Measurement Accuracy Enhancement with Multi-Event Detection using Deep Learning Approach in Raman Distributed Temperature Sensors

Abstract

In this work, we present a novel deep learning framework for multi-event detection with enhanced measurement accuracy from the measured data of a Raman Optical Time Domain Reflectometer (Raman-OTDR). We demonstrate the utility of a deep learning-based approach by comparing the results from three popular neural networks, i.e. vanilla recurrent neural network (RNN), long short-term memory (LSTM), and gated recurrent unit (GRU). Before feeding the experimentally obtained data to the neural network, we sanitize our data through a correlation filtering operation to suppress outlier noise spikes. Based on experiments with Raman-OTDR traces consisting of single temperature event, we show that the GRU is able to provide better performance compared to RNN and LSTM models. Specifically, a bidirectional-GRU (bi-GRU) architecture is found to outperform other architectures owing to its use of data from both previous as well as later time steps. Although this feature is similar to that used recently in one dimension convolutional neural network (1D-CNN), the bi-GRU is found to be more effective in providing enhanced measurement accuracy while maintaining good spatial resolution. We also propose and demonstrate a threshold-based algorithm for accurate and fast estimation of multiple events. We demonstrate a 4x improvement in the spatial resolution compared to post-processing using conventional total variational denoising (TVD) filters, while the temperature accuracy is maintained within ± 0.5 of the set temperature.

Full text

Measurement Accuracy Enhancement with
Multi-Event Detection using Deep Learning
Approach in Raman Distributed Temperature
Sensors
AMITABHA DATTA *, VISHNU RAJ, VI SWAN ATHA N SANKAR, SHE ETAL
KALYAN I,AND BAL AJI SRINIVASAN**
Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India
*Presently at CSIR-National Aerospace Laboratories, Bangalore, India
**balajis@ee.iitm.ac.in
Abstract:
In this work, we present a novel deep learning framework for multi-event detection
with enhanced measurement accuracy from the measured data of a Raman Optical Time Domain
Reflectometer (Raman-OTDR). We demonstrate the utility of a deep learning-based approach by
comparing the results from three popular neural networks, i.e. vanilla recurrent neural network
(RNN), long short-term memory (LSTM), and gated recurrent unit (GRU). Before feeding the
experimentally obtained data to the neural network, we sanitize our data through a correlation
filtering operation to suppress outlier noise spikes. Based on experiments with Raman-OTDR
traces consisting of single temperature event, we show that the GRU is able to provide better
performance compared to RNN and LSTM models. Specifically, a bidirectional-GRU (bi-GRU)
architecture is found to outperform other architectures owing to its use of data from both
previous as well as later time steps. Although this feature is similar to that used recently in one
dimension convolutional neural network (1D-CNN), the bi-GRU is found to be more effective in
providing enhanced measurement accuracy while maintaining good spatial resolution. We also
propose and demonstrate a threshold-based algorithm for accurate and fast estimation of multiple
events. We demonstrate a 4x improvement in the spatial resolution compared to post-processing
using conventional total variational denoising (TVD) filters, while the temperature accuracy is
maintained within ±0.5 𝑜𝐶of the set temperature.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed fiber optic sensors (D-FOS) based on Brillouin, Raman or Rayleigh scattering in
optical fibers are attracting widespread interest for several commercial applications [1
–
5]. A
common trade-off in all the above sensor systems is that of measurement accuracy versus spatial
resolution. Specifically, to meet the stringent spatial resolution requirement for some of the above
applications one has to launch a pulse of short duration. In such a scenario, the measurement
accuracy may be compromised due to the low signal to noise ratio, especially from the farther
sections of the sensing fiber. In order to preserve the measurement accuracy while maintaining
good spatial resolution, several post-processing techniques have been proposed in the literature. In
particular, various signal processing techniques have been proposed in the literature to mitigate the
trade-off between spatial resolution and temperature accuracy. Zhang et al. & Saxena et al. [6, 7]
proposed wavelet transform based signal processing of the back-scattered anti-Stokes/Stokes
signal to reduce temperature uncertainty. Noise reduction method based on a nonlinear median
filter has been proposed by Wang et al. [8]. In this approach the average maximum deviation in
the temperature measurement reduced from 4.1
𝑜𝐶
to 1.2
𝑜𝐶
in the 40-60
𝑜𝐶
temperature range.
An innovative approach based on ensemble empirical mode decomposition (EEMD) method for
signal denoising has been recently proposed by Pan et al. wherein the SNR is enhanced by 8.8

dB while maintaining the spatial resolution [9].
In our previous work, we have applied a total variation denoising (TVD) to suppress the noise
and improve the signal to noise ratio for the anti-Stokes signal in a Raman-OTDR system [10].
In this approach, a convex optimization based on majorization-minimization algorithm was
used to minimized the cost function which provide better noise reduction over conventional
Savitzky-Golay low pass filtering [11]. Recently, 2-D image processing of 1-D traces using
non-local mean (NLM) filtering has been proposed by Soto et al. through which they demonstrate
a 100-fold improvement in the sensor performance [12]. However, the NLM algorithm needs
apriori knowledge about the SNR of the data to properly set the values of window size and
smoothening parameter. As such, implementation of such an algorithm i.e., find an optimal value
for the above parameters could be non-trivial in the field environment.
Deep learning techniques [13] have recently been implemented with great success in multiple
domains, including computer vision [14], wireless communication systems [15,16], optical fiber
systems [17] etc. Similar exploration has also been recently extended to distributed fiber sensors,
as the deep learning approach promises to learn continuously based on data collected from the
field environment. In the context of improving spatial resolution, Silva et al. used a nonlinear
auto-regressive neural network architecture to process the response from a distributed temperature
sensor in which the features are hand-picked [18]. The results showed that both spatial resolution
as well as temperature resolution can be improved by using neural networks. Wu et al. proposed
a feed-forward image denoising convolutional neural networks to enhance the signal-to-noise
ratio (˜13.4 dB) without loss of measurement accuracy (temperature uncertainty and spatial
resolution) at low sampling rates [19]. A deep learning-based method for effective wavelength
detection for FBG sensor networks has been proposed by H. Jiang et al. [20]. Considering
the wavelength detection as a sequential learning problem, they have used a Long Short-Term
Memory (LSTM) based recurrent neural network for the wavelength detection. In order to
enhance the multiplexing capacity and measurement accuracy of FBG sensor system, Manie et
al. [21] proposed a recurrent neural network-based architecture to use in a ring structured FBG.
For the problem of real time detection and classification of intrusion using Distributed Acoustic
Sensing (DAS), Li et al. proposed a convolutional LSTM based solution [22]. The field test
results from a high-speed railway show that the proposed system is able to handle threat detection
even in the presence of strong noises and interference.
Laarossi et al. presented a denoising deep auto-encoder based approach for improving the SNR
of backscattered signals in a Raman Optical Time Domain Reflectometer (OTDR) [23]. The main
advantage of the presented method is the single shot enhancement of the SNR once the neural
network is trained. Zhongshu Zhang et al. [24] recently reported 1-D convolutional neural network
based denoising methodology for a Raman-OTDR temperature map. Unfortunately, the plots of
temperature as a function of length presented in this work do not reveal how well the temperature
transition regions corresponding to an event are captured by the network. Moreover, it is not clear
whether such an approach could be extended for an arbitrary spatial distribution of multiple events.
A novel deep learning framework for enhancement of spatial resolution and measurement
accuracy from the measured data of a Raman-OTDR has been explored in our present work. Here,
we consider the raw measurements as a data sequence and sanitize the data using correlation
filtering to remove any undesirable noise spikes before feeding it to a deep learning network to
achieve multi-event detection. We explore three popular models of deep learning for the data
processing: (i) Vanilla Recurrent Neural Network (RNN), (ii) Long Short-Term Memory (LSTM),
and (iii) Gated Recurrent Unit (GRU). Based on systematic studies, we find that the bi-directional
Gated Recurrent Unit (bi-GRU) is best suited for achieving low temperature uncertainty (
±
0.5

𝑜𝐶
) and 4-fold improvement in spatial resolution compared with conventional filtering (TVD).
We also demonstrate a data-driven threshold-based algorithm for rapid processing of temperature
map with multiple events.
Our work is organized as follows: Sec. 2 describes several possible RNN architectures for
post-processing the Raman-OTDR data, Sec. 3 discusses the implementation of the RNNs for
post-processing of the experimental data consisting of single event and also multiple events,
followed by a discussion of our approach in Sec. 4 before concluding in Sec. 5.
2. Recurrent neural network as filters
In this work, we view the post-processing of measured values as a process of filtering and propose
to use deep learning to develop efficient filters that can learn from the data used for training.
Noting that the measurement data from each trace can be seen as a sequential signal, we use deep
learning architectures which are designed to process sequential data. Recurrent Neural Networks
(RNN) are one of the most popular neural network architectures for processing sequential data.
2.1. Recurrent Neural Networks
In traditional feed forward neural networks, the input data is processed by each hidden layer
in a sequential manner and the output produced depends only on the input given as well as the
parameters on the network. This severely limits the applicability of feed forward neural network
on temporal data where each of the data points are potentially dependent on the past data points.
Recurrent Neural Networks (RNNs) are introduced to solve this problem [25]. In RNNs, recurrent
directed connections between the nodes allow the data to flow both in forward direction as well as
backward direction. By using a recurrent connection, RNN units can retain information about the
past data points it has seen and combine it with the current input to produce an output. The working
principle of a simple RNN is shown in Fig. 1. At every step, input
𝑥𝑡
is fed into the recurrent
cell, producing an output
ℎ𝑡
. The output
ℎ𝑡
depends on both the current input
𝑥𝑡
as well as the
previous state saved inside the cell about past inputs (denoted by recurrent/loop connection). This
enables a RNN to processes sequential data with different lengths. The unrolled representation at
right hand side shows how data flows through the network during the processing. As one can see,
Fig. 1. Working principle of an RNN. The output
ℎ𝑡
depends on both the current input
𝑥𝑡as well as the previous state saved inside the cell about past inputs.
RNN maintains an internal hidden state which gets updated as the sequential data flows through
the recurrent unit. Through the introduction of this hidden state, RNNs are able to capture the
required information about the past data points and can efficiently combine it with present input
data point in a sequence to make predictions. Since the entire past history of the input sequence

is represented in the hidden state representation, RNNs can theoretically deal with sequences
of infinite length where both long term and short term dependencies between data points may exist.
I. Vanilla RNN
The Vanilla RNN is the simplest recurrent neural network structure available in literature. It
stores information about the past observations in the sequence by maintaining a hidden state
inside the unit. Let
𝑥𝑘
be the input at data points at
𝑘th
position in the sequence. Then, Vanilla
RNN computes a hidden state,
ℎ𝑘
, which is the abstraction of all information until
𝑘th
data point
as
ℎ𝑘=tanh(𝑊𝑖 ℎ𝑥𝑘+𝑏𝑖 ℎ +𝑊ℎℎ ℎ(𝑘−1)+𝑏ℎℎ).(1)
Here,
ℎ(𝑘−1)
refers to the hidden state at
𝑘−
1index. During the learning phase, the parameters
𝑊𝑖ℎ , 𝑏𝑖 ℎ, 𝑊ℎ ℎ
and
𝑏ℎℎ
are updated using an optimizer based on the loss incurred. In a Vanilla
RNN, both the output and the hidden state representation is the same:
ℎ𝑘
. One of the main
disadvantages of Vanilla RNN is the capability to deal with long term relationships in sequences.
As one can see from (1), Vanilla RNN maintains a simple relationship with all the past data
through a single hidden state. This causes Vanilla RNNs to forget the information about distant
past observations as it sees more and more input points. Eventually, this could lead to failure in
identifying long term relationships in the sequence.
II. Long Short Term Memory (LSTM)
LSTM units have proposed as as a possible solution to forgetting problem in Vanilla RNNs [26,27].
Instead of maintaining a simple hidden state, LSTM maintains a separate hidden state
ℎ𝑘
, cell
state
𝑐𝑘
and output
𝑜𝑘
. The operations happening inside an LSTM unit is given below. Here

is
used to denote a Hadamard product.
𝑖𝑘=𝜎(𝑊𝑖𝑖 𝑥𝑘+𝑏𝑖𝑖 +𝑊ℎ𝑖 ℎ𝑘−1+𝑏ℎ𝑖 )(2)
𝑓𝑘=𝜎(𝑊𝑖 𝑓 𝑥𝑘+𝑏𝑖 𝑓 +𝑊ℎ 𝑓 ℎ𝑘−1+𝑏ℎ 𝑓 )(3)
𝑔𝑘=tanh(𝑊𝑖 𝑔𝑥𝑘+𝑏𝑖𝑔 +𝑊ℎ 𝑔 ℎ𝑘−1+𝑏ℎ𝑔 )(4)
𝑜𝑘=𝜎(𝑊𝑖𝑜 𝑥𝑘+𝑏𝑖𝑜 +𝑊ℎ𝑜 ℎ𝑘−1+𝑏ℎ 𝑜)(5)
𝑐𝑘=𝑓𝑘𝑐𝑘−1+𝑖𝑡𝑔𝑘(6)
ℎ𝑘=𝑜𝑘tanh(𝑐𝑘)(7)
Instead of directly dealing with current input
𝑥𝑘
, LSTM first computes an input gate value
𝑖𝑘
and
a forget gate value
𝑓𝑘
. Both of these values are calculated using a sigmoid activation function
which outputs a value between
−
1and
+
1. The value of
𝑓𝑘
is used to selectively discount the
effect of previous cell state
𝑐𝑘−1
. This discounted past information is then added to the current
information via the input gate value calculated as
𝑖𝑘
. This produces the next cell state
𝑐𝑘
. The
output for this round
𝑜𝑘
is computed as based on current input and previous hidden state. Finally,
the hidden state for this round
ℎ𝑘
using the current output
𝑜𝑘
and cell state
𝑐𝑘
. This method of
selectively passing the information from past observations along with the ability to maintain a
separate cell state enables LSTM to capture long term dependencies in the sequence.
III. Gated Recurrent Units (GRU)
GRUs are proposed as simpler recurrent units which can capture long term dependencies in
the sequence [28]. Instead of maintaining separate cell state and hidden state, GRUs use two
novel operations for combining data; they use a reset gate
𝑟𝑘
and a update gate
𝑧𝑘
to combine the
current data point with past observations. The mathematical operations inside a GRU are given

below:
𝑟𝑘=𝜎(𝑊𝑖𝑟 𝑥𝑘+𝑏𝑖𝑟 +𝑊ℎ𝑟 ℎ(𝑘−1)+𝑏ℎ 𝑟 )(8)
𝑧𝑘=𝜎(𝑊𝑖𝑧 𝑥𝑘+𝑏𝑖 𝑧 +𝑊ℎ𝑧 ℎ(𝑘−1)+𝑏ℎ 𝑧 )(9)
𝑛𝑘=tanh(𝑊𝑖 𝑛𝑥𝑘+𝑏𝑖𝑛 +𝑟𝑘∗ (𝑊ℎ𝑛 ℎ(𝑘−1)+𝑏ℎ𝑛 )) (10)
ℎ𝑘=(1−𝑧𝑘) ∗ 𝑛𝑘+𝑧𝑘∗ℎ(𝑘−1)(11)
In this work, we show the applicability of the entire above RNN variant in the problem of
enhancement of temperature uncertainty and spatial resolution.
2.2. Architecture of the model
We use a multi-layer RNN architecture followed by a dense layer for post-processing the Raman
OTDR data. The architecture of the proposed deep learning model is given in Table-1. We
Table 1. Architecture of the deep learning model
Layer Name Number of hidden units Activation function
Input layer 1None
RNN-1 30 tanh(·)
RNN-2 20 tanh(·)
RNN-3 10 tanh(·)
Dense Layer 1𝜎(·)
have used a recurrent neural network with three hidden recurrent layers followed by a fully
connected dense layer. The first three layers are used to capture the sequential dependency in
the data observed followed by a dense layer to act as a regression predictor and provide real
valued temperature. Each of the recurrent layers holds an internal state which captures sequence
characteristics. By reducing the number of hidden nodes at each layer, we force each of the layers
to only retain the statistical characteristics of the state and discard the random noise. Since the
hidden dimension is getting reduced, the network will learn to capture only the necessary details
filtering the raw data rather than propagating the noise. As such, this bottleneck architecture
guides the network to perform neural filtering.
2.3. Network training
In our work, we have created a large training data set using simulations performed on a Raman-
ODTR model. In a Raman-OTDR, the distributed temperature data is obtained by observing
the Stokes and anti- Stokes power as a function of time for a given pulsed excitation of the
sensing fiber. This constitutes a forward model, wherein for a given input temperature map,
transmitter parameters, receiver parameters and fiber parameters, the backscattered Stokes and
anti-Stokes traces can be accurately estimated. The block diagram of such model is illustrated in
Fig. 2. In our previous studies, we have carried out a detailed noise analysis of Raman-OTDR
receiver [29,30]. We have found that the most dominant noise term is the thermal noise from the
optical receiver. Such noise sources are added to the estimated Stokes, anti-Stokes traces and
the corresponding results have been experimentally validated. The corresponding temperature
map, which mimics the experimentally observed data is computed and used for our network
training. Based on such a model, we ran simulations where we have used an optical laser source

Fig. 2. Model of Raman-OTDR used for generating the simulation data
operating at 1550 nm with 80 mW input power and 80 ns pulse width corresponding to the 8 m
spatial resolution. In this work, a 11.5 km long standard singlemode fiber (SMF-28) has been
used for the sensing fiber. The simulations were performed with temperature maps consisting of
single event with three different event width (8, 32, 217 m) and different temperature range (27 to
90
𝑜𝐶
with a step of 5
𝑜𝐶
). The simulation output i.e. temperature maps, each of 330 length
index have been used to train the model and validation purpose. Temperature map obtained from
the simulation model is used as an input feature and the target is the set temperature (square
profile) map of the recurrent neural network. Overall, we have generated
∼
200 such temperature
maps, which were divided for training model (70%of samples) and validation (30%of samples).
During the training phase, the data samples are provided to the neural network model, and the
system is adjusted according to the error observed. The validation data is used for network
generalization and to halt training of the neural network when the generalization stops improving
network performance. The networks are implemented in PyTorch. The maximum epoch is set to
be 1000. Since the task involves estimating real valued temperature output, we use Mean Square
Error (MSE) as the loss objective to minimize. Through a systematic architecture search, we
found that increasing the depth of the network is not helping in improving the quality of our
estimation. Specifically, we use three RNN layers followed by a fully connected dense layer
for estimation. Since the events are symmetric about baseline, if our post-processing module
detects any event below room temperature the corresponding data is flipped along the y-axis
for the estimation. Finally, the estimated data is reverse flipped to exhibit the correct measured
data. The Mean Square Error (MSE) between the estimated output and the actual temperature is
used as the cost function to minimize. Adam optimizer [31] is used to train the neural network
with learning rate (
𝜂∼
10
−2
), learning rate decay for first moment (
𝛽1∼
0.99), and learning rate
decay for second moment (
𝛽2∼
0.999) parameter. Once the training process is finished, the

(a) (b)
(c)
Fig. 3. The training loss and validation loss plot for the different neural architectures:
(a) RNN (b) LSTM and (c) GRU
well-trained models can be directly applied for the single event and multi-event temperature
estimation. Fig. 3 shows the loss evolution as a function of number of epochs during the training
and validation phase of RNN, LSTM and GRU models. Overall, the training losses reduce as the
number of iterations increases. However, the loss plots exhibit certain spikes beyond a certain
number of epochs. This is because of inappropriate learning rate and momentum at that epoch.
This has been corrected in the successive epochs by back-propagating the loss in the network,
decaying the learning rate and adjusting the momentum by the optimizer. It is interesting to note
that the GRU has significantly reduced undulations compared to other networks, signifying a
stable parameter update. Another key point to note here is that the validation loss is lowest in
GRU compared to the other architectures, implying generalization of the network.
In the following section, we present results for both unidirectional (uni) and bidirectional (bi)
estimation using the proposed architecture and applicability of the above mentioned sequence
processing models in the context of post-processing of Raman-OTDR data. We compare the
performance of each of the above neural architectures in enhancing the temperature uncertainty
and spatial resolution.

3. Implementation of RNN for enhancement of system performance
In this section, we introduce our deep learning receiver-based experimental setup consisting of a
Raman optical time domain reflectometer (OTDR). A correlation filter has been used to sanitize
the data, followed by demonstration of single event detection and multi-event detection based on
experimental data.
3.1. Deep learning receiver based experimental setup
Our Raman-OTDR based distributed temperature sensing system shown in Fig. 4 consists of
a pulsed semiconductor laser (1550 nm, 85 mW, 10 nm FWHM), an avalanche photo-diode
(APD) based low noise receiver (3.5 MHz bandwidth), and a Field Programmable Gate Array
(FPGA)-based digital circuit to acquire data as well as provide control and synchronization. The
back-scattered responses are digitized at the receiver using a 10-bit ADC operated at a sampling
frequency of 48 MHz. The digitized data is fed to the FPGA-based data acquisition system which
is also capable of averaging the signals through the use of a pair of pipelined SRAMs. It is well
known that the anti-Stokes component of the Raman backscattered signal is strongly dependent
on the temperature. Hence, by taking the ratio of the anti-Stokes intensity and the Stokes intensity
or Rayleigh backscattered intensity, one can accurately measure the temperature across the length
of the sensing fiber using optical time domain reflectometry (OTDR) principle [32].
In our approach, the backscattered anti-Stokes signal is measured from both forward and
backward directions in a loop configuration as illustrated in Fig. 4a. Here, the two ends of
the sensing fiber are connected to a 1 x 2 optical switch, allowing pulses to be launched into
the test fiber segments either in the forward (Port-F) or the backward (Port-B) direction. The
anti-Stokes voltage trace is averaged over 2
18
iterations in our data acquisition system. We have
used a pre-calibrated commercial electrical thermometer (RTD) with 0.5
𝑜𝐶
accuracy to monitor
the temperature in our temperature-controlled chamber (TCC). Specifically, we have used the
experimental setup shown in Fig. 4b where the testbed consists of four spools of standard single
mode fiber (SMF-28) whose total length is 11.5 km. We have used 2 km long fiber spools at either
end of the fiber under test (FUT), which are maintained at room temperature and used as reference
for the temperature measurement. Two fiber segments of length 200 m are placed in a TCC and
another 100 m fiber is placed in a refrigerator allowing for measurement of temperatures above
and below the ambient temperature. Two spans of 3 km long fiber is placed on either end of the
100 m fiber section to spatially separate them from the two 200 m fiber sections. The geometric
mean of the normalized single-ended anti-Stokes signal measured in both forward direction
𝑃𝑓(𝑧)
and backward direction
𝑃𝑏(𝑧)
provides a measure of the temperature as a function of
distance.
𝑃𝑚(𝑧)=q𝑃𝑓(𝑧)𝑃𝑏(𝑧)(12)
In order to extract the temperature from the measured anti-Stokes signal traces,
𝑃𝑚(𝑧)
can be
written as [33]
𝑃𝑚(𝑧)=𝐾
𝑒𝑥 𝑝 (Δ𝐸
𝑘𝐵𝑇𝑚) − 1(13)
where
Δ𝐸
is the peak phonon energy of the host glass (corresponding to a frequency shift of 13
THz in fused silica fibers),
𝑘𝐵
is the Boltzmann constant and Kis a calibration constant which
may be uniquely determined for a given system by performing a reference measurement of the
anti-Stokes backscattered power (
𝑃𝑟
) using a standoff section of fiber maintained at a controlled
reference temperature (
𝑇𝑟
) at both ends of the sensing fiber. Based on such a measurement, the
temperature profile
𝑇𝑚(𝑧)
can be obtained using the following expression which is an elegant

(a)
(b)
Fig. 4. (a) Schematic diagram of our reference-free self-calibrated Raman-OTDR
system based on a deep learning receiver (highlighted in yellow) (b) Picture of the
test-bed where the temperature measured by the Raman-OTDR is compared with the
reference temperature from a pre-calibrated RTD.
alternative compared to previously developed ratio based calibration algorithm [34] :
𝑇−1
𝑚=𝑘𝐵
Δ𝐸𝑙𝑛 (𝑒 𝑥 𝑝 Δ𝐸
𝑘𝐵𝑇𝑟−1𝑃𝑟
𝑃𝑚+1(14)
The above measured signal in both forward direction
𝑃𝑓(𝑧)
and backward direction
𝑃𝑏(𝑧)

needs to be sanitized to suppress any noise spikes before it is processed using our neural network
for a threshold-based multi-event detection. Such sanitization may be carried out by correlating
the measured signal with the laser pulse sequence used for the Raman OTDR measurement. This
step may be mathematically explained as follows: A Raman-OTDR can be modeled as a discrete
linear time invariant system. The output (y[n]) signal is a convolution of the laser pulse sequence
x[n] with the backscattered response (b[n]), which is then corrupted by additive white Gaussian
noise (AWGN), N[n] at the receiver [35,36]. This can be expressed as:
𝑦[𝑛]=𝑥[𝑛] ∗ 𝑏[𝑛] + 𝑁[𝑛](15)
At the receiver, we correlate the original probe sequence x[n] with the output signal y[n] to
obtain,
𝑥[𝑛] ⊕ 𝑦[𝑛]=𝑥[𝑛] ⊕ (𝑥[𝑛] ∗ 𝑏[𝑛] + 𝑁[𝑛]) =𝑏[𝑛] + 𝑥[𝑛] ⊕ 𝑁[𝑛](16)
where
∗
represents the convolution operation and
⊕
represents the correlation operation. Since
the auto-correlation (x[n]
⊕
x[n]) approximates to a delta function, b[n] can be accurately
estimated and is only limited by the receiver bandwidth. It is to be noted that the probe sequence
x[n], which is a square-shaped pulse in our case is poorly correlated with the noise N[n], and
hence the second term in (16) yields a much lower value compared to the first term. Thus, a
correlation filtering operation is performed to suppress the noise spikes at the front end of the
learning receiver (highlighted box in Fig. 4a).
The detailed steps involved in the calibration of the above Raman-OTDR are as follows [34]:
a. Measure forward and backward anti-Stokes traces (
𝑃𝑓(𝑧)
and
𝑃𝑏(𝑧)
) across the sensing fiber
as well as the stand-off fiber.
b. Normalize the two traces such that their initial values are consistent.
c. Apply correlation filtering to sanitize the traces using (16).
d. Calculate the geometric mean (GM) of the above single-ended anti-Stokes signal in both
forward and backward directions (𝑃𝑚,𝑃𝑟).
e. Calculate the temperature map using (14)
f. Compare the measured temperature with the reference temperature value for the ambient
temperature along with several set temperature values, and extract any offset as well as scaling
factor.
g. Incorporate the above calibration values (offset/scaling) in the temperature calculation and
verify the Raman-OTDR performance over the desired temperature range.
To illustrate the utility of this correlation operation, we have conducted an experiment in which
two segments of length 200 m each are placed in a temperature-controlled chamber (TCC) at
72
𝑜𝐶
, and another 100 m fiber segment is placed in a refrigerator at -8
𝑜𝐶
. The correlation
operation not only helps to suppress spurious spikes in the measured signal, but also improves
the signal to noise ratio (SNR) without compromising the temperature event-related transitions.
The suppression of the noise spikes in the measured data is highlighted in Fig. 5a. The effect of
the correlation operation is more apparent in the histogram plot of temperature map before and
after correlation as shown in Fig. 5b. One can note that correlation operation has significantly
reduced the standard deviation in the temperature uncertainty due to the receiver noise. As such,
the correlation filter not only enhances the SNR of the signal but also helps to efficiently sanitize
our data by removing outlier noise spikes which could possibly be detected as a false positive
event during our deep learning step.
In the learning receiver, an event detection methodology based on a data-driven threshold has
been proposed to localize the temperature change across the sensing range. We have calculated
the threshold value based on mean (m
∼
26.2
𝑜𝐶
) and standard deviation (
𝜎∼
3.2
𝑜𝐶
) of the
measured data with respect to a reference temperature (
𝑇𝑟
). If the correlation filtered event

(a)
(b)
Fig. 5. (a) Comparison of conventional and correlation filtered forward anti-Stokes
voltage traces (b) Histogram of temperature map before correlation filter and after
correlation filter
exhibits a value > m
±𝜎
, then 330 length index i.e. 660 m of sensing window was selected around
the the peak of the event. The above threshold detection step identifies the starting point as well
as the end point of the event of interest, which allows for acceleration of the training and testing
process in the deep learning. The localized window corresponding to the event is then forwarded
to the trained RNN network as sequential data. The trained RNN network observes the complete
sequence inside the event window and estimates the output. Finally, the estimated temperature map
is obtained by stitching the data from the trained RNN network with the TVD filtered baseline data.
In network testing for the Raman-OTDR temperature measurement, we have used two different
experimental conditions, viz. a single event temperature map and also a multiple event temperature
map. Multiple event temperature estimation is carried out through a test case consisting of a
controlled three event laboratory demonstration.

(a)
(b)
Fig. 6. Single event temperature map estimation using unidirectional RNN, LSTM,
uni-GRU & bi-GRU models illustrating the superior performance of the bi- GRU
model compared to the other models (a) Estimated temperature map (b) Temperature
error map.
3.2. Single event temperature map: Testing
As mentioned earlier, we have trained the RNN with different architectures using simulated data
for single event estimation with several different temperature values and event width. In order to
test the trained model, we use pristine data (data set has not been seen by the network before)
collected from the above experimental setup with the sensing fiber subjected to a set temperature
of 55
𝑜𝐶
over a spatial extent of 20 m. The temperature map estimated by the uni-RNN,
uni-LSTM, uni-GRU & bi-GRU models are shown in 6a. The corresponding temperature error
calculated by subtractuing the estimated temperature from the set temperature for the different
models is shown in 6b.

As seen from the figure, the uni-RNN & uni-LSTM models are not able to capture the leading
& trailing edge i.e. the transition region of the event. Further, one can observe the presence of
spurious spikes at the baseline for such data. On the other hand, both uni-GRU and bi-GRU are
able to perform reasonably well and capture the transition region. However, the uni-GRU model
exhibits higher levels of error compared to bi-GRU model. In general, the uni-RNN based deep
learning algorithm may be used to model time series data, but it suffers from the problem of
vanishing gradient over long time dependencies. Therefore, it exhibits difficulty in capturing
long term features in the data set. Both LSTM and GRU may be considered as a solution to this
problem of vanishing gradient during back propagation in time. Specifically, LSTM introduces
input and forget gates to deal with how much data is fed to the next time step. GRU is a relatively
recent development in RNNs which replaces the complex operations by LSTM with a simple
update gate for keeping information. Even though simpler than LSTM, GRU has been shown to
be performing better than LSTM in our test cases. Furthermore, bi-GRU model performs better
than uni-GRU because the data from both the previous and next steps are available for estimation
resulting in higher estimation accuracy. To check the estimation efficiency of the bi-GRU model
Fig. 7. Single event with three different temperature magnitude estimation
for a wide range of temperature values, we used experimental data collected for 3 different set
temperatures - one close to the ambient temperature (35 𝑜𝐶), one intermediate temperature (55
𝑜𝐶
) and another at relatively high temperature (90
𝑜𝐶
). The corresponding experimental data as
well as the estimated data using the bi-GRU network is shown in Fig. 7. We observe that the
estimation for the case where the set temperature is close to ambient has slightly higher error due
to the proximity to the noise floor level. For higher temperatures, the error is much lower, which
confirms that the proposed bi-GRU model is not over-fitted and is able to estimate the different
temperature levels accurately.
Recently, an one-dimensional convolutional neural network (1-D CNN) has been demonstrated
to provide excellent performance for a similar distributed temperature sensing application [37].
The 1-D CNN architecture consists of an one dimensional input layer, a convolution layer with
kernel size 3 and one filter channel to extract basic features from the Raman-OTDR data. It
is followed by a series of 18 1-D convolution, rectified linear units (ReLU), and 1-D batch
normalization (BN) with kernel size 7 and 64 filter channels to extract more abstract features.
The last convolution layer consisting of 1 filter with kernel size 3 is given to a fully connected
layer to extract the output. The model is run for 200 epochs with batch size 16 using Adam

optimizer [31] with
𝜂∼
10
−2
, with
𝐿2
-regularization value of 5
𝑥
10
−2
for generalization. In
order to understand the performance of our bi-GRU network with respect to the above 1-D CNN
model, we compared the estimated data obtained from single event raw measurement data.
(a)
(b)
Fig. 8. (a) Performance comparison of 1-D CNN & bi-GRU estimation. The 1-D CNN
estimation exhibits more fluctuations both in the baseline as well as in the event region
compared to bi-GRU, (b) RMS temperature error for bi-GRU estimation is observed to
be lower compared to 1-D CNN.
The single event map with two different temperatures (55
𝑜𝐶
and 90
𝑜𝐶
) estimated by bi-GRU
and 1-D CNN are shown in the 8a. One can observe that both the deep learning models perform
quite well in estimating the set temperature. However, the bi-GRU network seems to be perform
slightly better from the perspective of temperature error, both in the baseline as well as within the
event. This may be confirmed through a plot of the RMS temperature error for the data estimated
through bi-GRU & 1-D CNN with respect to the set temperature.

As mentioned above, a key performance parameter for the Raman-OTDR measurement is the
RMS error in the temperature as a function of the sensing length. This may be quantified by
subtracting the measured temperature from the expected temperature i.e., the set temperature.
One can estimate RMS temperature error by calculating the standard deviation of the temperature
error as a function of sensing length. To extract such information, the standard deviation is
calculated across a fixed sensing length where the temperature is expected to be relatively uniform
i.e. a fixed bin size. In our experimental Raman-OTDR system, one data point corresponds to 2
m of sensing length. The RMS temperature error for the two cases is calculated by observing the
standard deviation of the temperature error over a bin consisting of 31 data points corresponding
to a physical distance of 62 m and plotted the same across the sensing length. The results
illustrated in Fig. 8b clearly shows the lower RMS temperature error for the data estimated
through bi-GRU compared to the 1-D CNN model. It is to be noted though that the computational
complexity 1-D CNN model is less compared to the bi-GRU and hence relatively easy to deploy.
In contrast, the bi-GRU has a memory element which increases the computationally complexity
while providing better performance in terms of the measurement accuracy. We have compared
the computational time (training as well testing time) for bi-GRU and 1-CNN network using
NVIDIA Tesla K80 GPU processor. The time taken for training by the bi-GRU model and
1D-CNN model is 1000 s and 212 s respectively for a 200 length index temperature map. The
time taken for testing the bi-GRU and 1D-CNN model using 5 samples of testing data is 0.056 s
and 0.0473 s respectively. Although the training time for bi-GRU is higher compared to 1-D
CNN, the testing time for both the networks are comparable.
3.3. Multiple event temperature map: Testing
In the work presented above, we discussed the superior performance of bi-GRU model for
estimating the temperature map in the single event case. We extend this to the case of multiple
temperature events in the temperature map. To demonstrate the performance of the network
for multiple temperature event estimation we use the experimental data collected from the
11.5 km long spools of SMF, consisting of two segments of length 200 m each placed in a
temperature-controlled chamber (TCC) at 72
𝑜𝐶
, and another 100 m fiber segment placed in
a refrigerator at -8
𝑜𝐶
(same as that used in 5a). As mentioned earlier, the anti-Stokes trace is
measured from both directions alternatively using the optical switch, and the traces are digitally
averaged over 2
18
iterations. A correlation filtering operation is performed to sanitize the data by
removing outlier noise spikes as discussed earlier, and the corresponding temperature map is
deduced using (14).
As discussed earlier, we employ a threshold based event detection algorithm to locate the
temperature change across the sensing range so that the training and testing process may be
accelerated at the deep learning receiver. We have chosen a nominal value of length index as
330 (
∼
660 m) for training the network. Once the above three events have been detected, a
section corresponding to the chosen length index around each detected event is forwarded to the
bi-GRU model as sequential data. Then the trained bi-GRU network is allowed to estimate the
temperature of the individual events. Finally, the consolidated temperature map is deduced by
stitching the individual estimated events with the baseline data replaced by TVD filtered data.
The multiple event temperature map estimated by bi-GRU is compared with conventional TVD
(
𝛼
, degree of smoothing
∼
0.9 ) and correlation-filtered data is shown in 9a. One can infer that
set temperature and the estimated temperature using bi-GRU model agree very closely across all
the events with an maximum error between set temperature & estimated temperature is 2
𝑜𝐶
at the event near the 10 km location. Although TVD filter eliminates the noise significantly in
the temperature map, it comes at the cost of compromising the spatial resolution of the detected
events and is discussed further in the following section.
The RMS temperature error in the estimated temperature map is obtained by calculating

(a)
(b)
Fig. 9. (a) Multi-event temperature map estimation using bi-GRU network compared
with correlation filtered data and TVD-filtered data (b) RMS temperature error
computed along the length of the sensing fiber for bi-GRU estimation is consistent with
a parabolic fit.
the standard deviation of the temperature error as a function of the length. To extract such
information, the standard deviation of a bin consisting of 100 successive data points is calculated
along the length of fiber and is presented in 9b. The data is seen to fit reasonably well with a
parabolic trend, as expected [33]. Since the loop scheme that is used in our work is the geometric
mean of the anti-Stokes backscattered signal for the pump pulse launched from either ends of
the sensing fiber, the signal to noise ratio (SNR) of the measured trace is worse near either ends
compared to the middle region of the sensing fiber. The significant deviation of the estimated
RMS temperature error with respect to the fit values around the 2 km, 7 km, and 10 km locations
are attributed to the events at those locations. In any case, the RMS temperature error across the

entire length of sensing fiber is found to be less than 0.5
𝑜𝐶
for the bi-GRU estimated temperature
map.
4. Discussion
As discussed in the Introduction section, post-processing of data in distributed fiber sensors is an
important step to ensure good measurement accuracy without compromising spatial resolution.
For example, previous work has established that the noise level from such sensors could be
significantly reduced using a traditional low pass filter or total variational denoising (TVD).
Unfortunately, such a denoising process typically compromises the spatial resolution with which
the event is detected [38]. In other words, it is quite challenging to achieve a perfect matched filter
response from conventional filtering techniques. In contrast, deep learning-based approaches
where the data processing is based on learning achieved from previously measured data itself
and the measurement conditions could potentially help to achieve superior results i.e., the
measurement accuracy could be enhanced without sacrificing spatial resolution.
Let us consider an example from the data from the experiments presented above. As discussed in
Fig. 10. Comparison of the temperature map estimated using the bi-GRU model with
respect to the raw data, the TVD-filtered data, and the data estimated using 1-D CNN.
Sec. 3.1, we have used 80 ns pulses in our experiments, which corresponds to a spatial resolution
of 8 m typically. This is apparent in the TVD filtered data shown in Fig. 10. Note that the spatial
resolution for such data is limited not only by the pulse width but also the receiver bandwidth.
Since such information is known apriori, the network may be trained to address such limitations.
As seen in Fig. 10, the bidirectional-GRU and the 1-D CNN models support a spatial resolution
of 2 m, with the bi-GRU architecture providing slightly lower measurement uncertainty. We
have also run simulations for different pulse widths such as 40 ns and 160 ns, and confirmed
that we observe a similar spatial resolution enhancement for the bi-GRU estimation. From this
perspective, the deep learning approach provides a pathway for achieving a spatial resolution that
is not only as good as that obtained from a matched filter [39], but potentially even better [40].
Another important issue related to the above proposed multi-event estimation algorithm is
the threshold for detecting the events. Lower value of threshold could possibly lead to spurious
event detection, whereas higher value could result in non-detection of events corresponding
to temperature close to the ambient temperature. While the fixing of the threshold based

on the standard deviation of measured data may sound reasonable, this needs to be tested
with more sets of data. Specifically, since the noise level is not uniform across a typical
distributed fiber sensor map it may be prudent to fix the threshold based on the local noise
level. Nevertheless, it is noteworthy that our data-driven approach is valid for any arbitrary
distribution of events, unlike previous work where they have considered only a limited set of events.
Finally, the estimation of any neural network is highly influenced by the target fed to the
network. In our studies, we have used a square temperature profile for the events in the sensing
fiber. This has been influenced by our previous work on the experimental demonstration of
a reference-free Distributed Anti-Stokes Raman Thermometry (DART) scheme for real-time
power line monitoring in overhead power transmission (OPGW/OPC) cables [10]. Temperature
experienced by the optical fiber embedded in the power cable is estimated through a simple heat
transfer model considering the conduction/convection/radiation properties of the power cable
and is experimentally validated to fit a square shape profile. Moreover, such a square temperature
profile is consistent with previous publications over past three decades by several reputed research
groups [7, 12, 41
–
44]. Presently, we are investigating the performance of our deep learning
receiver for fire detection in tunnels where the temperature event profile is not square in shape.
However, that is beyond the scope of the present work.
From this perspective, there is a relevant question - can the shape of an event be predicted
apriori? For example, the measured temperature at any location in the sensing fiber is typically
governed by a set of differential equations corresponding to the physical event. Is it possible
to train the network based on the solutions of these differential equations? This leads to the
possibility of using Physics Inspired Neural Networks (PINNs) [45, 46] for distributed fiber
optic sensors. Such an approach may also ensure that the estimation is more realistic and hence
mitigate any potential failure modes of our deep learning approach.
5. Conclusion
In this work, we demonstrate the ability of a deep learning-based optical receiver to improve
the spatial resolution and measurement accuracy of Raman distributed fiber optic sensors. Our
learning receiver consists of a correlation filtering operation on the experimental data to sanitize
the data by suppressing outlier noise spikes before feeding it to the neural network. The filtered
data is processed through three popular models, i.e. Vanilla Recurrent Unit (RNN), Long Short-
Term Memory (LSTM), Gated Recurrent Unit (GRU) for enhancement of temperature uncertainty
and spatial resolution. The GRU model is observed to provide better performance compared
to RNN and LSTM models. Specifically, we note that bi-GRU architecture outperforms other
neural architectures since it uses data from both previous as well as later time steps for estimation.
In comparison with the highly popular one dimension convolutional neural network (1D-CNN),
the bi-GRU is found to be more effective in providing enhanced measurement accuracy while
maintaining good spatial resolution. One potential roadblock for deep learning-based approaches
is their ability to accurately estimate multiple events at arbitrary locations, since they require
extensive training for such a scenario. To address this issue, we proposed and demonstrated a
threshold-based algorithm to accurately localize the various events, isolate them and then perform
the estimation process. Finally, we demonstrate an improvement in the spatial resolution for
a sample event compared to conventional total variational denoising (TVD) filters, while the
RMS temperature accuracy is maintained within
±
0.5
𝑜𝐶
of the set temperature. It is to be
noted that the proposed approach is not just limited to Raman-OTDR based temperature sensing
but potentially applicable to other distributed fiber optic sensors to improve their measurement
accuracy.

Funding
The authors acknowledge generous funding from the Department of Science and Technology,
Government of India (IMP/2019/000512) in support of the above work.
Acknowledgments
The authors acknowledge technical discussions with A. Bekal, PP. Prasanth, and Manobala
Sankar.
Disclosures
We hereby declare that there is no conflicts of interest in this research work.
References
1. X. Bao and L. Chen, “Recent progress in brillouin scattering based fiber sensors,” Sensors 11, 4152–4187 (2011).
2.
G. Bolognini and A. Hartog, “Raman-based fibre sensors: Trends and applications,” Opt. Fiber Technol.
19
, 678–688
(2013).
3.
A. Ukil, H. Braendle, and P. Krippner, “Distributed temperature sensing: review of technology and applications,”
IEEE Sensors J. 12, 885–892 (2011).
4.
Q. Chai, Y. Luo, J. Ren, J. Zhang, J. Yang, L. Yuan, and G.-D. Peng, “Review on fiber-optic sensing in health
monitoring of power grids,” Opt. Eng. 58, 072007 (2019).
5.
A. Datta, S. Viswamurthy, M. Augustin, N. Gupta, R. Sundaram et al., “Experimental studies using distributed fiber
optic sensor for aircraft structural health monitoring applications,” in International Conference on Fibre Optics and
Photonics, (Optical Society of America, 2014), pp. M3C–4.
6.
L. Zhang, X. Feng, W. Zhang, and X. Liu, “Improving spatial resolution in fiber raman distributed temperature sensor
by using deconvolution algorithm,” Chin. Opt. Lett. 7, 560–563 (2009).
7.
M. K. Saxena, S. Raju, R. Arya, R. Pachori, S. Ravindranath, S. Kher, and S. Oak, “Raman optical fiber distributed
temperature sensor using wavelet transform based simplified signal processing of raman backscattered signals,” Opt.
& Laser Technol. 65, 14–24 (2015).
8.
X. Wang, T. Liu, and H. Wang, “Research on noise reduction approach of raman-based distributed temperature sensor
based on nonlinear filter,” Open J. Appl. Sci. 9, 631–639 (2019).
9.
L. Pan, K. Liu, J. Jiang, C. Ma, M. Tian, and T. Liu, “A de-noising algorithm based on eemd in raman-based
distributed temperature sensor,” IEEE Sensors J. 17, 134–138 (2016).
10.
A. Datta, H. Mamidala, D. Venkitesh, and B. Srinivasan, “Reference-free real-time power line monitoring using
distributed anti-stokes raman thermometry for smart power grids,” IEEE Sensors J. 20, 7044–7052 (2019).
11.
R. W. Schafer, “What is a savitzky-golay filter?[lecture notes],” IEEE Signal processing magazine
28
, 111–117
(2011).
12.
M. A. Soto, J. A. Ramirez, and L. Thevenaz, “Intensifying the response of distributed optical fibre sensors using 2d
and 3d image restoration,” Nat. communications 7, 1–11 (2016).
13. Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” nature 521, 436–444 (2015).
14.
A. Voulodimos, N. Doulamis, A. Doulamis, and E. Protopapadakis, “Deep lear ning for computer vision: A brief
review,” Comput. intelligence neuroscience 2018 (2018).
15.
V. Raj and S. Kalyani, “Backpropagating through the air: Deep learning at physical layer without channel models,”
IEEE Commun. Lett. 22, 2278–2281 (2018).
16.
V. Raj and S. Kalyani, “Design of communication systems using deep learning: A variational inference perspective,”
IEEE Transactions on Cogn. Commun. Netw. 6, 1320–1334 (2020).
17.
B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-end
deep learning of optical fiber communications,” J. Light. Technol. 36, 4843–4855 (2018).
18.
L. C. B. da Silva, J. L. A. Samatelo, M. E. V. Segatto, J. P. Bazzo, J. C. C. da Silva, C. Martelli, and M. J. Pontes,
“Narx neural network model for strong resolution improvement in a distributed temperature sensor,” Appl. optics
57
,
5859–5864 (2018).
19.
H. Wu, C. Zhao, R. Liao, Y. Chang, and M. Tang, “Performance enhancement of rotdr using deep convolutional
neural networks,” in Optical Fiber Sensors, (Optical Society of America, 2018), p. TuE16.
20.
H. Jiang, Q. Zeng, J. Chen, X. Qiu, X. Liu, Z. Chen, and X. Miao, “Wavelength detection of model-sharing fiber
bragg grating sensor networks using long short-term memory neural network,” Opt. express
27
, 20583–20596 (2019).
21.
Y. C. Manie, P.-C. Peng, R.-K. Shiu, Y.-T. Hsu, Y.-Y. Chen, G.-M. Shao, and J. Chiu, “Enhancement of the
multiplexing capacity and measurement accuracy of fbg sensor system using iwdm technique and deep learning
algorithm,” J. Light. Technol. 38, 1589–1603 (2020).
22.
Z. Li, J. Zhang, M. Wang, Y. Zhong, and F. Peng, “Fiber distributed acoustic sensing using convolutional long
short-term memory network: a field test on high-speed railway intrusion detection,” Opt. Express
28
, 2925–2938
(2020).

23.
I. Laarossi, A. P. Franco, O. Conde, M. Quintela, and J. M. López-Higuera, “Rotdr signal enhancement via deep
convolutional denoising autoencoders trained with domain randomization,” in Seventh European Workshop on
Optical Fibre Sensors, vol. 11199 (International Society for Optics and Photonics, 2019), p. 111993N.
24.
Z. Zhang, H. Wu, C. Zhao, and M. Tang, “High-performance raman distributed temperature sensing powered by deep
learning,” J. Light. Technol. (2020).
25.
H. Salehinejad, S. Sankar, J. Barfett, E. Colak, and S. Valaee, “Recent advances in recurrent neural networks,” arXiv
preprint arXiv:1801.01078 (2017).
26.
F. A. Gers, J. Schmidhuber, and F. Cummins, “Learning to forget: continual prediction with lstm,” in 1999 Ninth
International Conference on Artificial Neural Networks ICANN 99. (Conf. Publ. No. 470), vol. 2 (1999), pp. 850–855
vol.2.
27.
K. Greff, R. K. Srivastava, J. Koutník, B. R. Steunebrink, and J. Schmidhuber, “Lstm: A search space odyssey,” IEEE
transactions on neural networks learning systems 28, 2222–2232 (2016).
28.
K. Cho, B. Van Merriënboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y. Bengio, “Learning
phrase representations using rnn encoder-decoder for statistical machine translation,” arXiv preprint arXiv:1406.1078
(2014).
29.
A. Datta, B. K. Lagishetty, and B. Srinivasan, “Performance evaluation of temperature sensing system based on
distributed anti-stokes raman thermometry,” in Optical Sensors, (Optical Society of America, 2010), p. JThA4.
30.
A. Datta, D. Venkitesh, and B. Srinivasan, “Study of fundamental noise limits in distributed anti-stokes raman
thermometry systems,” in Proc. Frontiers Opt. Photon. Conf., (2011).
31. D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).
32. A. Rogers, “Distributed optical-fibre sensing,” Meas. Sci. Technol. 10, R75 (1999).
33.
M. A. Soto, A. Signorini, T. Nannipieri, S. Faralli, G. Bolognini, and F. Di Pasquale, “Impact of loss variations
on double-ended distributed temperature sensors based on raman anti-stokes signal only,” J. Light. Technol.
30
,
1215–1222 (2012).
34.
A. Datta, U. Gajendran, V. Srimal, D. Venkitesh, and B. Srinivasan, “Precise, rugged spectrum-based calibration of
distributed anti-stokes raman thermometry systems,” in 2011 Asia Communications and Photonics Conference and
Exhibition (ACP), (IEEE, 2011), pp. 1–6.
35.
M. Nazarathy, S. A. Newton, R. Giffard, D. Moberly, F. Sischka, W. Trutna, and S. Foster, “Real-time long range
complementary correlation optical time domain reflectometer,” J. Light. Technol. 7, 24–38 (1989).
36.
A. Datta, V. Srimal, and B. Srinivasan, “Performance enhancement of raman optical time domain reflectometer
using golay codes,” in Photonics 2010: Tenth International Conference on Fiber Optics and Photonics, vol. 8173
(International Society for Optics and Photonics, 2011), p. 81731R.
37.
Z. Zhang, H. Wu, C. Zhao, and M. Tang, “High-performance raman distributed temperature sensing powered by deep
learning,” J. Light. Technol. 39, 654–659 (2020).
38.
S. Zaslawski, Z. Yang, and L. Thévenaz, “On the 2d post-processing of brillouin optical time-domain analysis,” J.
Light. Technol. 38, 3723–3736 (2020).
39.
H. Gabbard, M. Williams, F. Hayes, and C. Messenger, “Matching matched filtering with deep networks for
gravitational-wave astronomy,” Phys. review letters 120, 141103 (2018).
40.
D. George and E. A. Huerta, “Deep learning for real-time gravitational wave detection and parameter estimation:
Results with advanced ligo data,” Phys. Lett. B 778, 64–70 (2018).
41.
J. P. Bazzo, F. Mezzadri, E. V. da Silva, D. R. Pipa, C. Martelli, and J. C. C. da Silva, “Thermal imaging of
hydroelectric generator stator using a dts system,” IEEE Sensors J. 15, 6689–6696 (2015).
42.
M. Höbel, J. Ricka, M. Wüthrich, and T. Binkert, “High-resolution distributed temperature sensing with the
multiphoton-timing technique,” Appl. optics 34, 2955–2967 (1995).
43.
D. Hwang, D.-J. Yoon, I.-B. Kwon, D.-C. Seo, and Y. Chung, “Novel auto-correction method in a fiber-optic
distributed-temperature sensor using reflected anti-stokes raman scattering,” Opt. express 18, 9747–9754 (2010).
44.
Z. Wang, J. Chang, S. Zhang, S. Luo, C. Jia, S. Jiang, B. Sun, Y. Liu, X. Liu, and G. Lv, “An improved denoising
method in rdts based on wavelet transform modulus maxima,” IEEE Sensors J. 15, 1061–1067 (2014).
45.
M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework
for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys.
378
,
686–707 (2019).
46.
C. Sherman, R. Mellors, and J. Morris, “Subsurface monitoring via physics-informed deep neural network analysis
of das,” Tech. rep., Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States) (2019).