esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Best Antenna Selection Mode  
### Best Antenna Serving U\({}_{1}\) (Bas-1)  
In this scheme, the source node selects the best antenna for maximal performance at \(U_{1}\). This strategy can optimize the performance of the system in the scenario where \(U_{2}\) performance is guaranteed due to superior normalized channel gain and the source prefers a suitable antenna to serve \(U_{1}\). Subsequently, the selected antenna, denoted by \(k_{1}^{*}\), can be formulated as  
\[k_{1}^{*}=\arg\ \max_{k=1,2,\ldots,K}\ G_{1}^{(k)}. \tag{22}\]  
Let \(F_{G_{n}}^{(k_{n}^{*})}(\gamma)\) be the CDF of \(G_{n}^{(k_{n}^{*})}\), it immediately follows that \(F_{G_{2}}^{(k_{1}^{*})}(\gamma)=F_{G_{2}}(\gamma)\), thus the outage probability and the Ergodic Capacity at \(U_{2}\) in this scheme is similar to those in \(RAS\), i.e., \(OP_{2}^{BAS-1}=OP_{1}^{RAS}\) and \(E_{x_{2}}^{BAS-1}=E_{x_{2}}^{RAS}\). In addition, the ordered random variables \(G_{1}^{(k_{1}^{*})}\) can be re-expressed as  
\[G_{1}^{(k_{1}^{*})}= \max(\min\left(\bar{G}_{1}^{(1)},\bar{G}_{2}^{(1)}\right),\min \left(\bar{G}_{1}^{(2)},\bar{G}_{2}^{(2)}\right),\ldots,\min\left(\bar{G}_{1} ^{(K)},\bar{G}_{2}^{(K)}\right)). \tag{23}\]  
It can be noticed that \"\(\min\left(\bar{G}_{1}^{(k)},\bar{G}_{2}^{(k)}\right)\)\", where \(k\in[1,K]\), are identically distributed and are dependent due to the mutual interference terms, i.e., \(I_{1}\) and \(I_{2}\). By rules of combinatorics, the CDF of \(G_{1}^{(k_{1}^{*})}\) can be derived as  
\[F_{G_{1}}^{(k_{1}^{*})}(\gamma)= 1+\sum_{k=1}^{K}\binom{K}{k}(-1)^{k}\Pr\bigg{(}\bigcap_{t=1}^{k} \min(\bar{G}_{1}^{(t)},\bar{G}_{2}^{(t)})>\gamma\bigg{)} \tag{24}\] \[= 1+\sum_{k=1}^{K}\binom{K}{k}(-1)^{k}\Pr\bigg{(}\min\left(\frac{ \min((X_{1,t})_{t=1}^{k})}{I_{1}},\frac{\min((X_{2,t})_{t=1}^{k})}{I_{2}} \right)>\gamma\bigg{)}\] (25) \[= 1+\sum_{k=1}^{K}\binom{K}{k}(-1)^{k}\exp\bigg{(}-C_{1}\left(\frac {k\gamma}{\mu_{1}\alpha_{1}}\right)^{\frac{2}{q}}-C_{2}\left(\frac{k\gamma}{ \mu_{2}\alpha_{2}}\right)^{\frac{2}{q}}\bigg{)}. \tag{26}\]Substituting (26) into (13) yields similar integrals as in (16), thus by use of (16), one can obtain the closed-form of the Ergodic Capacity as \(U_{1}\) for \(BAS-1\) scheme as  
\[\begin{split} E_{x_{1}}^{BAS-1}=&-\frac{1}{\mu\alpha 2}\frac{\theta_{1}}{\mu_{2}-1}\sum_{k=1}^{K}{(k)}(-1)^{k}\left\{H_{1,2}^{2,1} \left(C_{1}\left(\frac{k}{\mu_{1}\alpha_{1}\alpha_{2}}\right)^{\frac{2}{\eta} }+C_{2}\left(\frac{k}{\mu_{2}\alpha_{2}\alpha_{2}}\right)^{\frac{2}{\eta}} \left|\begin{array}{c}(0,2\eta^{-1})\\ (0,1),(0,2\eta^{-1})\end{array}\right.\right)\\ &\quad-H_{1,2}^{2,1}\left(C_{1}\left(\frac{k}{\mu_{1}\alpha_{1}}\right)^{\frac {2}{\eta}}+C_{2}\left(\frac{k}{\mu_{2}\alpha_{2}}\right)^{\frac{2}{\eta}} \left|\begin{array}{c}(0,2\eta^{-1})\\ (0,1),(0,2\eta^{-1})\end{array}\right.\right)\right\}.\end{split} \tag{27}\]
## 2 Materials and Methods
### Hierarchy Model Construction
#### 2.2.3 Calculating Weights  
The characteristic vector \(\rm W\) of the comparison judgment matrix is the relative importance vector of the elements. At present, the methods used to calculate the eigenvalues of the matrices and their corresponding eigenvectors mainly include the square root method, the geometric average method, the sum product method, the power method, and so on. This research used the square root method. With \(\rm n\times n\) Matrix \(\rm A=\{a_{ij}\}\), the steps taken to calculate the matrix eigenvalue and corresponding eigenvector with the square root method are as follows:  
1. Calculate the product of elements in each line of comparison of judgment matrix \(\rm A\): \[\rm M_{i}=\prod_{j=1}^{n}a_{ij},\ i=1,\ 2,\ \ldots,\ n\] (1)
2. Calculate the \(\rm n\)th root of \(\rm M_{i}\): \[\rm\overline{W}_{i}=\sqrt[5]{M},\ i=1,\ 2,\ \ldots,\ n\] (2)
3. Calculate the eigenvector of the comparison judgment matrix. Normalize the vector \(\rm\overline{W}=\left[\rm\overline{W}_{1},\rm\overline{W}_{2},\ldots,\rm \overline{W}_{n}\right]^{T}\) to obtain the eigenvector \(\rm W=\left[\rm W_{1},\rm W_{2},\ \ldots,\rm W_{n}\right]^{T}\). \[\rm W_{i}=\rm\overline{W}_{i}/\sum_{j=1}^{n}\ \rm\overline{W}_{j},\ i=1,\ 2,\ \ldots,\ n\] (3) This vector is the calculated weight.
4. Carry out a consistency test for the judgement matrix. The comparison judgment matrix was obtained with an evaluator, through a comparison, in pairs, and the results were inevitably biased; therefore, it was necessary to determine the consistency. The consistency inspection steps are as follows 1. Calculate the maximum eigenvalue of the comparison judgment matrix: \[\rm\lambda max=\sum_{i=1}^{n}\left(AW\right)_{i}/nW_{i}\] (4) 2. Calculate the random consistency ratio (CR): \[\rm Consistency\ index:\ CI=\frac{\rm\lambda max-n}{n-1}\] (5) Random consistency ratio : \[\rm CR=\frac{CI}{RI}\] (6) where \(\rm n\) is the matrix order and \(RI\) is the average random consistency index, the values of which are shown in Table 3.
# SSTrack: An Object Tracking Algorithm Based on Spatial Scale Attention
## 4 The Experiments
### Comparison with the Popular Trackers
#### 4.2.2 TrackingNet  
TrackingNet [42], the first large-scale object tracking dataset, consists of video sequences exclusively captured in real outdoor scenarios. The training dataset is exceptionally rich, encompassing over 30,000 video sequences and 14 million annotated bounding boxes. The test set comprises 511 sequences. Like GOT-10k, tracking results are evaluated online, providing a relatively fair assessment standard for object tracking algorithms. The evaluation metrics include precision (P), normalized precision (NP), and success rate (SUC). Experimental results are presented in Table 2.  
Leveraging the powerful feature extraction capabilities of the Swin Transformer, SwinTrack outperforms other tracking algorithms across various evaluation metrics. However,  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **AO (\%)** & **SR\({}_{0.5}\) (\%)** & **SR\({}_{0.75}\) (\%)** & **Speed/fps** \\ \hline OURS & 71.5 & 81.9 & 65.5 & 28 \\ SwinTrack [15] & 69.9 & 80.1 & 63.9 & 45 \\ CSwinTT [39] & 69.6 & 80.0 & 63.1 & 6 \\ TransT [14] & 68.9 & 79.7 & 61.5 & 15 \\ TrDimp [13] & 68.8 & 80.4 & 58.6 & 12 \\ TrSiam [13] & 67.3 & 78.7 & 58.5 & 14 \\ Siam RCNN [40] & 65.0 & 72.8 & 59.8 & 4 \\ Ocean [41] & 61.1 & 71.6 & 49.2 & 34 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experiments and comparisons on GOT-10k.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **P (\%)** & **NP (\%)** & **SUC (\%)** \\ \hline OURS & 79.9 & 86.7 & 81.9 \\ CSwinTT [39] & 79.5 & 86.6 & 81.7 \\ SwinTrack [15] & 78.4 & 85.7 & 81.1 \\ TransT [14] & 73.1 & 83.3 & 78.4 \\ TrDimp [13] & 73.1 & 83.3 & 78.4 \\ TrSiam [13] & 72.7 & 82.9 & 78.0 \\ SiamPRN++ [20] & 73.3 & 69.4 & 80.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experiments and comparisons on TrackingNet.  
due to the lack of utilization of spatial scale features, SwinTrack lags behind the SSTrack by 1.5%, 1%, and 0.8% on the three respective metrics.
## 3 Results and Discussion
### FTIR Analysis  
The FTIR spectra provide information of functional group or biomolecules on the surface of the biosynthesized AgNPs. In the present study, FTIR analysis was performed to identify the potential functional group in _L. plantarum_ TA4 which responsible in the reduction and stabilization of AgNPs. The obtained FTIR spectrum is shown in Figure 5. Several intense bands are observed on the biosynthesized AgNPs at 3197, 2924, 1634, 1518, 1450, 1209, 1030, and 961 cm\({}^{-1}\) (Table 2), whereas the cell biomass of _L. plantarum_ TA4 showed intense bands at 3254, 1636, 1551, 1456, 1224, 1078, and 994 cm\({}^{-1}\). The bands obtained from the cell biomass of _L. plantarum_ TA4 were used as references, where the functional group was involved in the synthesis and stabilization process. A broad band located at 3197 cm\({}^{-1}\) (was shifted from 3254 cm\({}^{-1}\) in cell biomass) can be assigned to the stretching vibration of hydroxyl group (-OH) and amine group (N-H stretching vibration in primary and secondary amines of amino acids, peptides and proteins) [45] implied their involvement in the synthesis of AgNPs. The band at 2924 cm\({}^{-1}\) corresponds to the C-H stretching vibration which not observed in the cell biomass, and the band at 1634 cm\({}^{-1}\) could be attributed to C=O stretching of Amide I in addition to peptide bond which may involve in the stabilization of AgNPs as reported by [PERSON] et al. [45]. Meanwhile, the intense band at 1518 cm\({}^{-1}\) corresponds to Amide II (N-H\({}_{2}\) deformation in primary amide and N-H bending and C-N stretching in secondary amide). The band at 1450 cm\({}^{-1}\) could be assigned to C-H bending mode of methyl and methylene group in protein and same band was also observed in the cell biomass. Concurrently, the band of 1209 cm\({}^{-1}\) in AgNPs (which was shifted from 1224 cm\({}^{-1}\) in cell biomass) corresponds to C-N stretching and PO\({}_{2}\)- asymmetric stretching. Moreover, the band observed at 1030 cm\({}^{-1}\) in AgNPs can be assigned to C-O stretching of carboxyl group, which was shifted from 1078 cm\({}^{-1}\) in cell biomass. Lastly, the small band (994 cm\({}^{-1}\) in cell biomass) shifted toward a lower wave number was observed at 961 cm\({}^{-1}\), which can be assigned to the bending vibration of C=C group. In this study, the obtained functional groups on biosynthesized AgNPs (hydroxyl, protein, and carboxyl) verified the presence of biomolecules from the cell membrane of _L. plantarum_ TA4, which was involved in the biosynthesis process.  
Figure 4: Size distribution of biosynthesized AgNPs by dynamic light scattering (DLS) analysis.
# Matching Quality Detection System of Synchronizer Ring and Cone
## 1 Introduction
According to related research, the most common failure mode of the synchronizer is crash [12], which can cause operational noise or even hardware damage. This is because the friction coefficient is too low due to wear or local thermomechanical effects. In addition, a friction coefficient that is too high will result in a higher thermo-mechanical load of the synchronizer, increasing the risk of cone seizure [13]. In order to avoid these failures, it is necessary to detect the matching degree of the synchronizer ring and synchronizer cone. Since the synchronizer ring is a thin-walled component, it is easily deformed during heat treatment, but the ring gear cannot be processed thereafter. Therefore, in the case where a single component cannot fully satisfy the requirements, it is necessary to ensure quality of matching of the synchronizer ring and cone to ensure performance. If they do not fit well enough, it will affect the contact angle, the contact mode, and the average radius of the friction surface. Wear due to normal use also changes the coefficient of friction. These will all affect friction and deteriorate the synchronization performance. This makes detecting the match quality a problem that needs to be solved. However, the traditional red lead powder detection method [14] for detecting matching quality requires manual recognition, so its accuracy is insufficient. Therefore, the problems of how to establish quantitative criteria, and how to design a machine to detect them need to be studied. In order to quantitatively detect matching quality after the workpiece is formed, to meet the needs of industrial production, a friction torque based detection system for matching quality between synchronizer ring and cone is designed in this paper. In Section 2, the theoretical model of the friction cone in the synchronization process is introduced. In Section 3, the acceptance criteria are established by the residual sum of squares (RSS), and the quality of the synchronizer is determined by measuring the friction torque and the backup gap. In Section 4, this synchronizer ring and cone matching quality detection system is implemented. The system is mainly used for quality detection of synchronizer ring and cone in the current automobile gearbox before packing. It improves the consistency of the synchronizer ring and synchronizer cone, which makes the synchronizer lighter and more reliable during shifting of the gearbox. According to market research, the system designed and implemented in this paper is advanced and original.
## 7 Discussion
### Comparison of Hardware Resource Requirements with Existing Mainstream Models  
The existing method supports bilingual capabilities in Mandarin and Uyghur, which is relatively rare among large language models. Specifically, support for Uyghur in the agricultural field is uncommon in other studies. Compared to ChatGPT and ChatGLM, which support multiple languages [46] such as English and Chinese, their support for minority languages is limited, and they do not support Uyghur.  
The existing method is optimized for professional knowledge in the agricultural field, including knowledge of agricultural development history, crop cultivation, animal husbandry, and other agricultural fields. This targeted optimization makes the model more accurate and efficient in handling agriculture-related issues. In contrast, general large language models may have limitations in deep understanding and generation in specific fields. Professional models, on the other hand, focus on highly relevant sustainable development goals. This emphasizes the importance of careful model selection, considering task requirements, cost, complexity, and transparency [47].  
When running OPT-175B on a single 16 GB GPU, ChatGPT achieves significantly higher throughput with FlexGen compared to the most advanced offloading systems, reaching a generation throughput of 1 token/second for the first time with an effective batch size of 144. In the HELM benchmark test, FlexGen can benchmark a 30B model equipped with a 16 GB GPU on 7 representative sub-scenarios within 21 h [47].  
The existing method can be normally deployed and run on a graphics card configured with 4 cores and 4 GB of video memory, significantly reducing hardware requirements and making the model more accessible and applicable. As shown in Table 8, compared to ChatGPT, Llama-2, ChatGLM, and Wenxin Yiyan, which have higher hardware requirements and require a high-performance distributed GPU integrated computing environment, the existing method has lower hardware demands.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model Name** & **Loss** & **Accuracy** & **Recall** & **F1 Score** & **Train Time** & **Data Type** \\ \hline Transformer & 0.067 & 0.984 & 0.984 & 0.984 & 3.9 & Chinese And Uyghur \\ \hline LSTM & 0.140 & 0.687 & 0.831 & 0.831 & 5.2 & Chinese And Uyghur \\ \hline TKAN & 0.346 & 0.653 & 0.653 & 0.653 & 7.1 & Chinese And Uyghur \\ \hline Transformer & 0.066 & 0.986 & 0.986 & 0.986 & 4.1 & Chinese And Tibetan \\ \hline \hline \end{tabular}
\end{table}
Table 7: Training result data of different models and corpora of different language categories.
## 4 Results
### In Vivo Carotid  
Figure 8 shows the in vivo cross section carotid images reconstructed by different methods. Regions indicated by the circle and box were selected to calculate image metrics. We can see that SLSC reduces clutter and noise; however, the tissue intensity degrades at a large depth. CMSB images show an improved contrast compared with the DAS image and an improved tissue intensity compared with DAS and DMAS images. In comparison with CMSB (\(\delta\) = 0.5), LOCw-CMSB reduces noise in the carotid artery and CMSB (\(\delta\) = \(\delta_{ac}\)) improves the tissue smoothness, respectively. LOCw-CMSB (\(\delta\) = \(\delta_{ac}\)) obtains a better performance inside the carotid artery and the anatomical structures are more distinguishable in comparison with CMSB (\(\delta\) = 0.5).  
Table 5 lists image quality metrics of carotid images. Compared with DAS, DMAS and SLSC obtain an improvement and degradation of 51.9% and 23.0% in contrast, respectively. CMSB-based methods obtain an improved CR, gCNR, and sSNR over DAS and DMAS. LOCw-CMSB improves the CR by 9.0% and 15.7% compared with CMSB (\(\delta\) = 0.3) and CMSB (\(\delta\) = 0.5), respectively, and the gCNR and sSNR of LOCw-CMSB are slightly higher than that of CMSB (\(\delta\) = 0.5). The gCNR and sSNR of CMSB (\(\delta\) = \(\delta_{ac}\)) are 7.2% and 17.3% larger than that of CMSB (\(\delta\) = 0.5), whereas CR is almost preserved. In addition, LOCw-CMSB (\(\delta\) = \(\delta_{ac}\)) leads to improvements of 14.7%, 6.0%, and 13.3% in CR, gCNR, and sSNR over CMSB (\(\delta\) = 0.5). This demonstrates the high image quality of LOCw-CMSB (\(\delta\) = \(\delta_{ac}\)) when imaging soft tissues.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**FWHM (mm)**} & \multicolumn{3}{c}{**Cyst at 15 mm Depth**} & \multicolumn{3}{c}{**Cyst at 42.9 mm Depth**} \\  & & **CR (dB)** & **gCNR** & **sSNR** & **CR (dB)** & **gCNR** & **sSNR** \\ \hline DAS & 0.59 & \(-\)32.7 & 0.98 & 1.99 & \(-\)22.0 & 0.61 & 1.90 \\ DMAS & 0.46 & \(-\)50.3 & 0.86 & 1.48 & \(-\)35.8 & 0.39 & 1.30 \\ SLSC & - & \(-\)29.0 & 1.00 & 4.97 & \(-\)32.3 & 1.00 & 2.83 \\ CMSB & 0.33 & \(-\)62.5 & 1.00 & 2.01 & \(-\)47.3 & 0.88 & 1.65 \\ (\(\delta\) = 1.3) & 0.27 & \(-\)59.5 & 1.00 & 2.01 & \(-\)44.8 & 0.92 & 1.71 \\ LOCw- & 0.27 & \(-\)74.1 & 1.00 & 1.98 & \(-\)66.1 & 0.85 & 1.54 \\ CMSB & 0.27 & \(-\)56.8 & 1.00 & 2.95 & \(-\)44.9 & 0.96 & 2.36 \\ LOCw- & 0.27 & \(-\)72.0 & 1.00 & 2.86 & \(-\)66.0 & 0.93 & 2.09 \\ (\(\delta\) = \(\delta_{ac}\)) & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Image metrics of experimental cyst images.
# Influence of the Flexible Tower on Aeroelastic Loads of the Wind Turbine
## 3 Calculation Method
### Solving Structural Equations of Motion  
For a general external excitation \(P(t)\), the Newmark method is used in this paper to solve the multi-degree-of-freedom equations of motion.  
The Newmark method approximates the velocity and displacement of the system at the moment \((t+\Delta t)\) by two assumptions.  
\[\dot{x}_{t+\Delta t}=\dot{x}_{t}+\left[(1-\beta)\ddot{x}_{t}+\beta\ddot{x}_{t +\Delta t}\right]\Delta t \tag{46}\]  
\[x_{t+\Delta t}=x_{t}+\dot{x}_{t}\Delta t+\left[\left(\frac{1}{2}-\alpha \right)\ddot{x}_{t}+\alpha\ddot{x}_{t+\Delta t}\right]\Delta t^{2} \tag{47}\]  
where \(\alpha\) and \(\beta\) are the parameters adjusted according to the accuracy and stability requirements of the integration. When \(\alpha=1/6\), \(\beta=1/2\), it is the linear acceleration method; when \(\alpha=1/4\), \(\beta=1/2\), it is the average acceleration method; when \(\alpha=1/2\), \(\beta=1/2\), it is the the central difference method; when \(\alpha=1/8\), \(\beta=1/2\), it is the variable acceleration method.  
From Equations (44) and (45), we can solve that:  
\[\ddot{x}_{t+\Delta t}=\frac{1}{\alpha\Delta t^{2}}(x_{t+\Delta t}-x_{t})-\frac {1}{\alpha\Delta t}\dot{x}_{t}-\left(\frac{1}{2\alpha}-1\right)\ddot{x}_{t} \tag{48}\]  
\[\dot{x}_{t+\Delta t}=\dot{x}_{t}+(1-\beta)\Delta t\ddot{x}_{t}+\beta\Delta t \ddot{x}_{t+\Delta t} \tag{49}\]  
When \(\beta\geq 0.5\) and \(\alpha\geq 0.25(0.5+\beta)^{2}\), the Newmark method is the unconditionally stable format. The equations of motion can be solved by the following steps.  
1. Initial Calculation 1. Firstly, the overall characteristic matrices \(K\), \(M\) and \(C\) of the vibrating system are calculated. 2. From the initial conditions \(x_{0}\) and \(\dot{x}_{0}\), \(\ddot{x}_{0}\) is calculated. \[\ddot{x_{0}}=M^{-1}\big{(}F_{0}-C\dot{x_{0}}-Kx_{0}\big{)}\] (50)
3. Step \(\Delta t\) is selected with parameters \(\alpha\), \(\beta\) and calculate the integration constants. \[A_{1}=\frac{1}{\alpha\Delta t^{2}},A_{2}=\frac{\beta}{\alpha\Delta t},A_{3}= \frac{1}{\alpha\Delta t},A_{4}=\left(\frac{1}{2\alpha}-1\right),A_{5}=\frac{ \Delta t}{2}\left(\frac{\beta}{\alpha}-2\right),A_{6}=\left(\frac{\beta}  
1. The equivalent load vector \(\overline{F}\) at moment \(t+\Delta t\) is determined. \[F=F_{t+\Delta t}+\big{[}A_{1}x_{t}+A_{3}\dot{x}_{t}+A_{4}\ddot{x}_{t}\big{]}M+ \big{[}A_{2}x_{t}+A_{\theta}\dot{x}_{t}+A_{3}\ddot{x}_{t}\big{]}C\] (52) 2. The displacement at moment \(t+\Delta t\) is calculated. \[x_{t+\Delta t}=\overline{K}^{-1}\overline{F}_{t+\Delta t}\] (53) 3. The velocity at time \(t+\Delta t\) and the acceleration are solved. \[\ddot{x}_{t+\Delta t}=\frac{1}{\alpha\Omega t^{2}}(x_{t+\Delta t}-x_{t})-\frac {1}{\alpha\Delta t}\dot{x}_{t}-\bigg{(}\frac{1}{2\alpha}-1\bigg{)}\ddot{x}_{t}\] (54) \[\dot{x}_{t+\Delta t}=\dot{x}_{t}+(1-\beta)\Delta t\ddot{x}_{t}+\beta\Delta t \ddot{x}_{t+\Delta t}\] (55)
## 2 Data Preprocessing for Feature Extraction
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Parameter Definition** \\
**Notation** & \\ \hline \(x_{n}\) & Sampled input data at interval \(T_{d}\) \\ \hline \(T_{d}\) & Sampling interval for input data \\ \hline \(y_{n}\) & RMS level for the \(n\)-th sample in \(Path-\alpha\) \\ \hline \(C\) & Normalization coefficient for RMS calculation \\ \hline \(L_{n}\) & Window size for RMS calculation \\ \hline \(y_{\alpha}\) & RMS pattern feature from \(Path-\alpha\) \\ \hline \(y^{*}\) & Preprocessed signal after passing through the \(BPF\) in \(Path-\beta\) \\ \hline \(W\{f\}\) & Weighting function applied in the frequency domain \\ \hline \(f_{L}\) & Lower frequency bound for the frequency windowing operation \\ \hline \(f_{H}\) & Upper frequency bound for the frequency windowing operation \\ \hline \(k\) & Amplification ratio applied within the frequency range \([f_{L},\ f_{H}]\) \\ \hline \(y^{**}\) & Signal after applying the amplitude weighting and \(IFT\) \\ \hline \(FT\{\cdot\}\) & 1D Fourier transform operation \\ \hline \(IFT\{\cdot\}\) & 1D Inverse Fourier transform operation \\ \hline \(y_{\beta}\) & RMS pattern feature from \(Path-\beta\) \\ \hline \(y_{rms}\) & Final RMS pattern feature after combining \(y_{\alpha}\) and \(y_{\beta}\) \\ \hline \(y_{fray}\) & Frequency pattern feature derived from the frequency response magnitude \\ \hline \end{tabular}
\end{table} 
Table 1: Nomenclature for data preprocessing. RMS pattern features in Figure 1, the frequency pattern feature is obtained by converting the preprocessed signal \(y^{*}\), after passing through the BPF block, into frequency-domain data using the 1D FT, as shown in Equation (5):  
\[y_{freq}=FT\{y^{*}\}, \tag{5}\]  
This process results in the final frequency pattern feature \(y_{freq}\). Figure 2 provides a visual representation of the pattern features extracted from the RMS and frequency components of leak and noise signals. Figure 2a illustrates the RMS pattern features, with the \(x\)-axis divided into two sections. The left side corresponds to RMS levels computed directly without filtering in \(Path-\alpha\), while the right side represents RMS levels calculated after filtering and amplitude weighting in \(Path-\beta\). For the leak feature shown in Figure 2a, the RMS pattern exhibits an increasing trend in \(Path-\beta\), whereas for the noise feature, external noise is effectively filtered, leading to a decreasing trend in the RMS pattern size. Figure 2b displays the frequency pattern. The 1D RMS and frequency pattern features are further integrated with domain-specific features obtained from multiple sensors to train the proposed model. Figure 3 demonstrates the sequential alignment of these pattern features along the channel direction, using data gathered from four sensors to form two-dimensional (2D) tensor features. This method combines features from various sensors, structuring the resulting 2D tensor as input for the proposed model, as discussed in Section 3.
# The Bearing Surface Defect Detection Method Combining Magnetic Particle Testing and Deep Learning
## 6 Experiment Results and Analysis
### Compare the Improved Model with the Basic Model  
The improved YOLOv5 model was compared with the baseline model in terms of mAP curve and training loss curve, as shown in Figures 17 and 18, respectively. Figure 17 illustrates the comparison of training loss curves, while Figure 18 presents the mAP curve comparison. It can be observed from Figures 17 and 18 that, in comparison to the baseline model, the improved model exhibited lower training loss values and higher detection accuracy.