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Dynamic temperature compensation model based on nonuniform temperature field change
Infrared Physics and Technology 101 (2019) 25–31
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Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Regular article
Dynamic temperature compensation model based on nonuniform temperature field change
T
⁎
Qian Shu , Shaosheng Dai, Hewen Nie, Weinan Yi Chongqing Key Laboratory of Signal and Information Processing, School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, No. 2 Chongwen Road, Nan’an District, Chongqing 400065, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Rotary kiln temperature measurement Variation of temperature field Atmospheric transmittance Compensation model
As the development of infrared temperature measurement technology, the research of the surface temperature monitoring system of rotary kiln based on infrared scanning has attracted the attention of experts in related fields. However, the non-contact characteristics of infrared bring many irresistible factors to the temperature measurement accuracy of rotary kiln, one of which cannot be ignored is the ambient temperature. In order to ensure the accuracy and stability of the system in temperature monitoring, the current research focuses on analyzing the influence of ambient temperature and establish a reasonable and effective temperature compensation model. In this paper, we analyze the influence of ambient temperature on temperature measurement in rotary kiln is analyzed based on the components of radiation received by infrared detector. The radiation received by infrared detector includes target radiation, reflection of ambient radiation and atmospheric radiation. It is found that the environmental temperature mainly affects the reflective radiation and atmospheric radiation of the environment, which cause the accuracy of temperature measurement drop. Therefore, this paper analysis the influence of ambient temperature on these two parts, and we put forward a dynamic temperature compensation model Based on nonuniform temperature field change, which improves the accuracy of temperature measurement by 5 percentage points.
1. Introduction Rotary kiln, known as rotary calcining kiln. It belongs to building materials equipment and is widely used in cement, metallurgy, glass and environmental protection industries. At present, there are three main types of surface temperature monitoring methods for rotary kiln [1]. The first is artificial observation method, although this method is easy and has low complexity, it has a great influence on human factors; the second type is thermocouple contact temperature measurement, which has a higher accuracy than the first type, however, the loss is serious and the stability is poor due to contact with rotary kiln; the third is the most widely used infrared temperature measurement technology. The surface temperature monitoring system of rotary kiln based on infrared scanning (ISTM) has obvious advantages, but the temperature measurement accuracy of the system is not high because of the influence of environment. Recently, there are many studies on compensation models for the influence of environment on the accuracy of infrared temperature measurement. Ochs proposed a pixel-wise calibration method which achieves high dynamic range by using fewer reference sources [2], Zhao Bin proposed an environment temperature
⁎
compensation model based on neural network algorithm [3]. A nonlinear mapping was established between the measured value of detector, the ambient temperature and the actual target temperature. The compensation coefficients were obtained through a certain amount of sample learning and training. For stable ambient temperature, these methods can achieve good results, but in view of the change of ambient temperature, this method needs to constantly update the reference temperature, which limits the real-time performance of temperature correction. Shi Dongping summarized two main compensation methods for environmental impact: reflection compensation method and incident compensation method [4]. This theory can be applied to target temperature measurement without considering atmospheric attenuation. If long-distance measurement (such as rotary kiln surface temperature measurement) needs reasonable improvement. Therefore, this paper combines the infrared temperature measurement principle and the field environment of rotary kiln to build a temperature compensation model for the system, which can overcome the non-uniformity of ambient temperature distribution and consider the influence of atmospheric attenuation in long-distance temperature measurement of rotary kiln. So as to achieve real-time and more accurate temperature
Corresponding author. E-mail address: [email protected] (Q. Shu).
https://doi.org/10.1016/j.infrared.2019.05.021 Received 27 February 2019; Received in revised form 20 May 2019; Accepted 27 May 2019 Available online 29 May 2019 1350-4495/ © 2019 Published by Elsevier B.V.
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Fig. 1. The composition of the detector receiving radiation.
temperature and the interference of these two parts. In this paper, the core idea of compensation model is to reasonably determine the parameters for specific application scenarios. The main parameters that need to be determined in the above formula are Tamb , Tamt , τ . For the first two temperature data, we can obtained through the temperature measuring instrument in the field. The determination of atmospheric transmittance needs to be determined according to the temperature field around the rotary kiln.
monitoring. 2. The effect of environmental temperature According to the principle of infrared temperature measurement, the radiation received by infrared detector includes target radiation and reflection of ambient radiation [5]. These radiations are attenuated and radiated through the atmosphere and reach the detector. The specific composition is shown in Fig. 1. We can see that the radiation arriving at the detector is mainly divided into three parts: the radiation emitted by the target, the reflected radiation of the environment and the radiation of the atmosphere. According to Fig. 1, the received radiation energy of the detector can be obtained as follows:
Wtot = ετWobj + (1 − ε ) τWamb + (1 − τ ) Wamt
3. The acquisition of atmospheric transmittance Atmospheric attenuation of infrared radiation mainly includes absorption and scattering attenuation. According to the absorption curves of H2O and CO2 at different wavelengths, it can be seen that the absorption rate is high in the infrared band selected for the surface temperature monitoring of rotary kiln. At this time, the scattering effect of atmosphere is so small that the scattering attenuation of atmosphere can be neglected. Thus, the absorption of H2O and CO2 is only considerate here, and the atmospheric transmittance τ can be calculated according to the following formula:
(1)
ε is the emissivity of object. The rotary kiln is generally coiled and welded automatically by carbon steel or alloy steel plate. In the process of using, the wear degree and dust distribution on the surface of the rotary kiln are nearly uniform. After investigating and analyzing the rotary kiln, we set the emissivity to 0.7, and add an emissivity finetuning function to compensate the changes in emissivity after long-term use on the remote terminal. This paper mainly analyses the influence of ambient temperature on the accuracy of temperature measurement. τ is the atmospheric transmittance, it is related to ambient temperature. Wobj represents the radiation energy on the surface of the target object, Wamb is the reflected radiation energy of environmental near rotary kiln, and Wamt is the environmental radiation energy of the atmosphere. According to Stephen Boltzmann's law [6,7], the relationship between the radiation energy of the target object and the surface temperature T can be obtained as follows:
τ = τH2 O *τCO2
τH2 O represents the transmittance of H2O, and τCO2 represents the transmittance of CO2. To calculate τH2 O in a certain length of atmospheric path, the first step is to calculate the content of H2O in the distance, and the content of H2O is measured by condensable water, and known as precipitable water, which is the thickness of the H2O condensed into a water layer in a container with the same cross-section as the beam along the direction of light. Its unit is mm ·km−1 which can be calculated by the following formulas.
(2)
W = σT n
σ = 5.67032 × 10−8 W·m−2·k−4 is the Stephen-Boltzmann constant and the Eq. (1) can be rewritten as follows: n n n n TISTM = ετTobj + (1 − ε ) τTamb + (1 − τ ) Tamt
ρw = RH *ρs
(6)
W = ρw *x H2 O
(7)
Formula above, W is the millimeter value of condensable water at a given distance, ρs is the quality of saturated water vapor at current temperature which can be obtained by looking up tables [8]; RH is relative humidity; ρw is the water vapor content in actual environment; x H2 O is horizontal distance of light propagation direction. Since the height of the rotary kiln is less than 10 m from the ground, the influence of the height on the transmittance can be neglected. After calculating the water vapor content of the known distance length, the transmittance of water vapor in the current atmospheric environment can be obtained by looking up the table CO2 which is the only gas that mixes approximately uniformly in the atmosphere for infrared absorption molecules. The transmittance of CO2 in atmospheric environment can be obtained directly by looking up table method. From the above analysis, it is clear that τH2 O is susceptible to the influence of ambient temperature. Therefore, the influence of ambient temperature on the transmittance of H2O is mainly considered when considering the influence of ambient temperature on the transmittance. In addition, the ambient temperature field has shown a trend of attenuation because of the high temperature of the rotary kiln. In order to best reflect the infrared radiation on the rotary kiln, it is necessary to obtain the real-time
(3)
TISTM is the target temperature measured by ISTM, Tobj represents the real temperature on the surface of the target object, Tamb is the ambient temperature near the rotary kiln, and Tamt is the temperature of the atmosphere, that is the natural air temperature which not affected by the heat dissipation of the rotary kiln. n is a constant related to the wavelength of infrared thermal imager. When the wavelength is 3 − 5 μm , n = 9.2554 ; the wavelength is 8 − 12 μm , n = 3.9889 . From the above analysis, the temperature measured by ISTM includes the interference of various radiations in the environment, the influence of environmental reflection radiation and atmospheric transmission. Thus, the temperature calculation formula of rotary kiln’ surface can be obtained as follows: 1
T9 (1 − ε ) 9 (1 − τ ) 9 ⎞ 9 Tobj = ⎜⎛ ISTM − Tamb − Tamt ⎟ ετ ε ετ ⎝ ⎠
(5)
(4)
Therefore, in order to improve the accuracy of temperature measurement, it is necessary to find out the relationship between ambient 26
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atmospheric transmittance according to the actual temperature field distribution.
Table 1 The tools and simulation software.
3.1. Distribution of temperature field around rotary kiln At different temperatures, the quality of saturated water vapor is different, due to the high temperature on the surface of rotary kiln and the continuous heat dissipation process, the temperature distribution around the rotary kiln is not uniform. Many errors will occur when calculating the atmospheric transmittance. Therefore, the influence of the high temperature operation of rotary kiln on the distribution of temperature field in the surrounding environment should be carefully analyzed, because the high temperature state of rotary kiln is continuous, the heat transfer between rotary kiln and air near surface can be regarded as a stable process approximately. This section takes the ambient temperature near the surface of rotary kiln Tamb and the ambient temperature of ISTM Tamt as the boundary temperature, and then finds out the distribution of temperature field between the surface of rotary kiln and the ISTM. Under the action of heat convection, the rotary kiln continuously emits heat outward. Therefore, the environmental temperature of the rotary kiln surface is mainly affected by the heat emitted from rotary kiln. It is assumed that the environment of the rotary kiln is stable. According to the law of thermodynamics, when the environment reaches the state of thermal equilibrium, the temperature will not change with time. In addition, according to the literature, the influence range of high temperature heat sources with different temperatures on environmental temperature has differences [9]. To solve this problem, this paper takes the no. 1 rotary kiln of Southwest Cement Company as an example to collect the environmental temperature of characteristic points. The rotary kiln model is Φ4*60m , the temperature measuring system is installed on the tower 30 m away from the center of the rotary kiln and ensure that the height of the system is consistent with that of the rotary kiln. Because the vertical height of rotary kiln is 7–8 m, the pressure in this height has little change, so the influence of vertical height on temperature can be neglected. A two-dimensional coordinate axis is established with the center of the rotary kiln as the coordinate origin and the horizontal and vertical direction of the rotary kiln as the coordinate axis. The distribution of the sampling feature points is shown in the left of Fig. 2. Acquisition of 21 points in horizontal direction with 3 m spacing, along the vertical direction of the rotary kiln moving 3 m for each acquisition. (Near the rotary kiln, there are observatories which can be used to measure temperature, and the temperature which distance from the rotary kiln 3 m or more is measured at the level of the ground.) The environmental temperature and measurement tools at the time of the experiment are shown in the right of
Name
Model or version
Remarks
MATLAB Blackbody ISTM ISTM Ruler Ambient thermometer
R2017b JQ-100MYZ3C Hardware entity Software terminal 50 m UT333
Infrared point thermometer
raytek raynger st60+
Data analysis and fitting Standard heat source emitters Temperature Data Acquisition Observation and data save Distance calibration Measuring ambient temperature and humidity Measuring the Real Temperature of Rotary Kiln
Fig. 2. The tools and simulation software used in the experiment are shown in Table 1. The temperature data collected on site are shown in Table 2. There are many data in Table 2, and it is difficult to analyze the decay law of temperature with distance. The data in Table 2 is described in the form of three-dimensional graph as shown in Fig. 3. We can see from Fig. 3 that when the vertical distance from the rotary kiln is unchanged, the temperature fluctuation in the horizontal position is not large. The average value of all the horizontal temperature at a vertical distance from the rotary kiln can be regarded as the environmental temperature, it also can be described that the temperature is Td at the distance from the rotary kiln d meter. The temperature trend is shown in Fig. 4. The temperature distribution around the rotary kiln has obvious stratification phenomenon. In the first part, the temperature decreases linearly. When the temperature approaches the ambient temperature, the temperature keeps stable basically. The relationship between the ambient temperature distribution and the distance can be obtained by linear fitting with the average temperature as Eq. (8):
− 1.82d + Tamb d ⩽ 9m Td = ⎧ Tamt d > 9m ⎨ ⎩
(8)
Within the range of 9 m from the rotary kiln, the temperature decreases monotonously, which mainly due to the continuous heat dissipation of the rotary kiln and the thermal convection of the environment. The attenuation should take the environmental temperature of the rotary kiln surface as the boundary. Therefore, the Tamb in the Eq. (8) is the environmental temperature measured when the distance from the rotary kiln is very close. When the temperature decreases to close to the ambient temperature, the temperature reaches a balance with the environment. The second part Tamt is the ambient temperature at the installation position of ISTM. These two temperature values can be obtained by the field temperature measuring equipment, so that the
Fig. 2. The plan and tools Experimental. 27
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Table 2 The temperature data collected on site. Characteristic point temperature/°C Horizontal coordinates x/m
−30 −27 −24 −21 −18 −15 −12 −9 −6 −3 0 3 6 9 12 15 18 21 24 27 30
Vertical coordinates y/m 0
3
6
9
12
15
18
21
24
27
30
29.4 28.6 28.1 29 29.1 29 29.1 29.2 29.5 28 29.1 28.3 29.4 28.3 28.2 29.2 29.1 29.1 28 29 29.1
21.6 21.4 21.8 21.4 21.1 21.4 21.3 22 21.3 21.5 21.9 21 21.4 21.8 21.2 21.9 21 22 21.5 21.3 21.5
16.2 16.4 16.3 16.8 16.3 16.3 16.5 17 16.7 16.4 16.4 16.7 16 16.4 16.5 16.3 16.9 16 16 16.5 17
12.7 12.4 12.1 12.3 12.2 12.9 12.7 12.2 12.7 12.8 12.8 12.6 12 12.1 12 12.5 12.5 13 12.8 12.2 12.1
12.6 12.1 12.1 12.1 12 12.7 12.8 12.1 12.8 12.3 13 12.6 12.1 12.9 12.4 12.6 12.5 12.9 12.5 12.6 12.5
12.9 13 12.7 12.1 12.5 12.4 12.7 12.9 12.7 12.4 12.6 12.7 12.9 12.6 12.6 12.8 12.7 12.9 12 12.9 12.5
12.9 12.8 12 12.2 12.2 12.5 12.3 12.3 12.3 12.4 12 12.1 12.8 12.3 12 12.3 12.3 13 12.7 12.9 12.3
11.9 11.9 11.9 11.9 11.1 11.7 11.2 11.3 11.4 11.5 11.9 11.5 11.9 11.2 11.1 11.6 11.5 11.1 11.8 11.7 11.3
11.3 11.9 12.3 11 12.4 11.5 12.3 11.3 12.3 11.5 11 12.5 11.7 11.5 11.6 12.1 11.8 11.3 12.3 12.3 11.7
11 12.5 11.3 12.1 11.5 11.3 11.9 11.3 12.2 11.9 12.1 11.3 12.1 11.5 11.8 11.3 11.6 11.8 12.2 12.3 11.1
11.1 12 11.5 11.4 11.4 11.1 11.4 11.5 12 11.7 11.2 11.2 11.7 11.8 11.5 11.8 11 11.2 11.8 11 11.8
Fig. 3. The three-dimensional distribution of surface temperature field in rotary kiln.
the environmental temperature attenuation part, and T2amt is the stable environmental temperature:
temperature distribution near the rotary kiln can be obtained. The atmospheric radiation is related not only to the transmittance but also to the atmospheric temperature. According to the distribution of the field temperature field, the third part of Eq. (4) should consider the change of the atmospheric temperature. Therefore, the following deformation can be obtained form Eq. (4):
T1amt =
Tobj
(10)
3.2. Calculation of atmospheric transmittance
1
T9 (1 − ε ) 9 (1 − τ1) 9 (1 − τ2) 9 ⎞ 9 = ⎜⎛ amb − Tamb − ( T1amt + T2amt ) ⎟ ε ετ1 ετ2 ⎝ ετ1 ⎠
Tamb + Tamt , T2amt = Tamt 2
To obtain the transmittance of H2O, there are two parameters need to be obtained by looking up tables: saturated water vapor content ρs at different temperatures and atmospheric transmittance of water vapor. The first parameter is only related to environmental temperature. In order to build the model easily, we obtain the relationship between the
(9)
Among them, τ1, τ2 are the atmospheric transmittance of the environmental temperature attenuation part and the environmental temperature stabilization part respectively. T1amt is the average temperature of 28
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Fig. 4. The distribution of ambient temperature.
Fig. 6. The whole temperature compensation correction model.
W1 = RH ∗
9
∫x=0 975.6*e(−(
W2 = RH ∗ 975.6*e (−(
Table 3 The data measured in the field. Field data values
Tamb (°C) Tamt (°C) RH
28.8 11.4 71.8%
ρs =
∗ 21
(13)
τ¯1H2 O = (τ3.0 + τ3.1 + τ3.2+⋯+τ4.9)/20
(14)
τ¯2 H2 O = (τ3.0 + τ3.1 + τ3.2+⋯+τ4.9)/20
(15)
τ¯1H2 O is the average transmittance of H2O in d ⩽ 9 m , τ¯2 H2 O is the average transmittance of H2O in d > 9 m . Using the same method, the transmittance of CO2 with a horizontal distance of 30 m is approximately obtained from the transmittance of CO2 with a horizontal distance of 0.1 km within the range of 3 ∼ 5 μm , All values are added and averaged.
environmental temperature and ρs by fitting the data in the table. The second parameter is mainly determined by precipitation and the band of the detector. It is different in the specific situation, so we still obtained this parameter by looking up tables. First, the fitting curve of the saturated water vapor content ρs at ambient temperature − 25°C ∼ 54°C is shown in Fig. 5. In Fig. 5, 80 points in the standard table are selected to fit the curve. In order to be closer to the empirical value, this paper chooses the Gauss function to fit the data. The fitting results are as follows: T − 156.7 2 975.6*e (−( 67.94 ) )
Tsysl − 156.7 2 ) ) 67.94
(12)
The temperature distribution is stratified and the saturated water vapor content is different at different temperatures, the condensable water millimeter value W in the linear attenuation part (d ⩽ 9 m ) of ambient temperature is obtained by integral method, using W1 representation. For the other part (d > 9 m ), the ambient temperature of the temperature measuring system is taken as the criterion, using W2 representation. The medium wave infrared detector selected by ISTM which band at 3 ∼ 5 μm . The W1, W2 can be obtained by adding and averaging all the values within the range of 3 ∼ 5 μm [10,11].
Fig. 5. The fitting curve of ρs at different ambient temperature.
Variables to be tested
−1.82x + Tsurh − 156.7 2 ) ) 67.94 dx
τ¯CO2 = (τ3.0 + τ3.1 + τ3.2+⋯+τ4.9)/20 ≈ 0.907
(16)
τ¯CO2 is the average transmittance of CO2. Then the atmospheric transmittance in two distance regions is obtained according to the following formula. τ1 = τ¯1H2 O *¯τCO2, τ2 = τ¯2 H2 O *¯τCO2
(17)
τ1 is the transmittance in d ⩽ 9 m , τ2 is the transmittance in d > 9 m . For the subjects of this experiment, the data measured in the field are shown in Table 3: According to the above analysis, the W1, W2 of condensable water in the experimental environment can be calculated by the value in Table 3.
(11)
T is the ambient temperature of the current position. Combined with the analysis of the environmental temperature field around the rotary kiln in the previous section, in order to get the millimeter value of condensable water with known horizontal distance, it is necessary to calculate the water vapor content in different temperature ranges in stages. According to the distance distribution of temperature field, The millimeter value of condensable water from rotary kiln to ISTM is calculated in two parts. The calculation formulas are as follows:
W1 = 0.12 mm, W2 = 0.16 mm
(18)
Combined with τH2 O and τCO2 , the atmospheric transmittance of condensable water with a millimeter value of 0.1 mm, 0.2 mm can be obtained within the range of 3 ∼ 5 μm : 29
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Fig. 7. Remote Temperature Monitoring Interface of Rotary Kiln. Table 4 The corresponding relationship. Actual feature points location (kiln head as origin) Characteristic points corresponding sequence number Actual feature points location (kiln head as origin) Characteristic points corresponding sequence number
0 0 31.2 364
2.4 28 33.6 392
4.8 56 36 420
7.2 84 38.4 448
τ1 = τ¯1H2 O *¯τCO2 = 0.98*0.907 ≈ 0.89 (19)
By substituting the above data into Eq. (9), the dynamic temperature compensation model based on the variation of non-uniform temperature field can be obtained as follows: 9
T 9 Tobj = ⎜⎛ amb − 0.429*1. Tamb − 0.177*T19amt + 0.159T29amt ⎟⎞ ⎝ 0.623 ⎠
(
)
12 140 43.2 504
14.4 168 45.6 532
16.8 196 48 560
19.2 224 50.4 588
21.6 252 52.8 616
24 280 55.2 644
26.4 308 57.6 672
28.8 336 60 700
accuracy of temperature measurement proposed in Section 3, we obtain the surface temperature Tamb of rotary kiln, the ambient temperature Tamt and relative humidity RH through field equipment, and then summarize the temperature compensation correction model based on ambient temperature in Fig. 6. The model is embedded in the core processing board of the infrared temperature measurement system and compared with the version without any compensation. The appearance of Rotary Kiln and remote monitoring interface of the temperature measurement system developed by our team is shown in Fig. 7: The system collects 700 points per row. In order to facilitate comparison, the spot thermometers is used to measure the characteristic temperature points on the surface of rotary kiln as the standard point to observe the temperature measurement without compensation and after compensation. According to the surface fabrication technology and surface temperature distribution of rotary kiln [12], the kiln head is taken as the starting point, and a temperature point is measured every 2.8 m as the standard temperature point. That is to say, the temperature data collected by the system are recorded once at each 26 points. The corresponding relationship between the data is shown in Table 4. According to the above correspondence, the surface temperature of rotary kiln is compared with the temperature measured by the system without considering the influence of ambient temperature and the system with compensation model in this paper. The experimental data are arranged as follows: From the trend in Fig. 8, we can see that the measured results of ISTM are lower than the actual values without considering the influence
Fig. 8. The Error comparison.
τ2 = τ¯2 H2 O *¯τCO2 = 0.99*0.907 ≈ 0.9
9.6 112 40.8 476
1 9
(20)
4. Compensation model and experimental verification According to analyzing the influence of ambient temperature on the 30
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5. Conclusion
Table 5 Comparison of Different Temperature Measurement Models. Distance (m)
The actual measured temperature (°C)
Temperature without considering ambient temperature (°C)
Error
Temperature considering ambient temperature (°C)
Error
0 2.4 4.8 7.2 9.6 12 14.4 16.8 19.2 21.6 24 26.4 28.8 31.2 33.6 36 38.4 40.8 43.2 45.6 48 50.4 52.8 55.2 57.6 60
283.7 89.4 412.6 389.1 376.9 381.5 362.4 368.2 355.9 214.7 108.4 313.7 374.9 349.7 350.9 348.3 363.4 368.9 373.4 369.8 112.5 276.3 133.4 321.9 319.7 270.4
244.2 62.0 373.8 355.6 344.3 350.0 333.8 339.4 331.1 198.2 97.4 292.8 352.8 327.5 328.1 325.1 338.9 340.0 341.2 337.5 89.3 244.0 107.5 285.1 279.2 229.4
−39.50 −27.42 −38.82 −33.54 −32.58 −31.46 −28.62 −28.76 −24.79 −16.55 −10.97 −20.89 −22.13 −22.22 −22.85 −23.23 −24.51 −28.90 −32.24 −32.32 −23.17 −32.29 −25.86 −36.77 −40.51 −41.00
257.38 65.32 393.96 374.75 362.91 368.94 351.8 357.77 348.98 208.85 102.69 308.62 371.81 345.16 345.76 342.62 357.18 358.35 359.58 355.7 94.15 257.18 113.35 300.52 294.26 241.78
−26.32 −24.08 −18.64 −14.35 −13.99 −12.56 −10.60 −10.43 −6.92 −5.85 −5.71 −5.08 −3.09 −4.54 −5.14 −5.68 −6.22 −10.55 −13.82 −14.10 −18.35 −19.12 −20.05 −21.38 −25.44 −28.62
Based on the analysis of the working environment of rotary kiln and the principle of infrared temperature measurement, this paper establishes a compensation model for the environmental factors affecting the accuracy of temperature measurement. According to the source of infrared temperature measurement receiving radiation, we find out the influence of ambient temperature on each part of the system, mainly including the environmental reflection radiation on the surface of rotary kiln and the influence on atmospheric transmittance. Through realtime acquisition of the environmental temperature near the rotary kiln and the atmospheric temperature near the ISTM, compensate for the impact of ambient temperature, so as to improve the accuracy of system in different environments. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 61671094) and the National Science Foundation of Chongqing Science and Technology Commission (No. CSTC2015JCYJA40032). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.infrared.2019.05.021. References
of ambient temperature, which is consistent with the theoretical analysis. In this paper, the measured value of the system after model compensation is closer to the real value. According to the calculation formula of the average error Eave , we can see the obvious advantages of the compensation model in this paper. N
∑i = 1 Eave =
i − Ti |Ttest actual | i Tactual
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× 100%
N
(21)
i represents the temperature measurements of the ISTM system for Ttest point i, represents the true temperature at point i measured by the Raytek hand-held thermometer. N represents the number of characteristic points. In this experiment, the value of N is 26. By substituting the data in Table 5 into the Eq. (21), the average errors without considering and considering the ambient temperature can be calculated as follows:
1 2 Eave = 10.58% Eave = 5.75%
(22)
1 Eave is the mean error without considering the ambient temperature, 2 is the mean error under the compensation model of ambient and Eave temperature in this paper. The proposed model in this paper improves the accuracy of infrared scanning temperature measurement system by nearly 5 percentage points.
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Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Regular article
Dynamic temperature compensation model based on nonuniform temperature field change
T
⁎
Qian Shu , Shaosheng Dai, Hewen Nie, Weinan Yi Chongqing Key Laboratory of Signal and Information Processing, School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, No. 2 Chongwen Road, Nan’an District, Chongqing 400065, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Rotary kiln temperature measurement Variation of temperature field Atmospheric transmittance Compensation model
As the development of infrared temperature measurement technology, the research of the surface temperature monitoring system of rotary kiln based on infrared scanning has attracted the attention of experts in related fields. However, the non-contact characteristics of infrared bring many irresistible factors to the temperature measurement accuracy of rotary kiln, one of which cannot be ignored is the ambient temperature. In order to ensure the accuracy and stability of the system in temperature monitoring, the current research focuses on analyzing the influence of ambient temperature and establish a reasonable and effective temperature compensation model. In this paper, we analyze the influence of ambient temperature on temperature measurement in rotary kiln is analyzed based on the components of radiation received by infrared detector. The radiation received by infrared detector includes target radiation, reflection of ambient radiation and atmospheric radiation. It is found that the environmental temperature mainly affects the reflective radiation and atmospheric radiation of the environment, which cause the accuracy of temperature measurement drop. Therefore, this paper analysis the influence of ambient temperature on these two parts, and we put forward a dynamic temperature compensation model Based on nonuniform temperature field change, which improves the accuracy of temperature measurement by 5 percentage points.
1. Introduction Rotary kiln, known as rotary calcining kiln. It belongs to building materials equipment and is widely used in cement, metallurgy, glass and environmental protection industries. At present, there are three main types of surface temperature monitoring methods for rotary kiln [1]. The first is artificial observation method, although this method is easy and has low complexity, it has a great influence on human factors; the second type is thermocouple contact temperature measurement, which has a higher accuracy than the first type, however, the loss is serious and the stability is poor due to contact with rotary kiln; the third is the most widely used infrared temperature measurement technology. The surface temperature monitoring system of rotary kiln based on infrared scanning (ISTM) has obvious advantages, but the temperature measurement accuracy of the system is not high because of the influence of environment. Recently, there are many studies on compensation models for the influence of environment on the accuracy of infrared temperature measurement. Ochs proposed a pixel-wise calibration method which achieves high dynamic range by using fewer reference sources [2], Zhao Bin proposed an environment temperature
⁎
compensation model based on neural network algorithm [3]. A nonlinear mapping was established between the measured value of detector, the ambient temperature and the actual target temperature. The compensation coefficients were obtained through a certain amount of sample learning and training. For stable ambient temperature, these methods can achieve good results, but in view of the change of ambient temperature, this method needs to constantly update the reference temperature, which limits the real-time performance of temperature correction. Shi Dongping summarized two main compensation methods for environmental impact: reflection compensation method and incident compensation method [4]. This theory can be applied to target temperature measurement without considering atmospheric attenuation. If long-distance measurement (such as rotary kiln surface temperature measurement) needs reasonable improvement. Therefore, this paper combines the infrared temperature measurement principle and the field environment of rotary kiln to build a temperature compensation model for the system, which can overcome the non-uniformity of ambient temperature distribution and consider the influence of atmospheric attenuation in long-distance temperature measurement of rotary kiln. So as to achieve real-time and more accurate temperature
Corresponding author. E-mail address: [email protected] (Q. Shu).
https://doi.org/10.1016/j.infrared.2019.05.021 Received 27 February 2019; Received in revised form 20 May 2019; Accepted 27 May 2019 Available online 29 May 2019 1350-4495/ © 2019 Published by Elsevier B.V.
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Fig. 1. The composition of the detector receiving radiation.
temperature and the interference of these two parts. In this paper, the core idea of compensation model is to reasonably determine the parameters for specific application scenarios. The main parameters that need to be determined in the above formula are Tamb , Tamt , τ . For the first two temperature data, we can obtained through the temperature measuring instrument in the field. The determination of atmospheric transmittance needs to be determined according to the temperature field around the rotary kiln.
monitoring. 2. The effect of environmental temperature According to the principle of infrared temperature measurement, the radiation received by infrared detector includes target radiation and reflection of ambient radiation [5]. These radiations are attenuated and radiated through the atmosphere and reach the detector. The specific composition is shown in Fig. 1. We can see that the radiation arriving at the detector is mainly divided into three parts: the radiation emitted by the target, the reflected radiation of the environment and the radiation of the atmosphere. According to Fig. 1, the received radiation energy of the detector can be obtained as follows:
Wtot = ετWobj + (1 − ε ) τWamb + (1 − τ ) Wamt
3. The acquisition of atmospheric transmittance Atmospheric attenuation of infrared radiation mainly includes absorption and scattering attenuation. According to the absorption curves of H2O and CO2 at different wavelengths, it can be seen that the absorption rate is high in the infrared band selected for the surface temperature monitoring of rotary kiln. At this time, the scattering effect of atmosphere is so small that the scattering attenuation of atmosphere can be neglected. Thus, the absorption of H2O and CO2 is only considerate here, and the atmospheric transmittance τ can be calculated according to the following formula:
(1)
ε is the emissivity of object. The rotary kiln is generally coiled and welded automatically by carbon steel or alloy steel plate. In the process of using, the wear degree and dust distribution on the surface of the rotary kiln are nearly uniform. After investigating and analyzing the rotary kiln, we set the emissivity to 0.7, and add an emissivity finetuning function to compensate the changes in emissivity after long-term use on the remote terminal. This paper mainly analyses the influence of ambient temperature on the accuracy of temperature measurement. τ is the atmospheric transmittance, it is related to ambient temperature. Wobj represents the radiation energy on the surface of the target object, Wamb is the reflected radiation energy of environmental near rotary kiln, and Wamt is the environmental radiation energy of the atmosphere. According to Stephen Boltzmann's law [6,7], the relationship between the radiation energy of the target object and the surface temperature T can be obtained as follows:
τ = τH2 O *τCO2
τH2 O represents the transmittance of H2O, and τCO2 represents the transmittance of CO2. To calculate τH2 O in a certain length of atmospheric path, the first step is to calculate the content of H2O in the distance, and the content of H2O is measured by condensable water, and known as precipitable water, which is the thickness of the H2O condensed into a water layer in a container with the same cross-section as the beam along the direction of light. Its unit is mm ·km−1 which can be calculated by the following formulas.
(2)
W = σT n
σ = 5.67032 × 10−8 W·m−2·k−4 is the Stephen-Boltzmann constant and the Eq. (1) can be rewritten as follows: n n n n TISTM = ετTobj + (1 − ε ) τTamb + (1 − τ ) Tamt
ρw = RH *ρs
(6)
W = ρw *x H2 O
(7)
Formula above, W is the millimeter value of condensable water at a given distance, ρs is the quality of saturated water vapor at current temperature which can be obtained by looking up tables [8]; RH is relative humidity; ρw is the water vapor content in actual environment; x H2 O is horizontal distance of light propagation direction. Since the height of the rotary kiln is less than 10 m from the ground, the influence of the height on the transmittance can be neglected. After calculating the water vapor content of the known distance length, the transmittance of water vapor in the current atmospheric environment can be obtained by looking up the table CO2 which is the only gas that mixes approximately uniformly in the atmosphere for infrared absorption molecules. The transmittance of CO2 in atmospheric environment can be obtained directly by looking up table method. From the above analysis, it is clear that τH2 O is susceptible to the influence of ambient temperature. Therefore, the influence of ambient temperature on the transmittance of H2O is mainly considered when considering the influence of ambient temperature on the transmittance. In addition, the ambient temperature field has shown a trend of attenuation because of the high temperature of the rotary kiln. In order to best reflect the infrared radiation on the rotary kiln, it is necessary to obtain the real-time
(3)
TISTM is the target temperature measured by ISTM, Tobj represents the real temperature on the surface of the target object, Tamb is the ambient temperature near the rotary kiln, and Tamt is the temperature of the atmosphere, that is the natural air temperature which not affected by the heat dissipation of the rotary kiln. n is a constant related to the wavelength of infrared thermal imager. When the wavelength is 3 − 5 μm , n = 9.2554 ; the wavelength is 8 − 12 μm , n = 3.9889 . From the above analysis, the temperature measured by ISTM includes the interference of various radiations in the environment, the influence of environmental reflection radiation and atmospheric transmission. Thus, the temperature calculation formula of rotary kiln’ surface can be obtained as follows: 1
T9 (1 − ε ) 9 (1 − τ ) 9 ⎞ 9 Tobj = ⎜⎛ ISTM − Tamb − Tamt ⎟ ετ ε ετ ⎝ ⎠
(5)
(4)
Therefore, in order to improve the accuracy of temperature measurement, it is necessary to find out the relationship between ambient 26
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atmospheric transmittance according to the actual temperature field distribution.
Table 1 The tools and simulation software.
3.1. Distribution of temperature field around rotary kiln At different temperatures, the quality of saturated water vapor is different, due to the high temperature on the surface of rotary kiln and the continuous heat dissipation process, the temperature distribution around the rotary kiln is not uniform. Many errors will occur when calculating the atmospheric transmittance. Therefore, the influence of the high temperature operation of rotary kiln on the distribution of temperature field in the surrounding environment should be carefully analyzed, because the high temperature state of rotary kiln is continuous, the heat transfer between rotary kiln and air near surface can be regarded as a stable process approximately. This section takes the ambient temperature near the surface of rotary kiln Tamb and the ambient temperature of ISTM Tamt as the boundary temperature, and then finds out the distribution of temperature field between the surface of rotary kiln and the ISTM. Under the action of heat convection, the rotary kiln continuously emits heat outward. Therefore, the environmental temperature of the rotary kiln surface is mainly affected by the heat emitted from rotary kiln. It is assumed that the environment of the rotary kiln is stable. According to the law of thermodynamics, when the environment reaches the state of thermal equilibrium, the temperature will not change with time. In addition, according to the literature, the influence range of high temperature heat sources with different temperatures on environmental temperature has differences [9]. To solve this problem, this paper takes the no. 1 rotary kiln of Southwest Cement Company as an example to collect the environmental temperature of characteristic points. The rotary kiln model is Φ4*60m , the temperature measuring system is installed on the tower 30 m away from the center of the rotary kiln and ensure that the height of the system is consistent with that of the rotary kiln. Because the vertical height of rotary kiln is 7–8 m, the pressure in this height has little change, so the influence of vertical height on temperature can be neglected. A two-dimensional coordinate axis is established with the center of the rotary kiln as the coordinate origin and the horizontal and vertical direction of the rotary kiln as the coordinate axis. The distribution of the sampling feature points is shown in the left of Fig. 2. Acquisition of 21 points in horizontal direction with 3 m spacing, along the vertical direction of the rotary kiln moving 3 m for each acquisition. (Near the rotary kiln, there are observatories which can be used to measure temperature, and the temperature which distance from the rotary kiln 3 m or more is measured at the level of the ground.) The environmental temperature and measurement tools at the time of the experiment are shown in the right of
Name
Model or version
Remarks
MATLAB Blackbody ISTM ISTM Ruler Ambient thermometer
R2017b JQ-100MYZ3C Hardware entity Software terminal 50 m UT333
Infrared point thermometer
raytek raynger st60+
Data analysis and fitting Standard heat source emitters Temperature Data Acquisition Observation and data save Distance calibration Measuring ambient temperature and humidity Measuring the Real Temperature of Rotary Kiln
Fig. 2. The tools and simulation software used in the experiment are shown in Table 1. The temperature data collected on site are shown in Table 2. There are many data in Table 2, and it is difficult to analyze the decay law of temperature with distance. The data in Table 2 is described in the form of three-dimensional graph as shown in Fig. 3. We can see from Fig. 3 that when the vertical distance from the rotary kiln is unchanged, the temperature fluctuation in the horizontal position is not large. The average value of all the horizontal temperature at a vertical distance from the rotary kiln can be regarded as the environmental temperature, it also can be described that the temperature is Td at the distance from the rotary kiln d meter. The temperature trend is shown in Fig. 4. The temperature distribution around the rotary kiln has obvious stratification phenomenon. In the first part, the temperature decreases linearly. When the temperature approaches the ambient temperature, the temperature keeps stable basically. The relationship between the ambient temperature distribution and the distance can be obtained by linear fitting with the average temperature as Eq. (8):
− 1.82d + Tamb d ⩽ 9m Td = ⎧ Tamt d > 9m ⎨ ⎩
(8)
Within the range of 9 m from the rotary kiln, the temperature decreases monotonously, which mainly due to the continuous heat dissipation of the rotary kiln and the thermal convection of the environment. The attenuation should take the environmental temperature of the rotary kiln surface as the boundary. Therefore, the Tamb in the Eq. (8) is the environmental temperature measured when the distance from the rotary kiln is very close. When the temperature decreases to close to the ambient temperature, the temperature reaches a balance with the environment. The second part Tamt is the ambient temperature at the installation position of ISTM. These two temperature values can be obtained by the field temperature measuring equipment, so that the
Fig. 2. The plan and tools Experimental. 27
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Table 2 The temperature data collected on site. Characteristic point temperature/°C Horizontal coordinates x/m
−30 −27 −24 −21 −18 −15 −12 −9 −6 −3 0 3 6 9 12 15 18 21 24 27 30
Vertical coordinates y/m 0
3
6
9
12
15
18
21
24
27
30
29.4 28.6 28.1 29 29.1 29 29.1 29.2 29.5 28 29.1 28.3 29.4 28.3 28.2 29.2 29.1 29.1 28 29 29.1
21.6 21.4 21.8 21.4 21.1 21.4 21.3 22 21.3 21.5 21.9 21 21.4 21.8 21.2 21.9 21 22 21.5 21.3 21.5
16.2 16.4 16.3 16.8 16.3 16.3 16.5 17 16.7 16.4 16.4 16.7 16 16.4 16.5 16.3 16.9 16 16 16.5 17
12.7 12.4 12.1 12.3 12.2 12.9 12.7 12.2 12.7 12.8 12.8 12.6 12 12.1 12 12.5 12.5 13 12.8 12.2 12.1
12.6 12.1 12.1 12.1 12 12.7 12.8 12.1 12.8 12.3 13 12.6 12.1 12.9 12.4 12.6 12.5 12.9 12.5 12.6 12.5
12.9 13 12.7 12.1 12.5 12.4 12.7 12.9 12.7 12.4 12.6 12.7 12.9 12.6 12.6 12.8 12.7 12.9 12 12.9 12.5
12.9 12.8 12 12.2 12.2 12.5 12.3 12.3 12.3 12.4 12 12.1 12.8 12.3 12 12.3 12.3 13 12.7 12.9 12.3
11.9 11.9 11.9 11.9 11.1 11.7 11.2 11.3 11.4 11.5 11.9 11.5 11.9 11.2 11.1 11.6 11.5 11.1 11.8 11.7 11.3
11.3 11.9 12.3 11 12.4 11.5 12.3 11.3 12.3 11.5 11 12.5 11.7 11.5 11.6 12.1 11.8 11.3 12.3 12.3 11.7
11 12.5 11.3 12.1 11.5 11.3 11.9 11.3 12.2 11.9 12.1 11.3 12.1 11.5 11.8 11.3 11.6 11.8 12.2 12.3 11.1
11.1 12 11.5 11.4 11.4 11.1 11.4 11.5 12 11.7 11.2 11.2 11.7 11.8 11.5 11.8 11 11.2 11.8 11 11.8
Fig. 3. The three-dimensional distribution of surface temperature field in rotary kiln.
the environmental temperature attenuation part, and T2amt is the stable environmental temperature:
temperature distribution near the rotary kiln can be obtained. The atmospheric radiation is related not only to the transmittance but also to the atmospheric temperature. According to the distribution of the field temperature field, the third part of Eq. (4) should consider the change of the atmospheric temperature. Therefore, the following deformation can be obtained form Eq. (4):
T1amt =
Tobj
(10)
3.2. Calculation of atmospheric transmittance
1
T9 (1 − ε ) 9 (1 − τ1) 9 (1 − τ2) 9 ⎞ 9 = ⎜⎛ amb − Tamb − ( T1amt + T2amt ) ⎟ ε ετ1 ετ2 ⎝ ετ1 ⎠
Tamb + Tamt , T2amt = Tamt 2
To obtain the transmittance of H2O, there are two parameters need to be obtained by looking up tables: saturated water vapor content ρs at different temperatures and atmospheric transmittance of water vapor. The first parameter is only related to environmental temperature. In order to build the model easily, we obtain the relationship between the
(9)
Among them, τ1, τ2 are the atmospheric transmittance of the environmental temperature attenuation part and the environmental temperature stabilization part respectively. T1amt is the average temperature of 28
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Fig. 4. The distribution of ambient temperature.
Fig. 6. The whole temperature compensation correction model.
W1 = RH ∗
9
∫x=0 975.6*e(−(
W2 = RH ∗ 975.6*e (−(
Table 3 The data measured in the field. Field data values
Tamb (°C) Tamt (°C) RH
28.8 11.4 71.8%
ρs =
∗ 21
(13)
τ¯1H2 O = (τ3.0 + τ3.1 + τ3.2+⋯+τ4.9)/20
(14)
τ¯2 H2 O = (τ3.0 + τ3.1 + τ3.2+⋯+τ4.9)/20
(15)
τ¯1H2 O is the average transmittance of H2O in d ⩽ 9 m , τ¯2 H2 O is the average transmittance of H2O in d > 9 m . Using the same method, the transmittance of CO2 with a horizontal distance of 30 m is approximately obtained from the transmittance of CO2 with a horizontal distance of 0.1 km within the range of 3 ∼ 5 μm , All values are added and averaged.
environmental temperature and ρs by fitting the data in the table. The second parameter is mainly determined by precipitation and the band of the detector. It is different in the specific situation, so we still obtained this parameter by looking up tables. First, the fitting curve of the saturated water vapor content ρs at ambient temperature − 25°C ∼ 54°C is shown in Fig. 5. In Fig. 5, 80 points in the standard table are selected to fit the curve. In order to be closer to the empirical value, this paper chooses the Gauss function to fit the data. The fitting results are as follows: T − 156.7 2 975.6*e (−( 67.94 ) )
Tsysl − 156.7 2 ) ) 67.94
(12)
The temperature distribution is stratified and the saturated water vapor content is different at different temperatures, the condensable water millimeter value W in the linear attenuation part (d ⩽ 9 m ) of ambient temperature is obtained by integral method, using W1 representation. For the other part (d > 9 m ), the ambient temperature of the temperature measuring system is taken as the criterion, using W2 representation. The medium wave infrared detector selected by ISTM which band at 3 ∼ 5 μm . The W1, W2 can be obtained by adding and averaging all the values within the range of 3 ∼ 5 μm [10,11].
Fig. 5. The fitting curve of ρs at different ambient temperature.
Variables to be tested
−1.82x + Tsurh − 156.7 2 ) ) 67.94 dx
τ¯CO2 = (τ3.0 + τ3.1 + τ3.2+⋯+τ4.9)/20 ≈ 0.907
(16)
τ¯CO2 is the average transmittance of CO2. Then the atmospheric transmittance in two distance regions is obtained according to the following formula. τ1 = τ¯1H2 O *¯τCO2, τ2 = τ¯2 H2 O *¯τCO2
(17)
τ1 is the transmittance in d ⩽ 9 m , τ2 is the transmittance in d > 9 m . For the subjects of this experiment, the data measured in the field are shown in Table 3: According to the above analysis, the W1, W2 of condensable water in the experimental environment can be calculated by the value in Table 3.
(11)
T is the ambient temperature of the current position. Combined with the analysis of the environmental temperature field around the rotary kiln in the previous section, in order to get the millimeter value of condensable water with known horizontal distance, it is necessary to calculate the water vapor content in different temperature ranges in stages. According to the distance distribution of temperature field, The millimeter value of condensable water from rotary kiln to ISTM is calculated in two parts. The calculation formulas are as follows:
W1 = 0.12 mm, W2 = 0.16 mm
(18)
Combined with τH2 O and τCO2 , the atmospheric transmittance of condensable water with a millimeter value of 0.1 mm, 0.2 mm can be obtained within the range of 3 ∼ 5 μm : 29
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Fig. 7. Remote Temperature Monitoring Interface of Rotary Kiln. Table 4 The corresponding relationship. Actual feature points location (kiln head as origin) Characteristic points corresponding sequence number Actual feature points location (kiln head as origin) Characteristic points corresponding sequence number
0 0 31.2 364
2.4 28 33.6 392
4.8 56 36 420
7.2 84 38.4 448
τ1 = τ¯1H2 O *¯τCO2 = 0.98*0.907 ≈ 0.89 (19)
By substituting the above data into Eq. (9), the dynamic temperature compensation model based on the variation of non-uniform temperature field can be obtained as follows: 9
T 9 Tobj = ⎜⎛ amb − 0.429*1. Tamb − 0.177*T19amt + 0.159T29amt ⎟⎞ ⎝ 0.623 ⎠
(
)
12 140 43.2 504
14.4 168 45.6 532
16.8 196 48 560
19.2 224 50.4 588
21.6 252 52.8 616
24 280 55.2 644
26.4 308 57.6 672
28.8 336 60 700
accuracy of temperature measurement proposed in Section 3, we obtain the surface temperature Tamb of rotary kiln, the ambient temperature Tamt and relative humidity RH through field equipment, and then summarize the temperature compensation correction model based on ambient temperature in Fig. 6. The model is embedded in the core processing board of the infrared temperature measurement system and compared with the version without any compensation. The appearance of Rotary Kiln and remote monitoring interface of the temperature measurement system developed by our team is shown in Fig. 7: The system collects 700 points per row. In order to facilitate comparison, the spot thermometers is used to measure the characteristic temperature points on the surface of rotary kiln as the standard point to observe the temperature measurement without compensation and after compensation. According to the surface fabrication technology and surface temperature distribution of rotary kiln [12], the kiln head is taken as the starting point, and a temperature point is measured every 2.8 m as the standard temperature point. That is to say, the temperature data collected by the system are recorded once at each 26 points. The corresponding relationship between the data is shown in Table 4. According to the above correspondence, the surface temperature of rotary kiln is compared with the temperature measured by the system without considering the influence of ambient temperature and the system with compensation model in this paper. The experimental data are arranged as follows: From the trend in Fig. 8, we can see that the measured results of ISTM are lower than the actual values without considering the influence
Fig. 8. The Error comparison.
τ2 = τ¯2 H2 O *¯τCO2 = 0.99*0.907 ≈ 0.9
9.6 112 40.8 476
1 9
(20)
4. Compensation model and experimental verification According to analyzing the influence of ambient temperature on the 30
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5. Conclusion
Table 5 Comparison of Different Temperature Measurement Models. Distance (m)
The actual measured temperature (°C)
Temperature without considering ambient temperature (°C)
Error
Temperature considering ambient temperature (°C)
Error
0 2.4 4.8 7.2 9.6 12 14.4 16.8 19.2 21.6 24 26.4 28.8 31.2 33.6 36 38.4 40.8 43.2 45.6 48 50.4 52.8 55.2 57.6 60
283.7 89.4 412.6 389.1 376.9 381.5 362.4 368.2 355.9 214.7 108.4 313.7 374.9 349.7 350.9 348.3 363.4 368.9 373.4 369.8 112.5 276.3 133.4 321.9 319.7 270.4
244.2 62.0 373.8 355.6 344.3 350.0 333.8 339.4 331.1 198.2 97.4 292.8 352.8 327.5 328.1 325.1 338.9 340.0 341.2 337.5 89.3 244.0 107.5 285.1 279.2 229.4
−39.50 −27.42 −38.82 −33.54 −32.58 −31.46 −28.62 −28.76 −24.79 −16.55 −10.97 −20.89 −22.13 −22.22 −22.85 −23.23 −24.51 −28.90 −32.24 −32.32 −23.17 −32.29 −25.86 −36.77 −40.51 −41.00
257.38 65.32 393.96 374.75 362.91 368.94 351.8 357.77 348.98 208.85 102.69 308.62 371.81 345.16 345.76 342.62 357.18 358.35 359.58 355.7 94.15 257.18 113.35 300.52 294.26 241.78
−26.32 −24.08 −18.64 −14.35 −13.99 −12.56 −10.60 −10.43 −6.92 −5.85 −5.71 −5.08 −3.09 −4.54 −5.14 −5.68 −6.22 −10.55 −13.82 −14.10 −18.35 −19.12 −20.05 −21.38 −25.44 −28.62
Based on the analysis of the working environment of rotary kiln and the principle of infrared temperature measurement, this paper establishes a compensation model for the environmental factors affecting the accuracy of temperature measurement. According to the source of infrared temperature measurement receiving radiation, we find out the influence of ambient temperature on each part of the system, mainly including the environmental reflection radiation on the surface of rotary kiln and the influence on atmospheric transmittance. Through realtime acquisition of the environmental temperature near the rotary kiln and the atmospheric temperature near the ISTM, compensate for the impact of ambient temperature, so as to improve the accuracy of system in different environments. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 61671094) and the National Science Foundation of Chongqing Science and Technology Commission (No. CSTC2015JCYJA40032). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.infrared.2019.05.021. References
of ambient temperature, which is consistent with the theoretical analysis. In this paper, the measured value of the system after model compensation is closer to the real value. According to the calculation formula of the average error Eave , we can see the obvious advantages of the compensation model in this paper. N
∑i = 1 Eave =
i − Ti |Ttest actual | i Tactual
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× 100%
N
(21)
i represents the temperature measurements of the ISTM system for Ttest point i, represents the true temperature at point i measured by the Raytek hand-held thermometer. N represents the number of characteristic points. In this experiment, the value of N is 26. By substituting the data in Table 5 into the Eq. (21), the average errors without considering and considering the ambient temperature can be calculated as follows:
1 2 Eave = 10.58% Eave = 5.75%
(22)
1 Eave is the mean error without considering the ambient temperature, 2 is the mean error under the compensation model of ambient and Eave temperature in this paper. The proposed model in this paper improves the accuracy of infrared scanning temperature measurement system by nearly 5 percentage points.
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