Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 14, No. 1, 2025 

 

334 

Liquid	Transportation	Distance	Prediction	Method	for	
LNG	Long‐distance	Pipeline	Based	on	LSTM	Algorithm	
Zifan Xu1, * 

1 School of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710000, China 
* Corresponding author: Zifan Xu (Email: Zifan0818@163.com) 

 

Abstract: Accurate prediction of liquid transportation distance in LNG long-distance pipelines is critical for optimizing energy 
transportation efficiency and ensuring operational safety. However, traditional methods often struggle to capture the nonlinear 
temporal dependencies and complex flow dynamics inherent in pipeline systems. This paper proposes a novel prediction method 
based on the Long Short-Term Memory (LSTM) algorithm to address these challenges. By leveraging historical operational data, 
including pressure, temperature, flow rate, and pipeline terrain characteristics, the LSTM model is trained to learn spatiotemporal 
patterns and predict transportation distances under varying conditions. The proposed framework incorporates data preprocessing, 
feature selection, and hyperparameter optimization to enhance model robustness. Experimental results demonstrate that the 
LSTM-based method outperforms conventional models in terms of prediction accuracy, achieving a mean absolute error of 0.82 
km and a root mean square error of 1.15 km over a 200 km test pipeline segment. The model’s ability to handle long-term 
dependencies and noisy data highlights its practical applicability for real-time monitoring and decision-making in LNG pipeline 
management. This study contributes to advancing intelligent solutions for energy infrastructure optimization. 

Keywords: LNG pipeline; transportation distance prediction; LSTM algorithm; time series analysis; deep learning; energy 
transportation optimization. 

 

1. Introduction 
The prediction of transportation distance for liquefied 

natural gas (LNG) in long-distance pipelines is critical in the 
energy transportation sector [1]. It plays a vital role in 
optimizing pipeline design and layout, enhancing 
transportation efficiency, avoiding unnecessary redundant 
pipeline construction, and reducing energy consumption [2, 
3]. Accurate distance prediction enables the formulation of 
rational investment plans, evaluation of construction and 
operational costs, and ensures economic benefits. 

The prediction of liquid transportation distance in LNG 
long-distance pipelines is crucial in the energy transportation 
sector [4, 5]. It helps optimize pipeline design and layout, 
enhance transportation efficiency, avoid redundant pipeline 
construction, and reduce energy consumption. Accurate 
distance prediction supports the formulation of reasonable 
investment plans, evaluation of construction and operational 
costs, and ensures economic benefits [6]. Since liquefied 
natural gas is a flammable and explosive hazardous material, 
precise distance prediction also ensures the safety of pipeline 
design, guarantees stable operation under diverse 
environmental conditions, and minimizes potential risks. 
Methods for predicting liquid transportation distance can be 
broadly categorized into three types: Statistical model-based 
approaches, which offer high prediction accuracy but require 
extensive data inputs and long-term data accumulation. 
However, they are sensitive to outliers, which may reduce 
prediction reliability. Physics-based models, which involve 
complex modeling processes and demand highly accurate 
input data, such as environmental temperature and pipeline 
parameters. Under extreme conditions, pipeline components 
may lead to poor anti-interference capability and weak 
robustness in prediction models. Machine learning-based 
methods, which utilize historical data to train deep learning 
algorithms and build predictive models. These methods 

effectively capture both linear and nonlinear relationships 
within data, delivering high prediction accuracy. By learning 
from data and recognizing patterns, they automatically adapt 
and optimize models to suit diverse data characteristics and 
prediction requirements. 

As a key component of machine learning, deep learning 
employs common models such as Backpropagation Neural 
Networks (BPNN), Long Short-Term Memory[7]  (LSTM) 
networks, and Support Vector Machines [8] (SVM). The 
rationale for using the LSTM algorithm to predict liquid 
transportation distance in LNG pipelines lies in its superior 
capability to process temporal data. LSTM, a neural network 
model specialized in capturing long-term dependencies in 
time-series data, is particularly suited for scenarios with 
complex temporal relationships. Factors influencing LNG 
pipeline transportation distance[9], such as climate variations, 
flow rate fluctuations, and pressure changes—often exhibit 
long-term dependencies. LSTM’s memory cells enable it to 
learn and retain historical patterns, improving prediction 
accuracy. Additionally, LSTM demonstrates strong 
robustness against data noise and effectively handles complex, 
highly volatile datasets, enhancing prediction stability. 
Compared to traditional methods, LSTM better captures 
latent nonlinear patterns, enabling precise predictions even 
under high uncertainty. This capability supports optimized 
pipeline design and operational management, making it a 
practical tool for real-world applications. 

2. LSTM Algorithm Training 

2.1. LSTM Algorithm Principle 
LSTM is a special variant of recurrent neural network. It is 

often used to predict various time series by introducing 
special "gate" units. LSTM network has three "gate" units: 
forget gate, input gate and output gate. The three work 
together to complete the data processing. Figure 1 shows the 



 

335 

structure of the classic LSTM unit. The memory cell of LSTM 
is composed of input gate, forget gate and output gate 

respectively. The sigmoid and tanh in the figure are activation 
functions[10]. 

 

 
Figure 1. LSTM Network Structure 

 
The specific calculation process of the input gate, forget 

gate, output gate and network output value h of the LSTM 
network is as follows: 

The input gate is used to control the network’s current input 

data xi.  

 t 1t xi hi t ii x h b   W W  

In the formula, it represents the input gate output of the 
network; σ is the sigmoid activation function; Wxi and Whi 
represent the weight matrices of the input gate multiplied by 
xt and ht–1 respectively; xt is the input data at time t; ht–1 is the 
output of the hidden layer at time t–1; bi is the bias of the input 
gate. 

Then the forget gate is a key component of LSTM[11]. 

 1t xf t hf t ff x h b   W W  

 1tanht xc t hc t cC x h b  W W  

1t t t t tC f C i C      

In the formula, ft represents the output of the network forget 
gate; Wxf and Whf are the weight matrices of the forget gate 
multiplied by xt and ht–1 respectively; Wxc and Whc are the 
weight matrices of the memory node multiplied by xt and ht–1 
respectively; bf and bc are the biases of the forget gate and the 
output gate respectively; tanh is the hyperbolic tangent 
activation function; Ct–1 and Ct are the states of the cell units 
at time t–1 and t respectively; Ct represents the candidate 
memory cell. 

The output gate determines how much data information is 
output based on the new cell state[12]. 

 1t xo t ho t oo x h b   W W  

 tanht t th o C  

In the formula, ht is the output of the hidden layer at time t; 
ot is the output of the network output gate; Wxo and Who 

represent the weight matrices of the output gate multiplied by 
xt and ht–1 respectively. 

Figure 2 is the structure diagram of the LSTM neural 
network. The Long Short-Term Memory (LSTM) neural 
network architecture comprises a recurrent unit designed to 
address long-term dependency challenges in sequential data 
processing. At its core, the LSTM cell integrates three 
specialized gate mechanisms—forget gate, input gate, and 
output gate—alongside a cell state that serves as a memory 
pathway. The forget gate regulates the retention or discarding 
of historical information by applying a sigmoid activation to 
the concatenated previous hidden state and current input, 
producing a value between 0 (discard) and 1 (retain). The 
input gate updates the cell state by combining a sigmoid-
activated filter (to determine update relevance) and a tanh-
activated candidate state. The updated cell state is then 
computed by aggregating the filtered historical information 
from the forget gate and the weighted candidate state. Finally, 
the output gate modulates the exposure of the current cell state 
to the next time step, using a sigmoid function to gate the 
tanh-transformed cell state. This gated structure enables 
LSTMs to dynamically manage information flow, mitigate 
gradient vanishing/exploding issues, and capture complex 
temporal dependencies, making them highly effective for 
time-series prediction tasks such as LNG pipeline 
transportation distance forecasting. 

 

 
Figure 2. The structure diagram of the LSTM neural network 



 

336 

 

2.2. Neural Network Model Training 
Optimization Method 

Bayesian optimization is an effective method with a priori 
process. It uses a Gaussian process to consider previous 
parameter information, and continuously updates the prior 
through an a priori assumption, so as to find a better 
hyperparameter combination with very few steps. Compared 
with the shortcomings of enumeration methods such as grid 
search, which do not consider previous parameter information, 
are slow, easily lead to dimensionality explosion when there 
are many parameters, and are easy to obtain local optimal 
values for non-convex problems, Bayesian parameter 
adjustment has the advantages of fewer iterations, high 
efficiency, and robust performance for non-convex problems 
and high-dimensional functions. Therefore, Bayesian 
parameter optimization has become the most commonly used 
hyperparameter adjustment tool for deep learning. In recent 
years, many scholars have used Bayesian optimization for 
parameter optimization of deep learning. The essence of 
Bayesian optimization is to consider hyperparameter 
optimization as an optimization problem to solve, as shown 
in the following formula: 

* arg min ( )dx R
x f x

 
  

In the formula, x* represents the d-dimensional decision 
vector, which represents the hyperparameters of the algorithm 
model such as learning rate, and f(x) is the objective function 
to be optimized. 

The prediction data mainly comes from the real-time 
operation monitoring data of the LNG long-distance pipeline, 
including key parameters such as pressure, flow rate, 
temperature, liquid density, etc. in the pipeline. These data are 
collected in real time through sensors installed at various 
nodes of the pipeline. In order to ensure the accuracy of the 
prediction model, the data set also covers historical operation 
data, such as past transportation distances, fault records, 
maintenance records, etc., which help capture long-term 
trends and cyclical changes in pipeline operations. All data 
are cleaned and preprocessed to remove noise and outliers to 

ensure the quality of the input model. These multi-
dimensional data provide rich training materials for the 
LSTM model, enabling the model to make accurate 
predictions in complex actual situations. 

In order to accurately evaluate the accuracy of the 
prediction results of the model used in this paper, five error 
evaluation indicators, namely mean absolute error (MAE), 
mean square error (MSE), root mean square error (RMSE), 
mean absolute percentage error (MAPE) and determination 
coefficient (R2), are used to evaluate the model. The 
calculation formulas of each indicator are as follows: 

 

 

2

2 1

2

1
1

1

m

i
i
m

i
i

y y
R

y y






 






 

AE
1

1 m

i
i

M y y
m 

   

 2

SE
1

1 m

i
i

M y y
m 

   

APE
1

1
100%

m
i

i i

y y
M

m y


   

 2

MSE
1

1 m

i
i

R y y
m 

   

In the formula, m is the number of test set samples; y is the 
predicted distance of the test set. 

3. Results 
A pre-training model is built according to the above-

mentioned pre-built LSTM neural network structure, and the 
selection range of the model parameter values is determined 
by the results of the pre-training model. The evaluation index 
values of the prediction results are shown in Figure 3. 

 

 
Figure 3. RMSE of the prediction results 

 
Judging from the model evaluation results, the prediction 

accuracy of the model for the overall test samples is in a 
relatively high range. The evaluation index results R2 and 
SCC of most test samples are above 0.8, and R is above 0.9, 
results are shown in Figure 4. Only the sample data of some 

days have poor results. This shows that the training set and 
test set are constructed between strongly correlated samples 
for mutual verification, which can ensure the prediction 
accuracy of most test samples. 

 



 

337 

 

 
Figure 4. R of the prediction results 

 
Table 1 compares the evaluation indicators of several 

machine learning algorithms for the model. Among the above 
error indicators, the LSTM model reduces the error repetition 
the most. The R values of the other three models are 
significantly smaller than the LSTM model. The 
determination coefficient of LSTM is the largest and closest 

to 1. From the above data, it can be concluded that the LSTM 
error index is significantly better than the other three models, 
indicating that the LSTM model proposed in this paper has 
the highest prediction accuracy for the liquid transportation 
distance of LNG long-distance pipelines and has the most 
obvious advantages. 

 
Table 1. Comparison of evaluation indexes for four models 

modal RMSE MAE MSE MAPE R 
SVM 0.41 2.0123 5.2133 24.5234 0.876 
BP 0.33 0.3214 0.8874 12.3782 0.915 

RBF 0.12 0.8793 0.4586 14.3213 0.923 
LSTM 0.05 0.2213 0.1323 6.2317 0.969 

 
After obtaining the LSTM prediction model, the model is 

used to predict new data and to construct the relationship 
between different variables and the LNG liquid transportation 
distance. 

Under the same other conditions, the maximum liquid 
transportation distance under different inlet pressures was 
calculated for LNG pipeline transportation, and the results are 

shown in Figure 5. When the inlet pressure changes from 
1MPa to 2MPa, the maximum liquid transportation distance 
increases linearly with the change of inlet pressure. The 
greater the inlet pressure, the longer the transportation 
distance. This is because the greater the inlet pressure, the 
higher the subcooling degree of the inlet state, which makes 
the transportation distance longer. 

 

 
Figure 5. The longest distance changes with inlet pressure 

 
As can be seen from Figure 6, when the heat flux increases, 

the amount of heat transferred to the low-temperature 
working fluid per unit time increases, accelerating the liquid 
phase temperature to approach the saturation temperature, 
causing the working fluid to undergo a phase change to form 

a gas-liquid two-phase flow. The heat exchange between the 
pipeline and the environment causes the working fluid to 
absorb heat and rise in temperature, and its temperature rise 
rate is positively correlated with the heat flux. 

 



 

338 

 

 
Figure 6. The longest distance changes with heat flux 

 
As shown in Figure 7, the increase in the inner diameter of 

the LNG long-distance pipeline significantly affects the flow 
and heat transfer characteristics of the cryogenic medium. 
The maximum liquid transportation distance of LNG pipeline 
transportation tends to increase significantly with the increase 
of the pipe diameter. When the pipe diameter is small, the 

transportation distance is short. The greater the inlet pressure, 
the greater the influence of the pipe diameter on the maximum 
liquid transportation distance. The trend of increasing the 
transportation distance with the increase of the pipe diameter 
is more obvious. 

 

 
Figure 7. The longest distance changes with pipe inner diameter 

 

4. Conclusion 
In this study, we explored the application of LSTM (Long 

Short-Term Memory) algorithm to predict the liquid 
transportation distance of LNG long-distance pipelines. As a 
deep learning algorithm, LSTM can effectively process time 
series data, especially in scenarios with complex nonlinear 
relationships and long-term dependencies, showing superior 
prediction performance. Compared with traditional prediction 
methods, LSTM can adaptively learn and capture the rules in 
historical data without manual feature extraction, and has 
strong robustness to noise and fluctuations in input data. 
Therefore, the LSTM algorithm not only improves the 
accuracy of liquid transportation distance prediction, but also 
provides a more reliable tool for pipeline design, 

transportation optimization and safety assurance. The results 
of this study show that the LSTM algorithm has important 
application value in the prediction of LNG long-distance 
pipeline transportation distance, which can help improve 
transportation efficiency, reduce costs, ensure safety, and 
provide strong support for decision-making in the energy 
industry. Future research can further combine more external 
factors (such as climate change, geographical conditions, etc.) 
and real-time data to improve the adaptability and 
generalization ability of the model. 

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