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Abstract
The general neural networks (NNs) based on classification convert the Brillouin frequency shift (BFS) extraction in Brillouin-based distributed sensing to a problem in which the possible BFS output of the sensing system belongs to a finite number of discrete values. In this paper, we demonstrate a method of applying NNs with adaptive BFS incremental steps to signal processing for Brillouin optical correlation-domain sensing and achieve higher accuracy and operation speed. The comparison with the conventional curving fitting method shows that the NN improves the BFS measurement accuracy by 2–3 times and accelerates the signal processing speed by 1000 times for simulated signals. The experimental results demonstrate the NN provides 1.6–2.7 times enhancement for BFS measurement accuracy and 5000 times acceleration for the BFS extraction speed. This method supplies a potential solution to online signal processing for real-time Brillouin sensing.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Brillouin-based distributed optical fiber sensing has been extensively investigated owing to its capability to measure temperature and strain along a single piece of optical fiber and its application in structural health monitoring, etc [1–6]. Among the various configurations proposed to realize the distributed measurement, the correlation-domain techniques have the merits of high spatial resolution and random accessibility to measuring points compared with the time-domain techniques [1]. Brillouin optical correlation-domain sensing includes two major configurations: Brillouin optical correlation-domain analysis (BOCDA) utilizing stimulated Brillouin scattering (SBS), or the interaction of the counter-propagating pump and probe light with the acoustic wave [7,8], and Brillouin optical correlation-domain reflectometry (BOCDR) utilizing spontaneous Brillouin scattering (SpBS), which benefits from single-end accessibility but suffers from a relatively low signal-to-noise ratio (SNR) [9,10]. Some approaches have been proposed in BOCDA and BOCDR to accelerate the measurement speed and achieve the real-time measurement of dynamic strain. For instance, ultrahigh-speed BOCDR with a sampling rate of up to 100 kHz was demonstrated by converting the Brillouin gain spectrum (BGS) to a synchronous sinusoidal waveform [11]. However, this approach achieved real-time distributed measurement at the sacrifice of deteriorated spatial resolution, measurement accuracy, and strain dynamic range. High-speed distributed sensing can also be achieved by employing the slope-assisted method in BOCDA/R, but the method suffers from drawbacks including limited dynamic range and measurement accuracy [12,13]. The single-point strain sampling rate of BOCDA can also be improved to 200 kHz with a cm-level spatial resolution by using a voltage-controlled oscillator (VCO) to scan the pump-probe frequency interval and adopting a lock-in amplifier (LIA)-free scheme [14,15]. Nevertheless, the approach simply increases the BGS acquisition speed, and the following signal processing is implemented offline. Therefore, the time for the post-processing is not considered and the scheme is not truly real-time.
Lorentzian curve fitting (LCF) is the signal processing method commonly used to extract the accurate Brillouin frequency shift (BFS), the parameter proportional to temperature or strain, in both time-domain and correlation-domain configurations. This conventional method produces results with high measurement accuracy but has the drawbacks of significant computation load that requires long processing time, hindering the measurement from being fast and real-time. Therefore, machine learning algorithms that have exhibited remarkable performances in data science and many other different fields are adapted into the signal processing stage for Brillouin-based optical fiber sensing. Concretely, neural networks (NNs) [16–18] and support vector machines (SVMs) [19,20] have been employed in the post-processing of Brillouin optical time-domain analysis (BOTDA) and verified to be effective in increasing the processing speed by at least hundreds of times without sacrificing the sensing accuracy. Some other advanced machine learning methods are also introduced into the BOTDA to further enhance the performances [21,22].
We have proposed the prototype of NN-based signal processing in correlation-domain sensors to make the sensing systems more reliable and efficient [23]. The idea is similar to the work done in BOTDA, but the realization is not feasible in the same manner because the operating principles and the BGS structures of the correlation-domain Brillouin sensors are quite different. In this paper, we demonstrate by simulation and experiment that a fully connected three-layer NN model is sufficient to process the BGSs in correlation-domain sensing. Comparing with the offline processing by the conventional curve fitting method, the NN improves the BFS extraction speed by thousands of times without the cost of other performances. In addition, a NN approach with adaptive BFS incremental steps is proposed to increase the efficiency of the model training and implementation for the real correlation-domain systems, especially for those with large dynamic ranges.
Although BOCDA and BOCDR have distinct principles, according to the theoretical studies, it is shown that the formula describing the two configurations, and thus the forms of the Brillouin spectra should be equivalent [10,24]. It is known that the Brillouin spectra obtained by the correlation-domain sensing methods are the superposition of the ‘real’ BGS generated by the correlation peak (CP) and the background signal that is the accumulation of signal generated from the non-correlation positions. We will see in the next section how NN processes the composite Brillouin spectra as a whole without seeking a way to reduce the background signal.
2. Principle and simulation
In this section, the principle of applying NN to the Brillouin correlation-domain sensing systems will be illustrated. The simulated BGS datasets will be used to testify the performance of NN in BFS extraction and its merits over the traditional curve fitting method.
2.1 Principle of NN for Brillouin optical correlation-domain systems
Figure 1 illustrates the principle of NN-assisted signal processing for Brillouin optical correlation-domain sensing systems. The training datasets contain a number of BGS samples labeled with different BFS or temperature/strain. As the output of a sensor, the BFS is intuitively treated as a continuous variable. In this paper, we introduce NN into Brillouin correlation-domain sensing as a classification algorithm, and the BFS needs to be discretized to a finite number of evenly spaced values covering the dynamic range. In other words, the possible BFS labels for each BGS sample belong to a series of discrete values.
The BGS dataset with discrete BFS labels (training dataset) is then fed into a NN. If each BGS sample is constituted by n sampling points, then the input layer of NN should have n+1 neurons (represented by red circles in Fig. 1), including x1, x2, x3… xn for the n-dimensional input vector and one additional neuron for the bias. The entire (n+1)-dimensional vector can be expressed as x(1). In the next stage, the algorithm is implemented by one or more hidden layers (represented by green circles in Fig. 1), each of which contains some neurons. The neurons in the l-th layer can be named as x(l) i, and the vector can be named as x(l).
Each of the neurons in the (l+1)-th layer can be calculated by using the neurons in the previous layer and the weight vector θ(l) ij as
in which g(z) is the sigmoid function that can be expressed asThe sigmoid function is used to activate each neuron and normalize it to the range from 0 to 1, before delivering the value of neurons to the next hidden layer. Equation (1) can be simplified by using vectors and matrices as
where Θ(l) is the weight matrix that connects the l-th and (l+1)-th layers.The output layer is the final stage of NN (represented by blue circles in Fig. 1), hence there is no need to activate these neurons. The number of neurons in the output should be the same as the number of BFS labels in the training datasets, and each neuron corresponds to one class of BFSi. The NN algorithm will find the neuron with the maximum value in the output layer and determines the BFS class that one BGS sample is most likely to belong to. The backpropagation algorithm optimizes the weight matrix Θ to make all BGS samples in the training datasets agree with their labels at utmost. In other words, by adjusting the weight parameters, the algorithm tries to minimize the cost function
When new BGS samples without BFS labels come (test dataset), NN with well-trained weights can predict their BFSs immediately by classifying each of them into one of the BFS classes through the search for the maximum probability shown by the neurons in the output layer.
The incremental step of the BFS labels defines the upper limit of the BFS measurement accuracy. However, a smaller BFS label incremental step leads to a greater number of neurons in the output layer, given the same dynamic range. Consequently, the target BFS class number also increases and raises the requirement for immense computational cost in model training, while most of the BFS classes in the trained model are redundant for a sensing application. Thus, we need to make a compromise between the BFS incremental step and the dynamic range, or we can find some ways to make the incremental step adaptive.
2.2 Simulation of BGS datasets
Simulation is used to generate the BGS datasets. Since at least tens of BFS classes are required to train the NN and the incremental step of the BFS label is expected to be small, it is impractical to generate the BGS training datasets experimentally by tuning the temperature/strain applied on the optical fiber under test subtly.
The simulation is done by assuming the laser frequency is sinusoidally modulated, and the beating spectrum SB is expressed by a series of discrete first-kind Bessel functions [25]
The local BGS is known to be the convolution between the beating spectrum ${S_B}$ and intrinsic Brillouin spectrum, and the overall BGS is the integral of local BGS over the entire fiber length as
in which ${ \otimes _f}$ indicates convolution in the frequency domain, and the intrinsic Brillouin spectrum $g(x,f)$ can be expressed by where ${g_B}$ is the Brillouin gain coefficient, ${\nu _B}(x)$ is the location-dependent BFS, and $\Delta {\nu _B}$ is the full width at half maximum (FWHM) of the BGS.In order to generate BGS samples belonging to different BFS classes, the simulation was performed assuming that the fiber under test has uniform temperature/strain distribution but different temperature/strain was applied to a short section centered at the CP, which then introduces a frequency offset of the Brillouin spectrum. Specifically, the intrinsic BFS that normally equals to 10.86 GHz in silica optical fibers (at telecom wavelength) was set to 0, and then the BFS was defined as the frequency offset between the Brillouin peak and 0.
Figure 2 shows examples in four classes of BGS with different BFS labels (100 MHz, 200 MHz, 300 MHz, and 400 MHz). The frequency range is from −500 MHz to 500 MHz, and the point number for each BGS is 10001. The real Brillouin spectrum can be treated as a spine added to the volcano-shaped background noise, and it is difficult to extract the BFS correctly when the power level of the background noise is higher than that of the real Brillouin spectrum. For each of the BFS classes in Fig. 2, the BGS samples were simulated with strained section length equals 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 times the nominal spatial resolution $\Delta z$ of BOCDA/R, which can both be expressed by [7,10]
Fig. 2. Examples in four classes of simulated BGS with different BFS labels: (a) BFS = 100 MHz, (b) BFS = 200 MHz, (c) BFS = 300 MHz, and (d) BFS = 400 MHz. The simulation was performed with FWHM = 30 MHz, strained section lengths of 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 times the nominal spatial resolution, and over the frequency range from −500 MHz to 500 MHz.
Except for the BGS samples for 0.7$\Delta z$∼1.0$\Delta z$ strained section length in BFS = 100 MHz class and 1.0$\Delta z$ strained section length in BFS = 200 MHz class, all the other examples in Fig. 2 exhibited the BGS shapes that have a background noise power level higher than the real Brillouin signal. It means that a simple maximum search method cannot find the correct BFS in these BGSs. It is worth mentioning that a shorter strained section length, especially when it is much shorter than the nominal spatial resolution $\Delta z$, is more difficult to be measured. Additionally, a large frequency offset from 0 is also a factor influencing the correctness of the measurement, because when the BFS becomes larger, the real Brillouin spectrum slides down from the summit to the foot of the “volcano”, and its power level becomes lower compared with the background noise. This is also the reason why dynamic range limitation exists in BOCDA/R.
The simulation was conducted at $\Delta f$ = 4 GHz, and ${f_m}$ = 1 MHz. The ${g_B}$ value makes no difference to the results and was set to 1, as the BGS is normalized before processing. The strained section length was set to the range from 0.5$\Delta z$ to 1.4$\Delta z$ with 0.1$\Delta z$ incremental step (10 cases), and the FWHM was set to the range from 30 MHz to 69 MHz with 1 MHz step (40 cases). The BFS label was set to the range from 100 MHz to 395 MHz with 5 MHz step (60 cases). Therefore, there should be 60 classes of simulated BGSs with different BFS labels, and each class had 40×10 = 400 BGS samples. Totally, there were 400×60 = 24000 samples in the simulated BGS dataset.
Two additional BGS datasets with the same structure were created for NN training, whose BFS was set to the range from 300 MHz to 359 MHz with 1 MHz step (60 classes), and from 300.0 MHz to 311.8 MHz with 0.2 MHz step (60 classes), while the other parameters were kept unchanged. These simulated BGS datasets covered only part of the dynamic range from 0.5$\Delta z$ to 1.4$\Delta z$ and the NN trained with these training datasets cannot predict the strained section length below 0.5$\Delta z$ or above 1.4$\Delta z$, but these datasets were sufficient to demonstrate our proposed method as a proof-of-principle. If a dataset with a wider dynamic range is expected to be used, more BFS classes need to be created and it will be extremely computationally expensive to implement the following algorithm on a personal computer unless we seek a hardware solution such as graphics processing units (GPUs) and field-programmable gate arrays (FPGAs) [26]. Also, the simulation only considers one single uniformly strained section centered at the optical fiber. The NN trained with these training datasets cannot predict more complicated situations such as two or more sections are applied with varied strains along the same optical fiber.
2.3 Double-peak Lorentzian curve fitting for BFS search
LCF is commonly used in Brillouin optical time-domain sensing to extract the BFS in the Brillouin spectra. However, in Brillouin optical correlation-domain sensing, the inherent volcano-shaped background noise cannot be easily removed with traditional methods. Therefore, we propose double-peak Lorentzian curve fitting (DP-LCF) for real BFS search while viewing the background noise as another peak in the Brillouin spectrum. The double-peak Lorentzian curve can be expressed by
The BGS dataset generated in Section 2.2, whose BFS labels were set to the range from 300 MHz to 359 MHz with 1 MHz step, was used to verify the feasibility and the performance of DP-LCF. The simulated ideal BGS samples are free of random noise and the SNR equals ∞. In this paper, we did not count the contribution of the background noise in the SNR calculation, but only random noises added to the ideal BGS samples were considered in SNR. Besides the ideal case (SNR = ∞), random noises of three different amplitudes were added to all the 24000 BGS samples to generate three noisy BGS datasets with SNR = 20 dB, 15 dB, and 10 dB. These simulated data are utilized to show the influence of random noise on DP-LCF.
Figure 3 shows one example of simulated BGS data (BFS = 400 MHz, FWHM = 30 MHz, SNR = ∞, 20dB, 15dB, and 10dB) and fitted double-peak Lorentzian curve. The results show that the BFSs found by the DP-LCF are 398.9574 MHz, 398.9683 MHz, 399.0576 MHz, and 399.2903 MHz. Each of these results is close to the real value 400MHz. The statistics of the BFS error are shown in Table 1, including the standard deviation (SD), root mean squared error (RMSE), and maximum error (absolute value). The average time needed to fit a BGS using DP-LCF is also listed in Table 1. The algorithm was implemented using MATLAB on a personal computer with Intel Core i7-10510U. The method used for fitting was nonlinear least squares. The initial condition and the possible range for the parameters need to be determined before implementing DP-LCF, otherwise, the algorithm may not converge within a finite number of iterations and cannot reach a reasonable result. For BGS with distinct BFS labels, sometimes different initial conditions and ranges are used to avoid the divergence of the algorithm.
Fig. 3. Simulated BGS data (BFS = 400 MHz, FWHM = 30 MHz) and fitted double-peak Lorentzian curve: (a) SNR = ∞, (b) SNR = 20 dB, (c) SNR = 15 dB, and (d) SNR = 10 dB.
Table 1. Statistics of BFS error extracted by DP-LCF and time for fitting each BGS
The statistics listed in Table 1 illustrates that the BFS error increased by small amounts with the deterioration of SNR. The reason may be that the fitting process smoothed the random variation of BGS, thus the SNR did not impose a significant effect on the resultant BFS error. Notably, the maximum BFS error (absolute value) for SNR = ∞ was slightly worse than that for SNR = 20 dB. Considering that the BGS shapes for SNR = ∞ and SNR=20 dB were similar to each other and that DP-LCF induces randomness, it may be treated as a normal phenomenon. The value in the RMSE column was remarkably larger than the value in the SD column, which means the fitted BFS is “biased”, or the mean of BFS error was not close to zero. The reason should be that the double-peak Lorentzian model did not exactly match the ideal BGS, so DP-LCF induced the error mostly in “one-direction” instead of in “two-direction” randomly, and then the resultant BFS error was biased.
The average time needed to fit one BGS varied from 174.2 ms to 191.1 ms. The time is irrelevant to SNR but depends on the data size, the fitting algorithm, and also the hardware and software used to implement the algorithm. When we used the provided condition to fit all the 24000 BGS samples, the overall time consumed was over 1.2 hours. It means that DP-LCF is quite a computationally expensive method, especially when a large number of BGS is needed to be processed, which hinders the realization of online signal processing in Brillouin optical correlation-domain sensing.
2.4 NN for BFS extraction
The three simulated BGS datasets prepared in Section 2.2 (BFS label steps = 5 MHz, 1 MHz, and 0.2 MHz) are used in the verification of NN for BFS extraction. Random noises of different amplitudes were added to each BGS sample in the datasets to generate noisy BGS with SNR = 20 dB, 15 dB, and 10 dB, as we did in Section 2.3. Consequently, we have 3×4 = 12 types of BGS datasets, each of which contains 24000 BGS samples. In every dataset, 70% BGS samples (16800 samples) were used as the training dataset and 30% BGS samples (7200 samples) were used as the test dataset.
The three-layer NN designed for the BFS extraction has a 10002-801-60 structure. The input layer has 10002 neurons for the 10001 sampling points in each BGS and one additional neuron for the introduction of the bias. The one hidden layer has 801 neurons including one for the bias. This number can be adjusted to test NNs with different hidden layers. The output layer contains 60 neurons for the 60 BFS classes. The designed NN structure is applicable for all the 12 types of BGS datasets.
As the BFS label has been discretized to 60 classes, the extracted BFS error is also discrete. Therefore, BFS error here can be represented using histograms, by showing the number of BGS samples belonging to each BFS error class. The best situation is that the BFS error belongs to the zero class, which means the BFS extraction is exactly correct. However, when the BFS error is classified into the classes adjacent to the zero class, it is also acceptable especially when the BFS incremental step is a small value. It is clear that more BGS samples are expected to fall into the zero class and fewer BGS samples are expected to belong to classes further away from the zero class. Thus, the histograms representing the BFS error can be reasonably approximated by a normal distribution with zero mean.
Figure 4 shows the 3×4 = 12 histograms of BFS error extracted by NN for the 12 types of BGS datasets. Row 1, Row 2, and Row 3 indicate BFS step = 5 MHz, 1 MHz, and 0.2 MHz; Column 1, Column 2, Column 3, and Column 4 indicate SNR = ∞, 20 dB, 15 dB, and 10 dB, respectively. The histograms illustrate the number of BGS samples belonging to each BFS class for the 12 different cases, both for the training set and the test set. The normal distribution fitting curves for the histograms are also shown in Fig. 4.
Fig. 4. Histograms of BFS error extracted by 10002-801-60 NN for BGS datasets, with 70% data used as training set and 30% data used as test set. (a) step = 5 MHz, SNR = ∞, (b) step = 5 MHz, SNR = 20 dB, (c) step = 5 MHz, SNR = 15 dB, (d) step = 5 MHz, SNR = 10 dB, (e) step = 1 MHz, SNR = ∞, (f) step = 1 MHz, SNR = 20 dB, (g) step = 1 MHz, SNR = 15 dB, (h) step = 1 MHz, SNR = 10 dB, (i) step = 0.2 MHz, SNR = ∞, (j) step = 0.2 MHz, SNR = 20 dB, (k) step = 0.2 MHz, SNR = 15 dB, and (l) step = 0.2 MHz, SNR = 10 dB.
Table 2 lists the statistics for all the 12 histograms shown in Fig. 4, including SD, RMSE, maximum BFS error (absolute value), and correct percentage (%), which means the percentage of the samples in the datasets that are exactly classified into the BFS error = 0 class. These four indices were calculated both for the training and test sets for comparison. Additionally, Table 2 also includes a column showing the average time needed to predict the BFS for each BGS sample in the test set.
Table 2. Statistics of BFS error extracted by NN and time needed to process each BGS
The SD and the RMSE increased with the deterioration of SNR both for the training set and the test set. The SD and the RMSE of the test set were always larger than those of the training set. It is reasonable because the weights of the NN were trained only using the samples in the training set, while the samples in the test set were used for verification of the trained model. Therefore, the trained model worked best with the training set. As samples in the training and test sets were selected randomly from the same original BGS datasets, the trained model also worked appropriately with the test set, so it turned out that the SD and the RMSE of the training and test sets did not differ by a significant amount. Unlike the statistics shown in Table 1, the RMSE in Table 2 was only slightly larger than or almost the same as the corresponding SD for each training or test set, which means the BFS error obtained by NN was not “biased”, and the mean of error was close to zero.
For the step = 5 MHz case, the classification worked out by NN was rough and did not reach an accuracy better than 5 MHz. Even though the SD and RMSE were relatively small and most samples were classified into the zero-error class, it does not mean the result was truly reliable. For the step = 1 MHz case, the classification was finer, and more BGS samples belonging to the zero-error class in the step = 5 MHz case fell into the neighboring classes. Consequently, the histograms spread out, and the SD and the RMSE became larger. For the step = 0.2 MHz case, the classification was done by the NN in the most delicate manner and the BFS error was depicted by the histograms with higher precision. Accordingly, the bars in the histograms assembled close to the zero-error class and the SD and RMSE became lower than the step = 1 MHz case but still higher than the step = 5 MHz.
The maximum BFS error (absolute value) listed in Table 2 should be integral multiples of the corresponding BFS label step as expected. The correct classification percentages shown in Table 2 are also reasonable. The correct classification rate decreased drastically as the BFS classification step became finer.
The comparison between the statistics in Table 1 and Table 2 states that the BFS measurement accuracy was improved by adopting the NN. If the SD and the RMSE are used as the criterion, there is a twofold to threefold enhancement. If the maximum BFS error is used as the criterion, the improvement will be threefold to fourfold depending on the SNR.
The average time needed to predict the BFS for each BGS sample varied from 168.4 µs to 256.2 µs. The time is highly relevant to the hardware and software we use. The comparison between the average time needed to fit one BGS using DP-LCF and using NN under the same conditions shows that the NN reduced the time spent on the signal processing by 1000 times.
3. Experiment
In Section 2, the simulated BGS datasets for Brillouin optical correlation-domain sensing were used to testify the effectiveness of NN on improving the BFS extraction accuracy and speed over the traditional curve fitting method. In this part, real BOCDR signals obtained experimentally are used to verify the theory.
The experimental setup of the BOCDR system was shown in Fig. 5. It is basically the same as that in previous reports [9,10] but with lock-in detection scheme [27]. By applying intensity modulation to the reference light, the resultant BGS can be restored with a high SNR by setting appropriate parameters for the lock-in amplifier. A detailed description of the experimental setup and the principle of the lock-in detection scheme can be found in Ref. [27].
The fiber under test was a 100 m single-mode fiber (SMF). Two sections of dispersion-shifted fibers (DSFs) with lengths of 0.4 m and 1.5 m were fused near one end of the SMF. As the BFS of the DSF was about 350 MHz lower than that of the SMF, we used the DSF to provide the equivalent effect of applying a large strain of 7000 µε, given that the strain coefficient is 0.05 MHz/µε. Applying large BFS change in the experiment is essential to testify that the BOCDR system can perform distributed strain sensing appropriately under a significant dynamic range, which is not the strong point of conventional signal processing schemes.
The normalized BGS distribution near one end of the fiber under test is shown in Fig. 6. The laser modulation frequency fm was 940–960 kHz to scan the CP, and the modulation amplitude was 4 GHz, which gave a nominal spatial resolution of 25 cm and a measurement range of 105 m. The location of the CP was defined to 0 m when fm equaled 940 kHz, and then the fiber terminated at 12.5 m in Fig. 6. The two DSF sections at around 6.0 m and 9.0 m were clearly observed.
Fig. 6. Normalized BGS distribution near one end of the fiber under test, with DSF sections fused at around 6.0 m and 9.0 m locations, which provide an equivalent effect of applying 7000 µε. The fiber terminates at 12.5 m.
Next, different signal processing methods were utilized to extract the BFS from the normalized BGS distribution in Fig. 6. The BFS distributions extracted by simple maximum search and DP-LCF are shown in Fig. 7. The maximum search found the longer DSF section at 8.6–10.1 m, but was not able to correctly measure the shorter DSF section at 5.5–6.0 m. It is because the real Brillouin signal power level was lower than the background noise, and a simple search for the maximum of the BGS did not give the information where the real Brillouin peak was located. Additionally, one point in the longer DSF section at about 8.8 m was mistakenly found to have a BFS much larger than its real value, which means the maximum search method is vulnerable to random induced errors.
Fig. 7. BFS distribution extracted by simple maximum search and DP-LCF. The DSF section at 8.6–10.1 m was detected by both methods, while the DSF section at 5.5–6.0 m was correctly measured only by DP-LCF.
On the contrary, the DP-LCF gave a reasonable result and found both the shorter and longer DSF sections correctly. The fitting used a nonlinear least square algorithm based on all data in each BGS, so it is robust to the random error of a single point.
The application of the NN to the experimental BGS data also requires the training of suitable models using BGS datasets. The limited amount of experimental BGS data we obtain cannot and is impractical to provide sufficient samples for all the different BFS label classes in the frequency measurement range. Therefore, training the NN model using simulated BGS data makes sense as long as the samples in the simulated dataset and experimental dataset labeled with the same BFS are similar and can be treated to be in the same class by the model. In this way, the simulated BGSs were used as the training dataset and the experimental BGSs were used as the test dataset.
Three training datasets were prepared with three different BFS label incremental steps (5 MHz, 1 MHz, and 0.2 MHz). The SNR was set to 20 dB because it is mostly compatible with the real experimental BGS. For step = 5 MHz, the strained section length was set to the range from 0.8Δz to 1.7Δz with 0.1Δz step (10 cases). The FWHM was set to the range from 40 MHz to 60 MHz with 0.25 MHz step (81 cases) because the FWHM of real BGS was found to be likely to lie around 50 MHz. The BFS label was set to the range from 10470 MHz to 10910 MHz (89 cases), which covered the needed frequency measurement range. Thus, we had a total of 10×81×89 = 72090 BGS samples in step = 5 MHz training dataset. The designed three-layer NN had a 385-201-89 structure. The number of neurons in the input layer must be the same as the sampling point number in each experimental BGS. The number of neurons in the hidden layer can be adjusted to optimize the algorithm, and the neuron number in the output layer is associated with the BFS label class number. The experimental BGSs were fed into the trained NN, and the BFS was predicted by the classification algorithm. The blue curve in Fig. 8 shows the BFS distribution extracted by NN with BFS step = 5 MHz. The DSF sections at 5.5–6.0 m and 8.6–10.1 m were clearly detected. The model trained by the simulated data had never “seen” the experimental data before, but still correctly provided the experimental BFS distribution with the knowledge learned from the training dataset, which means it is a rational method to use the simulation to generate the training datasets.
Fig. 8. BFS distributions extracted by NN with step = 5 MHz, 1 MHz, and 0.2 MHz. The DSF sections at 5.5–6.0 m and 8.6–10.1 m were clearly detected. The distance axis is magnified in the ranges of (a) 1.0–2.0 m, (b) 5.5–6.1 m, (c) 6.9–7.8 m, and (d) 8.5–10.1 m.
For step = 1 MHz and 0.2 MHz, if the simulated datasets are created covering the same BFS label range as the step = 5 MHz case, there will be redundantly many BFS classes, and the training process will be quite slow. As the result with step = 5 MHz clarified that the experimental BFS lies in two ranges: 10470–10540 MHz for the DSF and 10810–10910 MHz for the SMF, the NN was trained only in these two ranges. For step = 1 MHz, the BFS label was set to the range from 10480 MHz to 10540 MHz (61 cases) and from 10810 MHz to 10910 MHz (101 cases); for step = 0.2 MHz, the BFS label was set to from 10480 MHz to 10540 MHz (301 classes) and from 10830 MHz to 10890 MHz (301 classes). The strained section length and the FWHM were set to the same as those with step = 5 MHz. The structure of the three-layer NN should be 385-201-x, where x is the number of the BFS label class number. The red and yellow curves in Fig. 8 show the BFS distribution extracted by the designed NN with step = 1 MHz and 0.2 MHz. The three curves for step = 5 MHz, 1 MHz, and 0.2 MHz exhibited a similar trend but differed in details.
To view the BFS distribution in detail, the BFS distribution curves were magnified in the distance ranges of 1.0–2.0 m, 5.5–6.1 m, 6.9–7.8 m, and 8.5–10.1 m, as shown in Fig. 8 insets (a)–(d), respectively. The stepwise graphs illustrate that the BFS results processed by the NN were only a number of discrete values, and the interval of these discrete values followed the BFS label incremental step size. The step = 5 MHz case provided a coarse BFS result with 5 MHz precision, while the step = 1 MHz case gave more details with 1 MHz precision, and the step = 0.2 MHz case yielded the finest factor of the BFS distribution with 0.2 MHz precision.
The statistics of the BFS extracted by DP-LCF and NN with step = 5 MHz, 1 MHz, and 0.2 MHz are summarized in Table 3. The statistical work was performed on two sections with relatively uniform BFS distribution: 0–5.5 m for the SMF and 8.6–10.0 m for the DSF. The SD, the RMSE, and the maximum error (absolute value) obtained by NN were lower than those of DP-LCF, and decreased as the BFS step becomes finer. The SD and the RMSE of the BFS fitted by DP-LCF for the 0–5.5 m section were remarkably larger than the values for the 8.6–10.0 m section, and also larger than the values processed by NN. The reason for this may be that the DP-LCF performs weakly for the SMF section, which does not have a real double-peak spectrum shape; while the performance of NN is not influenced by the structure of the spectrum and only depends on the similarity among the BGS samples belonging to a single class. The comparison between the statistics for DP-LCP and NN step = 0.2 MHz shows that the enhancement of BFS accuracy by utilizing the NN for the SMF and the DSF sections was 2.7 times and 1.6 times, respectively.
Table 3. Statistics of BFS extracted by DP-LCF and NN with step = 5 MHz, 1 MHz, and 0.2 MHz for fiber sections at 0-5.5 m and 8.6-10.0 m, and average time needed to process each BGS
The average times needed to process each BGS by DP-LCF and NN are also listed in Table 3. The time needed to fit one BGS using DP-LCF was 111.7 ms, which is about half of the time needed to fit each simulated BGS in Section 2. Considering each experimental BGS had 385 sampling points and each simulated BGS in Section 2 had 10001 sampling points, we can conclude that the average time needed to fit one BGS is not simply proportional to the point number.
The average time needed to process one BGS using the NN varied from 22.05 µs to 24.95 µs. It is about tenfold less than the time used to process one 10001-point simulated BGS. Considering that the scale of the designed NN for the experiment is smaller than that designed for the simulated signal in Section 2, and that the matrice of smaller sizes are required to be multiplied in the computational process, 10 times lower computational cost is a reasonable result.
Eventually, the average time required to process a single BGS in our experiment by NN was 5000 times less than that by DP-LCF. It is an outstanding improvement in the perspective of signal processing efficiency. The NN is thus a promising tool for reducing the post-processing time significantly for Brillouin optical correlation-domain sensing systems.
4. Conclusion
In this paper, the NN was implemented on a personal computer using MATLAB. The speed was expected to be further improved by utilizing stronger hardware or developing optimized NN algorithms. The time needed to extract BFS for a single BGS is essential to realize a real-time Brillouin optical correlation-domain sensing system. Many types of research work focus on improving the sampling rate of BGS acquisition, but in most cases, the data is processed offline. To complete the signal processing online, in other words, to extract the BFS information instantly when the one BGS is acquired, the time needed to process one BGS should be much shorter than the BGS acquisition period. For instance, if the BGS acquisition sampling rate is 100 kHz for a certain sensing system, then the acquisition period is 10 µs, a signal processing time of 22 µs is still insufficient, as the post-processing costs at least twice the period of BGS acquisition. The NN implemented on hardware like GPU or FPGA will be a potential solution to this problem. The hardware can also assist to accelerate the training of a large-scale NN. Thus, we anticipate that a truly real-time sensing system that feedbacks the BFS immediately when each BGS is acquired can be realized in the near future by implementing NN on appropriate hardware without deterioration of system performances such as measurement accuracy, dynamic range, and spatial resolution. Note that this method is applicable to both BOCDA and BOCDR, though we performed an experiment using BOCDR only. In addition, the modulation waveform of the laser frequency is not limited to a sinusoidal waveform; different BGS shapes generated by arbitrary modulation waveforms [28,29] can also be processed by well-trained NN.
Funding
Changshu Institute of Technology (KYZ2019056Q); Japan Society for the Promotion of Science (17H04930, 20K22417, 21H04555); Murata Science Foundation; Telecommunications Advancement Foundation; Yazaki Memorial Foundation for Science and Technology ; Takahashi Industrial and Economic Research Foundation.
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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