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Abstract
We propose a deep learning demodulation method based on a long short-term memory (LSTM) neural network for fiber Bragg grating (FBG) sensing networks. Interestingly, we find that both low demodulation error and distorted spectrum recognition are realized using the proposed LSTM-based method. Compared with conventional demodulation methods, including Gaussian-fitting, convolutional neural network, and the gated recurrent unit, the proposed method improves the demodulation accuracy being close to 1 pm and achieves a demodulation time of 0.1s for 128-FBG sensors. Furthermore, our approach can realize 100% accuracy of distorted spectra recognition and complete the location of spectra with spectrally encoded FBG sensors.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber Bragg grating (FBG) sensors have been widely used in several fields, such as health monitoring of power grids [1], civil engineering [2], environment monitoring [3], and underground coal mining [4], because of their advantages, such as immunity to electromagnetic interference and adaptation to harsh environments. In recent years, wavelength division multiplexing (WDM) technology has been utilized to enhance the capabilities of FBG sensor networks [5]. It is desirable to improve the modulated accuracy and speed in larger-capability WDM-based FBG sensor networks, owing to the significant number of FBG sensors. The key to obtaining the temperature and stress parameters is the wavelength demodulation of the FBG sensors. Usually, the reflection spectrum waveform of an FBG sensor is a smooth Gaussian-like curve [6]. Distortions in the sensing system exist in the FBG reflection spectrum [7]. It exhibits excellent performance in symmetrical Gaussian spectral sensing signals with high signal-to-noise ratios (SNR) using conventional peak detection (CPD) algorithms, including the centroid [8], correlation [9], and Gaussian fitting methods [10]. However, it is difficult to handle asymmetric distortion spectra in FBG sensor networks using these conventional methods owing to the demodulation accuracy. Therefore, proposing a high-accuracy demodulation method for asymmetric distorted signals to enhance the reliability and survivability of FBG sensor networks is highly desirable.
Previously, Lamberti et al. [11] used the transfer-matrix approach to simulate the dynamic behavior of distorted FBG spectra, and the distorted spectra were demodulated using a fast phase-correlation algorithm. Chen et al. [12] designed an exponentially modified Gaussian fitting function to alter peak position. Wei et al. [7] established a spectral distortion model for practical applications, and studied the influence of spectral distortion on demodulation errors. Shang et al. [13] proposed correcting the spectrum using the first derivative of the asymmetric distortion spectrum and peak-sharpening algorithm. The demodulation accuracy of the asymmetric distortion spectra was improved by using these methods. However, these calculations are complex. This implies that the time cost of the demodulation system increases with an increase in the number of sensors.
Deep learning algorithms based on long short-term memory (LSTM) networks have been widely applied for the demodulation of FBG spectra. Since FBG wavelength detection is a nonlinear regression problem, the LSTM can extract features from the FBG spectrum using a multilayer network structure to demodulate its central wavelength. Zhang et al. [14] used LSTM to establish the relationship between strain values and load without a complex dynamic model, achieving the value of an FBG sensor axial dynamic strain. Wu et al. [15] demonstrated that LSTM could effectively mitigate FBG wavelength degradation in harsh environments. Jiang et al. [16] improved the detection accuracy and efficiency of an FBG sensing network in overlapping spectral conditions using LSTM. Moreover, few studies have focused on asymmetric spectral demodulation and location in the FBG sensing network.
In this work, we investigated spectral recognition and localization to identify whether the FBG reflective spectrum was normal or distorted and then located the distorted spectra. Furthermore, a demodulation algorithm based on the LSTM neural network model is proposed to improve the demodulation performance of the FBG sensing network. In addition, we compared the demodulation performance of our algorithm with that of two other methods based on deep learning: gated recurrent unit (GRU) networks [17] and convolutional neural networks (CNN) [18]. Distorted signal demodulation with an error of less than 1 pm was successfully achieved even for cases in which the signals were severely distorted. Accordingly, we determined that the demodulation speed of the algorithm remained very high as the number of FBG sensors increased.
2. Principles of algorithm
2.1 Principles of quasi-distributed FBG sensors network demodulation
Figure 1(a) presents a schematic diagram of the proposed quasi-distributed FBG sensor network system, which comprises a broadband source, 3-dB optical coupler, multi-channel optical switch, optical spectrum analyzer (OSA), personal computer (PC), and microcontroller. Optical signals from a broadband source are transmitted through an optical switch (OSW) and the FBG sensing channels. The reflection signals measured at the OSA from each FBG sensing channel contain multiple signals with different central wavelengths. Spectra were segmented and demodulated using an LSTM-based algorithm. The microcontroller controls the OSW and switches to another channel when the current channel fails [19].
Fig. 1. (a)System of FBG sensor network. (b)The partial reflective spectrum of a channel sensing FBGs.
To avoid overlapping of the FBG spectra, every FBG was assigned a wavelength range of 2 nm, and the partial waveform of the FBG reflection spectrum is illustrated in Fig. 1(b). We demodulate the wavelength of the FBG reflectivity. The one-channel FBG reflective spectrum ${R_i}(\lambda )$ can be considered as
where ${\lambda _{B,ik}}$ is the central wavelength of the k-th FBG in the i-th channel. The entire spectrum is segmented into n parts before the demodulation algorithm is used. For instance, an FBG in the wavelength range of 1550–1552 nm can be expressed using 2000 samples. Hence, the single FBG spectrum can be expressed as where $\Upsilon ({\cdot} )$ and $\lambda _{B,ik}^{\prime}$ denote the spectrum function of a single FBG and k-th FBG correlative wavelength, respectively. Essentially, the wavelength demodulation problem involves determining the solution of $\lambda _{B,ik}^{\prime}$ from the segmentation reflection spectrum ${R_{ik}}(\lambda )$. Hence, if we can obtain the inverse function, ${{\Upsilon }^{ - 1}}$, $\lambda _{B,ik}^{\prime}$ can be given by [16] eventually, the spectrum ${R_{ik}}(\lambda )$ central wavelength ${\lambda _{B,ik}}$ can be expressed as where C is the segmentation wavelength range ($C = 2$ nm), and ${\lambda _0}$ denotes the starting wavelength in the $i$-th channel. Equation (3) and (4) define the relationship between the FBG reflection spectrum ${R_{ik}}(\lambda )$ and the spectrum ${R_{ik}}(\lambda )$ central wavelength ${\lambda _{B,ik}}$ . However, owing to the influence of noise from the transmission process and external environment, the shape of the FBG reflection spectrum ${R_{ik}}(\lambda )$ was altered. Hence, it is difficult to achieve the inverse function ${{\Upsilon }^{ - 1}}$ using numerical methods. This means that the ${{\Upsilon }^{ - 1}}$ specific formula cannot be directly obtained using conventional methods. Therefore, we adopted deep learning algorithms to train the parameters of the ${{\Upsilon }^{ - 1}}$ model. The LSTM details are presented in Section 2.3.2.2 Principles of distorted spectral identification and location
In the proposed FBG sensor network, the OSW is used to switch different sensing channels, and the FBGCHi can discriminate between different channels. Figure 2(a) illustrates the principle of spectral location. Each FBGChi contained three FBGs to achieve FBG sensing channel discrimination. The spectral encoding method [20] was equipped with FBGChi.
Fig. 2. (a)Spectral encoding of FBG sensors in the FBG sensor network. (b), (c) Two states of the reflective spectrum of FBG.
In each channel, the first three FBGs were set as locators, and the other FBGs were utilized for optical sensing. The bands of each FBG sensor were separated by 2 nm intervals. The signal with the reflection spectrum of the FBG sensor was divided into two states based on the reflection spectrum. As shown in Fig. 2(b), one state is “0,” which represents the reflectivity of the FBG between 0.6 and 0.7. The other state is “1,” as shown in Fig. 2(c), which represents the reflectivity of the FBG between 0.8 and 0.9. The FBG sensor channel is encoded using “0” and “1” states. For instance, the second channel can be expressed as
where S denotes the state of the FBG sensor and the value of $S$ is 0 or 1. Hence, CH2 can be represented as {0,0,1}. To distinguish the characteristics of the spectrum, we divided the spectrum into two types: normal (N) and distortion (D) spectra. All FBG sensors in one channel can be encoded as follows: where n is the number of FBG sensors in a channel. T represents the type of spectrum. Therefore, when all FBG sensor states in the network are obtained, the position of the distorted FBG can be located. Here, we also used a deep learning algorithm to identify the spectrum state and locate the position of the distorted FBG.2.3 Principles of LSTM neural network
The LSTM neural network is a type of recurrent neural network (RNN). The model of the LSTM neural network was first established in 1997 by Hochreiter et al. [21] and then developed in 2000 by the team of Gers [22]. LSTM can solve long-time series problems [23–25], and it has been widely applied in FBG wavelength demodulation [14–16].
The block architecture of LSTM, shown in Fig. 3, contains three gates to process the input data, where ht-1 and ct-1 are the output signal and cell state at the previous time, respectively. The sigmoid neural layer, σ converts the input signal into a value between 0 and 1. Therefore, it was used to count the number of input signals that could be retained ht and ct denote the output signal and cell state at the current time, respectively. ${h_m}$ is the hidden vector. There are three gates in the LSTM network: forgetting gate ${f_t}$, input gate ${i_t}$, and output gate ${o_t}$. The value of each gate was determined as follows [14,16,23]:
In the LSTM network, we defined the spectrum of the FBG sequence $X = \{ {X_1}\textrm{,}{X_2}, \ldots ,{X_m}\}$.as the input and the central wavelength of the FBG spectrum Y = {${\lambda _B}$} as the output. Therefore, the network relationship between the input and output can be expressed as
where $H(\cdot )$ denotes the recurrent hidden layer function. Finally, the deep learning model LSTM network can realize the demodulation and recognition of distorted spectra.3. Simulation setup
Ideally, the reflectivity of FBG can be expressed as [6]
However, because of the practical fabrication process and degeneration in harsh environmental applications, the spectrum of FBG sensors has many possible distortions. Therefore, the FBG spectrum can adopt an asymmetric generalized Gaussian function, $\Re (\lambda )$ [7]
Fig. 4. (a) $W$= 0.2 nm, $\chi$= 1.8. (b) $W$= 0.2 nm, $\chi$= 2.2. (c) spectrum of a signal with a SNR of 20 dB, (d) spectrum of the (c) signal through the S-G filter.
The sensor network data for the model training were generated via a theoretical model using Eq. (13). The parameters settings are presented in Table 1. $\Delta {\lambda _B}$ represents the offset of the central wavelength.
Table 1. Parameter setting to construct training dataset for LSTM
In the simulation, the training and testing data comprised ideal and distorted spectra, and the entire spectra exhibited 20 dB Gaussian white noise. In total, 80000 training data sets were fed into the model based on the LSTM neural network as training data, and 20000 testing data sets were used to test the model performance. Before the training and testing processes, the S-G filter, which can retain the overall characteristics of the signal, was used to denoise the signals. Figure 4(b) illustrates the effect of the S-G filter [13], which reduces the influence of random noise in the spectrum and makes the spectrum curve smoother. We also discuss the influence of low SNR on the demodulation of our proposed method. As shown in Fig. 5, we tested the mean error of 128 spectra with different SNRs, and compared the original spectra without denoising and denoising spectra. After denoising with the S-G filter, the mean error was less than 1 pm when the signal-to-noise ratio was increased from 20 dB to 35 dB.
Fig. 5. The mean error of the proposed demodulation method decreases along with the SNR increase in the cases of original spectra and smoothing by the S-G filter.
The proposed neural network model is illustrated in Fig. 6. Two thousand sampling points were adopted as the input for the network, and the batch size (BS) was 32. Three LSTM layers containing 256 × 3 hidden units were used to obtain the features of the input points. Then, the linear layers connect all previous features to the last output, which can be the central wavelength of the FBG sensors. In the training process, a back-propagation algorithm is used to update all network parameters in the training process to improve the performance of the network properly. Simultaneously, the mean squared error (MSE) Loss, as a loss function, reduces the loss between the real and predicted values. We used the Adam stochastic optimization algorithm to train the network. The processor was Ten-Core Intel i5-12600 K CPU and NVIDIA RTX3060Ti, 8GB GDDR6 GPU, and the overall neural network model was trained and tested using PyTorch 1.11.
4. Results
Neural network algorithms were used for the wavelength demodulation of the distorted spectra. The loss incurred by the model was lower and the prediction result of the model was closer to the real value. As a loss function, MSE Loss can be expressed as
where ${\lambda _i}$ is the FBG sensor real central wavelength and ${\lambda _{pre,i}}$ is the model predicted FBG sensor central wavelength. BS = 32.We compared the MSE Loss of our demodulation model with those of the CNN and GRU schemes using the same training and testing data sets. In the CNN, the convolutional kernel size was set to three, and one convolutional layer and four dilation convolutional layers were used to obtain spectral features. In addition, three GRU layers containing 256 × 3 hidden units achieved the features of the input point. Figure 7 presents the training and validation MSE Loss of the three neural network models with increasing epochs. During the training process, the CNN training MSE Loss fluctuated considerably, and the training MSE Loss of the proposed model and GRU could stably reach <1. However, the validation MSE Loss for the proposed model is lower than that for the GRU, and the CNN validation MSE Loss still exhibits significant fluctuation as the epoch reaches 1000.
In addition, the performance of the LSTM-based algorithm was validated by identifying 128 spectra containing normal and distorted spectra. In Table 2, we compare our method with GRU [17], CNN [18], and conventional Gaussian-fitting methods [10]. The method achieves the lowest mean error of 1.013 pm, and the demodulation time is 0.102 s. Because Gaussian-fitting is suitable for spectrum demodulation of the ideal Gaussian model, it has a significant error in terms of serious spectral distortion. In general, the proposed LSTM-based algorithm can implement high precision and fast demodulation in FBG sensor networks.
Table 2. Comparison of different algorithms
An LSTM neural network model was adopted to recognize and locate the position of the distorted FBG. The network was designed as a classified model because there are two types of spectra. As shown in Table 3, even with the increase in FBG sensors, the state recognition accuracy of the FBG sensors can still reach 100% when using the neural network algorithm.
Table 3. FBG recognition ability of the algorithm
To test the ability of the proposed algorithm, we identified and located the distorted spectra. Three locations and nine sensing spectra were used to constitute the entire spectrum, as illustrated in Fig. 8. The three location spectra can realize eight channels and $C{S_4} = \{{0,1,1,N,N,D,D,D,D,N,N,D} \}$.
Table 4 lists the results of the proposed algorithm. In the 12 spectra, the first, second, and third spectra were designated as the location spectra, and the fourth to twelfth spectra were designated as the sensing spectra. The states of the first three spectra {0,1, 1} indicate the channel is 4-th. Here, state “0” represents the reflectivity of the spectrum in the range of 0.6–0.7, and state “1” represents the reflectivity of the spectrum in the range of 0.8–0.9. The distorted spectra (represented by D) were the sixth, seventh, eighth, ninth, and twelfth, respectively. The fourth, fifth, tenth, and eleventh spectra behave normally (represented by N) and are close to the ideal Gaussian model. The predicted and real central wavelengths of each FBG in the 4-th channel are also listed in Table 4. It is evident that the central wavelength error of each FBG is close to 1 pm. Hence, the proposed algorithm can precisely determine the location and recognize the spectra.
Table 4. Results of the location and recognition algorithm
5. Conclusion
In conclusion, a deep learning-based LSTM algorithm was utilized to demodulate the spectra in FBG sensing networks. Compared with the results of the demodulation accuracy and speed of GRU, CNN, and Gaussian-fitting, the proposed LSTM-based algorithm exhibits a better stability, and it can be inferred that the error could reach 1 pm when there are some distorted spectra in the FBG sensing network. Furthermore, 128 FBG spectra containing distorted and non-distorted spectra were demodulated simultaneously in only 0.1 s. An LSTM algorithm with a spectral encoding method was proposed to identify the spectra and locate the position of the FBG sensing network spectra. This method can accurately identify the current channel and locate distorted spectra within the channel. Therefore, the proposed methods are promising candidates for enhancing the sensing capability of FBG sensing networks.
Funding
National Natural Science Foundation of China (61905060); Scientific Research Project of the Department of Education of Hebei Province, China (ZD2021019); Natural Science Foundation of Hebei Province (F2022402007).
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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