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Abstract
We have proposed and demonstrated a denoising and extraction convolutional neural network (DECNN) composed of 1D denoising convolutional autoencoder (DCAE) and 1D residual attention network (RANet) modules to extract temperature and strain simultaneously in a Brillouin optical time-domain analysis (BOTDA) system. With DCAE for high-fidelity denoising and RANet for accurate and robust information extraction, integrated denoising and extraction of both temperature and strain have been realized for the first time under a single CNN framework. Both simulation and experiment have been conducted to statistically analyze the performance of the proposed scheme and compare it with the conventional equation solving method (CESM), which show that DECNN has large noise tolerance and robustness over a wide range of temperature/strain and signal-to-noise ratio (SNR) conditions. The mean standard deviation (SD) and root mean square error (RMSE) of the temperature/strain extracted by DECNN over a wide range of SNRs are only 0.2°C/9.7µɛ and 2°C/32.3µɛ at the end of 19.38 km long sensing fiber, respectively. At a relatively low SNR of 8.8 dB, DECNN shows 196 times better temperature/strain uncertainty and 146 times faster processing speed when compared with CESM.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin optical time-domain analysis (BOTDA) has attracted much research interest due to its excellent capability of distributed temperature and strain sensing for structural health monitoring (SHM) [1,2]. Brillouin gain spectrum (BGS) is usually measured to extract the Brillouin frequency shift (BFS) which is linearly dependent on the temperature and strain. However, there is cross-sensitivity of temperature and strain for Brillouin scattering, which makes it hard to simultaneously measure the temperature and strain. Several solutions have been proposed to achieve simultaneous measurement [3–13]. The hybrid sensing systems combining Brillouin scattering with Rayleigh/Raman scattering are used to extract both the temperature and strain [3,4]. But the hybrid systems significantly increase system complexity and cost when compared with a single BOTDA system. Instead of using single-peak BGS based BOTDA, multi-peak BGS based BOTDAs using specialty fibers are then proposed for reducing the system complexity and cost [5–8]. Using fibers with multi-peak BGS has been demonstrated to be an effective and simple way of simultaneous measurement of temperature and strain [9–13]. By measuring double-peak BGS, both the temperature and strain can be obtained by solving two BFS equations, which is the conventional equation solving method (CESM). Nevertheless, this method would result in large measurement uncertainties due to the small difference in temperature/strain coefficients of different peaks [12]. In CESM with two BFS equations, the BFS should be firstly obtained, and this is usually achieved by Lorentzian curve fitting (LCF) of the measured BGS. However, like the case of single temperature or strain measurement, the iterative feature of LCF algorithm is time-consuming, especially when the signal-to-noise ratio (SNR) is low [14].
Recently, some machine learning (ML) methods have been proposed to replace LCF to speed up the process, such as the Artificial Neural Network [14], Support Vector Machine (SVM) [15], Principal Component Analysis (PCA) [16], and some other machine learning methods [17–19]. Machine learning methods have faster processing speed and better accuracy than LCF. In the above works, machine learning methods are only used for single temperature or strain extraction. In 2019, B. Wang et al. used Deep Neural Network (DNN) to extract both the temperature and strain directly from the double-peak BGS of LEAF [19]. But in this work, the scheme can only be applicable to a narrow range of temperature and strain conditions, which is not practical for real applications. Moreover, the proposed DNN cannot tolerate large noise and thus is only feasible when the SNR is relatively high.
On the other hand, SNR is one of the most critical parameters for the BOTDA system, which determines the sensing distance, spatial resolution (SR), and measurement accuracy. Several image denoising technologies [20–23] have been applied to improve the SNR without additional hardware complexity. Most of the image denoising techniques will induce data loss after denoising [20], making high-fidelity denoising difficult. And it is demonstrated that the denoising along the axis of the frequency, i.e. the BGS at one location, brings no decisive improvement in measurement accuracy, since it is fundamentally redundant with LCF [24]. So in most of the past works, the denoising along the frequency axis consumes additional computing resources which makes the denoising inefficient. After denoising the temperature/strain information is still extracted using LCF, which is time-consuming. There is no such scheme integrating the functions of efficient high-fidelity denoising and information extraction under the same single framework. This is possible to finish under the same machine learning framework. Such a machine learning model can serve as a black box for data processing in BOTDA and can adapt to signals at different SNRs, especially useful for achieving fast and accurate extraction of both temperature and strain with large tolerance to noise.
In this paper, we propose and demonstrate a denoising and extraction convolutional neural network (DECNN) composed of two modules, i.e. 1D residual attention network (RANet) and 1D denoising convolutional autoencoder (DCAE), for simultaneous temperature and strain measurement. RANet can achieve highly accurate extraction of both temperature and strain with large tolerance to noise, while DCAE can realize efficient high-fidelity denoising without the loss of signal information and waste of computational resources. The performance of the proposed scheme is statistically analyzed and compared with CESM through both simulation and experiment. DECNN is demonstrated to work over a wide range of temperature/strain and SNR conditions, and shows at least 196 times better temperature/strain uncertainty and 146 times faster processing speed when compared with CESM at a relatively low SNR of 8.8 dB.
2. Principle and simulation
We firstly propose to use RANet for the extraction of both the temperature and strain and show its superiority in terms of measurement accuracy and noise tolerance when compared with CESM. Then, DCAE is introduced for denoising BOTDA signals. Finally, RANet and DCAE modules are integrated under a single CNN framework to form DECNN for the integrated denoising and information extraction.
2.1 RANet based simultaneous extraction of temperature and strain with large noise tolerance
As mentioned above, in CESM, the small difference in temperature and strain coefficients between the two peaks produces large calculation errors. Here we propose to use RANet to extract temperature and strain simultaneously with high accuracy and large noise tolerance. The structure of the proposed 1D RANet for the simultaneous extraction of temperature and strain is illustrated in Fig. 1(a). The double-peak BGS serves as the input for RANet, and after extracting and compressing the features of BGS through the convolution and pooling layers, the final output by the fully connected layer (FC) is the temperature and strain. The convolutional layer (Conv) of size 16 × 1 with stride 2 × 1 (i.e. the step of the convolution operation) extracts features from the input data through a large receptive field. After that, a max pooling layer with stride 2 × 1 is used to reduce the size of the feature by down-sampling with the maximum value. Then, the feature extraction module (FEM) is applied 3 times. The structure of our FEM is given in Fig. 1(b). The FEM has a residual attention block (RABlock) and a convolutional layer, where RABlock consists of a residual module (ResBlock) [25] and a convolutional block attention module (CBAM) [26]. ResBlock deepens the network and improves the mapping capability of the network, which effectively solves the problem of feature and information loss during extraction. CBAM including both channel and spatial dimensions allows the network to fully learn which information is meaningful and hence improves the accuracy of extraction. CBAM can be integrated into CNN architecture seamlessly with negligible overheads as a lightweight universal module. The last Conv of size 3 × 1 and stride 2 × 1 is used to compress the size of features while increasing the number of channels to avoid information loss. Following 3 FEMs, there are two feature compression modules (FCM) consisting of a ResBlock and a Conv. The main function of FCM is to re-extract and compress the features extracted by FEM. In the FCM module, channel compression of the features occurs in ResBlock. Conv of size 3 × 1 without padding reduces the size of features to achieve spatial compression. The structure of ResBlock in FCM is different from that in FEM due to the need to use a Conv of size 1 × 1 to match the number of channels for a skip connection. Note that the value of N is equal to the number of channels in the input to FEM and FCM, respectively.
Fig. 1. Structure of (a) RANet, (b) FEM, and (c) FCM. Conv: convolutional layer; FEM: feature extraction module; FCM: feature compression module; GAP: global average pooling layer; FC: fully connected layer; RABlock: residual attention block; CBAM: convolutional block attention module; ResBlock: residual block.
The final part of our RANet consists of a global average pooling layer (GAP) and two fully connected layers (FC). GAP greatly reduces the parameters of the network by spatial dimensionality reduction and regularizes the network to prevent overfitting while allowing the arbitrary size of the input. FC performs weighted integration of the learned high-level features, and finally outputs both the temperature and strain. It should be noted that after each Conv there are batch normalization (BN) and scaled exponential linear units (SELU). BN can avoid internal covariate shift during network training [17], making the training fast and efficient. Instead of using commonly used rectified linear units (ReLU) as the activation function, here we use SELU to increase the network non-linearity and to mitigate the gradient vanish problem [27], which enables faster training.
2.1.1 Dataset for training RANet
To improve the robustness of RANet, we construct the training dataset by simulation. We use theoretical double-peak Lorentzian BGS expressed in Eq. (1) to train RANet,
Table 1 shows the values of parameters in Eq. (1) used in the construction of the training dataset. In our case, the range of v is the same as the frequency scanning range during the acquisition of BGSs in the experiment. To further enhance the universality of the model, BGSs are generated with multiple ${\Gamma _B}$ and ${g_B}$. Note that BGSs must be normalized to ensure the efficient operation of RANet, so $g_B^{BGP1}$ is set to a fixed value (i.e. 1). To improve the tolerance of the model to noise, RANet is trained with noisy BGSs, which are obtained by adding Gaussian white noise to the clean BGSs. Considering long-distance sensing in practical applications, the SNR is set to a relatively low value of 10dB as an example. The above parameter setting is based on the pre-calibrated double-peak BGS of our fiber under test (FUT), which is a standard signal-mode fiber (SSMF), i.e. G.652.D commercial fiber made in Corning Optical Fiber Cable (Chengdu) Co., Ltd. Meanwhile, to make the model applicable to a wide range of temperature and strain conditions, multiple temperature and strain values are combined randomly to generate the BGSs for training. The two BFSs, i.e. $v_B^{BGP1}$ and $v_B^{BGP2}$, of the ideal double-peak BGS are determined by using pre-calibrated BFS-temperature/strain coefficients of our FUT. Note that in the training larger temperature and strain range can be used with the cost of more training time. This is definitely feasible as long as the two BGPs are not overlapped significantly. Finally, we have 845,397 simulated double-peak Lorentzian BGSs and 5,751 target temperature and strain combinations for training RANet. We randomly selected 90% of temperature and strain combinations as the training dataset and the rest serves as the validation dataset.
Table 1. Parameter setting to construct training dataset for RANet
2.1.2 Simulation results
After training, we use RANet to simultaneously extract the temperature and strain and compare its performance with CESM. The root mean square error (RMSE), representing the variance between the extracted temperature/strain and the real values, and standard deviation (SD), evaluating the fluctuations of the extracted temperature/strain, are used for the comparison of the accuracy. Some temperature and strain combinations that do not appear in the training dataset are randomly selected for generating testing BGSs. For each combination of temperature and strain, there are 200 BGSs generated for the demonstration. The temperature and strain distributions extracted by RANet and CESM for three different temperature and strain combinations are shown in Fig. 2. For all three cases, it is obvious that the results by CESM have large fluctuations when compared with those by RANet. Due to the induced calculated errors, the temperature and strain extracted by CESM deviate far from the real values. In contrast, both the temperature and strain fluctuations by RANet are small, and the extracted values are close to the real ones for all three cases. It implies that the measurement accuracy by RANet is much better than that by CESM. The detailed error performance for RANet and CESM are compared in Table 2, where 6 randomly selected temperature and strain combinations covering a wide temperature and strain range are shown. In Table 2, the worst SD and RMSE of the temperature/strain extracted by RANet are 2.0°C/75.5µɛ and 2.5°C/86.6µɛ, respectively. In comparison, the worst SD and RMSE by CESM are 61°C/2497.9µɛ and 61.4°C /2514.0µɛ, respectively. On average the SD and RMSE of the temperature and strain extracted by RANet are respectively 76 and 41 times lower than those by using CESM, indicating much better sensing accuracy by RANet.
Fig. 2. Temperature and strain distributions obtained by RANet (blue curve) and CESM (red curve), respectively.
Table 2. Comparison of the error performance between RANet and CESM
Furthermore, the error performance of RANet and CESM is analyzed and compared under different SNRs, as shown in Fig. 3. The temperature and strain values are set to be 38.5°C and 545µɛ, respectively, and the range of SNR varies from 7dB to 16dB with a step of 3dB by changing the noise level in the simulation. As shown in Fig. 3(a) and 3(b), both the SD and RMSE of the extracted temperature by using CESM increase significantly as the SNR decreases, while those by using RANet only have little increase. In Fig. 3(c) and 3(d), a similar trend is found for the case of strain extraction. RANet always outperforms CESM in terms of accuracy, especially when the SNR is relatively low. When the SNR is 7dB, the RMSE of the extracted temperature/strain by using CSME is 121.6°C/4981.4µɛ, while that by using RANet is only 6.9°C/273.3µɛ. We can see that RANet has a much larger tolerance to noise than CESM. The mean SD and RMSE of the temperature/strain extracted by RANet over the SNR depicted in Fig. 3 are only 1.75°C/69.2µɛ and 3.25°C/132.4µɛ, respectively. It is worth mentioning that RANet also performs well when the SNR is 7dB, despite the fact that it is trained only using simulated BGSs of 10dB SNR, which indicates the superior noise tolerance of RANet for simultaneous temperature and strain extraction.
Fig. 3. SD and RMSE of (a),(b) temperature and (c),(d) strain extracted from simulated BGSs by RANet and CESM under different SNRs.
2.2 DCAE based efficient high-fidelity denoising of BOTDA signals
DCAE is a variant of denoising autoencoder (DAE) [28], consisting of encoders and decoders. Convolutional layers in DCAE feature local connectivity and parameter sharing, enabling efficient feature extraction with fewer net parameters. The input data of DCAE is corrupted, and the robustness of feature extraction of DCAE is enhanced by restoring the corrupted data. We propose to use DCAE for denoising the time-domain Brillouin trace. The output of DCAE is the noise within the input data. By subtracting the output noise from the input data, the denoised data can be obtained at high fidelity.
The structure of the proposed DCAE is shown in Fig. 4. The structure of the decoding part is inversely symmetric to that of the encoding part. The decoding part consists of the transposed convolution layers (T-conv) instead of the convolution layers. In the encoding part, the noisy Brillouin trace is mapped into a low-dimensional feature space, where the latent features of the noise are extracted. Through the decoding part, the features of noise obtained by the encoders are restored into noise layer by layer. Note that all Convs and T-Convs of size 16 × 1 have a stride of 2 × 1 in DCAE. Encoder1 and Encoder2 have a similar structure, except that all convolutional layers of Encode2 have 32 filters. The change in the number of filters in Encode1 stems from the need to ensure that less valid information would be lost when the input data is significantly reduced in size. In the encoding and decoding parts, all Convs and T-Convs are followed by BN and SELU. Both Conv1 and Conv2 have only a single filter of size 1 × 1, which are used to generate the output. There are also two points to note. Firstly, we add skip connections to connect the corresponding encoders and decoders in the network. This operation shares the detailed features of each encoder with the corresponding decoder, reducing the loss of detailed features of the Brillouin signal during down-sampling by the encoders, while alleviating the gradient vanish problem [25]. Secondly, we introduce the attention mechanism [29]. The Brillouin time-domain trace and the output of Conv1 are concatenated through a skip connection, and a weight matrix is generated by Conv2 and Tanh activation function. The attention mechanism fully exploits the correlation between the input and output, allowing more robust noise information to be extracted from the Brillouin signal.
For DCAE training, we construct a dataset from the simulated Brillouin trace. Here, we simulate the Brillouin time-domain trace along a small section of fiber, where the transmission loss is negligible. The length of the time-domain trace is equivalent to a BGS sequence (200 BGSs). In order to make the DCAE model robust to most of the Brillouin time-domain traces, we assume there are two BFSs within the length of the time-domain trace, where the first section with a length of ${L_1}$ has a BFS of ${v_{B1}}$ and the following section with a length of ${L_2} = 200 - {L_1}$ has a BFS of ${v_{B2}}$. The Brillouin bandwidth is ${\Gamma _B}$. ${g_B}$ is set to be 1 since the Brillouin signal is normalized. To further enhance the universality and robustness of the model, those parameters vary within a range as depicted in Table 3, to generate the dataset for training. We fix the parameters ${v_{B1}}$ to avoid data duplication while including more cases of BFS combinations along the distance of ${L_1}$ and ${L_2}$. The value of ${v_{B1}}$ is fixed to the midpoint of the frequency scanning range to include more balanced cases of BFS variations. The Brillouin bandwidth in the experiment varies in the range of 40MHz -80MHz. Meanwhile, considering the spatial resolution (2m spatial resolution under 2.5GSample/s sampling rate in our case), ${L_1}$ varies from 50 to 150. Moreover, except for the values listed in Table 3, one more dataset where ${L_1}$ is set to be zero is also simulated for training. This simulates the case where there is no BFS variation along the fiber and makes the DCAE more robust to multiple conditions. Both the clean and noisy data are used for training. Because in the experiment, the actual resistance is defective, making the noise not satisfy the ideal Gaussian distribution [22]. So instead of adding ideal Gaussian noise to the data, we collect the output of the photodetector when the pump light is turned off, which serves as the actual noise added to the data for the DCAE training. Finally, to make the simulated Brillouin signal reflect the SR, a Gaussian filter with 50 MHz bandwidth is applied to the BFS distribution to generate smooth rising/falling edges [30]. Based on the setting of the above parameters, 1,920,000 Brillouin traces are generated, of which 90% of the dataset is used for training and 10% for validation.
Table 3. Parameter setting to construct training dataset for DCAE
For testing the DCAE after training, we simulate the double-peak BGS distribution using 400 BGSs including two BFS sections, where the first section corresponds to temperature and strain values of (25°C, 0µɛ) and the second section corresponds to (38.5°C, 545µɛ). Figures 5(a) and (b) show the BGS distribution without and with denoising by DCAE, respectively. The BGS at the fiber end and the Brillouin trace at the BFS of BGP1 with/without denoising are also shown in Figs. 5(c) and (d), respectively. After denoising by DCAE, the noise is significantly removed and the SNR is improved from 7.3dB to 18.5dB. Figures 5(e) and (f) show the BFS distributions of BGP1 and BGP2 for the raw data and denoised data, respectively. Due to denoising, the BFS uncertainty of BGP1 is reduced from 1.50MHz to 0.12MHz, and that of BGP2 is reduced from 2.63MHz to 0.16MHz. More importantly, the transition sections in Figs. 5(e) and (f) indicate that the spatial resolution remains almost the same after denoising, implying that the effective information is maintained and high-fidelity denoising is achieved.
Fig. 5. Simulated double-peak BGS distribution (a) without and (b) with denoising by DCAE; (c) BGS and (d) Brillouin trace at the BFS of BGP1 with and without denoising; the BFS distribution of (e) BGP1 and (f) BGP2 with and without denoising.
2.3 Integrated denoising and extraction of both temperature and strain by DECNN
It is desirable to have a machine learning model that integrates the functions of both high-fidelity denoising and information extraction and serves as a black box for data processing in BOTDA. Here we design such a model under a single CNN framework which we call DECNN. In the designed DECNN, we use DCAE as the module for efficient high-fidelity denoising and RANet as the module for simultaneous temperature and strain extraction with large noise tolerance. The structure of our DECNN is shown in Fig. 6. The architecture of DECNN contains two main steps: denoising and extraction. The noisy BGSs firstly pass through the encoders and decoders of the DCAE module which output the corresponding noise. The denoised BGSs are then obtained by subtracting the output noise from the input BGSs. Then they are used as the input of the RANet module, which extracts, compresses and maps the features of BGSs to simultaneously output the temperature and strain. The performance of DECNN is experimentally demonstrated in the next section.
3. Experiment setup and results
3.1 BOTDA experiment setup for data collection
In this section, we employ a conventional BOTDA setup to experimentally validate the proposed scheme. The setup is shown in Fig. 7. The output of a continuous wave (CW) laser working at 1550.12nm is split into two branches. At the upper branch, the CW light is modulated by a semiconductor optical amplifier (SOA) to generate a 20 ns pump pulse with high extinction ratio. An erbium-doped fiber amplifier (EDFA) is used to amplify the pump power. To suppress the polarization-dependent noise, a polarization scrambler (PS) is used. The light at the lower branch is modulated by an electro-optic modulator (EOM) based on carrier-suppressed modulation to provide the probe signal. The RF frequency is scanned from 10.75GHz to 11.15GHz with 1MHz step. After passing through the FUT, the probe signal is filtered to remove the higher frequency sideband by the FBG filter. Finally, it is detected by a 125 MHz photodetector and collected on an oscilloscope at a sampling rate of 2.5GSample/s. The peak power of the pump pulse is 11dBm and the probe power is −10dBm. The FUT is G.652.D single-mode fiber made by Corning Optical Fiber Cable (Chengdu) Co., Ltd. The length of the FUT is 19.38km with the last 6.8m section coiled on two micro-positioners and put inside an oven to apply different temperature and strain. Note that a relatively high sampling rate is used to collect sufficient data along the last 6.8m long FUT for statistical analysis of the error performance.
Fig. 7. BOTDA experiment setup. PC: polarization controller; EOM: electro-optic modulator; RF: radio frequency generator; VOA: variable optical attenuator; ISO: isolator; FUT: fiber under test; SOA: semiconductor optical amplifier; AFG: arbitrary function generator; EDFA: erbium-doped fiber amplifier; PS: polarization scrambler; PD: photodetector; OSC: oscilloscope.
The measured BGSs distribution along FUT is shown in Fig. 8(a) where 64 times averaging is used. The inset of Fig. 8(a) shows the normalized double-peak BGS at the end of FUT. The BFS as a function of temperature/strain is given in Figs. 8(b) and (c), where the BFS-temperature coefficient and BFS-strain coefficient of BGP1 are 1.9754 MHz/°C and 0.0483 MHz/µɛ, respectively, and those of BGP2 are 2.0351 MHz/°C and 0.0493 MHz/µɛ, respectively.
Fig. 8. (a) Measured BGSs distribution along FUT; (b) BFS as a function of temperature for BGP 1 and 2; (c) BFS as a function of strain for BGP 1 and 2.
3.2 Simultaneous temperature and strain extraction by using RANet
Here we firstly verify the performance of RANet for simultaneous temperature and strain extraction by experiment. Different values of temperature and strain are applied to the last 6.8m FUT, where the central section of 4.8m with relatively uniform strain is used for the subsequent analysis. The BGSs are collected with 64 times averaging, which corresponds to the SNR level of 11.5dB. Six different combinations of temperature and strain are randomly selected for the demonstration, all of which do not appear during the training of RANet. Figure 9 shows four groups of temperature and strain distributions extracted by CESM and RANet, respectively. The fluctuations of the temperature and strain extracted by CESM are quite large, with the temperature at some locations incorrectly reaching 200°C and −100°C, and the strain incorrectly reaching 7000µɛ and −6000µɛ. The extracted values by using CESM greatly deviate from the applied temperature and strain values. In contrast, the fluctuations by using RANet are small and the extracted values are close to the real values, indicating small uncertainty and RMSE of the extracted temperature and strain. The accuracy of the measured temperature and strain by RANet is much better than that of CESM. The detailed error performance is given in Table 4. It can be seen that the RMSE and SD by using RANet are much smaller than those by using CESM. In Table 4, the worst SD and RMSE of the temperature/strain extracted by RANet are 2.2°C/83.0µɛ and 4.7°C/205.4µɛ, respectively, while those by using CESM are 57.3°C/2346.4µɛ and 93.9°C/3919.5µɛ, respectively. By using RANet the SD and RMSE are respectively improved by 43 and 40 times on average in Table 4 when compared with that using CESM. Note that there is some SD and RMSE difference for different temperature and strain conditions. It is believed to originate from two factors: non-uniform strain applied on the fiber section and the low strain precision of the micro-positioner used in the experiment.
Fig. 9. Temperature and strain distribution along the central part of the last 6.8 m FUT extracted by RANet (blue curve) and CESM (red curve), respectively.
Table 4. Comparison of the error performance between RANet and CESM
To prove the robustness of RANet to different noise levels, the error performance is explored under different SNRs. The experimental BGSs are collected by using different averaging times, i.e. 16, 64, 256 and 1024, which correspond to the SNR levels of 8.8 dB, 11.6 dB, 14.5 dB and 16.9 dB at the end of FUT, respectively. For the demonstration, the applied temperature and strain values are set to be 31.2°C and 293µɛ, respectively. The results are shown in Fig. 10. It is evident that when the SNR decreases, both the SD and RMSE of the extracted temperature/strain by using CESM increase significantly, while those by using RANet have only a slight increase, which shows remarkable noise tolerance of RANet. When the SNR is 8.8 dB, the SD and RMSE of the temperature/strain extracted by CESM are 78.6°C/3224.7µɛ and 99.4°C/4159.4µɛ, respectively, while those for RANet are reduced to 1.5°C/70.6µɛ and 7.6°C/204µɛ. The SD and RMSE are at least 45 and 13 times lower than those by CESM, respectively. The mean SD and RMSE of the temperature/strain extracted by RANet over all the SNRs are only 0.7°C/37.9µɛ and 4.7°C/118.5µɛ, respectively. RANet not only has excellent accuracy for simultaneous temperature and strain extraction, but also exhibits strong tolerance to the noise when compared with CESM.
Fig. 10. SD and RMSE of (a),(b) temperature and (c),(d) strain extracted from experimental BGSs by RANet and CESM under different SNRs.
3.3 Integrated denoising and temperature/strain extraction by using DECNN
Although RANet has shown good noise tolerance, the SNR of the measured BGSs can still have an impact on the measurement accuracy, especially when the SNR is much lower. The denoising can further improve the measurement accuracy and make the performance better. As demonstrated by the simulation in Section 2.2, DCAE can be used to achieve efficient and high-fidelity denoising. Here we firstly show some experimental results to analyze the denoising performance by the DCAE module in DECNN. The last 6.8 m FUT is heated to 31.2°C and stressed to 293µɛ. 16 times of averaging are used for BGSs collection, corresponding to the SNR of 8.8 dB. Figures 11(a) and (b) show the BGS distributions along the last 19.2 m FUT before and after denoising by DCAE, respectively. The BGS at the end of FUT and the Brillouin time-domain trace at the BFS of BGP1 without/with denoising are also given in Figs. 11(c) and (d). It could be found that the noise level has decreased largely in the frequency and time domain after denoising by DCAE. The SNR is improved by 8.7dB after denoising. Figures 11(e) and (f) show the BFS distributions of BGP1 and BGP2 along the last FUT without/with DCAE denoising, respectively. The BFS profiles are obtained by using Lorentzian curve fitting. After denoising by DCAE, the BFS uncertainty of BGP1 decreases from 1.04 MHz to 0.15 MHz, and that of BGP2 decreases from 2.24 MHz to 0.11 MHz. This result shows that the denoising by DCAE along the axis of distance can provide efficient denoising, without waste of computational resources. The insets of Figs. 11(e) and (f) indicate that there is almost no deterioration in the spatial resolution after denoising, implying that the effective information has been maintained during denoising and high-fidelity denoising has been achieved.
Fig. 11. Measured BGSs distribution along the last 19.2 m FUT (a) without and (b) with denoising by DCAE; (c) BGS at the end of FUT and (d) Brillouin trace at the BFS of BGP1 with and without denoising; the BFS distribution of (e) BGP1 and (f) BGP2 with and without denoising. Insets: magnified view of the transition section.
As mentioned in Section 2.3, under the same single CNN framework, an end-to-end DECNN integrating the functions of both denoising and information extraction is designed. The experimental performance of DECNN is demonstrated firstly using the same collected data as in Fig. 11(a). Figure 12 shows the temperature and strain distributions extracted by DECNN. For comparison, the results by RANet and CESM are also given. It is obvious that the temperature and strain extracted by DECNN have fewer fluctuations and are closer to the actual values when compared with those extracted by RANet, which is due to the denoising by the DCAE module in DECNN. CESM has the worst accuracy among the three methods and some of the values extracted by CESM are even beyond the vertical range in Fig. 12 where the extreme temperature values at some locations are incorrectly extracted as 244.6°C and −121.9°C, and the extreme strain values are incorrectly extracted as 6407.7µɛ and −8612.9µɛ. The comparison of error performance between RANet and CESM under different SNRs is given in Fig. 10, here Fig. 13 shows the comparison between DECNN and RANet. The temperature and strain on the last 6.8m FUT are also set to be 31.2°C and 293µɛ, respectively. The experimental BGSs are collected with different averaging times, i.e. 16, 64, 256 and 1024, corresponding to the SNR levels of 8.8dB, 11.6dB, 14.5dB and 16.9dB, respectively. With the DCAE module added in DECNN, the SNR improvement are 8.7dB, 8dB, 7.1dB and 6dB, respectively. Thus, the SD and RMSE of the temperature/strain extracted by DECNN become lower than those by RANet, especially when the original SNR is relatively low, as shown in Fig. 13. For the case of 8.8dB original SNR, the error performance of DECNN, RANet, and CESM is given in Table 5. Compared with RANet, the SD of temperature/strain by DECNN has at least 3.7 times improvement, and the RMSE has more than 2.2 times improvement. Compared with the results of CESM in Fig. 10, the SD and RMSE by DECNN have been improved by at least 196 and 29 times, respectively. In Fig. 13, the mean SD and RMSE of the temperature/strain extracted by DECNN over all the SNRs are only 0.2°C/9.7µɛ and 2°C/32.3µɛ, respectively. The results prove that the proposed DECNN has better accuracy even for low SNRs when compared with RANet and CESM. In addition to the outstanding measurement accuracy, DECNN also exhibits fast processing speed. To process the total number of 484,500 BGSs along 19.83km FUT, DECNN takes approximately 4.6s based on the Python platform. For the same data, RANet and CESM require approximately 2.4s and 671.5s based on the same platform, respectively. This means the processing speed by DECNN is about 146 times faster than that of CESM. Compared with RANet, the measurement accuracy using DECNN is well improved with only a little increase in processing time. Note that the computer for data processing has an Intel Core i7-10700 CPU and an Nvidia GeForce RTX 2070 SUPER GPU. Therefore, DECNN provides a superior measurement accuracy for a wide range of SNR of the input data and can be used to reduce the data acquisition time (low averaging times) and processing time with little sacrifice of the measurement accuracy.
Fig. 12. (a) Temperature and (b) strain distribution along the central part of the last 6.8 m FUT extracted by DECNN (blue curve), RANet (red curve) and CESM (black curve), respectively.
Fig. 13. SD and RMSE of (a),(b) temperature and (c),(d) strain extracted from experimental BGSs by RANet and DECNN under different SNRs.
Table 5. Comparison of the error performance among DECNN, RANet and CESM
4. Conclusion
With DCAE and RANet modules integrated under a single CNN framework to form DECNN, integrated denoising and simultaneous extraction of temperature and strain by DECNN over a wide temperature/strain and SNR conditions is proposed and demonstrated. RANet shows great superiority over CESM in terms of measurement accuracy and noise tolerance. DCAE performs efficient high-fidelity denoising without the loss of effective signal information. For 19.38km sensing fiber, the mean SD and RMSE of the temperature/strain extracted by DECNN over a wide range of the SNRs are only 0.2°C/9.7µɛ and 2°C/32.3µɛ, respectively. Compared with CESM, DECNN shows 196 times better temperature/strain uncertainty and 146 times faster processing speed at a relatively low SNR of 8.8dB. We believe that the DECNN assisted BOTDA would be a potential candidate to for accurate sensing of both temperature and strain over a wide range of SNRs.
Funding
National Natural Science Foundation of China (62005087); Open Projects Foundation of State Key Laboratory of Optical Fiber and Cable Manufacture Technology (YOFC) (No. SKLD2006).
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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