Physics-informed DAS neural network paradigm
The experimental setup and application deployment of the DAS system are shown in Fig. 1a. In DAS, the laser is modulated into pulsed light and injected into the fiber under test (FUT). The location of any point along the FUT can be determined according to the round-trip time of pulsed light in the FUT. The Rayleigh backscattering light field generated on FUT interferes with the local light field to generate an interference signal. Since the phase change of the backscattering light field is linear with the strain on the optical fiber, the quantitative measurement of an acoustic wave can be achieved by acquiring phase information from the interference signal. When DAS is applied in field applications, the acoustic waves of target events and background interference events are received simultaneously, which makes it difficult to extract and analyze the target signals. For most DAS applications, the occurrence of target events is rare, such as seismic wave detection, structural health monitoring and pipeline monitoring. Therefore, the vast majority of DAS data consists of background data containing various environmental noises due to the high spatiotemporal density characteristic of DAS data. This leads to the requirement of a long-term data accumulation process to obtain a large number of target event data for the design of artificially designed algorithms or the training of conventional data-driven neural networks for DAS data processing, as shown in Fig. 1b. The data accumulation process may encounter difficulties when the application environment is complex and the background noise is intense.
Fig. 1: Schematic of the proposed physics-informed DAS neural network paradigm.
a Schematic diagram of the DAS system and its application. SMF single-mode fiber, RF radio frequency, AWG arbitrary waveform generator, AOM acousto-optic modulator, EDFA erbium-doped fiber amplifier, BPD balanced photodetector, ADC analog-to-digital converter, FUT fiber under test. The DAS system simultaneously detects both background and event signals in practical applications. b Traditional design process of DAS signal processing algorithms. ANN artificial neural network. A long-term data accumulation process is required to obtain a sufficient amount of event data, whether labeled or not. c Physics-informed DAS neural network paradigm. PIGN physics-informed generative network. The training of PIGN, noise-removal net, and classification network in the network paradigm does not require any real-world event data. PIGN is used to generate data, the noise-removal net is used to remove background noise, and the classification network is used for event recognition
In order to overcome the challenges of data accumulation process and significant background noise in DAS applications, a physics-informed neural network paradigm, including DAS data generation and denoising is proposed as shown in Fig. 1c. DAS physics-informed generative network (PIGN) is first proposed to produce massive generated event data. PIGN only needs to be constrained by the physical model of the target event in the training process, without the requirement of any RWD. For events that are difficult to be physically modeled, professional experience can be converted into empirical functions as training constraints for PIGN. The generated data can be regarded as noise-free target event signals. Using these generated noise-free ground truths, a DAS noise-removal net is proposed to eliminate complex environmental noise. The training dataset of the noise-removal net is composed of generated event data and easily obtainable real-world background data. Since the background environment is unique in different DAS application scenarios, it is difficult and unnecessary to physically model the background data. In practical DAS applications, DAS signals at most spatial locations belong to the background data, which is easy to obtain. Given the characteristics of DAS background data, the real-world background data should be directly collected for data analysis. The core purpose in most DAS applications is event recognition. Hence, a neural network for event classification is trained using generated event data and real-world background data. The proposed DAS data processing network paradigm does not require real-world event data during the entire training process. Once the noise-removal net and classification network have been trained, they can be directly applied to RWD for environmental noise removal and event recognition in the field.
Physics-informed generative network
The proposed framework does not require a fully precise physical model to operate effectively. However, its performance improves as the discrepancy between PIGN-generated data and RWD becomes smaller. The working principle of PIGN is shown in Fig. 2. Signals generated by different types of events often possess distinct spatiotemporal features. Since DAS data is two-dimensional, comprising temporal and spatial dimensions, it is capable of recording features of various events. The spatial and temporal features of an event can be delineated by viewing DAS data as an image and projecting curves along the respective axes, as shown in Fig. 2a. Typically, the temporal and spatial feature functions of a class of events can be derived from theoretical physical models based on research in related fields. For applications where the theory is underdeveloped or difficult to model due to the complex circumstances, the temporal and spatial feature functions can be derived from experiential knowledge of the expert. Using these feature functions, a large number of feature curves can be obtained to depict multiple cases of the event. PIGN is based on a U-Net structure, taking random data as input and generating event data as output. In PIGN, the temporal and spatial feature curves of the event are used as target curves for network training, as shown in Fig. 2b. The output data from the network are processed to obtain the predicted feature curves, which are then compared with the target curves using mean squared error as part of the loss function. Although high-quality image reconstruction often requires curve projections from multiple directions50, projection curves along the time and space dimensions have provided sufficient information for PIGN to learn the spatiotemporal features of the event.
Fig. 2: Principle of PIGN.
a Schematic of feature functions acquisition for DAS event data. After projecting DAS event data onto different dimensions, and combining physical models with professional experience, the corresponding feature functions of the events in the respective dimensions can be obtained. Feature curves of an individual event can then be derived from these feature functions. b Network structure and training process of PIGN. Network is based on the U-Net architecture. During training, the loss function is defined by assessing the gap between the feature curves of the output image and the target feature curves, while also incorporating constraints from the DAS system and real-world conditions
To narrow the gap between generated data and RWD, constraint functions based on real-world characteristics and the DAS system have been incorporated into the loss function. The design of the real-world constraint function must be tailored to the specifics of the target application. Since real-world signals are predominantly continuous in the time domain, the average of the squared temporal differences in the generated DAS signal is calculated and incorporated as a type of real-world physical constraint function R into the loss function, which can be expressed as:
$$\frac{1}{n-1}\mathop{\sum }\limits_{i=1}^{n-1}{(\Delta {I}_{i})}^{2}$$
(1)
where, n is the total number of samples in the time dimension. Note that I still denote the output image. With this continuous-signal constraint function, unreal spurious spikes in the generated data can be eliminated. In many scenarios, correlations in DAS data can be observed across multiple channels within dimensions such as space, time, and frequency. Taking the spatial dimension as an example, the spatial-correlation constraint function added to the loss function as another type of real-world constraints function can be expressed as:
$${(\mathop{\sum }\limits_{i}\mathop{\sum }\limits_{j}{C}_{{s}_{i}{s}_{j}}-{C}_{T})}^{2}$$
(2)
where \({C}_{{s}_{i}{s}_{j}}\) is the correlation coefficient between channel i and j, CT is the target value of the total correlation coefficient. Continuous signals and correlation constraint functions in other dimensions can be similarly constructed based on the characteristics of the event. In the applications presented below, the continuous-signal constraint and the spatial-correlation constraint serve as the real-world constraint functions. In addition to these constraints, the DAS instrumentation itself also introduces characteristic influences on the measured signals. Since phase wrapping is a common phenomenon and an important characteristic in DAS data, a phase wrapping algorithm should be applied to the objective feature functions as a type of DAS constraint function. Taking the temporal feature function T as an example, the phase wrapping constraint can be expressed as:
$$D(T(t))=T(t)-2\pi \left[\frac{T(t)+\pi }{2\pi }\right]$$
(3)
where \([.]\) is the floor function. Details about the real-world and DAS system constraint functions are provided in the supplementary material. By using the objective feature functions as learning targets and incorporating constraints from both the real world and the DAS system, PIGN can synthesize large amounts of DAS data for target events. Therefore, the full loss function of the PIGN network is expressed as:
$${W}_{0}({\Vert \tilde{T}-D({T}_{Event})\Vert }^{2}+{\Vert \tilde{S}-D({S}_{Event})\Vert }^{2})+\mathop{\sum }\limits_{n}{W}_{n}{R}_{n}$$
(4)
where D() is the DAS constraints function and R is the Real-world constraints function. W represents the weight. The specific functional forms of D() and R, as well as the number of R terms, may vary depending on the application scenario. We adopted an untrained mode for training, and details are in the supplementary materials.
Event recognition with PIGN
The effectiveness of PIGN is validated on a public DAS dataset through the event recognition task24. The public DAS dataset includes training and testing datasets for six distinct event classes, with each class having roughly 2000 training and 500 testing samples. The background, shake, and walk data are selected to validate the PIGN. Although the public dataset contains six event types, our expertise does not allow us to develop physical models for the remaining three. This underscores the importance of collaborating with domain experts who are capable of establishing the corresponding physical models.
Shaking can be described by a forced vibration model, while walking conforms to a pedestrian motion model (see Methods). Based on these physical models, combined with the model of DAS signal generation mechanisms, both temporal and spatial feature functions are derived for these two classes of events. Using these objective feature functions, PIGN can generate corresponding DAS event data, which is compared with RWD as shown in Fig. 3a. The generated data and RWD present similar structural patterns. For the public dataset used here, it is not specified whether the measurements correspond to differential phase or absolute phase. In our applications, however, the temporal feature models are typically constructed from sinusoidal functions, whose general form is preserved under integration or differentiation: the characteristic frequency of an event remains unchanged, and only the associated coefficients vary. Consequently, even without knowing whether the dataset reflects differential or absolute phase, the physical model can still capture the essential event characteristics. This indicates that the proposed PIGN approach does not require an exact correspondence between the physical model and the measured DAS signals; it suffices that the model represents the fundamental features of the underlying events.
Fig. 3: Event recognition performance on a public dataset.
a Examples of shake and walk DAS data from the public dataset and PIGN-generated dataset. Spat. spatial, Sat. saturation. PIGN can generate data that possesses the characteristics of signal saturation and phase wrapping observed in practical applications. b Flowchart of the training and testing process for the classification network. The training dataset comprises only easily accessible real-world background data and event data generated by PIGN, with no real-world event data included. c Event recognition results in different networks with the same real-world test data from a public dataset. RWD real-world data; Acc. accuracy, Prec, precision, Rec. recall. class 0: background; class 1: shake; class 2: walk. PIGN means training with generated event data, whereas RWD means training with real-world event data
Owing to the integration of the DAS system and real-world constraint functions, the generated data is capable of simulating signal saturation and phase wrapping. As shown in Fig. 3b, the generated event data and real-world background data are used as training data for training the classification network. The reason for using real-world background data is that it is easily accessible in practical DAS applications. After training, RWD is used for testing the model. Multiple classification networks were trained with varying amounts of RWD under the same network structure and parameters to compare with classification networks trained on generated data, as shown in Fig. 3c (statistical evaluation in Supplementary Materials). Three representative basic classification networks, convolutional neural network (CNN)51, residual network (ResNet)52, and convolutional neural network bidirectional long short-term memory (CNN-BiLSTM)53, were trained to demonstrate that the validity of the generated data is independent of the network architecture. The classification accuracies of the three types of networks trained with PIGN output data are above 70%, surpassing the 55% and 63.9% accuracies of ResNet and CNN-BiLSTM networks trained with 50 samples of RWD per class. To ensure reliability, the experiment of randomly selecting a small amount of RWD from the public dataset for network training was repeated 100 times. Figure 3c shows the result of one trial with relatively high accuracy (see Supplementary Materials for details). Networks initially trained with PIGN data were further finetuned using a small RWD dataset with 50 samples per class. This process led to accuracy improvements of 6.1, 11.9, and 22.3% for the CNN, ResNet, and CNN-BiLSTM networks, respectively, compared to networks trained on the same small RWD dataset. The finetuned CNN-BiLSTM reached an accuracy of 86.2%, exceeding the performance of ResNet when trained on a large dataset of RWD. All results in Fig. 3c were subjected to statistical significance testing, which shows that PIGN-Finetune and few-shot RWD exhibit a statistically significant difference. PIGN-Finetune consistently achieves superior performance, highlighting the effectiveness of the PIGN-generated data. The results demonstrate that the data generated by PIGN can effectively simulate RWD, and the classification network trained with generated data has comparable or superior performance to the networks trained with a limited amount of RWD. Compared with results trained with large amounts of RWD, the lower accuracy with PIGN-generated data is reasonable because the simplified physical models and broadly chosen parameters cannot fully reproduce the complexity of specific real-world scenarios. Moreover, the public dataset contains only subtle differences between its training and testing conditions, which inherently benefits models trained on real-world data.
Noise-removal net
Generated data from PIGN can also be utilized to train a DAS signal denoising network, addressing the challenge of severe environmental background noise interference in DAS applications.
Although end-to-end learning methods do not require a separate denoising network, some studies have shown that a specially trained denoising network can effectively improve the performance of various downstream tasks54,55. More importantly, the PIGN network cannot reproduce complex background noise and can only generate relatively idealized event signals. Consequently, the classifier trained on PIGN-generated data requires input with minimal noise. Therefore, in our proposed paradigm, denoising is necessary before the final downstream task. Since the public dataset was collected in a laboratory environment where background noise is not strong enough, we chose the application of belt conveyor fault monitoring, as shown in Fig. 4a, which involves significant environmental noise. Figure 4b shows typical DAS data in the temporal and spatial dimensions for belt conveyor monitoring (an enlarged version is provided in the Supplementary Material). Mechanical vibrations accompany the normal operation of the belt conveyor, causing significant background noise in DAS data. Due to the intense background noise and intermittent fault signals characteristic of belt conveyor monitoring applications, time-frequency DAS data were obtained by applying the short-time Fourier transform (STFT) to the time-domain DAS data at each spatial channel, enabling analysis of the signal’s time-varying frequency information. For less severe faults, the relatively weak fault signals are often overwhelmed by the background noise, making it difficult to distinguish fault signals from normal signals in both the time and time-frequency domains, as shown in Fig. 4c, d. Moreover, the vibrations from normal operation share similar mechanisms with the vibration induced by some types of faults, resulting in background noise in the normal signal has similar features with the fault data. Therefore, it is necessary to perform denoising to extract the target event signal.
Fig. 4: Schematic of the DAS noise-removal net.
a Schematic illustration of belt conveyor fault monitoring. b Example DAS data in belt conveyor monitoring. c Temporal DAS signals for normal and fault states in the belt conveyor. d DAS time-frequency diagrams for fault and normal state. The zoomed-in figure depicts the temporal variation of signals at 2 kHz for both fault and normal states. Due to the presence of intense background noise signals, it is difficult to distinguish normal and fault signals in both time and time-frequency domains. e The training process of DAS noise-removal net. STFT short-time Fourier transform. The DAS noise-removal net is based on the U-Net structure. f Testing process of the DAS noise-removal net. ReLU, rectified linear unit. After denoising, the fault signal can be distinctly observed at 2 kHz
The training and testing processes of the proposed DAS noise-removal net are shown in Fig. 4e, f. The first step is to obtain data generated by PIGN of fault events for training. In the belt conveyor fault monitoring application, building a theoretical physical model is very challenging due to the complex environment. Therefore, in this case, the objective feature functions used to train PIGN are established based on experiential knowledge (see Methods). Considering that each roller in the belt conveyor corresponds to a specific spatial position, and the signals from different rollers are nearly independent, the objective feature functions describe the time-frequency domain of the data at a single position. According to expert experience and related literature56, roller faults can be roughly divided into two types: sparse frequency and broadband frequency fault signals. The corresponding fault data generated by the trained PIGN are shown in Fig. 5 (more results in the Supplementary document). These generated fault data were then combined with real-world normal data to train the noise-removal network. After training, the noise-removal network can be used to extract background noise from the RWD. Subtracting the network output linearly from the input RWD gives the background-removed event feature signal, as shown in Fig. 4f. The ReLU operation is applied to ensure that the resulting event features do not contain meaningless negative values (see Supplementary Materials for details). The noise-removal net adopts a residual learning structure, focusing on learning the background data rather than directly extracting event features (see Methods). The main reasons are the accessibility of a substantial amount of real-world background signals, and the fact that low-frequency components within the background noise are more easily captured by the network, following the frequency principle in neural network training57. As shown in Fig. 4d, f (enlarged version in Supplementary Materials), after the background noise is removed by the noise-removal net, the subtle fault signal at a frequency of 2 kHz can be distinctly observed. Before background noise removal, the fault signal at 9 s is difficult to distinguish due to its comparable amplitude to background noise at other time points. After background noise removal, the fault signal at 9 s becomes clearly identifiable, with an amplitude at least twice as large as that at other time points.
Fig. 5: Examples of fault signals in belt conveyor from real-world data and PIGN-generated data.
Real-world data with intense fault signals are presented for clear demonstration, and show periodic impulsive features with varying intensities in the time domain. Due to strong low-frequency environmental noise during belt conveyor operation, both sparse frequency and broadband frequency faults in the real-world data have strong energy below about 1 kHz. The main difference is that sparse frequency faults show clear, strong frequency components above 1 kHz but low intensity in other bands, while broadband frequency faults have no obvious strong components beyond the low-frequency noise and maintain a certain intensity across the entire frequency range. PIGN-generated data possess characteristics similar to real-world data
The experiment was conducted at the belt conveyor simulation test site provided by Ningbo AllianStream Photonics Technology Co., Ltd, to acquire DAS data of normal rollers, eccentric rollers, split rollers, and cracked rollers (see Methods). The initial time-frequency data and the background removal results by the noise-removal net for the four classes are shown in Fig. 6a. The temporal and frequency feature curves are obtained by calculating the average energy in their respective domains. For the convenience of comparison, both the initial and denoised feature curves have been normalized individually. After denoising, the maximum amplitude of the normal data decreased from 1 to 0.15, primarily retaining an abnormal feature at 7 s. The frequency feature curve of the normal data after denoised changed little, and the temporal feature curve showed an approximately average decrease of 3.91 dB. Fault data from eccentric rollers, which exhibit broadband frequency features, as well as data from split and cracked rollers with sparse frequency features, were effectively denoised by the noise-removal network, preserving the essential fault signals while removing background noise. This is evident in the frequency feature curves, where the intensities of fault frequencies are enhanced by >3 dB, and in the temporal feature curves, which retain the intermittent fault signals from similar background noise signals and achieve an average >2.5 dB reduction in background noise. To demonstrate the benefit of background removal, different classification networks were trained using both the RWD collected from the simulation test site and the corresponding background-removed data, under the same network structure and parameter settings. The results on the same test data are shown in Fig. 6b. The training dataset includes 15 samples for each class, whereas the test data includes 30 samples for each class. All networks were trained with >200 epochs to reach a convergent state. The results indicate that the denoised data demonstrate accuracy improvements of 8.4, 4.2, and 1.6% in CNN, ResNet, and CNN-BiLSTM, respectively, when compared to the initial data. From the statistical comparison between CNN-initial and CNN-denoised, it shows a statistically significant difference in classification accuracy between the two networks. This demonstrates that applying the noise-removal network effectively improves the final classification performance, confirming that the noise-removal network can successfully suppress noise while preserving event-related features.
Fig. 6: Denoised results from the noise-removal net and fault diagnosis results in the belt conveyor simulation test site.
a Comparison of initial and denoised data for different classes. The noise-removal net can eliminate background noise while retaining fault signals with sparse or broadband frequency features. b Fault recognition results using initial and denoised data. Denoised data can achieve higher classification accuracy in various networks. c The classification performance of initial and denoised data in CNN under different training datasets with varying sample sizes. Compared to the initial data, the denoised data facilitates higher classifier accuracy
Given the inherent randomness in the network training, multiple training rounds with different random parameter settings were performed. After ten rounds of training, the CNN achieved average accuracies of 74.42% for denoised data and 70% for initial data, with standard deviations of 1.71 and 3.8%, respectively. This confirms the background noise removal capability of the noise-removal net. The denoised data show performance improvements across different network architectures, especially in simpler networks. Statistical evaluation of classification results is provided in the Supplementary Materials. The performance of initial and denoised data is compared across small training datasets of varying sizes, as shown in Fig. 6c.
Field test of belt conveyor fault detection
In the practical deployment of DAS, different sites of the same application often have distinct environments, resulting in poor generalization of traditional DAS data processing algorithms. For a specific application, events to be detected across different sites follow a similar basic physical model, and the corresponding DAS data should have similar features. The main difference in DAS data for these similar events at different sites lies in the environmental background noise. The proposed neural network paradigm, which leverages event data generated from PIGN and easily obtainable background data for training, facilitates fast deployment in different fields. Figure 7a illustrates the process of deploying a fault diagnosis network in a coal mine field of belt conveyor fault monitoring. The intrinsic mechanical vibration of the belt conveyor constitutes the primary background noise. Despite significant differences in machine type, running speed, load weight, and working environment between the simulation test site and the coal mine field, the background noise at both sites originates from mechanical rotating equipment vibrations. Hence, the noise-removal net originally trained for the simulation test site can be directly applied to the coal mine field to remove background noise. The application of the noise-removal network in the coal mine field scenario follows the same procedure as illustrated in Fig. 4f. The denoised results of different types of events are shown in Fig. 7b. The noise-removal net remains effective for field data, reducing background noise by >4 dB in the time feature curves, while significantly enhancing fault signal intensity by more than 6 dB in the frequency-domain feature curves. Even though the amplitude of background noise in the coal mine field is higher than that of the simulation test site, the denoising network still shows effective background noise removal capability. Normal data consisting of 450 samples collected at different times and locations over a single day at the coal mine field are processed by the noise-removal network to obtain denoised real-world normal data. Subsequently, the classification network is trained using PIGN-generated fault data and real-world background-removed normal data as inputs, corresponding to fault and normal classes, respectively. Importantly, real-world event data from the coal mine field is not involved in the training of any part of the network. During a four-month field monitoring period, a total of 23 roller faults occurred on the belt conveyor. Approximately ten samples were selected for each roller fault, combined with the normal data randomly selected at any time period during the 4 months, to form the test dataset. The performance of CNN-BiLSTM trained with generated and denoised normal data on the test dataset is shown in Fig. 7c. For comparison, the same network structure was trained with labeled RWD as training data. The real-world training dataset is an imbalanced dataset, in which 450 samples are in the normal class, and ten samples are in each of the two fault classes. Data augmentation of directly copying fault data and cost-sensitive learning methods are adopted to complete this unbalanced sample training task (see Supplementary Materials for details). The proposed approach, without requiring any real-world fault data for training, achieves a three-class classification accuracy of 85.6%, which is a 14.3% improvement compared to the 71.3% accuracy of the network trained with RWD. According to the statistical significance analysis in Fig. 7c, the network trained on PIGN-generated data exhibits a statistically significant improvement in classification performance compared with the network trained on RWD. This demonstrates the effectiveness of PIGN-generated data in serving as a surrogate for RWD in network training.
Fig. 7: Deployment of physics-informed DAS neural network paradigm in the coal mine field.
a Training and testing processes of PIGN, noise-removal net and classification network in the coal mine field. The noise-removal network, trained using background data from the belt conveyor simulation test site and PIGN-generated data, can be directly applied to remove background noise in field data from the coal mine. The training of the classification network does not require fault data from a simulation test or field. Dashed lines indicate the testing phase and solid lines indicate the training phase. b Comparison of initial and denoised data in the coal mine field of different classes. The noise-removal net, deployed directly from the belt conveyor simulation test site to the coal mine field, can still remove background noise and retain fault signals. c Fault recognition results of artificially designed algorithm and classification networks trained with denoised PIGN-generated data or RWD. Class 0, normal; Class 1, sparse frequency fault; Class 2, broadband frequency fault. In a binary classification task, class 0 and class 1 represent normal and fault, respectively. Physics-informed DAS neural network paradigm with PIGN and noise-removal net shows better classification performance than data-driven network and artificially designed algorithm
For practical applications, it is typically only necessary to establish whether a fault exists. Therefore, binary classification results are presented and additionally compared with a complex, manually designed fault diagnosis algorithm based on time-frequency analysis. This algorithm was deliberately designed after a comprehensive review of data spanning more than four months and has undergone meticulous parameter adjustment. Even with these manual efforts, the accuracy of the artificially designed algorithm is 86.6%, inferior to the accuracy of 91.8% achieved by the proposed paradigm. In practical use, once a small amount of real-world target event data were obtained, finetuning the network with RWD can further enhance fault diagnosis performance. After finetuning the pretrained network with labeled RWD consisting of ten samples per fault class, the accuracy for three-class and two-class classification reached 88.4 and 93.4%, respectively.