esa-sceva/satcom-chunk-collection huggingface dataset:
# Remaining Useful Life Prediction of Cutting Tools Using an Inverse Gaussian Process Model
## 1 Introduction
Thus, the precision here refers to the precision of the cutting process. The influence of the cutting tool on cutting precision is directly reflected on the surface of a workpiece, which mainly has a significant influence on surface roughness. Therefore, the roughness of cutting surface is regarded as the index of cutting precision in this study. The time that the tool can normally work while still meeting the surface roughness requirements is defined as the RUL. Compared with the wear of a tool, cutting precision criteria, such as the surface roughness, are more concerned with the actual cutting process [29]. Therefore, the failure criterion of the tool is generally not a decrease in its strength or stiffness but a decrease in its cutting precision. Traditional tool RUL prediction model focus on tool wear level. A conservative protection strategy could waste the RUL of the tool, increase unnecessary downtime and lead to a decrease in production efficiency. There are different mechanism models for the prediction of surface roughness have been studied [30; 31; 32; 33]. The limitation of mechanism models is that it needs a lot of strict experiments test conditions, which is time-consuming and costly. In addition, the application of artificial intelligence technology in surface roughness has been widely discussed [34; 35]. While these artificial intelligence models lack of discussion on tool wear degeneration, which is a very important factor related to surface quality. Thus, this paper proposes a dynamic evaluation method for RUL prediction, links the surface roughness to the wear of the tool, and the surface roughness criterion is modeled by a random threshold for the degradation state of the tool. The degradation of the wear process is modeled by an inverse Gaussian process, which has been successfully applied in degradation modeling [36]. Considering the quality variation of the tool, the degradation rate of the inverse Gaussian process is modelled as a random effect to improve the performance of the model. The rest of this study is organized as follows: In Section 2, an inverse Gaussian process with a variable drift coefficient is formulated to characterize the degradation process considering the dynamic wear degradation mechanism and individual heterogeneity. The relationship between the surface roughness and degradation in terms of wearing is defined, and the RUL evaluation model with a random failure threshold is proposed. The parameter estimation procedure based on an EM algorithm is also developed. Section 3 provides the implementation and validation of the proposed approach through simulation experiments and real-data examples. The conclusions of the paper are drawn in Section 4.
## 8 Conclusions  
In this paper, ISVD and MVMD for PD signal noise reduction are proposed. Through the analysis of the simulated and field-measured signals, the effect of the noise reduction method in this paper is verified, and the following conclusions are drawn:  
(1) The SVD algorithm with a guidance signal is proposed. The elements of the guidance signal are adaptively obtained by FSWT and the improved Rife method, and the guidance signal is added to the noisy PD signal to complete the narrowband interference suppression. At the same time, the various indicators of this method are better than the traditional SVD narrowband interference suppression method, even in the case of small narrowband interference amplitude.  
(2) MPA considering MAEE is used to realize the automatic optimization of MVMD modal decomposition number \(k\) and penalty factor \(\alpha\). The optimal decomposition of the noisy PD signal is realized, and the modal aliasing phenomenon is overcome. PD feature information can be accurately extracted to improve the accuracy of PD detection.  
(3) Through the wavelet threshold introduced by decomposition layer \(i\) and the new exponential attenuation threshold function, the fitting effect of the PD signal is enhanced and a better noise reduction effect is achieved. Through the noise reduction of simulated and field PD signals, the SNR, NCC and RMSE indexes of the overall noise reduction method in this paper are better than SVMD, IIE-MVMD and SVD-EWT, and the efficiency of the algorithm is the best.  
Although the method proposed in this paper has better noise reduction performance, the algorithm takes a long time. The complexity of the algorithm will be further improved in the future, thus reducing the time consumption of the algorithm.  
Conceptualization, J.C. and Y.W.; Methodology, J.C., Y.W., W.Z. and Y.Z.; Software, W.Z. and Y.Z.; Validation, W.Z. and Y.Z.; Writing--original draft, J.C.; Writing--review & editing, J.C.; Supervision, Y.W.; Funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by \"the Fundamental Research Funds for the Central Universities (Ph.D. Top Innovative Talents Fund of CUMTB)\", and in part by the National Natural Science Foundation of China under Grant 52474188.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Evaluating Indicator** & **S\_VMD** & **IIE-MVMD** & **SVD-EWT** & **ISVD-MVMD** \\ \hline Time/s & 8.972 & 1.435 & 2.042 & 1.984 \\ \(E_{\text{s}}\)/s\({}^{-1}\) & 1.29 & 5.03 & 8.14 & 11.25 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Comparison of duration and operating efficiency indicators of field-measured PD signals for different algorithms.
# Leveraging Digital Twin Technology for Sustainable and Efficient Public Transportation
## 2 Review of Different Aspects of Digital Twins
### Digital Twins in Urban Infrastructure
Digital twins enabled by high-speed network capabilities enable real-time communication among moving objects--vehicles and infrastructure--to enable higher functions such as autonomous driving, vehicle platooning, and remote driving. One of the ways that digital twins can analyze traffic conditions is by fusing 3D models of transportation infrastructure with real-time operational data. These models analyze data by utilizing AI and big data to visualize dynamic transportation scenarios. These virtual models contain realistic components such as roads, greenery, and vehicles, which create an immersive experience of urban traffic. Among various investigations on IoV, one has focused on digital twins, showing they can effectively optimize IoV data-sharing or increase the resiliency of the transportation network against disruptions. The researchers reported a system reduction in communication overheads (additional time, resources, or computational effort for managing and coordinating data transfer between different systems or components in a network) by upwards of 50%. Furthermore, they also reported improvement in the operational efficiency by almost 20% compared to traditional algorithms [19]. Digital twins can be applied at different levels of urban planning. One level is strategic planning for critical infrastructures like mobility systems and energy distribution. Another level of operational planning is for managing services, local mobility, and building performance. At the emergency level, digital twins can also be used to integrate resilience and sustainability for disaster preparedness. In smart city planning, digital twins can allow stakeholders to evaluate the impacts of proposed changes before they are implemented [17; 18]. Digital twins link physical environments with digital infrastructures through sensors, wireless networks, and cloud computing, handling a great volume of data. The data go through sophisticated models that run simulated scenarios, options for evaluation, and strengths-weaknesses before actual decisions are made. In addition, the digital twin allows for interacting in real time with the users; hence, it opens up the possibility of directly controlling city operations [19]. Furthermore, digital twins have also been used in Adaptive Traffic Signal Control (ATSC). One study developed a digital twin-based ATSC system that reduces and redistributes the waiting times of vehicles at intersections [50]. The method considers waiting times at both the target and upstream intersections. This can be useful in optimizing the traffic flow in congested networks. It is also scalable to city-wide applications, going a long way in improving the driving experience for urban commuters.
## 4 Results and Analysis
### Relationship Analysis  
The relationships between the in-situ AR and the MODIS NIR BRDF_R index, MODIS NDVI, and the CI are shown in this section.  
The MODIS NIR BRDF_R index is negatively correlated with the in-situ AR and has an \(R^{2}\) value of 0.5228, and the relationship is in the form of an exponential power function that reflects the geometric structure information for the vegetation [9; 10; 11]. The MODIS NDVI is positively correlated with the in-situ AR and has an \(R^{2}\) value of 0.579, which is comparable to that of the BRDF_R index, and the relationship is in the form of a power exponent that primarily reflects variations in the vegetation leaves [6; 7]. The results in Figure 4 show that the NIR BRDF_R index and NDVI are both sensitive indicators for characterizing the AR variation process over grassland.  
Figure 3: (**a–d**) Change profiles of the Moderate-resolution Imaging Spectroradiometer (MODIS) near-infrared (NIR) bi-directional reflectance distribution function (BRDF)_R index, MODIS normalized difference vegetation index (NDVI), average wind speed, and in-situ aerodynamic roughness (AR) from April to September in 2013–2014.  
The CI based on the NIR BRDF_R and the NDVI shows a stronger relationship with the in-situ AR, which is also in the form of an exponential power function, as shown in Figure 5. As the CI increases below 2.0, the AR decreases rapidly. With CI values between 2.0 and 6.0, the AR decreases more slowly before converging. The \(R^{2}\) value of 0.721 and the much higher aggregation degree indicate an obvious improvement of the fit compared with the result in Figure 4. Thus, the combination of the NIR BRDF_R index and the NDVI can provide a more accurate characterization of the AR dynamics related to grass growth. The proposed CI in this paper will provide significant guidance towards remote sensing-based AR estimations over grassland during growing season.  
Figure 4: Relationship between the MODIS NIR BRDF_R index and the field AR (**a**) and between the MODIS NDVI and the field AR (**b**).  
Figure 5: Relationship between the combination index (CI) and the field AR.
## Abbreviations  
The following abbreviations are used in this manuscript:  
ARBS Arbitrary Bit Sequence  
AWR Applied Wave Research  
BER Bit Error Rate  
BITW Bit Width  
CRLH Composite Right/Left-Handed  
CTLE Continuous Time Linear Equalizer  
DFE Decision Feedback Equalizer  
DSP Digital Signal Processing  
EQ Equalizer  
FEC Forward Error Correction  
FFE Feed-Forward Equalizer  
I/O Input/Output  
IL Insertion loss  
ISI Intersymbol interference  
LMS Least Mean Square  
MWO Microwave Office  
NRZ Non Return to Zero  
PAM Pulse Amplitude Modulation  
PCB Printed Circuit Board  
PRBS Pseudo Random Bit Sequence  
PRC Parallel RC Resistor Capacitor  
RLC Resistor inductor capacitor  
S Scattering  
SI Signal Integrity  
SLR Series LR
# Domain-Invariant Few-Shot Contrastive Learning for Hyperspectral Image Classification
## 4 Experimental Result and Discussion
### The Influence of Temperature Parameters on the Results  
In this part of the document, we carry out experimental research on the DIFSCL method to explore the effects of temperature coefficients on the results. As shown in Figure 13, the horizontal axis represents the values of the temperature coefficients, while the vertical axis corresponds to the Overall Accuracy (OA) values. The range of temperature coefficient values is from 0.1 to 0.5. When the temperature coefficient is set to 0.1, DIFSCL performs best on the UP dataset. When set to 0.5, it performs best on the IP dataset. When set to 0.2, it performs best on the Salinas dataset.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Variants** & **Crop** & \(L_{con}\) & \(L_{d}\) & **OA** & **AA** & **Kappa** \\ \hline \(v_{0}\) & ✓ & ✓ & ✓ & \(88.33\pm 3.65\) & \(89.50\pm 2.23\) & \(84.80\pm 4.49\) \\ \(v_{1}\) & ✗ & ✓ & ✓ & \(83.86\pm 2.39\) & \(84.38\pm 2.14\) & \(78.92\pm 2.91\) \\ \(v_{2}\) & ✓ & ✗ & ✓ & \(88.33\pm 2.38\) & \(89.49\pm 2.40\) & \(84.77\pm 2.99\) \\ \(v_{3}\) & ✓ & ✓ & ✗ & \(88.01\pm 2.84\) & \(88.94\pm 2.04\) & \(84.37\pm 3.55\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Ablation experiments of each module in UP dataset.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Variants** & **Crop** & \(L_{con}\) & \(L_{d}\) & **OA** & **AA** & **Kappa** \\ \hline \(v_{0}\) & ✓ & ✓ & ✓ & \(75.88\pm 2.02\) & \(84.64\pm 1.69\) & \(72.75\pm 2.31\) \\ \(v_{1}\) & ✗ & ✓ & ✓ & \(67.54\pm 3.37\) & \(78.58\pm 2.11\) & \(63.37\pm 3.69\) \\ \(v_{2}\) & ✓ & ✗ & ✓ & \(75.21\pm 2.38\) & \(84.83\pm 1.69\) & \(72.03\pm 2.65\) \\ \(v_{3}\) & ✓ & ✓ & ✗ & \(74.43\pm 2.72\) & \(83.76\pm 1.81\) & \(71.18\pm 3.02\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Ablation experiments of each module in IP dataset.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Variants** & **Crop** & \(L_{con}\) & \(L_{d}\) & **OA** & **AA** & **Kappa** \\ \hline \(v_{0}\) & ✓ & ✓ & ✓ & \(75.88\pm 2.02\) & \(84.64\pm 1.69\) & \(72.75\pm 2.31\) \\ \(v_{1}\) & ✗ & ✓ & ✓ & \(67.54\pm 3.37\) & \(78.58\pm 2.11\) & \(63.37\pm 3.69\) \\ \(v_{2}\) & ✓ & ✗ & ✓ & \(75.21\pm 2.38\) & \(84.83\pm 1.69\) & \(72.03\pm 2.65\) \\ \(v_{3}\) & ✓ & ✓ & ✗ & \(74.43\pm 2.72\) & \(83.76\pm 1.81\) & \(71.18\pm 3.02\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Ablation experiments of each module in Salinas dataset.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Variants** & **Crop** & \(L_{con}\) & \(L_{d}\) & **OA** & **AA** & **Kappa** \\ \hline \(v_{0}\) & ✓ & ✓ & ✓ & \(92.05\pm 0.91\) & \(94.99\pm 0.46\) & \(91.15\pm 1.01\) \\ \(v_{1}\) & ✗ & ✓ & ✓ & \(90.33\pm 1.64\) & \(93.50\pm 1.61\) & \(89.24\pm 1.81\) \\ \(v_{2}\) & ✓ & ✗ & ✓ & \(91.41\pm 1.27\) & \(94.33\pm 0.85\) & \(90.45\pm 1.40\) \\ \(v_{3}\) & ✓ & ✓ & ✗ & \(91.32\pm 0.90\) & \(94.11\pm 0.66\) & \(90.34\pm 1.00\) \\ \hline \hline \end{tabular}
\end{table}
Table 9: Ablation experiments of each module in Salinas dataset.
# Traffic-Aware Optimization of Task Offloading and Content
## 4 Joint Optimization for Offloading and Content Caching with Traffic Stream Prediction
### MOEA/D-Based Joint Optimization
#### 4.2.1 Tchebycheff Weight Aggregation Approach  
Among the various decomposition methods of MOEA/D, we choose to use the Tchebycheff approach because it can handle relatively more complex problems with a high computational efficiency. Then, the decomposition cost form of the sub-problem optimization problem of computing the content caching or offloading of tasks in a region is _minimize_\(g^{\text{tche}}(x\mid w,z^{*})=\underset{1\leq i\leq m}{max}\left\{\lambda_{i} \mid f_{i}(x)-w_{i}^{*}\right\}\), where, \(z^{*}=\left\{z_{1}^{*},z_{2}^{*}\right\}(i\in\{1,2,\ldots,P\})\) is the optimal value of \(\overline{T}^{i}(t)\) and \(E^{i}(t)\), \(w_{i}\) represents the weight of the \(i^{th}\) objective function for each \(x\), and \(P\) represents the population size defined by MOEA/D. In this paper, let \(f_{1}\) be the energy consumption of the area and \(f_{2}\) be the average time delay of the area. Decompose the multi-objective optimization problem into m subproblems according to the Tchebycheff ray uniform expansion, assign the objective weight of each subproblem, and obtain the subproblem weight matrix \(w=[w_{1},w_{2},\ldots,w_{i},\ldots,w_{m}]\), where \(w_{i}=(w_{i}^{1},w_{i}^{2})\) represents the weight vector of the \(i^{th}\) sub problem. Let \(w_{i}^{1\prime}=i\times\frac{1}{m+1}\), \(w_{i}^{2\prime}=1-w_{i}^{1\prime}\); \(w_{i}^{1}=\frac{\frac{1}{w_{i}^{1\prime}}}{\frac{1}{w_{i}^{1\prime}}+\frac{1} {w_{i}^{2\prime}}}\), \(w_{i}^{2}=1-w_{i}^{1}\).
## 4 Mean Squared Performance of Individual MISO APA Filters
### Steady-State Performance for MISO Filters
However, we can also assume the following approximations: \[\operatorname{Tr}\left(\operatorname{E}\left\{\mathbf{A}_{n}^{( j)}\right\}\right) \approx\operatorname{E}\left\{\frac{K_{j}}{\left\|\mathbf{x}_{n} \right\|^{2}}\right\}\] (48) \[\frac{1}{\operatorname{E}\left\{a_{11}^{(j)}\left[n\right]\right\}} \approx\operatorname{Tr}\left(\mathbf{R}_{n}^{(j)}\right)\] (49) that yield the following expression for the steady-state EMSE of the \(j^{\text{th}}\) MISO filter: \[\xi_{\infty}^{(j)}=\frac{\mu_{j}\sigma_{v}^{2}}{\left(2-\mu_{j}\right)} \operatorname{Tr}\left(\mathbf{R}_{n}^{(j)}\right)\operatorname{E}\left\{ \frac{K_{j}}{\left\|\mathbf{x}_{n}\right\|^{2}}\right\}\] (50) which depends proportionally on the value of the projection order \(K_{j}\).
## 4 Analytical Results for the Conduction-Convection Case  
### Consistency  
We calculate the truncation error in the most common way, where subscripts with \(t\) or \(x\) are for differentiation with respect to the time or space variables, respectively. The exact solution is substituted into the equation containing the finite difference formulas, and  
\[\tau=D_{t}^{+}u-D_{x}^{2}u+Ku \tag{29}\]  
is the truncation error. In our case,  
\[D_{t}^{+}u=\frac{u(x_{i}\,\ t^{n}+\Delta t)-u(x_{i}\,\ t^{n})}{\Delta t}\]  
is the usual first order forward difference operator for the time derivative. However, the second order central difference operator for the space derivative  
\[D_{x}^{2}u=\alpha\frac{u(x_{i}\ -\Delta x,\ t^{n}+\
icefrac{{\Delta t}}{{2}})-u (x_{i}\,\ t^{n})-u(x_{i}\,\ t^{n}+\Delta t)+u(x_{i}\ +\Delta x,\ t^{n}+\
icefrac{{ \Delta t}}{{2}})}{\Delta x^{2}}\]  
and the convection term  
\[Ku=Kpu(x_{i}\,\ t^{n}+\Delta t)+K(1-p)u(x_{i}\,\ t^{n})\]  
contain different time levels. The Taylor series expansion of \(u\) is substituted into Equation (29). The function \(u\) is supposed to be the exact solution, thus the identity \(u_{t}=\alpha u_{(2x)}-Ku\) is used. The obtained truncation error is  
\[\tau=\tau_{0}-\
icefrac{{1}}{{2}}K(2p-1)(Ku-\alpha u_{xx})h+\frac{1}{8}\bigg{(} K+\frac{2\alpha}{\Delta x^{2}}\bigg{)}u_{tt}h^{2}+\frac{1}{24}u_{(3t)}h^{2}, \tag{30}\]  
where \(\tau_{0}\) is the discretization error of the _standard_ central difference formula (used in, e.g., the FTCS method):  
\[\tau_{0}=-\frac{\alpha}{12}u_{(4x)}\Delta x^{2}-\frac{\alpha}{360}u_{(6x)} \Delta x^{4}-\frac{\alpha}{20160}u_{(8x)}\Delta x^{6}+\text{h. o. t.}. \tag{31}\]  
Figure 5: The temperature \(u\) as a function of the \(x\) variable in the case of the initial function \(\text{u}^{0}\), the reference solution at \(t^{\text{fin}}\), and the LH method for \(h=2\cdot 10^{-3}\) when the convection term is inside the numerator, and when it is implemented in a mixed way.  
The highest order term cancels out only if \(2p=1\). In the case of traditional methods, such as the FTCS scheme, the discretization error of the \(D_{t}^{+}\) and \(D_{x}^{2}\) operators depend on only \(\Delta t\) and \(\Delta x\), respectively. In those cases, the space- and time-dependent terms in the truncation error can be clearly separated. This does not hold in our case, where there is a term containing the ratio of \(\Delta t\) and \(\Delta x\). We can summarize these results in the following theorem.  
**Theorem 1**.: _When applied to PDE \(u_{t}=\alpha u_{xx}-Ku\), the algorithm given by Formulas (15) is conditionally consistent. The order of temporal consistency/convergence is two if and only if \(p=\
icefrac{{1}}{{2}}\). In this case, if the space and time step size tend to zero \(\Delta x\to 0\), \(h\to 0\), such that \(\frac{h}{\Delta x}\to 0\), then the error of the numerical solution compared to the analytical solution of the PDE tends to zero with \(h^{2}\)._
## 4 Experiments
### Dataset Construction and Evaluation Metrics
#### 4.1.2 Evaluation Metrics  
In this study, precision (\(P\)), recall (\(R\)), average precision (\(AP\)), mean average precision (\(mAP\)), frames per second (\(fps\)), and the number of parameters are utilized as evaluation metrics to assess the object detection performance of the model. The corresponding calculation equations are provided as follows:  
\[Precision=\frac{TP}{TP+FP} \tag{10}\]  
\[Recall=\frac{TP}{TP+FN} \tag{11}\]  
\[AP=\int_{0}^{1}P(R)dR \tag{12}\]  
\[mAP=\frac{1}{N}\sum_{k=1}^{N}R_{n}P_{n} \tag{13}\]  
\[fps=\frac{F_{i}}{T_{n}} \tag{14}\]  
In these equations, precision (\(P\)) measures the proportion of correctly predicted positive samples among all predicted positives; recall (\(R\)) measures the proportion of actual positive samples that are correctly identified; average precision (\(AP\)) evaluates the detection accuracy for a single class; mean average precision (\(mAP\)) indicates the mean detection accuracy across all classes; and frames per second (\(fps\)) reflects the average inference speed on the drilling cutting test dataset.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Dataset Classification** & **Quantity** \\ \hline Training Set & 2535 \\ Value Set & 568 \\ Test Set & 684 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Ratio of training group, value group, and test group.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Operating System** & **Windows 10** \\ \hline Deep learning framework & Pytorch:(version=2.3.0) \\ CPU & AMD Ryzen 5 5600 (3.50 GHz) \\ GPU & NVIDIA GeForce RTX 4060 Ti \\ CUDA & 12.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental environment configuration.  
To quantitatively assess the accuracy of velocity measurements in drilling cutting detection, this paper introduces two evaluation metrics: Velocity Accuracy (A) and Variance of Error (\(V\)), which are used to evaluate the model's performance in target velocity estimation.  
The equation for calculating Velocity Accuracy (A) is given as follows:  
\[Accuracy=1-\frac{|v_{d}-v_{r}|}{v_{r}}\in(0,1) \tag{15}\]  
In the equation, \(v_{d}\) represents the measured velocity of the object, while \(v_{r}\) denotes the true velocity of the object.  
The Variance of Error (\(V\)) metric is used to assess the stability of the discrepancy between the measured velocity and the true velocity. A smaller value indicates greater measurement accuracy. The calculation equation is as follows:  
\[\varepsilon_{i}=V_{d,i}-V_{r,i} \tag{16}\]  
\[\bar{\varepsilon}=\frac{1}{M}\sum_{i=1}^{M}\varepsilon_{i} \tag{17}\]  
\[\sigma_{\varepsilon}^{2}=\frac{1}{M}\sum_{i=1}^{M}(\varepsilon_{i}-\bar{ \varepsilon})^{2} \tag{18}\]  
In the equation, \(\varepsilon_{i}\) denotes the measurement error of the \(i\)-th target; \(v_{r,i}\) indicates the true velocity of the \(i\)-th target; \(v_{d,i}\) represents the measured velocity of the \(i\)-th target; \(M\) stands for the number of times the target has been measured; and \(\bar{\varepsilon}\) represents the average measurement error of the target.
## 4 Optimization Design Process and Results
### The Surrogate Model  
Kriging model [37] is an interpolation model for spatial modeling and prediction of random process/random field according to covariance function. Kriging model can obtain more accurate global optimal results than quadratic RSM model [38]. The model can be divided into regression model and correlation model. The regression model is the global approximation in the design space, and the correlation model can reflect the design spatial distribution structure of variables, which has an impact on the prediction accuracy of the model.  
The Kriging model as a type of surrogate model can effectively establish a global mapping between design variables and optimization objectives, with lower computational cost. The Kriging surrogate model was widely used in aerodynamic design optimization of high-speed train [39] and high-lift airfoil design optimization [40].