ORIGINAL RESEARCH
Optimizing Real-Time PM2.5 Predictions
with Deep Belief Networks: Synergistic
Role of Kriging Interpolation
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1
Yinchuan University of Science and Technology, Ningxia 710021, China
2
Xi’an University of Architecture & Technology, Xi’an 710055, China
Submission date: 2025-03-31
Final revision date: 2025-08-29
Acceptance date: 2025-10-02
Online publication date: 2026-03-26
Corresponding author
Chao Bian
Xi’an University of Architecture & Technology, Xi’an 710055, China
KEYWORDS
TOPICS
ABSTRACT
The aim of this study was to improve the accuracy and stability of fine particulate matter (PM2.5)
concentration prediction by integrating a deep belief network (DBN) and the kriging interpolation
algorithm. First, we utilized a binary particle swarm optimization algorithm to construct the evaluation
model, thereby identifying the main factors that most significantly influence the prediction of the
PM2.5 concentration. Second, we thoroughly analyzed the relationship between the real-time PM2.5
concentration in Xi’an City during different months (or days) and various traditional variograms to obtain
training samples for DBN. Finally, on the basis of the selected functions and sample data, we obtained
corresponding kriging model interpolation results. The experimental results showed that, compared with
the prediction errors of the traditional, spatiotemporal, and empirical kriging interpolation methods,
the proposed method yielded a prediction error of only 4.677%. This error was calculated using the Mean
Absolute Percentage Error (MAPE), which reflects the average percentage deviation between predicted
and actual PM2.5 concentrations. MAPE was chosen to facilitate comparison with previous studies in air
quality prediction. This method increases not only the accuracy of the interpolation algorithm but also
its robustness. The core contribution of this study is the introduction of a DBN to optimize the kriging
interpolation algorithm, significantly improving the accuracy and stability of PM2.5 concentration
prediction. We combined climate and meteorological data with a deep learning technique to enable
the model to adaptively select the most appropriate variogram, thereby more accurately simulating
the air quality during different seasons and in various environments. In summary, this study provides
a new and effective method for accurate air quality simulation, which has significant implications
for advancing meteorological research and improving environmental pollution conditions.
CONFLICT OF INTEREST
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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