esa-sceva/satcom-chunk-collection huggingface dataset:
# Concrete Gas Permeability: Implications for Hydrogen Storage Applications
## 3 Results and Discussion  
In light of the results obtained from the laboratory tests, a detailed analysis of the findings is presented below. Figure 1 provides an example of the oxygen permeability coefficient measured for one specific sample. Subsequent figures offer a comprehensive graphical representation of the data collected from all of the samples studied, encompassing the various conditioning states that were applied throughout the experiment. This approach allows for a thorough comparison of the effects observed under different conditions.  
Below are the results of the \(k_{\infty}\) obtained for each test condition, grouped by sample type and the presence or absence of cold joints. Equation (4) was used for the fitting process.  
Figures 2 and 3 display the values of k\(\infty\) for specimens 135 and 151, grouped by the type of gas used in the test and the type of conditioning. No clear trend can be observed based on the type of gas used, but for helium, the highest permeability value is obtained. Concerning the type of conditioning, the highest permeability value is obtained for dry concrete (air-exposed samples), while the lowest value is obtained for saturated concrete. This can be explained by the availability of pores for gas permeation. The trends for the specimens with cold joints are similar, but the values are higher by approximately two orders of magnitude.  
Figure 1: An example of one of the samples measured (O\({}_{2}\))—151 concrete, without cold joints, exposed to air.  
In order to use the equations mentioned, it is necessary to make the assumption that hydrogen's permeability is similar to helium's. This hypothesis is based on the experimentally obtained results, where no significant influence of the gas on the permeability value has been observed. The effect of humidity or the presence of cold joints is much greater.  
The main objective of this study was to simulate the concrete working as a barrier against hydrogen. Therefore, the model determined the amount of gas that would be released into the tank per unit of time and surface area.  
To observe the effect of thickness and internal tank pressure, hydrogen flow has been plotted on a logarithmic scale (Figures 7-12). The left side of each figure shows a 2D diagram, and the right side depicts the same in a contour plot.  
As expected, hydrogen flow increases with the internal gas pressure in the tank and decreases with an increase in the thickness of its wall. Additionally, it increases with a decrease in the moisture content in the concrete and the presence of cold joints, which act as easier and faster pathways for hydrogen.  
Figure 8: Hydrogen flow in 65% RH-conditioned specimens.  
Figure 6: Saturated: (**a**) permeability of specimens without cold joint; (**b**) permeability of specimens with cold joint.  
Figure 7: Hydrogen flow in air-exposed specimens.
# A Minimal GBT Model for Distortional-Twist Elastic Analysis of Box-Girder Bridges
## Appendix B Planar Frame Deflections  
The rectangular planar frame in Figure 4 was considered with prescribed displacements at joints caused by the known distortion \(\varphi=1\) and with the rotations \(\alpha\) unknowns. For a single beam, the stiffness matrix links shear forces and couples to displacements and rotations at the \(A,B\) ends:  
\[\left(\begin{array}{c}V_{i}\\ M_{A}\\ V_{B}\\ M_{B}\end{array}\right)=EI_{i}\begin{pmatrix}\frac{12}{b}&\frac{6}{l_{1}^{2}} &-\frac{12}{l_{1}^{3}}&\frac{6}{l_{2}^{2}}\\ \frac{6}{l_{1}^{2}}&\frac{4}{l_{1}^{2}}-\frac{6}{l_{1}^{2}}&\frac{2}{l_{1}^{2 }}\\ -\frac{12}{l_{1}^{3}}&-\frac{6}{l_{1}^{2}}&\frac{12}{l_{1}^{3}}-\frac{6}{l_{1}^ {2}}\\ \frac{6}{l_{1}^{2}}&\frac{2}{l_{1}^{3}}-\frac{6}{l_{1}^{2}}&\frac{4}{l_{1}^{3} }\end{pmatrix}\left(\begin{array}{c}v_{A}\\ \theta_{A}\\ v_{B}\\ \theta_{B}\end{array}\right) \tag{14}\]  
with \(l_{i}=b,h\) and \(l_{i}=\frac{t_{1}^{3}}{12}\), \(\frac{t_{1}^{3}}{12}\), when \(i=1,3\) and \(i=2,4\), respectively. It turns out that  
* when \(i=1,3\), \(v_{A}=-\frac{b}{2}\)\(v_{B}=\frac{b}{2}\), \(\theta_{A}=\theta_{B}=\alpha\), entailing \(M_{A}=M_{B}=-\frac{6 EI_{1}}{b}+\frac{6 EI_{1}}{b}\alpha\);
* when \(i=2,4\), \(v_{A}=\frac{h}{2}\) and \(v_{B}=-\frac{h}{2}\), entailing \(M_{A}=M_{B}=\frac{6 EI_{2}}{h}+\frac{6 EI_{2}}{h}\alpha\).  
Enforcing equilibrium at any joint (all the equilibrium conditions being equal for symmetries), it follows that  
\[\frac{6 EI_{1}}{b}(\alpha-1)+\frac{6 EI_{2}}{h}(\alpha+1)=0 \tag{15}\]from which \(\alpha\) is derived, as given in Equation (16). To evaluate the deflections of each beam, the elastic line equation \(EI_{i}V_{i}^{\prime\prime\prime\prime}(s)=0\) is integrated under the prescribed displacements at the end; namely  
* when \(i=1,3\), \(V\left(\mp\frac{b}{2}\right)=\mp\frac{b}{2}\), \(V^{\prime}\left(\mp\frac{b}{2}\right)=\alpha\), from which \(V_{i}=\frac{1}{2}s_{i}\left(3+\frac{4s_{i}^{2}(\alpha-1)}{b^{2}}-\alpha\right)\)
* when \(i=2,4\), \(V\left(\mp\frac{b}{2}\right)=\pm\frac{b}{2}\), \(V^{\prime}\left(\mp\frac{b}{2}\right)=\alpha\), from which \(V_{i}=\frac{1}{2}s_{i}\left(-3+\frac{4s_{i}^{2}(\alpha+1)}{b^{2}}-\alpha\right)\)
# Infection Control with Antimicrobial Solid-State ZnO Nanoparticles on Silk Fiborin Gauze
## 3 Results and Discussion
Furthermore, NP size influences interactions with cell transport and defense systems, affecting distribution kinetics. NPs smaller than 5 nm tend to overcome cell barriers non-specifically, while larger particles enter cells through various mechanisms such as pinocytosis [68]. It was demonstrated that smaller ZnO nanoparticles (30 nm) had a higher internalization effect compared to larger nanoparticles (80-100 nm) and the ionic form of zinc [65]. To improve the bactericidal effect of the gauze without modifying the cytotoxicity, more research should be performed to increase the release of Zn\({}^{2+}\) and maintain the low rate of ROSs formation. For example, strategies include surface modification with acidic coatings to promote dissolution, reduce particle agglomeration, or increasing the porosity of the gauze to allow better fluid penetration. In vivo experiments indicate rapid distribution of NPs smaller than 10 nm among all organs and tissues, contrasting with the localization of larger NPs (around 250 nm) in specific organs (liver and spleen) [69]. Our material, coated with ZnO nanoparticles larger than 100 nm, not only induces bacterial death but also preserves tissues and could support essential physiological processes involved in tissue repair. The low release of ROSs from our dressing enhances tissue safety, making it particularly suitable for clinical treatment of chronic diabetic wounds, aiming to improve wound healing and prevent bacterial infections [70,71]. The results of these in vitro studies lay the groundwork for further research in vivo, guiding the development of wound dressings that effectively combat bacterial growth and facilitate the healing process [72]. Given that silk-based materials have been approved by the FDA for a wide array of applications, such as wound dressing, and ZnO is FDA-approved for skin-protection and wound-care products, some of the regulatory considerations have already been addressed, but for full implementation in clinical settings, safety assessments, manufacturing scalability, and clinical efficacy studies will be required.
## 3 Method
### Embedding Layer
#### 3.1.1 Character Level Features  
In order to obtain rich word-level semantic representations, this paper uses a BERT pre-training model to obtain word-level feature vector representations of the corpus. The BERT pre-training model is based on the bidirectional transformer encoder, which is used to obtain word-level feature representation by masking the language model and next sentence prediction model to learn the sentence-level semantic relationship of text sequences for better extraction of text feature information [25].  
Figure 1: BERT-BiGRU-CRF model structure diagram. * Notes: The English translation of the input layer is “Qian Hong 68 by Yangtze River”.  
During BERT pre-training, the sequence \(S=\{c_{1},c_{2},c_{3},\dots,c_{n}\}\) corresponds to the input \(E=\{E_{1},E_{2},E_{3},\dots,E_{n}\}\), as shown in Figure 2, which is superimposed by three embedding features, namely character embedding \(e_{i}^{p}\), sentence embedding \(e_{i}^{e}\), and position embedding \(e_{i}^{p}\), where \(E_{i}=e_{i}^{t}+e_{i}^{s}+e_{i}^{p}\) and \(e_{i}\) denotes the embedding feature of each character. Two special markers [CLS] and [SEP] are added to the initial position of sequence X and between sentences, [CLS] identifies the start position of the sequence and [SEP] identifies the split between sentences. After multiple bidirectional transformer encoders, the vector E obtains the vector \(X^{b}=\{x_{1},x_{2},x_{3},\dots,x_{n}\}\), which contains rich semantics, where \(X\in\mathbb{R}^{n\times h_{bert}}\), \(h_{bert}\) denotes the hidden state dimension of BERT, and \(x_{i}^{b}\) denotes the BERT vector of the i-th character in the sequence.
## 5 Experiments and Evaluation
### Experimental Setting
#### 5.1.2 Baselines  
We compare the performances of our model with several state-of-art methods in personalized location recommender systems.  
**SVD-MFN**[51]: Singular Value Decomposition with Multi-Factor Neighborhood (SVD-MFN) takes a variety of factors into consideration so as to better predict the users' preferences for items. It aims to recommend the most similar items according to historical interactions. In our experiment, the geographic, temporal, and social factors are considered.  
**KNN**: The K-Nearest Neighbor (KNN) uses the similarity between users to recommend. It first finds \(K\) most similar users with the target, and then make recommendations based on the visiting behavior of these people.  
**CMF-UL**[34]: This is based on the collaborative matrix factorization but considers more interactions i.e., user-location, user-app and location-app information. Then, latent representations, \(U\) and \(L\), are used to obtain a scoring matrix and make recommendations.  
**CMF-U**: Compared with CMF-UL, this method only uses the user-location and user-app interactions for collaborative matrix factorization. That is, it only uses the users' behavior on app usage.  
**CMF-L**: Compared with CMF-UL, this method only uses the user-location and location-app interactions for collaborative matrix factorization. That is, it only uses the locations features represented by app usage.  
**SoRec**[52]: SoRec incorporates additional user-user relationships into user-location matrix. The relationships between users is obtained by calculating the cosine similarity on every two users according to app usage frequencies of different users.  
**SR-U**[53]: Unlike SoRec, which adds social information into matrix decomposition, SR-U uses social relationships as regularization term to constrain the distance between users' embedding vectors in the latent space. In SR-U, we also use the same similarity matrix in SoRec to construct social regularization terms.
## 3 Proposed Methods
### Obstacle Detection Method Based on Superpixel Point-Cloud Height (OD-SPH)
Figure 8 shows the probabilistic distribution of the above image, represented by \(PR_{SPH}\), and the classification result of the OD-SPH method (the decision threshold is set to 0.15). As can be seen from the figure, as \(PR_{SPH}\) is obtained from the height of the superpixel point cloud, there is no misjudgment in the obstacle area with a plane geometry, such as the hood of the vehicle. These areas are classified as the obstacle in Figure 8b, and this method makes up for the shortcoming of the OD-PNV method. However, in some areas close to the road surface (such as vehicle tires), the OD-SPH method has the problem of low discrimination, while the OD-PNV method does not have such a problem. Therefore, the fusion of these two methods can achieve complementary effects.
# Dynamic Quality Monitoring System to Assess the Quality of Asphal Concrete Payement
## 2 Development of the Dynamic Monitoring System for Asphalt Concrete
### _Composition of Digital Monitoring System_
#### 2.2.2 Quality Control System for Asphalt Mixture Mixing  
The quality control system for the asphalt mixture mixing process includes the data acquisition module, 5G network transmission module and data processing module to realize the dynamic monitoring of raw materials in the mixing station. The data-collection system of the mixing plant is constructed by installing an SBW series temperature transmitter (SBWR4560, Shanghai Automation Instrumentation CO., LTD, Shanghai, China) next to the discharge bin and METTLER--TOLEDOIND series load cells (SPC, METTLER TOLEDO, Shanghai, China) in the screening system of the reduction bin. This enables collection of the aggregate consumption, asphalt consumption, mixture mixing temperature and discharge temperature in real time, and calculates the asphalt aggregate ration and grading of each plate. The collected data is transmitted to the remote central server through the industrial control computer in the control room of the mixing plant (as shown in Figure 2). The data processing module of the system can provide a professional data analysis table and mixture grading curve to construction engineering and project managers.
## 3 Methods
### Joint Loss Function  
In image classification, by the existing deep-learning-based AD classification methods [3; 9; 10; 11; 12; 13], a common loss function is the cross entropy. In this paper, we first defined the cross-entropy as the following inter-loss function:  
\[\mathcal{L}_{inter}=-\frac{1}{N}\sum_{i=1}^{N}\sum_{k=1}^{3}\left[y_{i}\ln p_{i, k}\right] \tag{1}\]  
Figure 4: ResNet50 network. (a) Shortcut connection and (b) network structure.  
Figure 5: (a) Example of a DenseNet with two dense blocks and (b) DenseNet121 structure.  
where \(N\) is the number of samples. \(p_{i,k}\) is the softmax output, representing the probability that the \(i\)-th sample belongs to the \(k\)th class, and \(y_{i}\) represents the label. Here, \(y=1\), 2, and 3 correspond to BAPL1, BAPL2, and BAPL3, respectively.  
We then defined an intra-loss (i.e., center loss [20,21]) function that handles the intra-variation problem:  
\[\mathcal{L}_{intra}=\frac{1}{2}\sum_{i=1}^{N}||f_{i}-c_{yi}||^{2} \tag{2}\]  
where \(f_{i}\) is the feature vector of the \(i\)th sample and \(c_{yi}\) denotes the center of the feature class to which \(y_{i}\) belongs which is updated during the training by Equation (3). The update is operated on each batch (not on the entire training set).  
\[\begin{split}& c_{j}=c_{j}-\alpha*\Delta c_{j}=c_{j}-\alpha* \frac{\frac{\partial\mathcal{L}_{intra}}{\partial c_{j}}}{\partial c_{j}}\\ &=c_{j}-\alpha*\frac{\sum_{i=1}^{N}\delta(y_{i}==j)(c_{j}\text{-} f_{i})}{1+\sum_{i=1}^{N}\delta(y_{i}==j)}\end{split} \tag{3}\]  
where \(\delta\) is the delta function. In this paper, the learning rate \(\alpha\) was set to 0.5.  
Finally, the inter-loss (Equation (1)) and intra-loss (Equation (2)) are combined into a joint loss for training the network:  
\[\mathcal{L}=\mathcal{L}_{inter}+\lambda\mathcal{L}_{intra} \tag{4}\]  
where the parameter \(\lambda\) adjusts the balance between the inter-class and intra-class losses. Note that when \(\lambda\) = 0, the joint loss reduces to the conventional cross-entropy loss function used in the existing methods [3, 9, 10, 11, 12, 13].
## 3 Analysis of Three-Stage Incremental Cooperative Communication
### PER Analysis  
For three-stage incremental relaying, it is assumed that there are three potential relays, \(R_{1}\), \(R_{2}\) and \(R_{3}\), available to cooperate with the source. Let \(PER_{SR_{1}}\), \(PER_{SR_{2}}\), \(PER_{SR_{3}}\), \(PER_{R_{1}D}\), \(PER_{R_{2}D}\) and \(PER_{R_{3}D}\) represent the probability of error of the source-to-relay (\(R_{1}\)) (\(S-R_{1}\)), source-to-relay (\(R_{2}\)) (\(S-R_{2}\)), source-to-relay (\(R_{3}\)), (\(S-R_{3}\)), \(R_{1}\)-to-destination (\(R_{1}-D\)), \(R_{2}\)-to-destination (\(R_{2}-D\)) and \(R_{3}\)-to-destination (\(R_{3}-D\)) links, respectively.  
The three-stage relaying process fails if one of conditions mentioned in Table 2 occur.  
\begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Error-Free Links** & **Failed Links** & **Remarks** \\ \hline No link & \(S-D\), \(S-R_{1}\), \(S-R_{2}\) and \(S-R_{3}\) & No communication; the packet is dropped \\ \hline \(S-R_{1}\) & \(S-D\), \(S-R_{2}\) and \(S-R_{3}\) & \(R_{1}\) decodes and forwards, but \(R_{1}-D\) link fails \\ \hline \(S-R_{2}\) & \(S-D\), \(S-R_{1}\) and \(S-R_{3}\) & \(R_{2}\) decodes and forwards the data packet, but \(R_{2}-D\) link fails \\ \hline \(S-D\), \(S-R_{1}\), \(S-R_{2}\) and \(S-R_{3}\) & \(S-D\), \(S-R_{1}\), \(S-R_{2}\) and \(S-R_{3}\) & No more available link \\ \hline \(S-R_{1}\) and \(S-R_{2}\) & \(S-D\) and \(S-R_{3}\) & \(R_{1}-D\) and \(S-R_{2}\) links fail \\ \hline \(S-R_{2}\) and \(S-R_{3}\) & \(S-D\) and \(S-R_{1}\) & \(R_{2}\) and \(R_{3}\) decode and forward the packet, but \(R_{2}-D\) and \(R_{3}-D\) link fail \\ \hline \(S-R_{1}\) and\(S-R_{3}\) & \(S-D\) and \(S-R_{2}\) & \(R_{1}\) and \(R_{3}\) decode and forward the packet, but \(R_{1}-D\) and \(R_{3}-D\) links fail \\ \hline \hline \end{tabular}
\end{table}
Table 2: Conditions for the failure of the three-stage relaying process.  
Hence, the PER for the three-stage relaying scheme is given as:  
\[\begin{split}& PER_{CC}^{(3)}=PER_{SD}PER_{SR_{1}}PER_{SR_{2}}PER_{SR_{3}} \\ &+PER_{SD}(1-PER_{SR_{1}})PER_{SR_{2}}PER_{SR_{3}}PER_{RD}\\ &+PER_{SD}PER_{SR_{1}}(1-PER_{SR_{2}})PER_{SR_{3}}PER_{RD}\\ &+PER_{SD}PER_{SR_{1}}PE_{SR_{2}}(1-PER_{SR_{3}})PER_{RD_{3}D}\\ &+PER_{SD}(1-PER_{SR_{1}})(1-PER_{SR_{2}})(1-PER_{SR_{3}})PER_{RD _{1}D}\\ & PER_{R_{2}D}PER_{R_{3}D}\\ &+PER_{SD}(1-PER_{SR_{1}})(1-PER_{SR_{2}})PER_{SR_{3}}PER_{RD}\\ & PER_{R_{2}D}PER_{R_{3}D}\\ & PER_{R_{2}D}PER_{R_{3}D}\\ &+PER_{SD}PER_{SR_{1}}(1-PER_{SR_{2}})(1-PER_{SR_{3}})PER_{RD_{1}D} PER_{RD}\\ &+PER_{SD}(1-PER_{SR_{1}})PER_{SR_{2}}(1-PER_{SR_{3}})PER_{RD_{1}D} PER_{RD}\\ \end{split} \tag{4}\]
## 2 Review of Phase-Locked Loops
### Discrete Model
#### 2.2.2 Pole-Zero Mapping  
The idea behind the pole-zero mapping method is to use a set of heuristic rules to locate the poles and zeros using the map \(z=e^{ST}\). Then, the gain of a \(z\)-transform is set to describe a discrete equivalent transfer function that approximates the given transfer function in the \(s\)-plane.
## 6 Testing System  
The developed under-frequency preventive control strategy was tested on the Penghu Island power system and the actual historical system operating data for every 5 min were utilized. The single  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Notification**} & \
\begin{tabular}{c} **Demand-Charge Discount** \\ **(NTD/MW per month)** \\ \end{tabular} &
\begin{tabular}{c} **Energy-Charge Discount** \\ **(NTD/MWh)** \\ \end{tabular} \\ \hline
15-min ahead & 96,000 & 10,000 \\ \hline
30-min ahead & 86,000 & 10,000 \\ \hline
1-h ahead & 78,000 & 10,000 \\ \hline
2-h ahead & 72,000 & 10,000 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The rate discount provided by the Taiwan Power Company EDRP rule.  
line diagram of the Penghu system is presented in Figure 10. The Jian-Shan Power Plant has 12 diesel generator units with 129.6 MW of total installed capacity. The Hu-Si wind farm has 6 wind turbines with 6.0 MW of total installed capacity. Jong-Tun wind farm has 8 wind turbines with 7.2 MW of total installed capacity. The distributed solar photovoltaic (PV) has 10 MW of total installed capacity. In this work, the battery energy storage is assumed to be installed at the Hu-Si Substation for the purpose of management and maintenance. Additionally, the controllable load is assumed to be connected at Ma-Gong Substation (the main substation for the load center) for implementing the DLC and EDRP methods.  
Currently, the under-frequency load shedding scheme and the rescheduling scheme of diesel generators are the defense strategies applied in the Penghu Island power system. That is, if a system contingency occurs and frequency drops to below 57.4 Hz, the under-frequency load shedding relay will be automatically activated to shed the load and then system operators reschedule the diesel generators based on their experiences. However, the load-shedding operations are unexpected and involuntary and the existing diesel generator rescheduling scheme is not economic. Therefore, this work proposes four frequency support methods to ensure sufficient system frequency stability and minimal operating costs.
# Precise Calculation of Inverse Kinematics of the Center of Gravity for Bipedal Walking Robots
## 2 Materials and Methods
### CoG and ZMP Calculations  
The ITU Biped has a six-axis force-torque sensor at its ankle (ATI Mini85 F/T Transducer, ATI, Apex, NC, USA). ZMP is indirectly measured using the parameters shown in Figure 4.  
Because no torque is generated in parallel with the foot plane according to the definition of the ZMP [10], the position of the ZMP based on the reaction on the sensor created by the force and moment at the ZMP is calculated using Equations (15) and (16).  
\[p_{z}=\frac{M_{y}+l_{3}F_{z}}{F_{x}} \tag{15}\]  
\[p_{y}=\frac{l_{3}F_{y}-M_{z}}{F_{x}} \tag{16}\]  
Figure 4: Parameters used in ZMP calculations.  
Figure 3: Trajectory of the CoG and fixed foot positions.  
Individual CoGs of the robot bodies are calculated with Equation (18). Before using Equation (18), Equation (17) must be used for calculating positions of the bodies with respect to the inertial coordinate system.  
\[\mathbf{{{}^{0}}}\mathbf{{{}_{{T}}}_{n}}=\prod\limits_{n=0}^{n-1}{{{}^{n}}} \mathbf{{{}^{T}}}_{n+1} \tag{17}\]  
\[\mathbf{{{}_{{n}}}}={{{}^{0}}}\begin{bmatrix}c_{x}\\ c_{y}\\ c_{z}\\ 1\end{bmatrix} \tag{18}\]  
In the algorithm, the CoG of the robot is calculated using the CoGs given in Figure 1b in Equation (19).  
\[\mathbf{{{}_{{\mathbf{B}}}}}=\frac{{\sum\
olimits_{n=1}^{6}{({{}m_{n}} \mathbf{{{}_{{\mathbf{c}}}}}_{n})}_{R}+\sum\
olimits_{n=1}^{6}{({{}m_{n}} \mathbf{{{}_{{\mathbf{c}}}}}_{n})}_{L}+{{}m_{T}}\mathbf{{{}_{{\mathbf{c}}}}}_{ T}}}{{{{}m_{R}}+{m_{L}}+{m_{T}}}} \tag{19}\]
## 2 Materials and Methods
### Strain Gage to Observe Shear Strain along the Fault  
An array of 42 resistance strain gages were mounted along the fault on the bottom sample surface, which formed 14 strain gage groups, as shown in Figure 1. The strain gage groups were used to measure the shear strain along the fault and test the results derived from the DIC method. Each strain gage had a resistance grid of 3 \(\times\) 5 mm with a resistance value of 120.1 \(\pm\) 0.1 \(\Omega\). The sensitivity coefficient of the strain gage was 2.10 \(\pm\) 1%. Data were acquired by a 96-channel strain acquisition system [21]. The analog-to-digital conversion, sampling rate, and observation error of the device was 16 bit, 100 Hz, and \(\pm\)1.5 \(\mu\)e, respectively. The angles between the three strain gages in each strain gage group and the measured fault segment were 0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\). Correspondingly, the offsets of the centers of the three gages from the measured fault segment were 5.0, 12.2, and 6.1 mm, respectively. The plane strain tensor could be obtained by each strain gage group (the specific method was described in previous studies [21; 24]), and subsequently, the shear strain of the fault could be calculated.  
Figure 3: Influence of the side length of the subregion (\(R\)) on the correlation coefficient (CC) during the calculation of the DIC method. Crosses denote the mean value of 1-\(CC\), error bars indicate the standard deviations, and the cross and error bar in red correspond to the optimal subregion side length.