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Abstract
The Artificial Intelligence of Things (AIoT) turns passive fiber sensors into learning machines. It can be used to integrate intelligent nodes into a multi-dimensional sensing system. In this study, the temperature measurement system based on Brillouin Gain Spectrum (BGS) test setup is creatively implemented with the AIoT architecture; the training and testing stages of the neural network are divided into different layers of equipment to improve performance and reduce the network traffic. To enable the lightweight and low-power consumption edge computing device to extract accurate temperature from the BGS during testing, we have integrated the post-processing method inspired by curve fitting into the machine learning and proposed the efficient digital resampling filter. The resampling filter approach is achieved by the peak range algorithm with Gauss differential operator and digital band-pass filter. The evaluation results for different methods on the BGS datasets show the superior performance of our approach. Notably, the approach can increase temperature extraction accuracy and compress the sampling data. The RMSEA of the extraction temperature is 0.5635, which can bring an almost 21% accuracy increase over the classic method. Compared with the classic method of processing the original data on the same hardware platform, the amount of data post-processed by the filter is reduced by 75%; the time consumption is reduced by 22%.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The development of Artificial Intelligence of Things (AIoT) has brought new vitality to the application field of optical fiber sensing technology. The technique of the AIoT does not only aim at realizing the interconnection between objects and humans but also can make better performance on end-device data sampling, processing, and analysis [1–4]. The Brillouin-based distributed fiber-optic sensing is one of the essential sensing techniques, which attracts much attention due to its precise measurement of the temperature and strain in the ultra-long sensing range. Generally, in a Brillouin-based sensing system, by scanning the frequency of probe light and detecting the intensity gains of the probe signal, the BGS is attained. Then it reveals the temperature and strain by the Brillouin frequency shifts (BFS) can be calculated by fitting the distributed BGS. The different post-processing techniques for the BGS are currently used in the curve fitting method [5,6]. One type of them is to measure the spectral range of the BGS with a quadratic range. The BFS can be calculated for the portion of the BGS that can be approximated as a quadratic function [7]. The statistical analysis shows that the uncertainty of BFS estimated is affected by the signal-to-noise ratio (SNR) condition, the full width at half maximum (FWHM) of BGS, and the sweeping frequency interval [8,9]. In the current research, with the development of the boom in artificial intelligence technology, some efforts are being devoted to overcoming the fundamental limitations of the conventional Brillouin-based fiber-optic sensing implementations of the curve fitting method. The proposals typically imply using the artificial intelligence solution, particularly an artificial neural network (ANN), which is used to process the BGS and perform the requested discrimination [10]. In contrast to the traditional fitting method, the neural network method does not need to calculate the corresponding relationship between the sampling data and the target results. Instead, it can extract the results from the sampling acquisition through the BGS by the trained model.
The non-linear mapping ability of the neural network can process complicated input-output relationships. Many meaningful schemes are proposed to achieve faster processing and higher SNR with the optimized approach [11–13]. Among them, one type is realized by using the neural network methods; the pair of the spectral profile and the pre-acquired temperature label is processed by the neural network that will be deployed to extract the temperature of the BGS. More recently, we have proposed the variance weight sweeping frequency method that facilitates the estimation of the temperature [14]. Optimized frequency spacing and encoding sampling are used to reduce the number of frequency sweeping (FS) points and improve the efficiency of the sampling.
The techniques mentioned above showed their effectiveness. Though the neural network method is used to train and test the BGS with full-spectrum, it is relatively tedious and time-consuming from the perspective of the data. Through the comparison, whether curve fitting or machine learning method, the FS is widely used to obtain the BGS distribution along with the tested fiber. The approach to processing the BGS is a critical procedure. The curve fitting methods have made a lot of efforts by analyzing and using the characteristics of BGS to improve the efficiency [15–19]. The neural network paid more attention to making full use of different network models to train and test the BGS data to achieve high accuracy [20]. By integrating the advantage of the above two techniques, providing an effective solution to reduce the complexity of calculation, remove redundant data and realize a high accuracy sensing system is worthy of further research. It will be a trend to make full use of the signal process technology to enhance the data processing, which could be equivalent to resampling. The quality of the BGS often matters more than the quantity when making an estimate or a model based on a sample.
In this article, we demonstrate the enhanced accuracy, data efficiency, and large tolerance BGS data processing method offered by the AIoT-enabled resampling filter. To our knowledge, for the first time, a signal resampling method based on a neural network fast and directly extracts the sensing temperature from BGS. Benefits of the AIoT architecture, the neural network training stage can be achieved by the cloud server; the edge server loaded the model can directly extract the temperature by testing the BGS. It aims to improve learning performance as well as reduce network traffic, the major challenges to implementing the neural network testing method on the lightweight edge computing device. The goal of our study is to seek out the optimal FS range in the frequency sweep method with equal intervals. To reduce the number of data points in the neural network model. We propose the resampling filter inspired by the gradient change rate of BGS. It was realized by the peak range algorithm and digital band-pass filter. The comparative evaluation of performance using the various ways, it demonstrates that the resampling filter adopted by the neural network model achieved high accuracy with fewer data sampling. Specifically, the AIoT-enabled resampling filter reduced the data size of the model processing by almost 75%, shortened the measurement time by 22%, and enhanced the accuracy by 21%, paving the way toward data-efficient time-saving and high-accuracy optical sensing. The system framework we proposed has great potential in the field of distributed sensing applications.
2. Methods and results
2.1 Experiment setup and fundamental theory
The proposed AIoT-enabled BGS-temperature sensing system is shown in Fig. 1. The AIoT aims to embed AI and machine-learning techniques into IoT infrastructures to achieve high-accuracy performance. The system is implemented with the AIoT architecture and is mainly composed of three layers: (1) the Policy Layer; (2) the Transport Layer; (3) the Perceptual Layer.
Fig. 1. Schematic diagram of AIOT enabled BGS-temperature sensing system. The BGS test setup mainly includes TLS (Tunable Laser Source), PC (Polarization Controller), EOM (Electro-Optic Modulator), DC (Direct Current), ISO (Isolator), VNA (Vector Network Analyzer), EDFA (Erbium-Doped Fiber Amplifier), PD (Photo Detector), WB (Water Bath), FUT (Fiber Under Test).
In the Policy Layer, the cloud server and database deployed on the Wide Area Network (WAN) can be used as a remote, online, or managed backup service. It has powerful computing and storage capability and can process complex and time-consuming tasks. In the framework, it can be used as a centralized control center to enable, authorize, and manage the end device in and down layers or to dig deep into the wealth of data. The hardware description of the AIoT platform is as follows: The CPU model is Intel Xeon CPU E5-2690 v4 @ 2.60 GHz. The virtual address size is 48 bits. And the total memory size is 81444584 KB. The storage disk size is 100 TB.
In the Transport Layer, the system can take advantage of recently developed edge computing devices and machine-learning approaches. The digital resampling filter implemented in the edge server deployed in the Local Area Network (LAN) can directly process the BGS data from the downlink equipment. Then the data can be tested in the local edge server ANN model. The data can be compressed, packaged, and then uploaded to the remote AIoT server for training or other different application requests. The description of the Edge-computing station is as follows: Ascend 310 AI Processor. 2 x Da Vinci AI cores. 8 x A55 ARM cores (maximum frequency: 1.6 GHz). Typical power consumption: 70 W. The storage disk size is 64 GB.
In the Perceptual Layer. It mainly includes the BGS test setup. The process details involved in the conversion of BGS-temperature data from optical to electric as flows: The output laser with a wavelength of 1550 nm generated by the tunable laser source (TLS) travels through an optical coupler (OC) with 50:50 and a polarization controller. The continuous light with 1 mW power is rightward entered into the electro-optic modulator (EOM). The DC signal source is used to adjust the working point of the EOM. The output of the EOM as the probe signal passed through the erbium-doped fiber amplifier (EDFA1) and optical isolator (ISO) and into the fiber under test (FUT). In this experiment, we use the 1 km highly non-linear fiber (HNLF) as the FUT. The signal from the left branch was amplified to 18 mW by the EDFA2 as the pump signal. The pump signal was injected into the FUT via port1 of the circulator. The probe signal is amplified by Stimulated Brillouin Scattering (SBS) effect when the frequency difference is equal to the BFS. The probe signal is detected by a photodetector (PD). The BGS is obtained by scanning the frequencies of the probe signal with a Vector Network Analyzer (VNA). Specifically, for the convenience of temperature measurement, the FUT is enclosed in the water bath (WB) with 20–60 °C range, 1 °C resolution, and no strain. When adjusting the water WB temperature, the BGS under different temperature conditions can be obtained. The frequency range of the BGS is 9.07-9.35 GHz, and the frequency interval limit of the device is 0.175 MHz. The temperature information of the FUT can be extracted from the edge server in the upper layer device.
The method to post-process the BGSs is in Fig. 2. When the BGS is collected from the device, to calculate the accurate BFS traditionally, the frequency of peak gain is usually obtained when using the curve fitting method. It can conclude that the data near the peak gain range of the BGS may have great importance in Fig. 2(a). The projections of the original spectra on the x, y, and z axes are shown respectively in Fig. 2(b). Through further analysis, an evolution in the spectral shape can be noticed. As the gain power increases, the decay in the flanks becomes sharper, reaching the Gaussian decay rate for the high gain power values. The numerical differentiation was one of the techniques applied to remove the linear scatter effect, which polluted each spectrum, resulting from the stochastic nature of the particle packing of a sample. The role of numerical differentiation as a peak sharpening was utilized as a digital filter protocol to narrow the FS range in the analysis of the BGS data. We optimized the algorithm to determine the scope of FS, the BGS sliced into a small data size. Therefore, we implemented the algorithm and put forward the post-processed way by the resampling filter in Fig. 2(c). The filtered BGS data set was labeled by temperature, then divided into a training set and a test set. The training set was utilized for training an ANN model, and then the testing set data was used to test the model accuracy. The trained model can learn the complex relationship between the filtered data and the temperature label as it is shown in Fig. 2(d).
The AIoT-enabled BGS-temperature system allocates the training and testing process to the different devices. It aims to make intelligent sensing nodes to facilitate integration into the multi-dimensional application. The cloud server is responsible for analyzing and training the collected raw data, as shown in the blue block of Fig. 3. The cloud server determined the parameters of the resampling filter according to the raw BGS. Before entering the neural network model, the raw data has been processed by the resampling filter. In the experiment, in order to strengthen the ability of the trained model to adapt to the actual experimental environment and other uncertain factors, 400 sets of raw BGS were collected. To make the model more robust, the amount of the dataset is increased by adding noise to the raw BGS. Each temperature has 10 simulated BGSs with different SNRs from 19 dB to 56 dB. Then 4000 sets of BGS-temperature datasets have been preprocessed with the resampling filter. The model converts data to array representations, fitting a dataset to the training set and applying the learned model. The filtered sequence data of the BGS are normalized in the range of 0 to 1. The sigmoid function is used as an activation function in the neural network. Then, the input data are trained in the same structure of the neural network. The neural network model we proposed was constructed with three layers, including one input layer, one output layer, and a single hidden layer. Empirically, the one hidden layer neural network is preferred as the model for it can approximate any function that contains a continuous mapping from one finite space to another. To further optimize the model structure, the number of hidden layer neurons was changed several times, and we decided to use 50. Stochastic Gradient Descent (SGD) is used to reduce the loss value continuously. With the help of the optimization loss function and a large number of iterations, the ANN model learns to map the temperature to the BGS. At each training iteration, the ANN output is computed, and the error signal can be calculated. The training stage of the neural network model aims to minimize the Root Mean Square Error Average (RMSEA) and Standard Deviation (SD) given between the desired output and the actual network output. When the training stage is finished, the cloud server generates the trained model profile. The edge server loads the ANN model. It takes the BGSs post-processed by the resampling filter as input and makes predictions of the output temperature, as shown in the orange block of Fig. 3. The performance of the resampling filter method in ANN can be evaluated by the difference between the predicted value and the corresponding observed value. It is usually illustrated by the RMSEA and SD of the testing stage. To make full use of the data, we adopt cross-validation to evaluate the performance of the methods.
2.2 Peak range filter algorithm
Theoretically, the BGS has a Lorentzian shape in the low gain region and a Gaussian shape in the high gain limit. By calculating the skewness and kurtosis of the spectrum data, it is further verified that the high gain region of the BGS is a Gauss-like curve with a single peak and symmetry.
Mathematically, the technique is a simplified version of a converging Taylor series expansion, in which only the even order derivative terms in the expansion are taken. The filtered bands have been artificially narrowed so that the key point positions can be calculated. The BGS curves can be subjected to numerical differentiation. The second derivatives of both Gaussian and Lorentzian functions have a reduced width. It can be used to improve spectral resolution. Fourth derivatives can also be used when the signal-to-noise ratio in the spectrum is sufficiently high. The peak range filter method is based on this idea to find the critical component bands and the point positions. For analysis, we shall consider the case of $\mu $ = 0 (since one can simply translate the function to achieve the Gauss curve at the desired center) as the Eq. (1) and (2) below:
From the raw data, we can acquire an estimated value of the linewidth (FWHM). According to Eq. (3), the standard deviation can be estimated. Figure 4 shows the key method of the resampling filter to find the peak range band. We explain the algorithm to clarify its features. To define $x(k)$ as the raw BGS data with one dimension at time k. The $y(k)$ is the filter output data as expressed in Eq. (4).
When the 2nd differential operator is used, the window constrained width ${N^{2nd}}$ of the resampling filter is 2$\sigma $. The 4th differential operator is used, and the window constrained width ${N^{4th}}$ is 4$\sigma $ as shown in Eq. (5). By calculation, the constrained width is shown in Fig. 4(a), (b).
F(x) is the non-linear function described as Eq. (6):
The differential operator is used to extract the band, and the multi-order derivatives are compared and analyzed in the experiment. As the derivative order increases, the sampling frequency range corresponding to the even-order derivative increase accordingly. Note that the 2nd and 4th derivatives determined the constrained frequency bandwidth respectively, so the selected frequency band can vary over a wide numerical range for peaks of different widths. For this reason, if the peak widths vary substantially across the signal, it can be optimized for each region of the signal by using the method as shown in Fig. 4(d). By calculation, the corresponding frequency point range is extracted according to the differential operator. The 2nd order derivative of the BGS data point sequence ranged from 600 to 1000, it represents the filtered frequency range from 9.17 GHz to 9.24 GHz. And the filtered band of the BGSs determined by the 4th order derivative as reference point sequence ranged from 400 to 1200, it represents the filtered frequency range from 9.14 GHz to 9.28 GHz.
2.3 Comparative experimental analysis
For the effectiveness analysis of the resampling filter method, we carry it out in various ways. Firstly, the different frequency slice of the BGS data was adopted with the same number of sampling data points. We adopted the same numbers of sampling points in the different frequency ranges. As Fig. 5(a1) shows, the full sampling frequency range of 9.07GHz-9.35 GHz with 4 MHz step frequency as the blue bars represented, which is split into 9.14GHz-9.28 GHz with 2 MHz step frequency in the 4th differential resampling filter method as the green bars represented, 9.17GHz-9.24 GHz with 1 MHz step frequency in the 2nd differential resampling filter method as the red bars represented. The test result is shown in Fig. 5(a2). The red line represents the RMSE of the full frequency range of the BGS data. The green line represents the RMSE of the 4th differential resampling filter method, which is better than the red line. Furthermore, the blue line is the RMSE of the 2nd differential resampling filter method, whose RMSE is the minimum in three methods. The Mean, Max, Min, and SD of the RMSEs illustrate the deviation between the temperature extraction value and the temperature label. The $\mu $ and $\sigma $ represent the Mean and SD of the RMSEs in Fig. 5(a3). The corresponding RMSEA is 0.89, 0.69, and 0.57, respectively. And the SD of the three frequency ranges is 0.1, 0.05, and 0.09. The Mean of the RMSEs illustrates that the 2nd differential resampling filter can achieve lower error, and the SD of the RMSEs illustrates that the 4th differential resampling filter can achieve better stability under the condition of the same number of samples.
Fig. 5. (a1) Three different frequency intervals with the same number of sampling points. (b1) Three different FS band width of the BGS with the same frequency interval. (c1) Three different FS intervals with 0.25 MHz, 0.5 MHz, 1 MHz in the filtered frequency band. (a2), (b2), (c2) Line chart of the RMSEs by using the corresponding method. (a3), (b3), (c3) statistical character of the RMSEs by using the corresponding method.
Secondly, the different frequency slices of the BGS adopted the same frequency sweeping intervals at 1 MHz and obtained BGS data of the above three frequency range. As Fig. 5(b1) shows the different frequency ranges of the BGS with the same step frequency. The various lines show the trends of the RMSE in Fig. 5(b2), revealing the stability and applicability of the performance of different methods. The above statistical characteristic in the different methods is shown in Fig. 5(b3). It shows that the corresponding RMSEA is 0.72, 0.64, and 0.57, respectively. And the SD of the three frequency ranges is 0.18, 0.15, and 0.09. By comparison, it is found that with the resampling filter’s help, the data size processed by the ANN was reduced, and the extraction accuracy was improved.
For the stability analysis of the resampling filter method, to study the effect of the resampling frequency interval in the method. The raw data resampled 9.17-9.24 GHz with different frequency intervals. The numbers of the uniformly-spaced sample points selected from the original BGS data are 71, 141, and 281. It can be equated to the sweep frequency with step frequencies 1 MHz, 0.5 MHz, and 0.25 MHz. The obtained BGS data is shown in Fig. 5(c1). The temperatures extracted by different frequency intervals are very close in terms of accuracy within the FS range. As depicted in figure Fig. 5(c2) (c3), the corresponding RMSEA is 0.57, the SD is 0.12, 0.16, 0.09. It illustrates that the resampling filter can reduce the influence of the frequency interval on extraction accuracy. And the temperature extraction accuracy with filtered data points has better stability. When the resampling filter is implemented, setting the uniform frequency sweeping, high-accuracy temperature extraction can be achieved with less training and testing data by selecting the frequency range. The temperature extraction accuracy fluctuation in the 2nd differential resampling filter method is relatively soft or regular, which is an ideal result. Specifically, it is beneficial that sample fewer points to obtain a high accuracy result by using the resampling filter in the neural network.
To further analyze the advantage of the proposed resampling filter method, the post-processed BGS data in different frequency ranges with the same frequency interval was adopted in the neural network model. To evaluate the performance of the temperature extraction by the different portion of the BGS, then try to find out the relationship between the different portions of the sampling points and the accuracy of temperature extraction. As shown in Fig. 6, the BGS was divided into three portions, the rising portion is marked in blue, the portion of the 2nd Gauss resampling filter is marked in green, and the falling portion is marked in red. All of them are set to the same frequency bandwidth and frequency interval. The configuration of the neural network model is fixed, and the performance of the temperature extraction is shown in Fig. 7.
Fig. 7. Results of the three different portions processed in the ANN. (a) Line chart of the RMSEs. (b) Statistical characteristic of RMSEs. (c) The PSNR of the three different portions.
Comparing the results of the three different portions processed in the ANN, line chart of the RMSEs are shown in Fig. 7(a). It reveals the differences in the trends among the three portions of the BGSs data. The red line represents the RMSE of the rising portion of the BGS data. The green line represents the RMSE of the falling portion of the BGS data, which is better than the red line. Furthermore, the blue line is the RMSE of the peak portion of the BGS data in Gaussian resampling filter method, whose RMSE is the minimum in three methods. The above statistical characteristic with the different portions are shown in Fig. 7(b). The corresponding RMSEA is 0.96, 0.85, and 0.57, respectively. And the SD of the three frequency ranges is 0.24, 0.1, and 0.09. It is proved that the temperature extraction performance is improved by the resampling filter. By calculating the PSNR of the different portions of the BGS. Figure 7(c) shows that the PSNR of the filtered portion is higher than the other two portions. By comparison, the resampling filter obtained the high PSNR portion of the BGS, which contributed to enhancing the accuracy of the temperature extraction. This explains the rationality of introducing this parameter when we design the resampling filter algorithm. Table 1 summarizes the optimized performance of our approach. There is no universal optimum value for the frequency bandwidth and interval. It depends on peak sharpening and flatness, which are affected by the PSNR. But the baseline of the filtered frequency band is given by the 2nd and 4th derivatives in the proposed method. The filtered frequency band increased the PSNR of the BGS, which promoted the result. The data size, training time, and testing time have been reduced by the 2nd resampling filter method. It illustrates that the method has high efficiency in the training and testing stage. The method can help the model be optimized in a relatively short time and improve the rapid response capability in the application. Thus, the resampling filter can be used to get an ideal temperature extraction on the ANN model.
Table 1. Experimental results of different methods
3. Discussion
To further verify the reliability of the resampling filter, bootstrap resampling was adopted to evaluate the performance of the method. The bootstrap resampling is a non-parametric method of statistical inference which means that the parametric assumptions that ignore the nature of the raw data distribution are avoided. The BGS is resampled without replacement, and this is done repeatedly. This method can be used to boost the performance of machine learning models. We set the frequency interval of the bootstrap resampling as 1 MHz. Firstly, The original data of 9.17-9.24 GHz is shifted by 0.5 MHz and 1 MHz, respectively. Three groups of comparative experiments are carried out, as shown in Fig. 8(a1). As depicted in Fig. 8(a2), we found that the changing trend of output temperature with the BGS parameters remains unchanged when expanding the frequency range, which supports the correctness of the experimental rules. As depicted in Fig. 8 (a3), the corresponding RMSEA is about 0.6,0.62,0.57; the SD is 0.09. It is found that there is a slight difference in the accuracy of extracting temperature. It also implies one can adopt different start and end frequencies instead of the strict frequency alignment when using the resampling filter for temperature extraction. But as the resampling frequency deviates from the resampling filter frequency band, the error of temperature extraction increases gradually. According to the 75% membership, when the frequency offset is 17.5 MHz, the extraction accuracy decreases by 9%. Secondly, we selected 9.17-9.22 GHz, 9.18-9.23 GHz, and 9.19-9.24 GHz three frequency bands within the filtered frequency range as depicted in Fig. 8(b1). The lines of the RMSE show fluctuation in Fig. 8(b2). The corresponding RMSEA is about 0.62,0.69,0.7, the SD is 0.17, 0.17, 0.11 in the Fig. 8(b3). It shows that the narrower frequency range of the filtered frequency band was adopted to process in the model, and the error of the temperature extraction increased for insufficient data. It further illustrated the rationality of the 2nd derivatives Gauss resampling filter method.
Fig. 8. Results of the bootstrap resampling method. (a1) The selected frequency band with 70 MHz width shifted 0.5 MHz, 1 MHz from the filtered frequency band. (b1)Three different frequency ranges with the 50 MHz width in the filter frequency band. (a2), (b2) Line chart of the RMSEs by using the corresponding method. (a3), (b3) Statistical characteristics of RMSEs by using the corresponding method.
By adopting the bootstrap method, we evaluated the temperature extraction performance of the system under various conditions. It is further verified that the proposed digital resampling filter can outperform the classic method.
4. Conclusion
This work opens up a way of designing the digital resampling filter and provides an innovative method to realize high-precision temperature extraction. Thus, it is extremely attractive from a computational point of view and is a very pragmatic solution to a potentially time-consuming problem. Especially in the applications of continuous monitoring and security guard, efficiency and rapid response capability can play a very important role at a critical time. The results show that implementing the resampling filter in sweeping frequency with equal intervals can extract temperature fast and accurately, with the RMSEA 0.5635. In addition, the method mentioned not only overcomes the obstacle of time-consuming and data-gult drawbacks in the neural network, but also improves the stability, tolerance, and accuracy of temperature extraction. For a future line of inquiry, we plan to implement the technique on other optical-fiber sensing systems, in collaboration with researchers and based on feedback, further improve the performance and robustness of the framework toward real-world applications.
Funding
Science and Technology Project of Education Department of Jilin Province (JJKH20190110KJ); Jilin Scientific and Technological Development Program (20180201032GX, 20220201061GX); National Natural Science Foundation of China (61875070).
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.
Supplemental document
See Supplement 1 for supporting content.
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