Entropy Theory Research Articles

A node deployment and resource optimization method for CPDS based on cloud‐fog‐edge collaboration

AbstractWith the development of the Internet of Things (IoT) in power distribution and the advancement of energy information integration technologies, the explosive growth in network data volume caused by massive terminal devices connecting to the power distribution network has become a significant challenge. Multi‐terminal collaborative computing is a key approach to addressing issues such as high latency and high energy consumption. In this article, fog computing is introduced into the computing network of the power distribution system, and a cloud‐fog‐edge collaborative computing architecture for intelligent power distribution networks is proposed. Within this framework, an improved weighted K‐means method based on information entropy theory is presented for node partitioning. Subsequently, an improved multi‐objective particle swarm optimization algorithm (MWM‐MOPSO) is employed to solve the task resource allocation problem. Finally, the effectiveness of the proposed architecture and allocation strategy is validated through simulations on the OPNET and PureEdgeSim platforms. The results demonstrate that, compared to traditional cloud‐edge service architectures, the proposed architecture and task offloading scheme achieve better performance in terms of processing latency and energy consumption.

GTDI: a game-theory-based integrated drought index implying hazard-causing and hazard-bearing impact change

Abstract. Developing an effective and reliable integrated drought index is crucial for tracking and identifying droughts. The study employs game theory to create a spatially variable weight drought index (game-theory-based drought index, GTDI) by combining two single-type indices: an agricultural drought index (standardized soil moisture index, SSMI), which implies drought hazard-bearing conditions, and a meteorological drought index (standardized precipitation evapotranspiration index, SPEI), which implies drought hazard-causing conditions. In addition, the entropy-theory-based drought index (ETDI) is introduced to incorporate a spatial comparison with GTDI to illustrate the rationality of gaming weight integration, as both entropy theory and game theory belong to linear combination methods in the development of the integrated drought index and entropy theory has been applied in related research. Leaf area index (LAI) data are employed to confirm the reliability of GTDI in identifying drought by comparing it with SPEI, SSMI, and ETDI. Furthermore, a comparative analysis is conducted on the temporal trajectories and spatial evolution of the GTDI-identified drought to discuss GTDI's level of advancement in monitoring changes in hazard-causing and hazard-bearing impacts. The results show that GTDI has a very high correlation with single-type drought indices (SPEI and SSMI), and its gaming weight integration is more logical and trustworthy than that of ETDI. As a result, it outperforms ETDI, SPEI, and SSMI in recognizing drought spatiotemporally and is projected to replace single-type drought indices to provide a more accurate picture of actual drought. Additionally, GTDI exhibits the gaming feature, indicating a distinct benefit in monitoring changes in hazard-causing and hazard-bearing impacts. The case studies show that drought events in the Wei River basin are dominated by a lack of precipitation. The hazard-causing index, SPEI, dominates the early stages of a drought event, whereas the hazard-bearing index, SSMI, dominates the later stages. This study surely serves as a helpful reference for the development of integrated drought indices as well as regional drought prevention and monitoring.

A two-stage framework for site selection of deep-sea offshore wind-to-hydrogen projects based on GIS - MULTIMOORA method under Pythagorean triangular fuzzy environment

Constructing deep-sea offshore wind-to-hydrogen projects (DS-OWHP) is crucial to solve the problem of offshore electricity storage and consumption. Addressing the uncertainty of the decision-making environment, and the lack of a comprehensive indicator system, this paper proposes a two-stage decision framework based on Geographic Information System (GIS). In the first stage, GIS is used to analyze the suitability of study area and identify alternative sites. In the second stage, the fuzzy MCDM method is used to further optimize alternative sites. Firstly, a comprehensive evaluation indicator system is established, and the Pythagorean Triangular Fuzzy Number (PTFN) is used to describe evaluation information. Then, a combination of stepwise weight assessment ratio analysis (SWARA), entropy, and game theory is used to determine weights, and the Multi-Objective Optimization on the basis of a Ratio Analysis plus the Full Multipli-cative form (MULTIMOORA) method is used to rank alternative sites. Finally, the feasibility of framework is proved through a case study in Guangdong Province. The results show that average wind speed has the highest weight of 0.149, and alternative site A2 which is close to zhuahai is the optimal choice. Through sensitivity analysis and comparative analysis, the reliability and stability of proposed model is verified.

An integrated framework of deep learning and entropy theory for enhanced high-dimensional permeability field identification in heterogeneous aquifers

Accurately estimating high-dimensional permeability (k) fields through data assimilation is critical for minimizing uncertainties in groundwater flow and solute transport simulations. However, designing an effective monitoring network to obtain diverse system responses in heterogeneous aquifers for data assimilation presents significant challenges. To investigate the influence of different measurement types (hydraulic heads, solute concentrations, and permeability) and monitoring strategies on the accuracy of permeability characterization, this study integrates a deep learning-based surrogate modeling approach and the entropy-based maximum information minimum redundancy (MIMR) monitoring design criterion into a data assimilation framework. An ensemble MIMR-optimized method is developed to provide more comprehensive monitoring information and avoid missing key information due to the randomness of stochastic response datasets in entropy analysis. A numerical case of solute transport with log-Gaussian permeability fields is presented, with twelve scenarios designed by combining different measurement types and monitoring strategies. The results demonstrated that the proposed ensemble MIMR-optimized method significantly improved the k-field estimates compared to the conventional MIMR method. Additionally, high prediction accuracy in forward modeling is essential for ensuring reliable inversion results, especially for observation data with strong nonlinearity. The findings of this study enhance our understanding and management of k-field estimation in heterogeneous aquifers, contributing to the development of more robust inversion frameworks for general data assimilation tasks.

Exploring the effect of Cr and Mn on the intrinsic strength of the tensile properties of FeCoNi, FeCoNiMn, FeCoNiCr, and FeCoNiCrMn multi-principal element alloys using in-situ EBSD

As the composition elements in multi-principal element alloys increase, it can bring excellent mechanical properties. However, the strengthening mechanism of the additional element is still unclear. In this work, we establish a method based on the in-situ EBSD technology to explore the possible effect of additional elements on the intrinsic strength of tensile properties. We prepared four different multi-principal element alloys, including FeCoNi, FeCoNiMn, FeCoNiCr, and FeCoNiCrMn with similar initial status. We systematically investigated the evolution of the microstructure, dislocation density, twin boundary, grain size, and element distribution during the tensile process by in-situ EBSD and EDS. By carefully analyzing the results of four different multi-principal element alloys, the strength effects of the solid-solution hardening, grain-boundary hardening, twin boundary hardening, precipitate hardening, and dislocation hardening were peeled. The effect of the Cr and Mn element addition on the intrinsic strength can be explored. It is found that the element addition indeed increases the intrinsic strength from quaternary to quinary but not very clear from ternary to quaternary no matter Cr or Mn, which indicated that the intrinsic strength was more related to the number of elements in the alloy than to which element was present. This can be explained using the mixing entropy theory, which states that the intrinsic strength is enhanced when the mixing entropy is over a threshold between the MEA and HEA. This paper presents a method to study the individual factors affecting the tensile properties, which can help other researchers to better investigate HEA.

Risk analysis of accident-causing evolution in chemical laboratory based on complex network

Chemical laboratories usually have many high risks from various dangerous chemicals, dangerous devices, and experimental operators involved in the laboratory. Once a severe accident occurs, the accident consequence will significantly impact scientific research innovation and social progress. Aiming at laboratory safety problems, an accident evolution model is established to reveal the critical accident-causing factors and the most likely evolutionary path of accidents in the process of accident evolution. Firstly, the 24 model is used to identify the cause factors of laboratory accidents and the causal relationship between factors. Then, the complex network model of laboratory accident evolution is constructed with accident-causing factors as nodes and causal relationships between factors as edges. Secondly, using the TOPSIS method, four typical complex network characteristic indexes, including degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality, are constructed into a comprehensive evaluation index to reveal the key influencing factors in the accident evolution process. Finally, the fuzzy number is introduced to quantify the uncertainty of the accident evolution path. The most likely evolutionary path is obtained through the Dijkstra and risk entropy theory. Based on the data of 151 laboratory accidents from 2001 to 2022, the accident evolution analysis of chemical laboratories was carried out. The evolution results show that the maximum probability value is the evolution path of fire accidents, and the minimum probability value is the evolution path of electric shock accidents, which accords with the general statistical law of accidents. When applied to the actual laboratory, the safety management level of the laboratory can be effectively improved by controlling the key influencing factors and cutting off the accident evolution path.

Research on Critical Quality Feature Recognition and Quality Prediction Method of Machining Based on Information Entropy and XGBoost Hyperparameter Optimization

To address the problem of predicting machining quality for critical features in the manufacturing process of mechanical products, a method that combines information entropy and XGBoost (version 2.1.1) hyperparameter optimization is proposed. Initially, machining data of mechanical products are analyzed based on information entropy theory to identify critical quality characteristics. Subsequently, a quality prediction model for these critical features is established using the XGBoost machine learning framework. The model’s hyperparameters are then optimized through Bayesian optimization. This method is applied as a case study to a medium-speed marine diesel engine piston. After the critical quality characteristics in the machining process are identified, the machining quality of these vital characteristics is predicted, and the results are compared with those obtained from a machine learning model without hyperparameter optimization. The findings demonstrate that the proposed method effectively predicts the machining quality of mechanical products.

Searching for long timescales without fine tuning.

Animal behavior occurs on timescales much longer than the response times of individual neurons. In many cases, it is plausible that these long timescales emerge from the recurrent dynamics of electrical activity in networks of neurons. In linear models, timescales are set by the eigenvalues of a dynamical matrix whose elements measure the strengths of synaptic connections between neurons. It is not clear to what extent these matrix elements need to be tuned to generate long timescales; in some cases, one needs not just a single long timescale but a whole range. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to construct ensembles of networks, exploring the constraints required for long timescales to become generic. We argue that a single long timescale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning. Langevin dynamics that generates patterns of synaptic connections drawn from these ensembles involves a combination of Hebbian learning and activity-dependent synaptic scaling.

Development and application of a comprehensive evaluation index system for groundwater quality evolution patterns

In recent years, driven by rapid socio-economic development and intensified human activities, the groundwater quality has exhibited a concerning trend of degradation. The challenge lies in integrating the impacts of both natural and anthropogenic factors to establish a scientific evaluation framework for the evolution of groundwater quality. This study adopts the model of driving forces – pressures – state – impacts – responses (DPSIR) proposed by the European Environment Agency, in conjunction with the Analytic Hierarchy Process (AHP) and Information Entropy Theory (IET), and the Water Quality Index (WQI) evaluation methods, to construct an evaluation index system for groundwater quality evolution that encompasses driving forces, state, and response systems. Initially, twelve indicators relevant to groundwater quality are quantified by screening across three systems, and a functional relationship between the categorization and scoring of each indicator is established. Subsequently, the weights for each system and indicator are obtained through the AHP, and the objective weights of the indicators are determined using the IET. The scores of each indicator are then comprehensively calculated. Finally, based on the defined types of groundwater quality evolution patterns, an integrated assessment of the evolution of groundwater quality over various time periods is conducted. Taking the Shijiazhuang region as a case study and analyzing the hydrochemical data of groundwater from 1985 to 2015, the results indicate a shift in the groundwater quality evolution pattern from one dominated by natural factors to one primarily influenced by human activities (The comprehensive score of the evaluation index system has increased from 1.84 to 3.25). Among these, the application of fertilizers emerges as the most important driving factors affecting groundwater quality. Particularly, nitrate and total hardness (TH) have emerged as the most salient indicators of quality degradation, with a significant escalation in their composite scores. At the outset, nitrate registered a score of 0.408, while TH scored 0.326; yet, these values have sharply ascended to 0.716 and 0.467, respectively, by the advanced stage. The study concludes with a discussion on the accuracy, strengths, limitations, and applicability of the evaluation index system. The establishment of this evaluation framework provides a scientific basis for the management and protection of groundwater resources and serves as a reference for identifying groundwater quality evolution patterns in other regions.

Information density threshold of urban road traffic signs based on visual comfort

The content and density of traffic signs directly affect the operation of urban road traffic and drivers. To overcome the limitations of quantitative research on the density threshold of traffic signs on urban roads, a real vehicle experiment was conducted to record the psychological characteristics of drivers. Four psychological parameters of drivers—pupil area, fixation intensity, heart rate change rate, and heart rate variability—were explored. Subsequently, principal component analysis was used to present a new index, S, divided into 5 grade scales, to represent the driving visual comfort level. The information entropy theory was applied to quantify the amount of information on road traffic signs that are included in driving tests, and a regression relationship between the traffic sign information and comfort index S was established. The visual psychological load thresholds for different comfort levels were −2.289≤S < −1.526 for very comfortable, 1.526≤S < −0.763 for relatively comfortable, −0.763≤S ≤ 0.763 for comfortable, 0.763<S ≤ 1.526 for uncomfortable, and 1.526<S ≤ 2.289 for very uncomfortable. To maintain the visual comfort of drivers, the information density of traffic signs should be less than 0.373 bits/m and the maximum information density of traffic signs should not exceed 0.507 bits/m. This conclusion provides a reference for the rational layout of traffic signs on urban roads.

Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model

The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document} that are constrained to a scaled (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-sphere, equivalently a scaled (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables.

An overview of the development and applications of information entropy

With information entropy gradually taking the lead in modern information theory development, it begins to hold greater influence over multiple research areas as well as technology innovation. This paper aims to clarify peoples confusion with the development of entropy theory and provide a brief overview of the origin of entropy theory, including the original Shannons proposal, variants such as relative entropy and conditional entropy, and entropy concepts proposed by other scientists, such as Rnyi Tsallis entropy. The paper also includes the current application of entropy, studies hotspots, and predicts future entropy development trends. This research paper is able to add more coherence and consistency to information entropys development, helping more people to better understand the concept of entropy and its derivation. At the same time, with hotspots of entropy fields of study, this paper hopes to attract more people to devote themselves to studying entropy-related fields, and boost technological development.

Crucial time of emergency monitoring for reliable numerical pollution source identification

The Pollution source identification (PSI) is an important issue on river water quality management especially for urban receiving water. Numerical inversion method is theoretically an effective PSI technique, which employs monitored downstream pollutant breakthrough curves to identify the pollution source. In practice, it is important to know how much monitoring data should be accumulated to provide PSI results with acceptable accuracy and uncertainty. However, no literature reports on this key point and it seriously handers the numerical PSI technology to mature practical applications. To seek a monitoring guideline for PSI, we conducted extensively numerical experiments for single-point source instantaneous release taking Bayesian-MCMC method as the baseline inversion technique. The crucial time (Tc) phenomenon was found during the data accumulation process for Bayesian source inversion. After Tc, estimated source parameters subsequent sustained low error levels and uncertainty convergence. Results shown the presence of Tc impacted by the number and location of monitoring sections, while monitoring frequency and data error do not. Under different river hydrodynamic conditions, relative crucial time (Λ) is determined by the river's Peclet number, and minimum effective Λ was controlled by dispersion coefficient (Dx). Analytic spatial structure of Λ(U, Dx) was uncovered and this relationship successfully explained by the information entropy theory. Based on these findings, a novel design method of PSI emergency monitoring network for preparedness plan and a practical framework of PSI for emergency response were established. These findings fill the important knowledge gap in PSI applications and the guidelines provide valuable references for river water quality management.

Study on crack initiation mechanism of notched TC4 titanium alloy plate based on acoustic emission information entropy

ABSTRACT Titanium alloys are widely used in high-end manufacturing fields such as aerospace and nuclear energy due to their excellent mechanical properties and corrosion resistance, but it is prone to cracking under load, seriously affecting its performance and safety. Therefore, studying the crack initiation process of titanium alloys is of great significance for improving their service life and safety. In this study, TC4 titanium alloy material is taken as the research object, and the crack emergence mechanism during its tensile fracture process is investigated by combining tensile test and AE test. The experiments were carried out under displacement-controlled conditions, and crack emergence detection was carried out by two methods: AE characterisation parameters and AE information entropy, and SEM was used to observe and analyse the specimen fracture. The results indicate that the AE characteristic parameters of different notched specimens have the same evolution pattern, and this method can be used to predict crack initiation, but there is a certain degree of uncertainty. Compared with the former, the information entropy theory can more accurately predict crack initiation. Therefore, the analysis of the entropy of AE information can be used as a highly practical real-time condition detection method to provide effective detection means for engineering applications.

Estimating velocity distribution and flood discharge at river bridges using entropy theory – insights from computational fluid dynamics flow fields

Abstract. Estimating the flow velocity and discharge in rivers is of particular interest for monitoring, modeling, and research purposes. Instruments for measuring water level and surface velocity are generally mounted on bridge decks, and this poses a challenge because the bridge structure, with piers and abutments, can perturb the flow field. The current research aims to investigate the applicability of entropy theory to estimate the velocity distribution and the discharge in the vicinity of river bridges. For this purpose, a computational fluid dynamics (CFD) model is used to obtain three-dimensional flow fields along a stretch of the Paglia River (central Italy), where a historical multi-arch bridge strongly affects flood flows. The input data for the entropy model include the cross-sectional bathymetry and the surface velocity provided by the numerical simulations. A total of 12 samples, including three different flow conditions at four cross-sections, one upstream and three downstream of the bridge, are considered. It is found that the entropy model can be reliably applied upstream of the bridge, also when forced with a single (i.e., the maximum) value of the surface velocity, with errors on total discharge below 13 % in the considered case. By contrast, downstream of the bridge, the wakes generated by the bridge piers strongly affect the velocity distribution, both in the spanwise and in the vertical directions and for very long distances. Here, notwithstanding the complex and multimodal spanwise distribution of flow velocity, the entropy model estimates the discharge with error lower than 8 % if forced with the river-wide distribution of the surface velocity. The present study has important implications for the optimal positioning of sensors and suggests the potential of using CFD modeling and entropy theory jointly to foster greater knowledge of river systems.

Infrared and Harsh Light Visible Image Fusion Using an Environmental Light Perception Network.

The complementary combination of emphasizing target objects in infrared images and rich texture details in visible images can effectively enhance the information entropy of fused images, thereby providing substantial assistance for downstream composite high-level vision tasks, such as nighttime vehicle intelligent driving. However, mainstream fusion algorithms lack specific research on the contradiction between the low information entropy and high pixel intensity of visible images under harsh light nighttime road environments. As a result, fusion algorithms that perform well in normal conditions can only produce low information entropy fusion images similar to the information distribution of visible images under harsh light interference. In response to these problems, we designed an image fusion network resilient to harsh light environment interference, incorporating entropy and information theory principles to enhance robustness and information retention. Specifically, an edge feature extraction module was designed to extract key edge features of salient targets to optimize fusion information entropy. Additionally, a harsh light environment aware (HLEA) module was proposed to avoid the decrease in fusion image quality caused by the contradiction between low information entropy and high pixel intensity based on the information distribution characteristics of harsh light visible images. Finally, an edge-guided hierarchical fusion (EGHF) module was designed to achieve robust feature fusion, minimizing irrelevant noise entropy and maximizing useful information entropy. Extensive experiments demonstrate that, compared to other advanced algorithms, the method proposed fusion results contain more useful information and have significant advantages in high-level vision tasks under harsh nighttime lighting conditions.

Similarity searching for wafer bin maps by measuring shape, location, and size similarities of defect patterns

A wafer bin map (WBM) is a visual representation of the spatial distribution of defective chips on a wafer. WBMs showing specific defect patterns are usually a result of process-assignable causes; thus, it is important to identify them to eliminate assignable causes. With advances in semiconductor manufacturing technology, identifying new defect patterns, and diagnosing their causes have become critical. However, most existing methods for WBM analysis use a supervised learning approach, which only detects previously known defect patterns. The similarity-search approach is a suitable alternative for defining new defect patterns. The proposed method uses an unsupervised approach to search for similar WBMs by measuring the similarities of three spatial features of defect patterns–shape, location, and size–which are useful for defining new defect patterns and diagnosing their causes. These three similarities are achieved using tensor voting and the mountain function for shape similarity, Euclidean distance for location similarity, and a combination of defect count and average radius for size similarity. The overall similarity was assessed using the weighted average of the three similarities. The weights are determined by quantifying the uncertainty of each similarity based on information entropy theory to better distinguish between similar patterns. The experimental results demonstrate the effectiveness of the proposed method compared to existing methods and highlight its capability to identify and describe the spatial features of defect patterns.

Generalized Core Functions of Maximum Entropy Theory of Ecology

Core distributions of Maximum Entropy Theory of Ecology (METE) are the Spatial Structure Function (SSF) and the Ecosystem Structure Function (ESF). SSF is a by-species prediction of the clustering of individuals over space. ESF is a kind of container function that describes the probability space of how abundances are assigned to species and how metabolic energy is parti-tioned over individuals in a community. In this study, these core functions of METE are generalized by deriving the corresponding functions in the Tsallis q-entropy. Derivation used the method of Lagrange multipliers. The generalized SSF and ESF are expressed in terms of the q-exponential function. Numerical examples are provided to illustrate the generalized SSF.

Risk analysis and assessment method for infectious diseases based on information entropy theory

Infectious diseases risk is directly related to human life safety. After the COVID-19 pandemic, people have paid unprecedented attention to the risk of infectious diseases. Compared with treatment after the outbreak of the epidemic, identifying the influencing factors of infectious disease risk and quantitatively analyzing and assessing infectious disease risk before the outbreak of the epidemic plays an equally important role. This article focuses on the risk of irregular outbreaks of infectious diseases. On the one hand, a method based on information gain is proposed to calculate the weight of environmental factors directly related to infectious disease risk, to clarify the correlation between environmental factors and infectious disease risk. On the other hand, the risk calculation method based on risk weight number is proposed to calculate the risk level of different infectious diseases under the influence of specific environmental factors. Finally, the effectiveness and feasibility of the proposed method are verified through case analysis and discussion. By comparing it with other risk assessment methods, the advantages and disadvantages of the proposed method are demonstrated.

Effects of longitudinal ventilation and GHEs on geothermal energy extraction and HRC in high geothermal tunnels

With the excavation of deep tunnels, the problem of high geothermal heat is becoming more and more prominent. However, high geothermal heat can be utilized as a renewable energy source. In order to effectively reduce thermal damage and utilize geothermal energy, it is necessary to study the effects of longitudinal ventilation and ground heat exchanges (GHEs) on the heat-regulating circle of the surrounding rock. In this study, an experimental platform was designed and constructed in a laboratory to test different geothermal heat exchanger flow rates and ventilation air velocities and to monitor the heat extraction from the geothermal heat exchanger, the ventilation heat extraction, and the temperature field of the surrounding rock. The experimental results show that when the temperature field tends to be stabilized, the flow rate and ventilation velocity of the GHEs are closely related to the temperature distribution of the surrounding rock. The initial heat storage and heat replenishment capacity of the enclosing rock have a great influence on the heat extraction efficiency. Ventilation has a great influence on the heat extraction efficiency of GHEs, and the optimal wind speed range is 1.5∼2 m/s considering the cooling and heat extraction efficiency. When the wind speed is less than 1.5 m/s, the heat extraction efficiency of GHEs can be improved, and the total heat transfer can be increased. When the wind speed is greater than 1.5 m/s, the situation is reversed. The thermal entropy theory for circular tunnels is not fully applicable to arched tunnels containing GHEs.