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Abstract
We propose an ultra-high-temperature sensing method using a fiber Bragg grating (FBG) and demodulation technique based on support vector regression optimized by a genetic algorithm (GA-SVR). A type-I FBG inscribed by a femtosecond laser in a silica fiber was packaged with a tube and used as a temperature sensor. The external ambient temperature was retrieved from the transient FBG wavelength and its increase rate in reaching thermal equilibrium of the FBG with the external environment using GA-SVR. The temperature sensing in the range of 400 to 1000 °C was realized with an accuracy of 4.8 °C. The highest sensing temperature exceeded the FBG resisting temperature of 700 °C. The demodulation time was decreased to approximately 15 s, only 3.14% of the FBG sensor time constant. The proposed method could realize the external ambient temperature determination before the FBG temperature reached the thermal equilibrium state, which enables to attain a demodulation time shorter than the time constant of the FBG sensor and a sensing temperature higher than the FBG resisting temperature. This method could be potentially applied in temperature inspection of combustion and other fields.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber Bragg grating (FBG) sensors have numerous advantages, such as a high sensitivity, low cost, small size, robustness against an external electromagnetic radiation, and good corrosion resistance. They have been widely used in national defense, aerospace, industrial measurement, and other applications for temperature, strain, and vibration sensing [1–3]. High-temperature sensing techniques are highly demanded in various fields including petrochemical and aerospace fields. As all other contact temperature sensors, the FBG sensor can only determine the target temperature until it reaches the thermal equilibrium state, so that the heat resistance is the key issue of FBG sensors in high-temperature environments. Hence, the maximum sensing temperature of the FBG sensor depends on the FBG and package resisting temperature, while its response time depends on the cost time of the FBG reaching thermal equilibrium, generally referred to as time constant. Traditional FBGs are inscribed in a photosensitive fiber by an ultraviolet (UV) continuum wave or nanosecond pulsed light, which are gradually erased above 400 °C. Over the past two decades, numerous methods have been applied to improve the operating temperature of FBGs, such as hypersensitization through pre-irradiation [4], optimization of glass composition, use of regenerative FBGs [5], and direct fabrication of type-IIA [6] and type-II [7] gratings using UV nanosecond and femtosecond lasers. Among these methods, femtosecond laser micromachining has become the most promising method for realization of high-temperature-resistant FBGs. Limited by the fiber material, the reported highest resisting temperature of FBGs implemented in a silica glass is as high as 1200 °C [8], while that of FBGs in a sapphire fiber is 1612 °C [9]. However, the highest sensing temperature cannot be over the FBG resisting temperature for the common packaged sensors. Another approach to increase the sensing temperature of FBG sensors is by a specific packaging. Azhari proposed a novel package and realized sensing at an external ambient temperature of 1000 °C using a regular FBG standing at temperatures not higher than 300 °C [10]. In this method, the fiber is protected using air cooling and highly-oriented pyrolytic graphite with an excellent anisotropic thermal conductivity to minimize the radial heat transfer. However, it makes the sensor bulky, complex, and expensive. Furthermore, the complex package may increase the response time of the FBG sensor. Limited by the high-temperature resistance of sensors, no contact temperature sensors can detect the internal combustion temperature of advanced energy power systems such as rocket engines and heavy-duty gas turbines, where the temperature reaches values as high as 2500 °C. On the other hand, the FBG sensor and other contact temperature sensors can determine the external ambient temperature until they reach the thermal equilibrium state with the external ambient temperature. This kind of “thermal-equilibrium temperature sensing” method resulted in that the demodulation time of the external ambient temperature could not be shorter than the time constant of the contact temperature sensors, which limited their sensing speed as well as their applications in fast-real-time measurement fields.
In this paper, we propose an ultra-high-temperature sensing method using a FBG sensor and demodulation technique based on support vector regression optimized by a genetic algorithm (GA-SVR). A femtosecond-laser-inscribed type-I FBG in a silica fiber was packaged by a corundum tube and used as a temperature sensor. The external ambient temperature could be determined based on the transient FBG wavelength and its corresponding increase rate before the FBG reaches the thermal equilibrium state using GA-SVR. Experimental results show that this method could be applied for both constant- and increasing-temperature cases. The highest achieved sensing temperature was 1000 °C with an accuracy of 2.2 °C, which exceeds the FBG resisting temperature of 700 °C. The demodulation time was decreased to below 3.14% of the time constant of the FBG temperature sensor within 400–600 °C. This “non-thermal-equilibrium temperature sensing” method makes it possible to realize the external ambient temperature determination using a time smaller than the time constant of the FBG sensor and determine the external ambient temperature higher than the FBG resisting temperature. The method has potential applications for real-time temperature inspection of rocket engines, where ultra-high-temperature lasts few minutes.
2. Methods and experimental setup
2.1 Principle of ultra-high-temperature sensing using the fiber grating sensor
Figure 1 shows the structure of the FBG temperature sensor packaged with a corundum tube. The tube can be treated as a single-layer cylinder. The heating and temperature distribution on the tube wall are uniform. Assuming that the thermal equilibrium state is not destroyed in the experiment, the differential equation of sensor temperature versus time is [11]
where $\frac{{dT}}{{dt}}$ is the temperature variation rate, which can be calculated by the slope of the temperature evolution curve of the FBG temperature sensor, ${T_f}$ is the external ambient temperature, T is the wall temperature of the corundum tube, Γ is the heat transfer coefficient between the fluid and surface of the corundum tube, A is the surface area of the corundum tube, and ρ, ${c_p}$, and V are the density, specific heat capacity, and volume of the corundum tube, respectively.
Fig. 1. Schematic of the single-ended coaxially packaged FBG temperature sensor with a corundum tube.
According to Eq. (1), ${T_f}$ could be expressed by
For FBG sensors, the temperature is retrieved by the Bragg wavelength of the FBG using linear or nonlinear response functions, which can be expressed as
By substituting Eq. (3) into Eq. (2), we obtain
Generally, the external ambient temperature was obtained when the FBG sensor reached thermal equilibrium, i.e., when the wavelength variation rate $\frac{{d\lambda }}{{dt}}$ became zero. Thus, the sensor could determine the external ambient temperature in a period not shorter than its time constant. Nevertheless, Eq. (4) shows that the external ambient temperature ${T_f}$ can also be deduced from the transient FBG wavelength λ and its corresponding variation rate $\frac{{d\lambda }}{{dt}}$. This implies that it may not be necessary to deduce the external ambient temperature for FBG sensors reaching thermal equilibrium.
However, the relationship between the Bragg wavelength and temperature is nonlinear at high temperatures; i.e., neither u(λ) nor v(λ) is constant. On the contrary, even if the temperature can be retrieved from the Bragg wavelength of the FBG using linear functions, the heat transfer coefficient Γ varies with the sensor temperature T, resulting in a nonlinear relationship between $\frac{{d\lambda }}{{dt}}$ and λ as well as ${T_f}$. Hence, ${T_f}$ cannot be simply deduced by linear fitting methods.
Machine learning is a powerful method for nonlinear multi-parameter fitting problems. Therefore, we could use the transient FBG wavelength λ and its corresponding variation rate as input parameters and external ambient temperature as a target output for a machine learning analysis. In our experiments, the method of SVR was applied to resolve this problem. The Bragg wavelengths at different times could be directly attained by a spectrometer or optical spectrum analyzer (OSA). To improve the speed and accuracy of demodulation, the gradient method was used to obtain the wavelength variation rate at different times. For vector $\boldsymbol{H}(i),(i = 1,2, \cdots ,n)$, its gradient calculation is carried out by
where ${\boldsymbol{D}_H}(i),(i = 2, \cdots ,n - 1)$ is the gradient value. In the experiment, we recorded the wavelengths with a constant time interval (7.5 s). The wavelength variation rate was then obtained by2.2 SVR
SVR [12] is an application of support vector machine [13] to regression problems. For given training data set $({\boldsymbol{X}_i},{\boldsymbol{Y}_i}),i = 1,2, \cdots ,n,{\boldsymbol{X}_i} \in {R^n}$, the fitting function is
where $\boldsymbol{\omega }$ and b are the model parameters to be determined. In our case, $\boldsymbol{X} = (\frac{{d\lambda }}{{dt}},\lambda ),\boldsymbol{Y} = {T_f}$. Unlike traditional regression models, SVR only calculates the loss when the absolute value of the difference between f(X) and Y is larger than ɛ. As shown in Fig. 2, this is equivalent to building an interval band with a width of 2ɛ with f(X) as a center.Therefore, the SVR problem can be transformed into an optimization problem according to the structural risk minimization criterion. The objective function and constraint conditions of the SVR model based on the ɛ-insensitive loss function are [14]
2.3 GA-SVR
The SVR generalization performance depends on a good setting of the metaparameters C, ɛ and kernel parameter σ [14]. Typically, the values of these three parameters are searched by either the trial or simple grid search methods, which may lead to local optimal points. GA is an optimization algorithm based on evolution theory and genetics, which provides good parallelism, robustness, and global optimality [15]. We use the GA to optimize the above parameters to obtain a better generalization performance.
A flowchart of the GA combined with SVR parameter optimization is shown in Fig. 3. First, a set of SVR parameters of C, ɛ, and σ are randomly generated and encoded. Second, the population is initialized, and its fitness is calculated. If the fitness is larger than the threshold value, the optimal parameters are obtained by comparison. Otherwise, the population should be processed with selection, cross, and mutation methods. Afterward, the next progeny population is generated and its fitness is calculated again until it exceeds the threshold value. Finally, we obtain the optimal parameters and use the above parameters to train the SVR model.
2.4 Experimental setup
The experimental setup is shown in Fig. 4. The signal light from the broadband light source is guided into the sensing FBG via a circulator. The reflected light spectra of the FBG sensors are recorded by an OSA (Yokogawa Co., AQ6370D) with a wavelength resolution of 0.02 nm. The sensing FBG is placed in a tubular high-temperature furnace. The temperature of the tubular high-temperature furnace can be controlled from room temperature to 1200 °C with a nominal temperature error of ±1 °C between 300 and 1200 °C. Both OSA and furnace are controlled by a computer, which could acquire the spectra or Bragg wavelengths as well as the furnace temperature simultaneously in real time. In addition, the FBG used in the experiment is a type-I grating, written on a single-mode fiber (Corning SMF-28e+) by a femtosecond laser. Its grating strength is degraded when its temperature is higher than 700 °C. The inscription method and setup are described in detail in Ref. [16]. The FBG was packaged with a cylindrical corundum tube with a diameter of 10 mm and wall thickness of 2 mm.
Fig. 4. FBG temperature sensing system. THF: tubular high-temperature furnace, BLS: broadband light source, PC: personal computer.
The FBG sensor was calibrated in the tubular furnace. The inner chamber of the tubular high-temperature furnace was heated to the setting temperature and stabilized for approximately 10 min. The FBG sensor at room temperature initially was quickly inserted into the tube of the furnace. The Bragg wavelengths of the FBG sensor in the process of reaching the thermal equilibrium state were recorded by the OSA with a constant interval time of 7.5 s, which was limited by the OSA. This operation was repeated at a series of setting temperatures of the furnace. The Bragg wavelengths at different times during the FBG sensor reaching a series of setting temperatures were used to construct the training data set. In the experiment, we studied the abilities of the proposed method when the external ambient temperature was constant and continuously increasing. For the former case, the operation method was the same as the calibration process. For the latter case, the FBG sensor was kept in the furnace when the furnace temperature increased continuously.
3. Results and discussion
3.1 GA-SVR training
To make sure the good repeatability and stability of the packaged FBG sensor, the corundum tube was first kept at high temperature of 1050 °C for 2.5 h to improve its thermal shock resistance. After the temperature of the corundum tube dropped to room temperature, the FBG was packaged into the corundum tube to form the FBG sensor. Next, the sensor was annealed at 650 °C for 0.85 h and then 600 °C for 3 h to eliminate the influence of the degradation of the refractive index change of the type-I grating at high temperature [17]. Figure 5(a) shows the change of the wavelength and intensity of the FBG sensor as the annealing time. After annealing, the wavelength of the FBG sensor blue-shifted from 1556.552 nm to 1556.52 nm at 600 °C, this is because the refractive index decrease after annealing. Then the repeatability of our packaged FBG sensor was tested by putting the sensor from room temperature to a tubular high-temperature furnace with a temperature of 500 °C. The test results are shown in Fig. 5(b). The entire test process lasted for 45 days, among them, the first and second tests were carried on the first day, and the third and fourth tests were carried on the fifteenth and forty-fifth days, respectively. The four test results show that the packaged FBG sensor has a good repeatability.
Fig. 5. (a) Wavelength and intensity changes of the FBG sensor during annealing. (b) Repeatability of the wavelength verse time curve when the FBG sensor was put from room temperature to a tubular high-temperature furnace with a temperature of 500 °C.
Figure 6 shows the evolution of the FBG sensor wavelength while reaching the thermal equilibrium from room temperature to different external ambient temperatures of 400 to 1000 °C in steps of 50 °C. The wavelength of the FBG increased with the inserting time, and then saturated when the temperature of the furnace was below 600 °C. At furnace temperatures above 600 °C, the Bragg wavelengths of the FBG sensor were recorded until the FBG temperature reached approximately 600 °C, and then the FBG sensor was taken out of the furnace quickly to avoid grating damage. The wavelength of the FBG at 600 °C was calibrated in advance and used as a criterion for the FBG temperature. In addition, the increase rate of the wavelength increased as the furnace temperature increased, consistent with Eq. (1).
Fig. 6. Evolution of the FBG wavelengths during the FBG reaching thermal equilibrium from room temperature to different external ambient temperatures.
Based on the above results, the training data set in GA-SVR was constructed using the transient wavelength at a certain time as well as its increase rate as an input and external ambient temperature as an output (to construct their nonlinear relationship for demodulation and carry out the temperature demodulation offline modeling). Figure 7 depicts the training and testing phases of the GA-SVR model to obtain the external ambient temperature. To reduce the influence of the fluctuation of measured data, we fitted the actual measured curves of the training data set using Fourier series expansion, and then calculated the gradient of sampling points of the fitted curves to obtain the transient wavelength and its corresponding increase rate at different times (the time interval is 1 s). Figure 8(a) shows the measured data and their fitting curve at the external ambient temperature of 400 °C. The measured data could be well fitted. Then, we using the gradient method to obtain the increase rate of the FBG wavelength when the FBG wavelength shifted to different values during the FBG sensor temperature increased from room temperature to the external ambient temperature of 400 °C. Figure 8(b) shows the corresponding relationships between the wavelength increase rate and the transient FBG wavelength during the FBG sensor temperature increased from room temperature to different external ambient temperatures. The above transient wavelengths and their increase rates formed a training data set with two dimensions of the vector space of the GA-SVR demodulation model. Based on the training data set, we trained GA-SVR to obtain the FBG temperature sensing demodulation model in the range of 400 to 1000 °C (denoted as GA-SVR-50°C).
Fig. 8. (a) Temporal evolution of the FBG temperature sensor wavelength when the external ambient temperature is 400 °C (inset: magnified view of (a)). (b) Corresponding relationships between the transient FBG wavelength and its increase rate during the FBG sensor temperature increased from room temperature to different external ambient temperatures.
3.2 Constant external ambient temperature case
Through the following experiments, we demonstrate the application of the proposed method in the constant external ambient temperature case. The external ambient temperature was set in the range of 400 to 1000 °C with an interval of 50 °C (the data at 500 °C uses here is the first group of data in Fig. 5(b)), included in the training data set, while the temperatures that were not in the training data set were 425, 475, 525, 575, 623, 674, 722, 779, and 871 °C. First, we studied the temperature demodulation error at different sampling times, which was defined as the sampling time of the central point among three points used for calculation of the wavelength increase rate. Figure 9 shows the results for the external ambient temperatures of 600, 623, 722, and 1000 °C. The demodulation errors oscillated in a certain range as the inserting time increased. They were approximately -3.5 to +5.5, -4 to +6, -6 to +1, and -4.5 to +2.6 °C for the above four temperatures, respectively. This implies that the demodulation errors were at almost the same level for the FBG wavelength and its increase ratio at different stages when the FBG sensor temperature varied from the initial temperature to the final equilibrium state temperature. Even at the early stage of the FBG reaching the equilibrium state, the retrieved temperature did not exhibit considerable error. This implies that the proposed method can be used to demodulate the external ambient temperature before the FBG temperature reached the thermal equilibrium state. Limited by the wavelength sampling frequency of the OSA (the wavelength acquiring interval was 7.5 s), the earliest time for demodulation of the external ambient temperature was approximately 15 s (the third sampling point; the first sampling time is denoted as 0 s) when the first three points were obtained. However, the demodulation time could be decreased to as short as millisecond if a fast FBG wavelength integrator or spectrometer was applied.
Fig. 9. Demodulation error for the wavelength evolution curve of the FBG sensor in different time periods. The external ambient temperature was (a) 600, (b) 623, (c) 722, and (d) 1000 °C.
Figure 10(a) and 10(b) show the variation trends of the root mean square error (RMSE) and error percentage with the external ambient temperature. The temperature measured by a thermocouple set near the FBG sensor was used as a reference to calculate the RMSE and error percentage. The temperature was retrieved at a sampling time of 15 s. For the temperature included in the training data set, the RMSE fluctuated between 1.41 and 4.47 °C, while the error percentage fluctuated between 0.148% and 0.589%. For the temperature not included in the training data set, the RMSE fluctuated between 1.94 and 4.82 °C, while the error percentage fluctuated between 0.243% and 0.746%. The RMSEs did not differ for the external ambient temperatures included and not included in the training data set. The maximum error occurred when the external ambient temperature was 674 °C, when the RMSE was 4.82 °C and the error percentage was only 0.716%. This indicates that the established GA-SVR-50°C FBG temperature sensing demodulation model is convergent.
In addition, we use the other three groups of measured data under the external ambient temperature of 500 °C in Fig. 5(b) to verify the repeatability of our trained model. The RMSE is 2.53, 2.39, and 3.06 °C for the second, third, and fourth measured data, respectively. Note that the RMSE of the first measured data is 1.69 °C, although the RMSE increases compared to the first group data incorporated in the training data set, but the maximum error percentage is only 0.612%, which indicates that the FBG packaged with a corundum tube has a good repeatability.
Notably, for the external ambient temperature of 1000 °C, the external ambient temperature was retrieved when the FBG temperature reached only approximately 267 °C, before reaching the thermal equilibrium state. This implies that we successfully realized the temperature sensing at 1000 °C using the FBG temperature sensor with the temperature resistance at 700 °C. In addition, the FBG temperature was far from the maximum resisting temperature of the FBG, and hence the maximum sensing temperature could be considerably higher than 1000 °C if the sensor package allowed.
While FBG sensor can provide reliable temperature sensing in the short term, but their long-term functionality at high temperatures is affected by the drift of the Bragg wavelength, which may be caused by the dopant diffusion from the core [18,19]. Type-II grating with a quenching process is expected to reduce the error caused by the drift of the Bragg wavelength [8].
The response speed is another important parameter of the FBG temperature sensor in dynamic temperature measurements. Generally, the time constant was used to characterize the response speed of the FBG sensor, which was defined as the cost time required for the increased temperature to reach 63.2% of the surrounding temperature variation. For the common temperature sensing, the temperature resolved time has to be not smaller than the time constant of the FBG sensor because it is necessary for the sensor to reach the thermal equilibrium state. However, it is possible to resolve the external ambient temperature using a time smaller than the time constant of the FBG sensor for the proposed method. Table 1 shows the measured time constant of our FBG sensor at different external ambient temperatures and time when we could demodulate the external ambient temperatures using our method. The time constant of the FBG sensor varied from 472 to 616 s. These differences may be attributed to the large temperature changes. For our method, the temperature demodulation time could be as short as 15 s, and decreased to below 3.14% compared to the common FBG temperature sensing method using the same FBG sensor. In other words, the demodulation method based on GA-SVR can significantly improve the demodulation speed of the FBG temperature sensor.
Table 1. Comparison of Time Constants and Demodulation Times of the FBG Temperature Sensor
Of course, the FBG will reach the thermal equilibrium state and be destroyed when its temperature is above the FBG resisting temperature. However, the temperature increase rate of the FBG could be decreased using a low-thermal-conductivity material while the available time of the FBG sensor was increased as it is not necessary for the FBG to reach the thermal equilibrium. That’s why the corundum tube (with a thermal conductivity of 46 W/(m*°C) at 25 °C) was selected as the packaging material. In addition, limited by the wavelength sampling frequency of the OSA, the earliest time for demodulation of the external ambient temperature was approximately 15 s. A FBG integrator with a sampling frequency over 1 kHz is expected to improve the temperature demodulation speed. This method is very suitable for the temperature sensing in fields where the ultra-high-temperature state does not last very long, such as the temperature inspection of rocket engines, where the ultra-high-temperature state remains approximately 5 min. However, if the wavelength increase rate of the FBG sensor is too little, the resolution of the wavelength demodulation equipment would be a critical problem for resolving the FBG wavelength variation. Hence, the application of our proposed method where both long survival time and fast sampling frequency are required at the external ambient temperature much higher than FBG resisting temperature would be a great challenge. In addition, packaging tube with a good thermal stability at temperature above 2500 °C would also be another challenge.
3.3 Variable external ambient temperature case
Further, we studied the application of the temperature sensing demodulation method based on GA-SVR in the increasing-temperature case. We recorded the wavelengths of the FBG sensor during the furnace temperature increase from 454 to 600 °C with a temperature increase rate of 10 °C/min. The wavelength acquiring time interval was 7.5 s. The recorded wavelengths during the temperature increase and extracted temperature using the GA-SVR-50°C FBG temperature sensing demodulation model in the testing phase are shown in Fig. 11(a) and 11(b), respectively. The transient temperature recorded by the thermocouple (Omega, TJC36-CAXL-040U-24) is also plotted in Fig. 11(b) (red curve). Both temperatures measured by the FBG sensor and thermocouple exhibit increasing trends with a wave-like shape. Although the value was different, the wave period was approximately same (45 s). Note that the dependence of the wavelength of the FBG sensor on time in Fig. 11(a) doesn’t obviously show a wave-like upward trend like the thermocouple, because the minimum time constant of FBG sensor used here was approximately 472 s, which was much larger than that of the thermocouple (4.5 s in air). Hence, the response speed of this FBG sensor was not fast enough as thermocouple to reflect the external ambient temperature variation in real-time and the external ambient temperature could not be retrieved using this FBG sensor and the common FBG temperature sensing method. However, our proposed method reduced the demodulation time of the external ambient temperature to 15 s, decreased by more than one order of magnitude compared to the time constant of this FBG sensor. Hence the demodulation results show similar wave-like shape as the thermocouple.
Fig. 11. (a) Variable-temperature data acquisition experiment (the external ambient temperature was increased from 454 to 600 °C; inset: magnified view of (a)). (b) Temperature extraction results of variable-temperature data (inset: temperature difference between the FBG sensor and thermocouple).
The inset in Fig. 11(b) shows the temperature difference between the FBG sensor and thermocouple. The value varied from -3.3 to 8.44 °C. The RMSE in the range of 454 to 600 °C is 3.48 °C. This implies that the temperature extracted by the GA-SVR-50°C FBG temperature sensing demodulation model is consistent with that of the thermocouple, which indicates that the proposed method can measure the change in the external ambient temperature in real time. This also shows that the GA-SVR-50°C FBG temperature sensing demodulation model has a good generalization performance.
For the GA-SVR-50°C model, although the training data set was obtained under the FBG temperature increasing process, it would be always applicable whether the external ambient temperature increases or decreases, when the external ambient temperature is higher than the FBG temperature. Because the FBG temperature still keeps increasing in this case. This could be seen from Fig. 11(b), where the retrieved temperatures show oscillating upward trends, including both upward and downward trends. Hence it could also be applicable for the decreasing external ambient temperature when the external ambient temperature is higher than the FBG temperature. But this model has not considered the case that the external ambient temperature is lower than the FBG temperature, because complex equipment is need to move the FBG sensor from high temperature furnace to a chamber with low temperature. This work would be carried out in future work.
4. Conclusion
This paper presents a new method for ultra-high-temperature sensing using a FBG and demodulation technique based on GA-SVR. The processed wavelength evolution curve of the FBG temperature sensor was used to train the GA-SVR model, where the transient FBG wavelength and its corresponding increase rate were used as an input, while the external ambient temperature was used as an output of the demodulation model. The experimental results showed that the highest achieved sensing temperature was 1000 °C with an accuracy of 2.2 °C, exceeding the FBG resisting temperature of 700 °C. In addition, the demodulation time was decreased to below 3.14% of the time constant of the FBG temperature sensor in the range of 400–600 °C, which could enable a considerably faster real-time FBG temperature sensing than the common FBG temperature sensing method. This method provides ultra-high-temperature sensing using a FBG, which may be applied to the temperature monitoring of rocket engines.
Future research will focus on improving the temperature demodulation time as well as the accuracy and demodulating the temperature in the cooling stage of the FBG sensor.
Funding
National Key Research and Development Program of China (2019YFA0706402HZ); National Natural Science Foundation of China (62027822); National Natural Science Foundation of China (61905192); Fundamental Research Funds for the Central Universities (XJJ2016016).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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