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Abstract
FBG array sensors have been widely used in the multi-point monitoring of large structures due to their excellent optical multiplexing capability. This paper proposes a cost-effective demodulation system for FBG array sensors based on a Neural Network (NN). The stress variations applied to the FBG array sensor are encoded by the array waveguide grating (AWG) as transmitted intensities under different channels and fed to an end-to-end NN model, which receives them and simultaneously establishes a complex nonlinear relationship between the transmitted intensity and the actual wavelength to achieve absolute interrogation of the peak wavelength. In addition, a low-cost data augmentation strategy is introduced to break the data size bottleneck common in data-driven methods so that the NN can still achieve superior performance with small-scale data. In summary, the demodulation system provides an efficient and reliable solution for multi-point monitoring of large structures based on FBG array sensors.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber Bragg grating (FBG) sensors are widely used in engineering, military, and civil applications due to their small size, high immunity to electromagnetic interference, and high sensitivity [1–5]. In structural health monitoring (SHM), FBG sensors are often used to monitor the strain in modules to reflect the building’s health condition. Recently, FBG array sensors that allow optical multiplexing of multiple FBGs on a single fiber have been introduced to extend the monitoring range and flexibility of strain information transmitted [6,7].
Stress changes caused by external perturbations are encoded as wavelength shifts by the FBG, and acquiring and decoding wavelength information is essential to demodulate this physical quantity. Optical spectrum analyzer (OSA) is often used in the demodulation process of FBG sensors due to their ability to acquire wavelength information directly. However, the cumbersome data processing and the high price of OSA severely limit its large-scale use in practical engineering applications. To improve the flexibility of monitoring, the Mach-Zehnder interferometers [8,9], Tunable Fabry-Perot filters [10–12] and Matching grating filters [13,14] based on grating filters. Other devices have been proposed and propagated as demodulation strategies. The Mach-Zehnder interferometer can achieve rapid response and high resolution in dynamic measurements. The precision is susceptible to interference during static monitoring due to poor immunity to electromagnetic interference. The tunable method Fabry-Perot filtering method has a good filtering effect and high demodulation precision, but its demodulation speed is slow and high cost. The matched grating filtering method can resist substantial electromagnetic interference and simple structure. Nevertheless, each FBG needs to correspond to a matched FBG, so the number of detected FBGs is limited, and the demodulation speed is not high. They are significantly more costly and efficient in coping with FBG array sensor demodulation regarding hardware facilities and algorithms. Both contradict the original intention of low-cost and high-performance demodulation in engineering applications.
The FBG demodulation method based on array waveguide grating (AWG) has received much attention for its energy-saving and high-efficiency capabilities. Su et al. [15] used the filtering characteristics of AWG to reflect the FBG sensor’s central wavelength variation. Marrazzo et al. [16] used the power ratio between multiple channels to sense the wavelength shift. In terms of demodulation precision, they offer no advantages. It is more common to work on the hardware to improve the performance of AWG-based demodulation systems. Robertson et al. [17] replaced one FBG with two reflectance peaks that are not significantly different. Guo et al. [18] used a closed-loop piezoelectric motor to overcome the limitation of additional wavelengths on the interrogation range. However, they cannot simultaneously improve demodulation precision and range, making it challenging to trade between performance and cost. This drawback also limits the application of AWG in multipoint demodulation tasks for FBG array sensors. Gao et al. [19,20] achieved simultaneous monitoring of multiple FBG sensors using an AWG. Evenblij et al. [21] used AWG as an optical spectrum analyzer (OSA) to interrogate multiple FBG sensors simultaneously. However, they have a limited interrogation range of FBG array sensors, a complex system architecture, and limited multiplexing capability. Therefore, it is crucial to design a cost-effective interrogation devices to interrogate multiple fiber grating sensors.
In recent years, artificial intelligence (AI) techniques, especially machine learning (ML) techniques, have been applied and have made key breakthroughs in several fields. Researchers have also been inspired by applications in optics, such as fiber optic sensor demodulation systems [22], microstructured fiber (MOF) inverse design [23,24], optical imaging [25,26], and biomedical photonics [27,28]. Artificial neural networks (ANNs) mimic biological neural structures and functional information processing systems. ANNs are widely used in FBG sensor demodulation systems. An et al. [29] implemented temperature calibration of FBG sensors using a back propagation neural network (BPNN). Wang et al. [30] used a deep neural network (DNN) to detect the FBG’s central wavelength from the overlapping spectra. Ren et al. [31] used a cascaded neural network to implement a matched filter to demodulate multiple FBGs. Zhang et al. [32] used BPNN to compensate for the nonlinearity of the FBG sensing system. Some of our previous work [33] also implemented cost-effective FBG sensor demodulation systems using NN algorithms. Jiang et al. [34] used a long and short-term memory network to achieve fast determination of Bragg wavelengths for FBGs. Li et al. [35] proposed a multi-peak detection model based on an expansive convolutional neural network to reduce the signal demodulation error. However, in practice, the high number of collections, the difficulty and the need for human intervention have become bottlenecks in this data-driven approach. To this end, researchers proposed a deep learning (DL)-based data augmentation strategy, such as autoencoder [36] and generative adversarial networks (GAN) [37,38], to achieve models that train well on small-scale a priori dataset. Such DL-based data augmentation methods require additional model training and parameter tuning, and the results tend to deviate from the original data distribution, which makes them significantly less flexible.
To address the above problems, we proposed an NN-based demodulation system for calculating the absolute wavelength shift of the FBG array sensors. Transmitted intensities of AWG channels cover the peak wavelength variation caused by external strain and feed into an end-to-end NN model to establish the nonlinear relationship with absolute wavelength. Moreover, we adopted a practical data augmentation strategy to reduce the negative impacts of data scarcity on the model’s performance. Experiments show that the proposed system can achieve at least $\pm 4 pm$ of multi-peak absolute wavelength interrogation precision. In summary, the proposed method provides a cost-effective and high-performance demodulation platform based on FBG array sensors for multi-point monitoring tasks.
The remainder of this paper is organized as follows. Section 2 presents the theoretical analysis of the proposed demodulation system; Section 3 presents the artificial neural network model. Section 4 presents the experimental setup and performs the experiments. Section 5 concludes this paper.
2. Theory and method
2.1 Demodulation system
Figure 1 shows the AWG-based FBG array sensor demodulation system. Two motorized panning tables are used to fix the sensors and receive commands from the PC to apply strain to the sensors. The reflected light from the FBG array is split into two channels by a 2*2 coupler (splitting ratio: 50/50), and input to the AWG and an optical spectrum analyzer (OSA, YOKOGAWA AQ6370D). During the experiment, 9 channels of AWG were selected. AWG’s 8 channels were connected to the 8-channel MEMS optical switch (MEMS-FSW8-SM-A). Another channel and the output of the MEMS optical switch are connected to two channels of the optical power meter, respectively. Simultaneous acquisition of multi-channel signals can be achieved without complex optical signal conversion sequences during the measurement process. The acquired data is handed over to the PC for processing.
Fig. 1. Architecture of the FBG array sensor demodulation system includes the broadband light source, motorized panning table, optical circulator, AWG, controllable 8-channel MEMS optical switch, optical power meter, and PC.
The external disturbance causes a change in the spectrum of the FBG array sensor, so the transmitted light intensity (the area of the overlapping part of the sensor and AWG spectrum) at the output of the AWG channel will change. The obtained data is fed into the NN model, which is used to establish a nonlinear relationship between the transmitted light intensity and the peak wavelength. It can be expressed as Eq. (1).
2.2 Principle of demodulation
The spectrum consisting of multiple AWG channels and $n$ peaks of the FBG array is shown in Fig. 2. $FBG _{1}$ and $FBG _{2}$ are the two adjacent FBGs in the FBG array sensor. $\lambda _{FBG1}$ and $\lambda _{FBG2}$ are their central wavelengths, respectively. AWG’s two neighboring channels are $CH _{n}$ and $CH _{n+1}$, Their wavelengths are $\lambda _{n}$ and $\lambda _{n+1}$, respectively. The wavelength difference between adjacent FBGs is greater than twice that of adjacent channels of AWG, effectively avoiding problems such as transmission strength overlap caused by crosstalk between channels. Two adjacent AWG channels can form a filter. Take FBG1 as an example. The $I _{n}$ and $I _{n+1}$ are the transmitted light intensities of $n ^{th}$ and $n+1 ^{th}$ AWG channels, respectively. The wavelength shift of the FBG array sensor causes a change in the transmitted light intensity. Therefore, the central wavelength shift can be determined by the combination of transmitted light intensities of different filters. It can be expressed as Eq. (2).
Fig. 2. Spectra of AWG multichannel demodulation of FBG array sensors: the shaded part where the FBG spectrum and the AWG channel intersect is the transmitted part of the AWG.
3. Machine learning algorithms for demodulation systems
3.1 Artificial neural network model
A back propagation neural network (BPNN) is used to establish a nonlinear relationship between transmitted intensity and peak wavelength to demodulate the FBG array sensor. Figure 3 depicts the network’s system structure. The nine independent neurons make up the input layer. They are used to denote the output intensity of reflected light under the selected nine AWG channels ($I _{1} - I _{9}$). The intermediate hidden layer continuously modifies the weights to more accurately map the relationship between the basis functions of the input and output samples. The output layer represents the peak wavelengths ($\lambda _{1} - \lambda _{4}$) of the FBG array sensor, which is described by four independent neurons.
Fig. 3. The network structure used to establish the relationship between output intensity and peak wavelength is a three-layer hidden layer containing 9 independent neurons in the input layer and 99 neurons in each layer, and 4 independent neurons in the output layer.
Figure 4 depicts the network’s training process. The reflected light intensity ($I$) and weight ($w$) of the input AWG channel are multiplied and added ($e$), and the expected wavelength ($\lambda$) is derived by activating a nonlinear activation function ($f(e)$). The weights are adjusted based on the difference ($loss$) between the predicted and true values, and the network’s learning is completed during the weight modification phase. When the error reaches the required value, the training is complete in which $r$ denotes the learning rate and $W^{'}$ denotes the updated weights.
Fig. 4. The training process of a neural network: 1) Multiply the inputs with the corresponding weights and sum them. 2) Activate the nonlinear function. 3) Calculate the loss function. 4) Update the weights.
3.2 Data pre-processing
To avoid the impact of data incompleteness, variability, and instability on the demodulation precision of the system. The raw data are normalized before input to the signal processing module to improve the model precision and augment the convergence speed. The data are linearly scaled between [0,1] by max-min normalization. This normalization method preserves the zeros in the sparse features and can solve data with microscopic feature variance. Its transformation function can be expressed as Eq. (3).
3.3 Data augmentation
Data-driven models rely too much on large-scale a priori data, and sparser dataset cannot meet the demand for high performance and affect the demodulation precision. Data augmentation is crucial to improve the stability of the results. Deep learning-based data augmentation methods are cumbersome and require additional parameter tuning and iteration steps, which are not flexible enough. In addition, the data generated by deep learning-based data augmentation methods tend to deviate from the original data distribution, which has a negative impact. Based on the above problems, we introduce a data augmentation method in the training process, using a particular case of the Dirichlet distribution–$\beta$ distribution ($\beta$ distribution) for random augmentation of sparse data, whose probability distribution function can be expressed as Eq. (4), where the normalized B is the beta function, which can be described as Eq. (5).
Without affecting the original data, the training dataset is augmented with samples drawn from the $\beta$ distribution, and the augmentation process can be expressed as Eq. (6).
where $data _{1}$ and $data _{2}$ are two random sets of nine inputs $(I _{1} - I _{9})$ and corresponding four outputs $(\lambda _{1} - \lambda _{4})$ from the original data. $y _{1}$ and $y _{2}$ are two new sets of data based on the original data and the expansion of the $\beta$ distribution; m is the value extracted from the $\beta$ distribution when both $\alpha$ and $\beta$ are 0.2, and m and n can be expressed as in Eq. (7).The expanded value $y _{final}$ is obtained by taking the average value based on the expanded new data, which can be expressed as Eq. (8).
The original dataset is augmented according to the above principles, and the procedure is written as shown in Algorithm 1. The number of iterations and parameters can be flexibly adjusted according to the requirements without deviating from the original data distribution during the data augmentation process, thus enriching the data input to the network model.
Algorithm 1. Data augmentation
4. Experiments
4.1 Experimental setup
This experiment was carried out using the experimental set-up depicted in Fig. 1 and the FBG array sensor, which consists of four FBGs. The gratings used as Sen-FBGs are based on SMF-28e with central wavelengths of 1550 nm, 1552 nm, 1554 nm, and 1556 nm and 90 $\%$ reflectivity. The full width at half maximum (FWHM) of these fiber gratings are 0.7078 nm, 0.6981 nm, 0.7182 nm, and 0.6991 nm, respectively. The experiment’s ambient temperature was set at 26$^{\circ }$C.
At the beginning of the experiment, the FBG array sensor was held in place with two motorized panning tables, and the precision panning table was manually adjusted to tension the sensor. Record this time as the initial state. The nine channels CH25, CH26, CH27, CH28, CH29, CH30, and CH31 are selected to demodulate the FBG array sensor, where the peak wavelength interval between two adjacent channels is 0.8 nm, after actual measurement, the FWHM of each channel is $\sim$0.456 nm. The CH31 channel is connected directly to CH2 of the optical power meter, while the remaining eight channels are connected to CH1 using optical switches. The selected channels are shown in Fig. 5(a), and Fig. 5(b) depicts their combined spectra with the FBG array sensor, using them to demodulate four peak wavelengths in the 1550-1558 nm range. Peak 1, Peak 2, Peak 3, and Peak 4 are shown in the order from left to right, and the initial peak wavelengths are measured with OSA ($\lambda _{1}$ = 1550 nm, $\lambda _{2}$ = 1552 nm, $\lambda _{3}$ = 1554 nm, and $\lambda _{4}$ = 1556 nm).
Fig. 5. (a) The reflection spectrum of the AWG channel used. (b) Combined spectrum of FBG array sensor and AWG channel, where $\lambda _{1} - \lambda _{4}$ are the peak wavelengths of peaks 1, 2, 3, and 4, respectively.
During the experiment, a motorized translation stage with 5 $\mathrm{\mu}$s resolution was used to control the stretch relaxation of the FBG array sensor. The transmitted intensity of the AWG channel collected by the optical power meter from the PC was recorded, and the peak wavelength of the associated peak was collected by the OSA simultaneously. Figure 6(a) depicts the variation of the interference spectrum of the FBG array sensor during stretching, with the interference fringe gradually shifting to the right as the stretching proceeds. Figure 6(b) depicts the change of the spectra of the FBG array sensor during horizontal relaxation, with the interference fringes gradually shifting to the left as the relaxation proceeds.
Fig. 6. (a) and (b) is the schematic diagram of the shift of Peak $\#1$, $\#2$, $\#3$ and $\#4$ during stretched horizontally and relaxing horizontally, respectively.
Figure 7(a) shows the peak wavelength versus strain during stretching, where the four peak wavelengths of the FBG array sensor gradually increase as the stretching proceeds. Figure 7(b) depicts the gradual decrease in peak wavelength as relaxation proceeds.
Fig. 7. (a) and (b) are the peak wavelengths of Peaks $\#1$, $\#2$, $\#3$, and $\#4$ of the sensor versus strain during tension and relaxation, respectively.
Adam, Adagrad, RMSprop, and SGD were selected as the optimization methods to test the model’s viability during the FBG array sensor demodulation simulation. Before training the neural network, the learning rate and loss function were also established. Since several peak wavelengths are the desired outcome, a multi-objective loss function was utilized, which may be written as Eq. (9).
4.2 Horizontal stretch demodulation
To prove the demodulation performance of the system, four models, SGD, Adagrad, RMSprop, and Adam, were used to train the peak wavelength-AWG channel transmitted intensity data pairs acquired during horizontal stretching, which never appeared in the training dataset. Since the amount of a priori data can affect the training process, data augmentation was performed on the dataset generated during the stretching process. Figure 8 shows the distribution of the original data with the augmented data, and it can be seen that the augmented data are not separated from the original dataset.
The wavelength demodulation error is defined as the difference between the network output value and the OSA measurement to verify the model’s performance after data augmentation. The original and augmented dataset is fed into the network model for wavelength demodulation error detection. Figure 9(a) shows the demodulation error of the four peak wavelengths in the original dataset using the above training model. Figure 9(b) depicts the peak wavelength demodulation errors for the augmented dataset using the above training model. For the peak wavelengths of the four peaks, the peak wavelength demodulation errors returned by the model based on the original dataset are within $\pm$0.2 nm; based on the wavelength demodulation errors returned by the augmented dataset, all four models return error values within $\pm$0.05 nm, and notably, the peak wavelength demodulation errors returned by the Adam model are within $\pm$0.02 nm.
Fig. 9. (a) and (b) denote the demodulation errors of the Adam, Adagrad, RMSprop, and SGD trained networks at the four peak wavelengths in the stretched original dataset and the augmented dataset, respectively.
In the process of the comprehensive evaluation of the system, Mean Square Error (MSE), Root Mean Square Error (RMSE), $R^{2}$, and Mean Absolute Error (MAE) are used as metrics, which can be expressed as Eqs. (10)–(13).
To further validate the demodulation performance of the network model, the four evaluation functions (MSE, RMSE, $R^{2}$, MAE) and the peak wavelength query error mentioned above are used to evaluate the model based on the original and augmented dataset more comprehensively, respectively. The overall analysis of the demodulation performance of the network model based on the original dataset using MSE, RMSE, $R^{2}$, MAE, and wavelength query error is given in Table 1. Based on the original dataset, the proposed neural network model can achieve $\pm$68 pm in wavelength query accuracy, and all four training models can achieve good wavelength query capability.
Table 1. Statistical analysis of performance evaluation metrics (MSE, RMSE, $R^{2}$, and MAE) and demodulation errors for Adam, Adagrad, RMSprop, and SGD trained models in the horizontal stretch test raw dataset.
The overall analysis of the demodulation performance of the network model based on the augmented dataset using MSE, RMSE, $R^{2}$, MAE, and wavelength demodulation error is given in Table 2. It is worth noting that, based on the augmented dataset, the models trained by all four algorithms outperform the former in terms of wavelength demodulation performance, and all achieve $\pm$19 pm in wavelength demodulation precision. The model trained with Adam outperformed the other three algorithms when performing multi-peaked wavelength demodulation. Based on the augmented dataset, the models trained by Adam’s algorithm achieve $\pm$4 pm for the best interrogation precision.
Table 2. Statistical analysis of performance evaluation metrics (MSE, RMSE, $R^{2}$ and MAE) and demodulation errors for models trained by Adam, Adagrad, RMSprop, and SGD in the horizontal stretch test augmentation dataset.
4.3 Horizontal relaxation demodulation
In practical monitoring, nonlinear hysteresis is one of the essential factors affecting the demodulation performance of the system, and its presence reduces the system’s repeatability. In the experiments, to verify the system’s repeatability, the model is trained on the data obtained from the relaxation process of the FBG array sensors. Again, comparisons are made based on the original and augmented dataset. The peak wavelength demodulation errors of different algorithmic models in other dataset are shown in Fig. 9. Figure 10(a) depicts the peak wavelength demodulation error based on the original dataset within $\pm$0.3 nm. Figure 10(b) illustrates the peak wavelength demodulation error based on the augmented dataset. It is worth noting that after data augmentation, all four peak wavelength demodulation errors of these models for the FBG array sensors are within $\pm$0.05 nm.
Fig. 10. (a) and (b) denote the demodulation errors of the Adam, Adagrad, RMSprop, and SGD trained networks at the four peak wavelengths in the stretched original dataset and the relaxed dataset, respectively.
The performance analysis of the models using MSE, RMSE, $R^{2}$, and MAE based on the original and augmented dataset is given in Tables 3 and 4, respectively. Table 3 depicts the performance analysis of the models based on the original dataset, where the proposed neural network model can demodulate the peak wavelength of the FBG array sensor with a precision of $\pm$ 0.13 nm in the original dataset. Table 4 depicts the performance analysis of the models based on the augmented dataset, where the peak wavelength’s demodulation precision based on the four algorithmic models mentioned above is $\pm$ 0.033 nm. The network trained by the Adagrad model has the best precision $\pm$8.19 pm when demodulating multiple peak wavelengths of the FBG array sensor simultaneously. The network’s versatility and the demodulation system’s repeatability are confirmed by demodulating peak wavelengths with high precision in a series of evaluations.
Table 3. Statistical analysis of performance evaluation metrics (MSE, RMSE, $R^{2}$, and MAE) and demodulation errors for Adam, Adagrad, RMSprop, and SGD trained models in the relaxation stretch test raw dataset.
Table 4. Statistical analysis of performance evaluation metrics (MSE, RMSE, $R^{2}$ and MAE) and demodulation errors for models trained by Adam, Adagrad, RMSprop, and SGD in the relaxation test augmentation dataset.
4.4 Model performance analysis
To demonstrate the superiority of our proposed network model, we used a series of traditional machine learning algorithms to compare with Adam’s algorithm. The main ones include linear regression (LR), decision tree, support vector regression (SVR), and Gaussian process regression (GPR). An augmented dataset consistent with the training of the neural network algorithm was used in the training process. These algorithms’ performance is comprehensively evaluated using the four performance evaluation indicators of MSE, RMSE, $R^{2}$, and MAE mentioned in Section 4.2. The statistics of evaluation indicators are shown in Table 5. In the process of demodulating the FBG array sensor, the performance of the proposed network model is significantly better than that of traditional machine learning algorithms such as LR, SVR, GPR, etc. Our proposed system has significant advantages in multi-point monitoring based on FBG array sensors.
Table 5. In the tensile test augmented dataset, the LR, Tree, SVR, and GPR algorithms are statistically analyzed according to the performance evaluation indicators (MSE, RMSE, $R^{2}$ and MAE).
In addition, the proposed model does not need to be trained for a long time and does not require excessive resource consumption, as shown in Table 6.
Table 6. Training / Testing (mean value in stretch and relaxing) time and training-time resource consumption of the proposed model under each algorithm.
5. Conclusion
In conclusion, we propose a novel demodulation approach to calculate the absolute wavelength of FBG array sensors effectively. Within this approach, an AWG is used to convert the sensor’s wavelength variation to transmitted intensities that feed into an end-to-end neural network model for the relationship between transmitted intensities and wavelength. Moreover, a practical data augmentation method is introduced to relieve the negative impacts of data scarcity on demodulation performance. Extensive experiments show that our method can monitor wavelengths of multi-peak within an FBG array sensor, reaching a precision of $\pm 4 pm$. The method is expected to provide a practical platform for intelligent multi-point monitoring of large buildings.
Funding
Scientific Research Starting Foundation of Hainan University (KYQD(ZR)1882); Major Science and Technology Project of Hainan Province (ZDKJ2016015); National Key Technology Support Program (2015BAH55F01, 2015BAH55F04); Open Project Program of Wuhan National Laboratory for Optoelectronics (2020WNLOKF001); Major Science and Technology Program of Haikou City (2021-002); Natural Science Foundation of Hainan Province (2019CXTD400, 617079, 620RC554); National Natural Science Foundation of China (61762033, 61865005, 62175054).
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.
References
1. R. Li, Y. Tan, Y. Chen, L. Hong, and Z. Zhou, “Investigation of sensitivity enhancing and temperature compensation for fiber bragg grating (fbg)-based strain sensor,” Opt. Fiber Technol. 48, 199–206 (2019). [CrossRef]
2. K. O. Hill and G. Meltz, “Fiber bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]
3. D.-S. Jiang and W. He, “Review of applications for fiber bragg grating sensors,” J. Optoelectron. Laser 13, 420–430 (2002).
4. H. Wang, S. Li, L. Liang, G. Xu, and B. Tu, “Fiber grating-based strain sensor array for health monitoring of pipelines,” Structural Durability & Health Monitoring 13(4), 347–359 (2019). [CrossRef]
5. C. E. Campanella, A. Cuccovillo, C. Campanella, A. Yurt, and V. M. Passaro, “Fibre bragg grating based strain sensors: review of technology and applications,” Sensors 18(9), 3115 (2018). [CrossRef]
6. T. Berkoff and A. Kersey, “Fiber bragg grating array sensor system using a bandpass wavelength division multiplexer and interferometric detection,” IEEE Photonics Technol. Lett. 8(11), 1522–1524 (1996). [CrossRef]
7. S. Kumar and S. Sengupta, “Multi peak detection algorithm of fiber bragg grating using mexican hat wavelets and hilbert transform,” in 2022 IEEE India Council International Subsections Conference (INDISCON), (IEEE, 2022).
8. S.-T. Lin and Y.-R. Cheng, “Wavelength shift determination using a dual-path heterodyne mach–zehnder interferometer,” Opt. Commun. 266(1), 50–54 (2006). [CrossRef]
9. L.-B. Yuan, “Multiplexed fiber optic sensors matrix demodulated by a white light interferometric mach–zehnder interrogator,” Optics & Laser Technology 36(5), 365–369 (2004). [CrossRef]
10. J. Sun, X. Yuan, X. Zhang, and D. Huang, “Single-longitudinal-mode fiber ring laser using fiber grating-based fabry–perot filters and variable saturable absorbers,” Opt. Commun. 267(1), 177–181 (2006). [CrossRef]
11. W. Zhu, J. Wang, J. Jiang, X. Liu, and T. Liu, “A high-precision wavelength demodulation method based on optical fiber fabry-perot tunable filter,” IEEE access 6, 45983–45989 (2018). [CrossRef]
12. A. V. Harish, B. Varghese, B. Rao, K. Balasubramaniam, and B. Srinivasan, “Dynamic interrogator for elastic wave sensing using fabry perot filters based on fiber bragg gratings,” Ultrasonics 60, 103–108 (2015). [CrossRef]
13. D. Jia, Z. Yao, and C. Li, “The transformer winding temperature monitoring system based on fiber bragg grating,” International Journal on Smart Sensing & Intelligent Systems 8(1), 538–560 (2015). [CrossRef]
14. Y. Yu, X. Bu, B. Liu, and P. Yang, “Fiber bragg grating acoustic emission demodulation system,” in World Conference on Acoustic Emission, (Springer, 2017).
15. H. Su and X. G. Huang, “A novel fiber bragg grating interrogating sensor system based on awg demultiplexing,” Opt. Commun. 275(1), 196–200 (2007). [CrossRef]
16. V. R. Marrazzo, M. Riccio, L. Maresca, A. Irace, and G. Breglio, “Wide range awg-based fbg interrogation system with improved sensitivity,” in 2019 15th Conference on Ph. D Research in Microelectronics and Electronics (PRIME), (IEEE, 2019).
17. D. Robertson, P. Niewczas, and J. R. McDonald, “Interrogation of a dual-fiber-bragg-grating sensor using an arrayed waveguide grating,” IEEE Trans. Instrum. Meas. 56(6), 2641–2645 (2007). [CrossRef]
18. H. Guo, G. Xiao, N. Mrad, J. Albert, and J. Yao, “Wavelength interrogator based on closed-loop piezo-electrically scanned space-to-wavelength mapping of an arrayed waveguide grating,” J. Lightwave Technol. 28(18), 2654–2659 (2010). [CrossRef]
19. G. Z. Xiao, F. Sun, Z. Lu, and Z. Zhang, “Simultaneously interrogation of multi fiber bragg grating sensors by an awg based demultiplexer,” in SENSORS, 2005 IEEE, (IEEE, 2005).
20. G. Xiao, P. Zhao, F. Sun, Z. Lu, Z. Zhang, and C. Grover, “Interrogating fiber bragg grating sensors by thermally scanning a demultiplexer based on arrayed waveguide gratings,” Opt. Lett. 29(19), 2222–2224 (2004). [CrossRef]
21. R. Evenblij and J. Leijtens, “Space gator: a giant leap for fiber optic sensing,” in International Conference on Space Optics–ICSO 2014, (SPIE, 2017).
22. Z. Cao, S. Zhang, T. Xia, Z. Liu, and Z. Li, “Spectral demodulation of fiber bragg grating sensor based on deep convolutional neural networks,” J. Lightwave Technol. 40(13), 4429–4435 (2022). [CrossRef]
23. S. Park, S. H. Kayani, K. Euh, E. Seo, and H. Kim, “High strength aluminum alloys design via explainable artificial intelligence,” J. Alloys Compd. 903, 163828 (2022). [CrossRef]
24. K. Yanamandra, G. L. Chen, X. Xu, G. Mac, and N. Gupta, “Reverse engineering of additive manufactured composite part by toolpath reconstruction using imaging and machine learning,” Compos. Sci. Technol. 198, 108318 (2020). [CrossRef]
25. G. Wetzstein, A. Ozcan, S. Gigan, S. Fan, D. Englund, M. Soljačić, C. Denz, D. A. Miller, and D. Psaltis, “Inference in artificial intelligence with deep optics and photonics,” Nature 588(7836), 39–47 (2020). [CrossRef]
26. J. Sun, A. Tárnok, and X. Su, “Deep learning-based single-cell optical image studies,” Cytometry Part A 97(3), 226–240 (2020). [CrossRef]
27. B. C. Wilson, M. Jermyn, and F. Leblond, “Challenges and opportunities in clinical translation of biomedical optical spectroscopy and imaging,” J. Biomed. Opt. 23(03), 1 (2018). [CrossRef]
28. R. S. Romaniuk, “Biomedical, artificial intelligence, and dna computing photonics applications and web engineering, wilga, may 2012,” in Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2012, vol. 8454 (2012), pp. 77–89.
29. Y. An, X. Wang, Z. Qu, T. Liao, and Z. Nan, “Fiber bragg grating temperature calibration based on bp neural network,” Optik 172, 753–759 (2018). [CrossRef]
30. Y. Wang, J. Chen, and H. Jiang, “Wavelength demodulation of overlapping spectra in fbg sensor network based on deep neural network,” in 2020 IEEE 16th International Conference on Control & Automation (ICCA), (IEEE, 2020).
31. N. Ren, Y. Yu, X. Jiang, and Y. Li, “Improved multi-grating filtering demodulation method based on cascading neural networks for fiber bragg grating sensor,” J. Lightwave Technol. 37(9), 2147–2154 (2019). [CrossRef]
32. Z. Jian, Z. Hong, and R. Xian-wei, “Application of bp neural network in fbg sensing system performance improvement,” in 2008 International Conference on Electronic Packaging Technology & High Density Packaging, (IEEE, 2008).
33. S. Chen, F. Yao, S. Ren, G. Wang, and M. Huang, “Cost-effective improvement of the performance of awg-based fbg wavelength interrogation via a cascaded neural network,” Opt. Express 30(5), 7647–7663 (2022). [CrossRef]
34. H. Jiang, Q. Zeng, J. Chen, X. Qiu, X. Liu, Z. Chen, and X. Miao, “Wavelength detection of model-sharing fiber bragg grating sensor networks using long short-term memory neural network,” Opt. Express 27(15), 20583–20596 (2019). [CrossRef]
35. B. Li, Z.-W. Tan, P. P. Shum, C. Wang, Y. Zheng, and L. jie Wong, “Dilated convolutional neural networks for fiber bragg grating signal demodulation,” Opt. Express 29(5), 7110–7123 (2021). [CrossRef]
36. S. Araki, T. Hayashi, M. Delcroix, M. Fujimoto, K. Takeda, and T. Nakatani, “Exploring multi-channel features for denoising-autoencoder-based speech enhancement,” in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (IEEE, 2015).
37. X. Huang, P. Qian, and M. Liu, “Latent fingerprint image enhancement based on progressive generative adversarial network,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, (2020).
38. M. Yang, K. Hu, Y. Du, Z. Wei, Z. Sheng, and J. Hu, “Underwater image enhancement based on conditional generative adversarial network,” Signal Processing: Image Communication 81, 115723 (2020). [CrossRef]
