a composition of burning gases [4]. The multispectral sensor placed in a vibro- and acousto-isolated aluminum box. The small and robust embodiment based on photodetectors allows installing it on board of an aircraft. The metallic rig is used for the firm fixation of the sapphire rod on the combustor’s wall. It is worth noting that the sapphire rod supplied with the metallic rig gives the opportunity of the distant measurements without perturbing the hot gas flow. The fiber bundle can withstand temperatures up to 600 °C and allows simultaneous transmission of the radiation to the spectrometer and the multispectral sensor. The multispectral sensor-on-chip (PixelSensor, PixelTeq Inc., United States) consists of eight silicon photodetectors. Seven photodetectors are hard-coated with interference bandpass filters. The multispectral sensor allows to detect six channels in the visible region with central wavelengths: 426 nm, 458 nm, 514 nm, 558 nm, 609 nm, and 658 nm. Each channel provides 15 nm FWHM (full width at half maximum). The channel 850 nm was used as an indicator of the influence of IR radiation on the multispectral sensor. Despite the fact that the multispectral sensor already has interference bandpass filters, an additional IR-cut filter (SZS-21, Arli Ltd., Russia) was used in order to minimize an influence of IR emission on the characteristics of the multispectral sensor. The filter cuts the IR region beyond 660 nm. This ensured that the light intensity in the channel at 850 nm was at the zero level. The control board digitizes data using a 16-bit ADC (MCDC04, MAZeT, Germany) and then transmits data to a PC via USB.
The temperature of the hottest zones of the combustion chamber of GTE varies within a range of 600–2200 °C. Wien’s displacement law derived from Plank’s law describes black body radiation for the mentioned temperatures [19]. Aircraft engines use mostly kerosene, which produces soot during inefficient combustion process [20,21]. Soot particles inside combustion chambers are considered to have an emission spectrum being close to the blackbody emission spectrum. Thus, the temperature might be evaluated according to the soot’s emission spectrum. Wien’s displacement law in a certain region of wavelengths describes spectrum emission of soot only if there is enough information in the spectral range 0.4–0.8 lm [12]. Temperature determination by spectral pyrometry is based on relative measurements of the intensity in a wide spectrum of a luminous object that is soot. The governing equation of measuring the temperature within the combustion chamber is written as [17,22]:
C2 ln k5 I ln ðeC1 Þ ¼ kT
ð1Þ
The unknown value of the e constant can be compensated by detailed spectral information, specifically by comparison between the shape of the spectral intensities distribution and the shape of blackbody radiation. In the case of grey body emission, where e ¼ const, Eq. (1) describes a straight line in coordinates x ¼ C2 =k and y ¼ lnðk5 IÞ, that are referred to as the Wien’s coordinates. Thus, the angle of the line in these coordinates is inversely proportional to the temperature of soot without taking into account a coefficient of emission. Following the spectral pyrometry, the method might help with the evaluation of the real-time temperature inside the GTE combustion chamber.
T¼
m X
wj Iðkj Þ þ b
ð2Þ
j¼1
The spectral method based on the spectrometer validates the multi-wave approach and provides data which is used the evaluation of the coefficients of linear regression for the multispectral sensor-on-chip solution. In order to make the system more robust and applicable for usage on board, it is possible to avoid the application of the spectrometer that is used in spectral pyrometry. 3. Multispectral sensor
2.2. Multi-wave pyrometry 3.2. High-temperature sapphire optical unit Temperature measurement by the method of multi-wave pyrometry is based on registration of the object’s radiation brightness at several wavelengths [13]. A multispectral sensor with narrow-band interference filters was implemented for this method since it can detect several spectral channels in the desired spectral
The optical unit propagating the radiation of the flame from the combustion chamber must withstand extremely harsh conditions [23]. Therefore, this unit is equipped with a sapphire rod due to its high resistance to hazardous environments and ability to
M.V. Mekhrengin et al. / Measurement 139 (2019) 355–360
357
from the sapphire optical unit was taken as a temperature reference in our experiments. The scheme of the experimental setup for testing of the developed sensor is shown in Fig. 2. Emission from combustion products of aviation kerosene fuel is directed from the sapphire rod into the fiber bundle. Further, the spectrometer and the multispectral sensor process the emission spectra. The spectrometer operates in the wavelength range from 425 nm to 750 nm. 4.2. Sensor placement An object of study was GTE (D-30KP-2, PJSC «UEC-Saturn», Russia). Experiments were performed on the combustion chamber. The sectional view of the combustion chamber is shown in Fig. 3. In order to mount the sensor, an additional hole in the wall of the flame tube of the combustion chamber was drilled. The size of the drilled outlet was chosen taking into account the thermal expansion coefficient of the walls of the GTE. The connection place of the facility to the GTE is shown in Fig. 4. Fig. 1. Schematic diagram of the optical unit comprising the sapphire rod and the metallic rig.
transmit radiation from the combustion chamber to the detection unit. The heat resistance of sapphire was investigated and it was shown that its melting point is 2040 °C. [16,24]. Moreover, it allows transmitting of the optical radiation in the wavelength range from 250 nm to 5000 nm. The sizes of the sapphire rod and the metallic rig were chosen in accordance with the parameters of the combustion chamber. The design of the sapphire rod and the metallic rig for installation into the combustion chamber is shown in Fig. 1. The rig consists of two metallic parts. Three copper and two rubber-metallic rings are fixed between them. The rings let avoid the hot gas clearance leakage. The fiber bundle includes nine multimode silica fibers with 1030 lm core diameter and aluminum coating coiled into a helix. The bunch strand is placed in a protective shell made of stranded silica tapes while optical connectors of the fiber bundle are formed using kovar sleeves and high temperature glue. The materials used in construction withstand the temperatures up to 600 °C. The end of the fiber bundle is attached to the wall of the combustion chamber which temperature does not exceed 600 °C due to continuous air-cooling between the wall of the combustion chamber and the flame tube from outside.
4.3. Data acquisition and analysis Nine operation modes of the GTE were measured. Each operation mode was active during 90 s and then was switched in accordance with the change of air-to-fuel ratio (AFR). The data from the thermocouples, the spectrometer, and the multispectral sensors were obtained simultaneously during the operation of the GTE.
Fig. 2. Schematic diagram of the experimental setup for testing developed sensor.
4. Experiments on the GTE In order to estimate the temperature inside the combustion chamber, the described techniques were used. Spectral pyrometry was implemented using the spectrometer (ASP-150T, Avesta Ltd., Russia) and the multi-wave pyrometry was applied based on the multispectral sensor. The temperature of hot gases inside the combustion chamber was derived from the emission spectra of soot using both techniques. 4.1. Experimental setup The GTE test bench is equipped with a set of thermocouples. Five thermocouple combs are installed at the exit of the combustion chamber to measure the temperature field therein. Each thermocouple comb consists of five Cr/Al thermocouples. A signal produced by one of the closest combs at a distance of 5 cm away
Fig. 3. The sectional view of the combustion chamber of the GTE.
358
M.V. Mekhrengin et al. / Measurement 139 (2019) 355–360
Fig. 4. The developed facility attached to the GTE.
Fig. 5. The soot radiation spectra corresponding to six operation modes of the GTE obtained with the spectrometer in standard coordinates.
Exposition time of the spectrometer was set up at 200 ms and five spectra during one second were averaged in order to decrease the noise level. The multispectral sensor operated in a mode with integration time 125 ms and the gain factor of 20. Signals from the thermocouple located in the combustion chamber were registered every 1 s. Spectral pyrometry error evaluation was provided by the bootstrap error evaluation of uncertainty of linear function approximation [25,26]. A linear regression error was assessed as the maximum prediction temperature deviation from the results obtained by the spectral approach in order to quantify the uncertainty associated with a multi-wave pyrometry. 5. Results and discussions The GTE operated in nine modes with determined AFR and temperature. The characteristics of every operation mode are shown in Table 1. Emission spectra measured with the spectrometer are illustrated in Figs. 5 and 6 in the standard and the Wien’s coordinates, respectively. The temperature of gas flow in the dilution zone of the GTE was estimated using the aforementioned method of finding the temperature described in Measurement methods Section 2.1. The derived temperature demonstrated a stepwise run. That form matches the dependence of the fuel supply on time. The calculated and reference temperatures are represented in Fig. 7. The spectral data collected during the first five operation modes was distorted whereas the following data allows evaluating the gas temperature that matches fine with the thermocouple unit. The presented effect is due to stuck of soot from the gas flow on the surface of the sapphire rod and further soot disappearance under the influence of high temperatures. To eliminate distortions caused
Fig. 6. The soot radiation spectra in Wien’s coordinates of six operation modes of the GTE.
Fig. 7. The change of the temperature corresponding to the GTE operation modes 1–9 evaluated using spectral pyrometry and registered by the thermocouple unit.
Table 1 Operation modes of the GTE. Operation mode, m
AFR
T from the thermocouple, C
Name of the operation mode
1 2 3 4 5
5 4.5 4 3.5 3
690 765 850 960 1070
6 7 8 9
2.8 3.5 4 4.5
1120 955 870 810
Idling power Cruising power 3 Cruising power 2 Cruising power 1 Maximum continuous power Maximum power Cruising power 1 Cruising power 2 Cruising power 3
by the negative impact of soot on the optical input port, it is possible to adjust the depth of the setting of the metallic rig. As it is seen in Table 2 the spread of temperature values is about 1% of the temperature Tm (temperature of the operation mode m). The gas temperature was also evaluated by the multispectral sensor, which is a part of the developed system. As it is described in Measurement methods Section 2.2. the gas temperature obtained using the spectrometer was used to evaluate the weight coefficients of linear regression. Since the spectral data collected during the first five operation modes was distorted we used only the following data to calibrate the multispectral sensor (steps 6–9).
359
M.V. Mekhrengin et al. / Measurement 139 (2019) 355–360 Table 2 Error estimation of the temperature in all operation modes of the GTE evaluated from the spectrometer’s data. Operation mode, m
1
2
3
4
5
6
7
8
9
Total deviation, DT, °C DT/Tm, %
20.5 1.1
23.0 1.1
21.9 1.2
22.7 1.1
37.4 1.1
9.6 0.9
10.8 1.0
9.1 1.0
10.7 1.0
Fig. 8. (A) The soot emission spectrum detected with the multispectral sensor; (B) The temperature of the gas flow measured using spectral pyrometry and multi-wave pyrometry.
Table 3 Error calculation of the temperature in 6–9 operation modes of the GTE measured by the sensor-on-chip solution. Operation mode, m
6
7
8
9
Total deviation, DT, C DT/Tm, %
43.3 3.7
26.2 2.5
21.7 2.3
24.4 2.7
It is potentially possible to conduct the measurements in the hottest part of the GTE – primary zone. Moreover, the system potentially can work on the low emissive GTE because OH*, CH* and C*2 radicals that are used for evaluating the temperature might be detected in visible wave range by means of the developed system. Acknowledgements
Further, the temperature of gas flow was estimated from the data of the multispectral sensor using linear regression as it is described in Measurement methods Section 2.2. Fig. 8(A) shows the integral intensity of each channel depending on the operation mode (6–9) of the GTE. The schematic change of the angle of the slope is depicted and the corresponding temperatures are labeled. Fig. 8(B) shows the temperature curves which were measured by the spectrometer (spectral pyrometry) and multispectral sensor (multi-wave pyrometry). As it is shown in Fig. 8(B) the temperature pattern derived from the multispectral sensor matches with the temperature pattern derived from the spectrometer. As it is seen in Table 3 the deviation of temperature is about 3%. Thus, the field test proved the possibility of the multispectral sensor usage as a part of high temperature pyrometer despite it is more sensitive to soot contamination. 6. Conclusions Temperature measurement in the dilution zone of GTE was performed by the developed pyrometer based on the multispectral sensor-on-chip solution. The system measured the temperature in the range of 810–1120 °C. The relative temperature error was about 3% so it is a significantly positive result in favor of multiwave methods of temperature measurement. The time reaction of the developed system is limited by the exposition time of the used detection facilities, which was 125 ms. At the same time, the response of the thermocouple was 1 s, so the time response of 125 ms is enough for replacing the thermocouple. However, for future purposes, such as flame stability measurement, the response time of the system should be improved.
This work was done at ITMO University and was supported by the Ministry of Science and Higher Education of the Russian Federation (The unique identifier of the project: RFMEFI57816X0202; Contract № 14.578.21.0202 from October 3, 2016). The authors are grateful to Prof. A.F. Novikov for the fruitful discussion and assistance in the preparation of the manuscript to publication. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.measurement.2019.02.084. References [1] N. Docquier, S. Candel, Combustion control and sensor: a review, Prog. Energy Combust. Sci. 28 (2) (2002) 107–150, https://doi.org/10.1016/S0360-1285(01) 00009-0. [2] A.A. Inozemtsev, A.N. Sazhenkov, V.V. Tsatiashvili, T.V. Abramchuk, V.A. Shipigusev, T.P. Andreeva, A.R. Gumerov, A.N. Ilyin, I.T. Gubaidullin, Delopment and application of noninvasive technology for study of combustion in a combustion chamber of gas turbine engine, Thermophys. Aeromech. 22 (3) (2015) 359–369, https://doi.org/10.1134/ S0869864315030117. [3] A. Moll, A. Behbahani, G.C. Fralick, J.D. Wrbanek, G. Hunter, A review of exhaust gas temperature sensing techniques for modern turbine engine controls, in: 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference: Cleveland, Ohio, 2014, https://doi.org/10.2514/6.2014-3977. [4] M. Mekhrengin, V. Guryev, I. Meshkovskii, D. Smirnov, A. Sukhinets, Development of sensor for spectral monitoring of combustion processes in gas-turbine engines, IEEE East-West Des. Test Symp. (EWDTS) (2018) 876–879, https://doi.org/10.1109/EWDTS.2018.8524839. [5] J. Kojima, Y. Ikeda, T. Nakajima, Spatially resolved measurement of OH*, CH*, and C2* chemiluminescence in the reaction zone of laminar methane/air premixed flames, Proc. Combust. Inst. 28 (2) (2000) 1757–1764, https://doi. org/10.1016/S0082-0784(00)80577-9.
360
M.V. Mekhrengin et al. / Measurement 139 (2019) 355–360
[6] S. Pellerin, K. Musiol, O. Motret, B. Pokrzywka, J. Chapelle, Application of the (0, 0) Swan band spectrum for temperature measurements, J. Phys. D: Appl. Phys. 29 (1996) 2850–2865, https://doi.org/10.1088/0022-3727/29/11/019. [7] D.J. Ellis, V.P. Solovjov, D.R. Tree, Temperature measurement using infrared spectral band emissions from H2O, J. Energy Resour. Technol 138 (4) (2016), https://doi.org/10.1115/1.4032425 042001. [8] K.S. Kappagantula, C. Crane, M.L. Pantoya, Determination of the spatial temperature distribution from combustion products: a diagnostic study, Rev. Sci. Instrum. 84 (10) (2013), https://doi.org/10.1063/1.4822118 104902. [9] C. Purpura, E. Trifoni, M. Musto, G. Rotondo, R. della Ragione, Methodology for spectral emissivity measurement by means of single color pyrometer, Measurement 82 (2016) 403–409, https://doi.org/10.1016/j. measurement.2016.01.018. [10] L. Savino, M. De Cesare, M. Musto, G. Rotondo, F. De Filippis, A. Del Vecchio, F. Russo, Free emissivity temperature investigations by dual color applied physics methodology in the mid-and long-infrared ranges, Int. J. Therm. Sci. 117 (2017) 328–341, https://doi.org/10.1016/j.ijthermalsci.2017.03.028. [11] M. Musto, G. Rotondo, M. De Cesare, A. Del Vecchio, L. Savino, F. De Filippis, Error analysis on measurement temperature by means dual-color thermography technique, Measurement 90 (2016) 265–277, https://doi.org/ 10.1016/j.measurement.2016.04.024. [12] I. Gulyaev, A. Dolmatov, Spectral-brightness pyrometry: radiometric measurements, Int. J. Heat Mass. Transfer. 116 (2018) 1016–1025, https:// doi.org/10.1016/j.ijheatmasstransfer.2017.09.084. [13] M. Liang, B. Sun, X. Sun, J. Xie, Development of a new fiber-optic multi-target multispectral pyrometer for achievable true temperature measurement of the solid rocket motor plume, Measurement 95 (2017) 239–345, https://doi.org/ 10.1016/j.measurement.2016.10.033. [14] M.A. Khan, C. Allemand, T.W. Eagar, Noncontact temperature measurement. II. Least squares based techniques, Rev. Sci. Instrum. 62 (2) (1991) 403–409, https://doi.org/10.1063/1.1142134. [15] D. Bastrom, R. Johansson, K. Andersson, F. Johnsson, S. Clausen, A. Fateev, Measurement and modeling of particle radiation in coal flames, Energy Fuel. 28 (3) (2014) 2199–2210, https://doi.org/10.1021/ef402271g.
[16] J. Ru˚zˇicˇka, J. Houzˇvicˇka, J. Bok, P. Praus, P. Mojzeš, Single-crystal sapphire tubes as economical probes for optical pyrometry in harsh environments, Appl. Optics 50 (36) (2011) 6599, https://doi.org/10.1364/AO.50.006599. [17] A. Magunov, Spectral pyrometry (Review), Instr. Exp. Tech. 52 (4) (2009) 451– 472, https://doi.org/10.1134/S0020441209040010. [18] A. Magunov, Spectral pyrometry of objects with a nonuniform temperature, Russ. J. Appl. Phys. 55 (7) (2010) 991–995, https://doi.org/10.1134/ S1063784210070121. [19] J. Ballester, T. Garcia-Armingol, Diagnostic techniques for the monitoring and control of practical flames, Prog. Energ. Combust. 36 (4) (2010) 375–411, https://doi.org/10.1016/j.pecs.2009.11.005. [20] R.K. Mishra, S. Chandel, Soot Formation and its effect in an aero gas turbine combustor, Int. J. Turbo Jet. Eng. (2016), https://doi.org/10.1515/tjj-20160062. [21] H. Lee, S. Seo, Experimental study on spectral characteristics of kerosene swirl combustion, Procedia Eng. 99 (2015) 304–312, https://doi.org/10.1016/j. proeng.2014.12.539. [22] Y.B. Yu, W.K. Chow, Review on an advanced high-temperature measurement technology: the optical fiber thermometry, J. Thermodyn. (2009) 1–11, https:// doi.org/10.1155/2009/823482. [23] B. Liu, Z. Yu, C. Hill, Y. Cheng, D. Homa, G. Pickrell, A. Wang, Sapphire-fiberbased distributed high-temperature sensing system, Opt. Lett. 41 (18) (2016) 4405–4408, https://doi.org/10.1364/ol.41.004405. [24] K.T.V. Grattan, Z.Y. Zhang, T. Sun, Y. Shen, L. Tong, Z. Ding, Sapphire-ruby single crystal fibre for application in high temperature optical fibre thermometers: studies at temperatures up to 1500 °C, Meas. Sci. Technol. 12 (7) (2001) 981– 986, https://doi.org/10.1088/0957-0233/12/7/340. [25] J.-H. Kim, Estimating classification error rate: repeated cross-validation, repeated hold-out and bootstrap, Comput. Stat. Data Anal. 53 (11) (2009) 3735–3745, https://doi.org/10.1016/j.csda.2009.04.009. [26] C. Beleites, R. Baumgartner, C. Bowman, R. Somorjai, G. Steiner, R. Salzer, M.G. Sowa, Variance reduction in estimating classification error using sparse datasets, Chemometr. Intell. Lab. 79 (1–2) (2005) 91–100, https://doi.org/ 10.1016/j.chemolab.2005.04.008.