esa-sceva/satcom-chunk-collection huggingface dataset:
# A New Method for Fatigue Evaluation of Titanium Alloy Welded Structures
## 5 Verification of Augmented-Reverse Notch Equivalent Stress Method  
Based on the new three-parameter power function model of titanium alloy welded structures, the notch stress equivalent value method is modified using the proposed correction factor calculation method. In order to verify the effectiveness and accuracy of this method, the fatigue test data of two welded joints of different sizes are used. The augmented reverse notch equivalent stress method is verified. It should be noted that this fatigue test is a new fatigue test different from the above test.  
1. The existing T-joint is shown in Figure 9, and its material is TA5 titanium alloy. The same loading and restraint methods as those in literature [28] are adopted, and the loading position and loading direction are shown in Figure 9. Literature [28] analyzed the effect of MIG welding on the residual stress and fatigue performance of the T-joint at the weld toe. Combined with the analysis results obtained from the fatigue test, the correctness of the augmented-reverse notch equivalent stress method is verified.  
It can be seen from Figure 9 that the height \(H\) of the non-loaded plate is 30 mm, the thickness \(L\) of the non-loaded plate is 16 mm, the size \(h\) of the welding leg is 6 mm, and the thickness \(t\) of the loaded plate is 16 mm. The fatigue life calculated by the augmented-reverse notch equivalent stress method and the test life under the same load and constraint conditions are shown in Figure 10, and the maximum error is only 9.51%.  
Figure 10: Comparison of test results and prediction results of verification (1).  
Figure 9: T-joint for verification (1) [28].  
2. The existing cross joint is shown in Figure 11, and its material is TC4 titanium alloy, using the same loading and constraining methods as in the literature [29,30]. The loading position and loading direction are shown in Figure 11. Combined with the data obtained from the fatigue test, the correctness of the augmented-reverse notch equivalent stress method is verified.  
It can be seen from Figure 11 that the height \(H\) of the non-loaded plate is 20 mm, the thickness \(L\) of the non-loaded plate is 8 mm, the size \(h\) of the welding leg is 4 mm, and the thickness \(t\) of the loaded plate is 8 mm. The fatigue life calculated by the augmented-reverse notch equivalent stress method and the test life under the same load and constraint conditions are shown in Figure 12, and the maximum error that can be obtained is only 10.91%.  
It can be clearly seen from the above two verification examples that the fatigue life predicted by the augmented-reverse notch equivalent stress method is basically the same as the real test life, which strongly verifies the effectiveness and accuracy of the new method. However, due to the existence of uncontrollable factors such as internal micro-defects of the specimen, there may be a big difference between the test life and the fatigue life predicted by the augmented-reverse notch equivalent stress method.
## 2 Dynamic Model
### Dynamic Model with Friction  
By incorporating the friction forces, the equations of motion in Equation (14) can be expanded to the following:  
\[M(q)\ddot{q}+N(q,\dot{q})+f(\dot{q})=Q+B(q,t)^{T}\lambda. \tag{26}\]  
The differential-algebraic equations in Equation (16) then become:  
\[\left[\begin{array}{cc}M&B^{T}\\ B&0\end{array}\right]\left[\begin{array}{c}\ddot{q}\\ \lambda\end{array}\right]=\left[\begin{array}{c}Q-N-f\\ \dot{B}\dot{q}\end{array}\right]. \tag{27}\]  
The partitioned differential-algebraic equations are accordingly given by:  
\[\left[\begin{array}{ccc}M_{aa}&M_{ap}&{B_{a}}^{T}\\ M_{pa}&M_{pp}&{B_{p}}^{T}\\ B_{a}&B_{p}&0\end{array}\right]\left[\begin{array}{c}\ddot{q}_{a}\\ \ddot{q}_{p}\\ \lambda\end{array}\right]=\left[\begin{array}{c}Q_{a}-N_{a}-f_{a}\\ Q_{p}-N_{p}-f_{p}\\ \dot{B}\dot{q}\end{array}\right]. \tag{28}\]  
The inverse dynamics can still be presented in the compact expression given in Equation (19), but the vector \(\overline{N}\) should be modified to the following:  
\[\overline{N}=\Big{(}N_{a}+f_{a}+{B_{a}}^{T}({B_{p}}^{T})^{-1}\Big{)}(Q_{p}-N_ {p}-f_{p})+\Big{(}M_{ap}{B_{p}}^{-1}-{B_{a}}^{T}({B_{p}}^{T})^{-1}M_{pp}{B_{p} }^{-1}\Big{)}\dot{B}\dot{q}. \tag{29}\]  
It is worth mentioning that the friction forces can only be evaluated after the corresponding normal forces are evaluated, whereas the normal forces can only be computed after the corresponding Lagrange multipliers are computed. In fact, the Lagrange multipliers are not available at the initial time. For this reason, a statics formulation of the mechanism is used at the initial time to compute the normal forces. This is valid since the mechanism is at rest at the initial time. The detailed statics formulation used to obtain the static normal forces is not presented here to reduce the paper's length. In short, the static equations can be written based on the static equilibrium principle, and subsequently, can be presented as a linear system that can be solved for the normal forces, i.e., the reaction forces, by inverting the linear system.
# A Comprehensive Study on Deep Learning-Based 3D Hand Pose Estimation Methods
## 4 Datasets & Metrics
### Metrics  
The two most common metrics utilized to quantitatively evaluate 3D hand pose estimation methods is mean End-Point-Error (EPE) and Area Under the Curve (AUC) on the Percentage of Correct Keypoints (PCK). Mean EPE is the average 3D Euclidean distance between predicted and ground-truth joints. On the other hand, PCK measures the mean percentage of predicted joint locations that fall within certain error thresholds in comparison to correct poses. Table 2 demonstrates the top results in the most commonly utilized datasets and the employed metric(s), as well as the input data modality, leveraged during training of the method responsible for the state-of-the-art results. It should be noted that, since not all works evaluate their performance using both metrics, Table 2 includes only the reported results on each method, measured in mm as far as mEPE is concerned and within 20-50 mm error threshold for AUC.
## 6 Conclusions  
The MODIS-compatible VIIRS EVI was obtained via cross-calibration using a year-long global dataset (MODIS and VIIRS CMG) and was subsequently evaluated with an additional dataset not used for the calibration/optimization. The dataset for obtaining the optimum set of coefficients was selected in order for EVI (and angular) frequencies to be as uniform as possible across all view zenith angles, relative azimuthal angles, and EVI values. The evaluation results showed a significant decrease in the difference between the VIIRS EVI and MODIS EVI upon cross-calibration, the mean error (absolute value) and RMSE having decreased from 0.021 to 0.003 EVI units, and from 0.029 to 0.020 EVI units, respectively. The random and systematic errors in VIIRS data due to the VIIRS product generation algorithms are expected to decrease, which should further improve the performance of the MODIS-compatible VIIRS EVI upon re-calibration with a new, higher maturity level dataset.  
The cross-calibration methodology introduced in this study should be useful not only for the EVI cross-calibration, but also for cross-calibrating other vegetation indices, such as the NDVI and two-band EVI (EVI2) [40] and, thus, has the potential to contribute to addressing continuity of spectral vegetation indices across optical sensors for long term global vegetation monitoring.  
**Acknowledgments:** This work was supported by a NOAA JPSS contract (T.M.) and was partially supported by a JSPS KAKENHI Grant Number 15H02856 (H.Y.).  
**Author Contributions:** [PERSON] and [PERSON] designed the concept of this study, developed the calibration protocol, and wrote the manuscript; [PERSON] performed the numerical experiment; [PERSON] and [PERSON] participated in the discussions on the interpretation of results and contributed to editing and revision of the manuscript; [PERSON] assisted in the interpretation and discussion of results with his knowledge on the VIIRS algorithm and product characteristics.  
**Conflicts of Interest:** The authors declare no conflict of interest.
## 4 Results
### Model Testing  
The trained model was tested on other datasets with outer race bearing failures in order to validate its correct performance. In total, three different datasets were used for testing.  
Firstly, it was tested with IMS dataset no. 3, which has 4448 samples corresponding to 31 days and 10 h of motor operation. This motor works under the same conditions as the one used in IMS dataset no. 2.  
Three different datasets (Bearing1_3, Bearing1_4, and Bearing 1_7) from the FEMTO dataset were also used. Bearing1_3 has 2376 samples corresponding to 6 h and 36 min of motor operation; Bearing1_4 has 1429 samples corresponding to 3 h and 58 min of motor operation and Bearing1_7 has 2260 samples corresponding to 6 h and 16 min of motor operation. In all of them, the motor works at 30 Hz and 4 kN of load using an NSK6804 DD bearing, which has a BPFO of 168.34 Hz.  
Finally, two datasets (Bearing2_5 and Bearing3_1) from the XJTU-SY dataset were used, each with different motor operating conditions. The first one has a total of 339 samples, corresponding to 5 h and 39 min of motor operation working at 37.5 Hz with a load of 11 kN. The other one has a total of 2538 samples, corresponding to 42 h and 18 min of motor operation at 40 Hz with a load of 10 kN. The bearings used in both tests are LDK UER204, which has a BPFO of 115.61 Hz for the first dataset and a BPFO of 123.32 Hz for the second dataset.  
RUL predictions are shown in Figure 7 for each dataset. The errors in predicting RUL with IMS, FEMTO, and XJTU-SY datasets are also shown in Table 4. While predicting RUL with IMS dataset no. 3, the error is 0.71%. For FEMTO and XJTU-SY datasets, the errors are also compared with the errors reported in similar works that tested their model with those datasets. As can be seen, in the FEMTO Bearing1_7 dataset, the error is 2.08%, second only to that in the work by [PERSON] et al. [59]. In the FEMTO Bearing1_3 and FEMTO Bearing1_4 datasets, the errors are significantly lower than those in the rest of the works. The errors with the XJTU-SY dataset are always below 1.52%, improving the results obtained in the work presented by [PERSON] and [PERSON] [60]. All of these errors are positive, which means that the predicted RUL is overestimated. Overestimations are preferable because they lead to early  
Figure 6: RUL prediction with training data.  
predictions, allowing maintenance work or part replacements to be planned before motor failure occurs.  
Figure 7: RUL prediction. **(a)** IMS dataset no. 3. **(b)** FEMTO Bearing1_3. **(c)** FEMTO Bearing1_4. **(d)** FEMTO Bearing1_7. **(e)** XJTU-SY Bearing2_5. **(f)** XJTU-SY Bearing3_1.
## 3 Modeling Methodology
### Solvability Analysis of the Proposed CLC Control Strategy
 \tag{56}\]  
Let \(a_{M}(k)=a_{min}\), and if the speed difference between vehicles B and M satisfies \(v_{B}(k)-v_{M}(k)\geq a_{min}dt/2\) at the same time, the following inequality will be held after multi-step amplification. \[ \begin{array}{ll}S_{BM}(k+1)-&S_{safe,BM}(k+1)LPFB(k+1)\\ &\geq[v_{B}(k)-v_{M}(k)]dt-a_{M}(k)dt^{2}/2=0\end{array}  \tag{57}\]  
Hence, when \(y_{M}(k)>d/2\), the longitudinal distance constraint \(S_{BM}(k+1)\geq S_{safe,BM}(k+1)LPFB(k+1)\) will be satisfied at \(k+1\) step. To sum up, the above analysis, if \(v_{B}(k)-v_{M}(k)\geq a_{min}dt/2+d_{0}L_{3}\Delta y_{M_{min}}\) is satisfied, \(S_{BM}(k+1)\geq S_{safe,BM}(k+1)LPFB(k+1)\) will hold, given that \(S_{BM}(k)\geq S_{safe,BM}(k)\)\(LPFB(k)\). The proof of Lemma 3 is closed. \(\square\)  
**Lemma 4**. : _Given \(S_{MA}(k)\geq S_{safe,MA}(k)LPFB(k)\) is satisfied at \(k\) step, a feasible solution \(a_{M}(k)=a_{max}\) and \(a_{A}(k)=a_{min}\) can make \(S_{MA}(k+1)\geq S_{safe,MA}(k+1)LPFB(k+1)\) hold, if the speed difference between vehicles M and A satisfies \(v_{M}(k)-v_{A}(k)\geq(a_{min}-a_{max})dt/2+d_{0}L_{3}\Delta y_{M_{min}}\) for any step \(k\) (\(k=1,\ 2,\ \ldots,\ N\))._  
Proof. : The proof process of lemma 4 is similar to that of Lemma 3 and will not be repeated here. \(\square\)  
In summary, vehicle differences between the controlled vehicles (A and D) and their preceding vehicles in the LC-O and LC-T stages are provided as the Lemma 1 to Lemma 4 to ensure the sequential solvability of the optimization problem (39) and (40) in the proposed CLC control strategy. It should be noted that the above conclusion is based on the longitudinal distances among vehicles close to the critical longitudinal safety distance \(d_{0}\), if the longitudinal distance between the controlled vehicle and its preceding vehicle is greater than this critical value, then the speed difference between the controlled vehicle and its preceding vehicle is allowed to have a greater lower limit.
# Advances in Random Fiber Lasers and Their Sensing Application
## 4 Sensing Application
### Point-Sensing
This is partly because the detection of inaccessible parts and the real-time structural monitoring are impossible for conventional methods. Regular FBGs have been extensively studied for ultrasound sensing [122; 123], but the broadband reflection of FBGs suffers week response from broad bandwidth light source in the ultrasound sensing. The RFL based on RFGs is a better choice for ultrasound detection. As RFGs can offer strong random scattering and broadband spectral reflection. In 2017, RFGs were used as the ultrasound sensing head for the first time; meanwhile, they provided random feedback for the RFL [124]. As long as the effective length of the grating can be less than the wavelength of the ultrasound waves, ultrasound sensing would be realized. It proved that this RFL based on RFGs realized broadband ultrasound detection of 0.8 MHz with high SNR and responded to the harsh environment with variations of large temperature and strain. To improve the sensitivity, reduce the cost, and optimize the structure, a high-efficiency RFL based on RFGs was proposed in 2020 [125], making it possible for the high response of temperature and strain, as well as broad ultrasound bandwidth of 8 MHz. The setup of RFL based on the strong RFG for ultrasound detection is depicted in Figure 18. This configuration is implemented by a lasing resonance with high doped EDF (HD-EDF), which is pumped by a 980 nm laser through a WDM. The HD-EDF can effectively reduce the threshold of the pump source and the length of fiber with strong gain because of the high erbium concentrate. The RFG provides random feedback, and could be as a sensing head. It greatly broadens the bandwidth of sensing and shows the practical applications in ultrasound sensing. In the point-sensing system, gratings are the important passive devices, due to the high sensitivity for the change of the environment. They play the role of sensing elements, as well as provide feedback for RFLs. Thus, RFLs based on the FBGs and RFGs can apply in the remote sensing system, and ultrasound sensing system, respectively. FBGs and RFGs would perform broad bandwidth, high stability, high sensitivity, flexible multiplexing capability, and robustness in the sensing system. However,  
Figure 17: Scheme of RFL using FBG as a sensing element. gratings always require the etching technique artificially controlled. There is no doubt that the process of forming an RFL system has increased in complexity and difficulty.
## 4 Analysis of the Main Objectives
### Functional Mobility  
The Time up and Go (TUG) test was the most preferred test to quantify functional mobility. Significant differences in favor of the control group for the TUG test (\(p=0.027\)) were observed in the [PERSON] et al. study. While in favor of the VR group, significant differences were reported for TUG (\(p<0.001\)) by the study of [PERSON] et al. Also, after treatment, TUG changes (\(p=0.005\)) were found to be superior in [PERSON] et al. Group I of patients, compared to group III and group II, proved to be superior to group III, TUG (\(p=0.011\)). Effect sizes were very small and nonsignificant between groups for TUG (\(p=0.3\)) in the [PERSON] et al. study favoring RAGT + VR. In the experimental group, the study conducted by [PERSON] et al. yielded better results for all measurements, including the TUG test. The same happened for the control group. Analyzing the progression over time, from T1 to T2, the control group shows better results in all measurements, while the experimental group maintains improved results only for the TUG test. The study by [PERSON] et al. showed no significant differences in TUG both post-intervention and during the follow-up. Two studies did not provide assessments of functional mobility [28; 29].
## Appendix A Gradient: Divergence, and Curl in Cylindrical Coordinates
### Curl in Cylindrical Coordinates  
The calculation of _curl_ follows the same method, as _divergence_ calculated in cylindrical coordinates. The cross product is calculated between _nabla_ and vector field \(U(\rho,\phi,z)\).  
\[\begin{split}\
abla\times U&=\left(\hat{\rho}\frac{ \partial}{\partial\rho}+\frac{\hat{\phi}}{\rho}\frac{\partial}{\partial\phi}+ \hat{z}\frac{\partial}{\partial z}\right)\left(U_{\rho}\hat{\phi}+U_{\rho} \hat{\phi}+U_{z}\hat{z}\right)\\ &=\hat{\rho}\times\left(\hat{\rho}\frac{\partial U_{\rho}}{ \partial\rho}+U_{\rho}\frac{\partial\hat{\rho}}{\partial\rho}+\hat{\phi}\frac{ \partial U_{\phi}}{\partial\rho}+U_{\rho}\frac{\partial\hat{\phi}}{\partial \rho}+\hat{z}\frac{\partial U_{z}}{\partial\rho}+U_{z}\frac{\partial\hat{z}}{ \partial\rho}\right)\\ &+\frac{\hat{\phi}}{\rho}\times\left(\hat{\rho}\frac{\partial U_{ \rho}}{\partial\phi}+U_{\rho}\frac{\partial\hat{\phi}}{\partial\phi}+\hat{\phi} \frac{\partial U_{\phi}}{\partial\phi}+U_{\rho}\frac{\partial\hat{\phi}}{ \partial\phi}+z\frac{\partial U_{z}}{\partial\phi}+U_{z}\frac{\partial\hat{z}}{ \partial\phi}\right)\\ &+\hat{z}\times\left(\hat{\rho}\frac{\partial U_{\rho}}{\partial z} +U_{\rho}\frac{\partial\hat{\phi}}{\partial z}+\hat{\phi}\frac{\partial U_{\phi} }{\partial z}+U_{\phi}\frac{\partial\hat{\phi}}{\partial z}+z\frac{\partial U_{z}}{ \partial z}+U_{z}\frac{\partial\hat{z}}{\partial z}\right)\\ &=\hat{\rho}\times\left(\hat{\rho}\frac{\partial U_{\rho}}{\partial \rho}+0+\hat{\phi}\frac{\partial U_{\phi}}{\partial\rho}+0+2\frac{\partial U_{z}}{ \partial\rho}+0\right)\\ &+\frac{\hat{\phi}}{\rho}\times\left(\hat{\rho}\frac{\partial U_{ \rho}}{\partial\phi}+U_{\rho}\hat{\phi}+\hat{\phi}\frac{\partial U_{\phi}}{ \partial\phi}-U_{\phi}\hat{\rho}+z\frac{\partial U_{z}}{\partial\phi}+0\right) \\ &+\hat{z}\times\left(\hat{\rho}\frac{\partial U_{\rho}}{\partial z} +0+\hat{\phi}\frac{\partial U_{\phi}}{\partial z}+0+z\frac{\partial U_{z}}{ \partial z}+0\right)\\ &=\frac{\partial U_{\phi}}{\partial\rho}\hat{z}-\frac{\partial U_{z}}{ \partial\rho}\hat{\phi}-\frac{\partial U_{\rho}}{\partial\phi}\hat{z}+\frac{U_{ \phi}}{\rho}\hat{z}+\frac{1}{\rho}\frac{\partial U_{z}}{\partial\phi}\hat{ \rho}+\frac{\partial U_{\rho}}{\partial z}\hat{\rho}-\frac{\partial U_{\phi}}{ \partial z}\hat{\rho}\\ &=\hat{\rho}\left(\frac{1}{\rho}\frac{\partial U_{z}}{\partial\phi}- \frac{\partial U_{\phi}}{\partial z}\right)+\hat{\phi}\left(\frac{\partial U_{ \rho}}{\partial z}-\frac{\partial U_{z}}{\partial\rho}\right)+2\left(\frac{1}{\rho} \frac{\partial}{\partial\rho}\left(V_{\phi}\cdot\rho\right)-\frac{1}{\rho}\frac{ \partial U_{\rho}}{\partial\phi}\right)\end{split} \tag{15}\]
## 1 Introduction  
There is a growing concern that the technology, processes, and procedures used in digital investigations are not keeping abreast with the technology that criminals are using to perpetrate crime. This is generally due to a continual growth in cybercrime, increasing magnitudes of storage, a multitude of data evidence sources and continual increases in computational power. For these reasons, there exists a phenomenon, which we refer to as the \"large data problem in digital forensics\", which contributes to the increase in the \"backlog\" in of digital devices waiting to be digitally investigated. Various attempts have been made to identify the scale of the backlog, but estimates suggest between 6-12 months in 2004 [1] and rising to between 18-24 months in 2010 [2]. Similar patterns are reported in the US [3]. It should be noted that the backlog is only in part due to the increasing dataset sizes, part of the problem exists because of the increasing number of investigations coupled with too few investigators to investigate them.  
One of the major pragmatic problems facing digital investigators is that at the outset of an investigation it is not apparent where digital evidence will be located, if the evidence is successfully located, it is often difficult to ascertain which evidence source will be relevant to an investigation. This leads to a situation where an investigator has to image all potential sources of digital evidence and indeed every device that has been included as part of a seizure.  
The \"range\" of data sources increases considerably when an investigation involves social media and increases further still where numerous participants are involved. Added to this problem of an increasing multitude of data sources is the rapidly increasing storage sizes (and decreasing costs) available for purchase--typical hard disk capacities have increased from 10 Gb in the early 1980s to over a Tb in the 2010s.  
The advent and adoption of \"secure\" technologies threatens to render current approaches to digital forensic investigation more complex and problematic. Technologies, such as the growth in encryption, which now encompasses full disk encryption; secure network communication; secure processors; and anonymous routing potentially make the time taken to undertake digital investigations longer.  
Given this array of problems, we propose that it is necessary to review the ways in which digital investigations consider issues and we discuss the introduction of intelligent techniques in the investigative process. In this paper, we propose that there is a need to re-examine standard digital forensic processes and procedures, as well as the uses of investigative technology to adapt to advances in the criminal use of technology--this is done in the paper by consideration of intelligent forensics. A number of the key recent technological advances, which present particular challenges to law enforcement agencies, are analysed herein. We explore the concepts of _intelligence_ and propose that _digital forensic intelligence_ and _intelligent forensics_ can add significant value to investigations.