esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Theoretical Framework
### Bee Colony Optimization Algorithm
#### 3.1.1 Forward Pass
However, it can sometimes suffer from premature convergence to suboptimal solutions. The WSA, on the other hand, is designed to explore the search space more thoroughly by simulating wave propagation. By combining these two algorithms, the strengths of both can be leveraged, leading to improved exploration and exploitation of the solution space. 2. The integration of WSA can help accelerate the convergence of the optimization process. While BCO may take longer to find optimal solutions due to its reliance on the collective behavior of bees, the wave propagation mechanism in WSA can guide the search process more efficiently, allowing for faster identification of high-quality solutions. 3. One of the challenges in optimization problems is the tendency of algorithms to get trapped in local optima. The combination of BCO and WSA can enhance robustness against this issue. The wave search mechanism can introduce diversity in the search process, helping to escape local optima and explore new areas of the solution space. 4. In WSNs, the environment can be dynamic, with changing conditions and requirements. The hybrid approach can provide greater adaptability, as the wave search can quickly adjust to changes in the search landscape, while BCO can maintain a balance between exploration and exploitation. 5. In WSNs application, energy efficiency is critical; combining BCO with WSA can lead to more effective resource management. The hybrid algorithm can optimize the selection of cluster heads and data transmission paths, ensuring that energy consumption is minimized while maintaining high levels of data delivery and network performance. 6. The combination of BCO and WSA can be applied to a wide range of optimization problems beyond WSNs, including routing, scheduling, and resource allocation in various fields. This versatility makes the hybrid approach a valuable tool for researchers and practitioners looking to solve complex optimization challenges.
# Investigations into Picture Defogging Techniques Based on Dark Channel Prior and Retinex Theory
## 3 The Proposed Methods
### The Correction of the Transmittance Value in the Sky Area  
Due to the large average brightness of the sky region with almost no dark elements, the calculated transmittance value will be small and lead to the final result being over-amplified, resulting in color distortion in the sky region. The color attenuation prior proposed by [PERSON] et al. [30] estimates the depth map of the scene by building a linear model of depth versus brightness and saturation, which leads to better performance when dealing with the sky region, and therefore, we use the depth map estimated by the CAP to correct the transmittance value of the DCP in the sky region, which can more accurately reflect the fog concentration in these regions, thus making the CAP depth map in these regions able to compensate for the deficiency of the DCP.  
According to the color decay a priori method, the concentration of fog at any pixel point of a foggy image is positively correlated with the difference between the brightness and saturation of that pixel, as shown in Equation (26):  
\[c(x)\propto v(x)-s(x) \tag{26}\]  
where \(c(x)\) denotes the fog density at the pixel location, \(v(x)\) denotes the pixel brightness, and \(s(x)\) denotes the pixel saturation; the linear model expressing depth in relation to brightness and saturation is as follows:  
\[d_{cap}(x)=\theta_{0}+\theta_{1}\cdot v(x)+\theta_{2}\cdot s(x)+\varepsilon(x) \tag{27}\]  
where \(\theta_{1}\), \(\theta_{2}\), and \(\theta_{3}\) denote unknown linear coefficients (\(\theta_{0}\) = 0.121779; \(\theta_{1}\) = 0.959710; \(\theta_{2}\) = \(-\)0.780245), and \(\varepsilon(x)\) denotes a random 0. Equation (27) can be substituted into Equation (9) to produce the following:  
\[t_{cap}(x)=e^{-d_{cap}(x)} \tag{28}\]  
where \(t_{cap}(x)\) denotes the transmittance derived from the color attenuation prior. Subsequently, the sky region is detected using dual thresholds for luminance and saturation, as in Equation (29):  
\[mask(x)=\left\{\begin{array}{ll}1&,v(x)\geq T_{v}\cap s(x)\leq T_{s}\\ 0&,otherwise\end{array}\right. \tag{29}\]When the \(mask(x)\) value equals 1, it indicates the sky region in the image; a value of 0 signifies a non-sky area. \(T_{v}\) is the luminance threshold, and \(T_{s}\) is the saturation threshold, where \(T_{v}\) = 0.85, and \(T_{s}\) = 0.12 based on sky region statistics from 100 foggy images in the RESIDE dataset. Within the sky region, weights are adjusted based on luminance and saturation to prevent edge discontinuities caused by segmentation. A weighting function is employed to correct the transmittance in color-distorted areas, where \(t_{dcp}\) denotes the transmittance value obtained by the original dark channel a priori defogging algorithm, as in Equations (30) and (31):  
\[\beta(x)=\frac{v(x)-T_{v}}{\max(v(x)-T_{v})}.\frac{T_{s}-s(x)}{T_{s}} \tag{30}\]  
\[\widetilde{t}(x)=\beta(x)\cdot t_{cap}(x)+1-\beta(x)\cdot t_{dcp}(x) \tag{31}\]
# Enhanced Trajectory Tracking via Disturbance-Observer-Based Modified Sliding Mode Control
## Appendix B Low Pass Filter  
The Laplace transform of Equations (14)-(16) can be written as:  
\[\widetilde{x}_{1}=\overset{\sim}{x}_{2}-(l_{1}/e_{o})\overset{\sim}{x}_{1}, \tag{21}\]  
\[\widetilde{p}\overset{\sim}{x}_{2}=\overset{\sim}{x}_{3}-(l_{2}/e_{o}) \overset{\sim}{x}_{1}, \tag{22}\]  
\[\widetilde{p}\overset{\sim}{x}_{3}=G-\bigg{(}l_{3}/e_{o})\overset{\sim}{x}_{1}, \tag{23}\]  
Equation (21) can be further solved as:  
\[\overset{\sim}{x}_{1}(p+l_{1}/e_{o})=\overset{\sim}{x}_{2}, \tag{24}\]insert Equation (A17) into (A15):  
\[p\bigg{(}p+\frac{l_{1}}{\epsilon_{o}}\bigg{)}\widetilde{x}_{1}=\widetilde{x}_{3} -(l_{2}/\epsilon_{o})\widetilde{x}_{1},\] (A18)  
\[\bigg{(}p^{2}+\frac{l_{1}}{\epsilon_{o}}p\bigg{)}\widetilde{x}_{1}+(l_{2}/ \epsilon_{o})\widetilde{x}_{1}=\widetilde{x}_{3},\] (A19)  
\[\widetilde{x}_{1}\bigg{(}p^{2}+\frac{l_{1}}{\epsilon_{o}}p+\frac{l_{2}}{ \epsilon_{o}}\bigg{)}=\widetilde{x}_{3},\] (A20)  
\[\widetilde{x}_{1}=\frac{\widetilde{x}_{3}}{\left(p^{2}+\frac{l_{1}}{\epsilon_ {o}}p+\frac{l_{2}}{\epsilon_{o}}\right)},\] (A21)  
The Laplace transform of Equation (5) can be written as:  
\[px_{3}=G,\] (A22)  
use (A22) in (A16):  
\[p\widetilde{x}_{3}=px_{3}-\left(l_{3}/\epsilon_{o}\right)\widetilde{x}_{1},\] (A23)  
use Equation (A21) in (A23):  
\[p\widetilde{x}_{3}=px_{3}-(\frac{l_{3}}{\epsilon_{o}}).\frac{\widetilde{x}_{ 3}}{\left(p^{2}+\frac{l_{1}}{\epsilon_{o}}p+\frac{l_{2}}{\epsilon_{o}}\right) },\] (A24)  
\[p\widetilde{x}_{3}+\bigg{(}\frac{l_{3}}{\epsilon_{o}}\bigg{)}.\frac{\widetilde {x}_{3}}{\left(p^{2}+\frac{l_{1}}{\epsilon_{o}}p+\frac{l_{2}}{\epsilon_{o}} \right)}=px_{3},\] (A25)  
\[\widetilde{x}_{3}\bigg{(}p+\frac{l_{3}}{\epsilon_{o}p^{2}+l_{1}p+l_{2}} \bigg{)}=px_{3},\] (A26)  
\[\widetilde{x}_{3}\bigg{(}\frac{\epsilon_{o}p^{3}+l_{1}p^{2}+l_{2}p+l_{3}}{ \epsilon_{o}p^{2}+l_{1}p+l_{2}}\bigg{)}=px_{3},\] (A27)  
\[\frac{\widetilde{x}_{3}}{x_{3}}=\frac{\epsilon_{o}p^{3}+p^{2}l_{1}+pl_{2}}{ \epsilon_{o}p^{3}+p^{2}l_{1}+pl_{2}+l_{3}},\] (A28)  
it is known that (\(\widetilde{x}_{3}=x_{3}-\hat{x}_{3}\)):  
\[\frac{x_{3}-\hat{x}_{3}}{x_{3}}=\frac{\epsilon_{o}p^{3}+p^{2}l_{1}+pl_{2}}{ \epsilon_{o}p^{3}+p^{2}l_{1}+pl_{2}+l_{3}},\] (A29)  
\[1-\frac{\hat{x}_{3}}{x_{3}}=\frac{\epsilon_{o}p^{3}+p^{2}l_{1}+pl_{2}}{ \epsilon_{o}p^{3}+p^{2}l_{1}+pl_{2}+l_{3}},\] (A30)  
after solving further:  
\[\frac{\hat{x}_{3}}{x_{3}}=\frac{l_{3}}{\epsilon_{o}s^{3}+l_{1}s^{2}+l_{2}s+l_ {3}}.\] (A31)
## 3 Results
### Accuracy Analysis  
The implant planning software programs used in the studies reviewed were SimPlant(r) [19; 20; 22; 29; 30; 31; 32; 37; 38; 39; 40]; Procera Clinical Design(r) [25; 26; 27; 28]; Facilitate(tm) [24]; CoDiagnostix(r) [21; 34; 35]; ImplantViewer [36]; SMOP [41]; Maximil [33]; and 3 Shape Implant Studio [23]. With respect to the types of guide support used, mucosa-supported surgical guides were the most commonly used. Two studies [30; 37] compared three types of surgical guide (muocosa-, tooth- and bone-supported), one study [19] compared two types of guide supports, 11 studies [20; 25; 26; 27; 28; 32; 33; 36; 38; 39; 40] used only mucosa-supported guides, eight studies [21; 22; 23; 29; 31; 34; 35; 41] used only tooth-supported guides, and one study [24] used bone-supported guides exclusively. Deviation parameter data are summarized in Table 2. Angular deviations of placed implants, corresponding to different mandibular or maxillary locations, were described in 22 studies. The mean angular deviation of mucosa-supported guides among the studies ranged from 2.71\({}^{\circ}\) (minimum) to 5.14\({}^{\circ}\) (maximum). With bone-supported guides, it ranged from 2.49\({}^{\circ}\) to 5.08\({}^{\circ}\) and with the tooth-supported guides from 2.5\({}^{\circ}\) to 5.62\({}^{\circ}\). Measurements of coronal deviations were described in 22 studies. The mean coronal deviations of mucosa-, bone- and tooth-supported guides ranged from 0.87 mm to 2.05 mm, 0.71 mm to 1.60 mm, and 0.39 mm to 1.63 mm, respectively. Measurements of apical deviations were described in 21 studies. The mean apical deviations of mucosa-, bone- and tooth-supported guides ranged from 1.08 mm to 2.28 mm, 0.77 mm to 1.65 mm, and 0.28 mm and 1.84 mm, respectively.
# RGB-D Camera for 3D Laser Point Cloud Hole Repair in Mine Access Shaft Roadway
## 4 Data Processing
### Data Processing of the RGB-D Camera  
The Rosbag offline dataset recorded by the Realsense depth camera obtained the key frame of the dataset through Intel Realsense SDK to obtain the color image and depth image in the key frame. The basic image information of the color image and depth image,  
Figure 8: Before and after point cloud denoising. (**a**) Point cloud before denoising; (**b**) Point cloud after denoising.  
Figure 9: Before and after 3D laser point cloud registration. (**a**) Point cloud before registration; (**b**) Point cloud after registration.  
point cloud sensor data, and target coordinates under the camera coordinate system of the depth camera can be used to calculate the coordinate values of any pixel in the internal and external participating image of the depth camera in the world coordinate system.  
The pixel \((x,y)\) coordinates and the camera internal parameters provided by the color image in the camera coordinate system can obtain the \((x,\,y)\) coordinates in the camera coordinate system, and the depth image can directly provide the \((z)\) coordinates in the camera coordinate system, which enables us to obtain the point cloud data, as shown in Figure 10. The conversion formula between camera coordinate P and pixel coordinate PXY is as follows:  
\[\mathbf{Z}\mathbf{P}\mathbf{xy}=\mathbf{Z}\begin{bmatrix}\mathbf{x}\\ \mathbf{y}\\ 1\end{bmatrix}=\begin{bmatrix}\mathbf{f}_{\mathbf{x}}&0&\mathbf{c}_{\mathbf{x}}\\ 0&\mathbf{f}_{y}&\mathbf{c}_{\mathbf{y}}\\ 0&0&1\end{bmatrix}\begin{bmatrix}\mathbf{X}\\ \mathbf{Y}\\ \mathbf{Z}\end{bmatrix}=\mathbf{K}\mathbf{P} \tag{1}\]  
\[\mathbf{X}=\frac{\mathbf{Z}(\mathbf{x}-\mathbf{c}_{\mathbf{x}})}{\mathbf{f}_{\mathbf{x}}},\,\mathbf{Y}=\frac{ \mathbf{Z}(\mathbf{y}-\mathbf{c}_{\mathbf{y}})}{\mathbf{f}_{\mathbf{y}}},\mathbf{Z}=\mathbf{d} \tag{2}\]  
where: \(x\) and \(y\) are the pixel coordinate values; \(X\), \(Y\), and \(Z\) are the camera coordinate values; \(K\) is the camera internal parameter matrix; \(f_{x},f_{y}\), \(c_{x}\), and \(c_{y}\) are the camera internal parameters; and \(d\) is the depth value of each pixel measured by the depth camera.  
After obtaining the key frame point cloud model of each shaft roadway, it was necessary to carry out point cloud registration on the point cloud data of different key frames. The most classic and common registration method is the ICP algorithm. The point cloud data of the RGB-D camera key frame was registered through the ICP algorithm based on Python. The registration results are shown in Figure 11a,b. The Ply data format of the registered depth camera point cloud data was converted to the general point cloud data format of Las.  
Figure 10: Conversion of RGB image and depth image into point cloud data. (**a**) Color image; (**b**) Depth image; (**c**) Point cloud.
# Edge and Cloud Computing in Smart Cities
## 4 Application Domains
### Smart Energy and Power Systems  
The modernization of energy infrastructures relies on edge-cloud architectures for intelligent grid management, decentralized energy trading, and predictive maintenance. Edge computing enables real-time load balancing by continuously monitoring power consumption, detecting fluctuations, and dynamically adjusting distribution. This decentralized approach enhances grid resilience, preventing failures and optimizing resource utilization [136; 137; 138].  
Cloud analytics are crucial for predicting energy demand, optimizing renewable energy integration, and improving fault tolerance in power networks. AI-based predictive models refine energy consumption strategies by analyzing historical and real-time grid data, supporting efficient energy allocation [139; 140].  
The emergence of peer-to-peer energy trading platforms powered by blockchain and edge intelligence enables consumers to exchange surplus electricity securely. Smart contracts enforce automated transactions, reducing reliance on centralized power distribution authorities while fostering decentralized energy markets [141; 142].
## 2 Results and Discussion  
### Analysis of \"in Vivo\" VOCs  
The volatile compounds emitted by _O. sphegodes_ subsp. _sphegodes_, _O. bertolonii_ subsp. _benacensis_ and _N. tridentata_ species are listed in Table 1. We identified 67, 93 and 77 compounds, respectively. These VOCs belonged to the major chemical classes, such as hydrocarbons, aldehydes, ketones, alcohols, furans, phenols, free fatty acids and terpenes. As reported in Table 1, the aromatic profiles of the three orchid species showed some distinctive differences. The difference among VOCs extracted and detected from picked samples respect to \"_in situ_\" arisen from two variables. Firstly by sampling \"_in situ_\" we observe a general dilution factor of monitored headspace respect the vials (20 mL) because the special equipment is specially designed to promote air circulation to the contained plant during the SPME extraction. The second reason can take place to the cut operations made in order to collect the flowers. Some terpenes are contained into special plant organ, that damaged, are released in a headspaces vial. The main components of _O. sphegodes_ subsp. _sphegodes_ bouquet were represented by terpenes, free fatty acids and phenols, followed by alcohols, aldehydes and hydrocarbons in minor amounts. In particular, as reported in Table 1 and Figure 1, the most representative compounds detected were d-limonene (22.13%), formic acid (11.70%), \(\alpha\)-zingibirene (9.98%), phenol (9.65%), \(\alpha\)-pinene (4.65%) and undecane (3.56%). Among terpenes, in minor amounts, the presence of \(\beta\)-pinene (2.19%) and cyclosativene (2.47%) was revealed. Terpenes, ketones, and aldehydes, were the major constituents of _O. bertolonii_ subsp. _benacensis_ aroma, followed by hydrocarbons and alcohols. In particular 3,5-ocatadien-2-one (9.85%), caryophilene (6.73%), dodecanal (4.90%), 4-methyltetradane (4.69%), decanal (3.48%) and nonanal (3%) were the main compounds (Table 1 and Figure 1). _O. sphegodes_ subsp. _sphegodes_ and _O. bertolonii_ subsp. _benacensis_ are sexually deceptive orchids and numerous behavioral tests have shown that the _Ophrys_-pollinator relationship is highly specific: each _Ophrys_ species is pollinated by males of usually only one or a few pollinator species [14, 15, 16, 17]. In particular the pollinators of _O. sphegodes_ subsp. _sphegodes_ are small bees of the genus _Andrena_, especially _A. nigroaena_ and _A. limata_, while _O. bertolonii_ subsp. _benacensis O. bertolonii_ subsp. _benacensis_ is characterized by higher pollinator specificity with the main pollinator being the thymenopterous _Chalicodoma parietina_[18]. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Control**} & \multicolumn{3}{c}{_O. sphegeodes subsp. sphegodes_} & _O. betroloni subsp. benacensis_ & _N.
## 4 Experiments and Results
### Experiment Result
Since PA represents the proportion of the number of correctly predicted pixels in the total number of pixels, the proportion of black background is high, so a small numerical fluctuation can reflect a large gap. The performance of PP-LiteSeg on IoU, F\({}_{1}\)-score, and PA is basically consistent with the proposed CSTA, and its F\({}_{1}\)-score and PA are slightly higher than CSTA. However, the proposed CSTA network is much faster than other networks in fwt. It is sufficient to show that the comprehensive performance improvement of the proposed network is significant compared with other networks. Although the proposed network is slightly inferior to PP-LiteSeg in some metrics, the huge improvement in inference speed makes CSTA more \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **IoU** & **F\({}_{1}\)-Score** & **PA** & **fwt (ms)** \\ \hline ERFNet & 0.8009 & 0.8851 & 0.9795 & 19.5816 \\ CCNet & 0.7973 & 0.8814 & 0.9817 & 108.8108 \\ PP-LiteSeg & 0.9011 & 0.9474 & 0.9916 & 52.8683 \\ FLANet & 0.8967 & 0.9384 & 0.9907 & 39.2761 \\ Proposed & 0.9019 & 0.9461 & 0.9912 & 8.6956 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of segmentation evaluation results in proper exposure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **IoU** & **F\({}_{1}\)-Score** & **PA** & **fwt (ms)** \\ \hline ERFNet & 0.7463 & 0.8452 & 0.9805 & 19.5031 \\ CCNet & 0.5646 & 0.7106 & 0.9674 & 108.3623 \\ PP-LiteSeg & 0.7052 & 0.8177 & 0.9803 & 53.0378 \\ FLANet & 0.7268 & 0.8334 & 0.9797 & 39.4803 \\ Proposed & 0.8355 & 0.9059 & 0.9889 & 18.5327 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of segmentation evaluation results in overexposure. suitable for real-time application scenarios. Table 2 shows the results of quantitative comparison of segmentation performance between the proposed method and other methods in overexposure environment. In the overexposure environment, the proposed method combining image inpainting and image segmentation is compared with other segmentation methods. Quantitative comparisons are performed on IoU, F\({}_{1}\)-score, PA, and fwt. The quantitative comparison results of the proposed method have a huge improvement over ERFNet, CCNet, PP-LiteSeg, and FLANet. The results show that the performance of the proposed method in the overexposed environment is much better than the existing image segmentation methods. In addition, the fwt value of the proposed method is also the lowest, which indicates that the optimization of MAE network module is successful. It not only meets the requirements of improving segmentation quality, but also meets the requirements of improving processing speed. However, the inference time of the system is longer in the condition of overexposure. The reason is that the inpainting preprocessing of overexposed images adds extra time overhead. However, as far as the current level of GPU chip development [42; 43; 44; 45] is concerned, it can fully meet the real-time requirements of embedded devices.
## 2 Methodology
### Mathematical Model of the MPP+Porous Structure  
Based on the sound absorption mechanism of porous sound-absorbing materials, the Johnson-Champoux-Allard model is chosen to describe the sound absorption coefficient of the material. The transfer matrix of a porous sound-absorbing material \(P\) is:  
\[P=\begin{bmatrix}\cos(k_{p}D_{p})&j\sin(k_{p}D_{p})\\ \frac{j}{Z_{p}}\sin(k_{p}D_{p})&\cos(k_{p}D_{p})\end{bmatrix} \tag{8}\]  
where \(k_{p}\) and \(Z_{p}\) are the wave number and characteristic impedance of the porous material, respectively, which are calculated as follows:  
\[k_{p}=\omega\sqrt{\frac{\rho(\omega)}{K(\omega)}} \tag{9}\]  
\[Z_{p}=\sqrt{\rho(\omega)K(\omega)} \tag{10}\]  
where \(\rho(\omega)\) and \(K(\omega)\) are the effective density and bulk modulus of the porous material, respectively, which are expressed as:  
\[\rho(\omega)=\frac{\alpha_{\infty}\rho_{0}}{\phi}\Bigg{[}1-j\frac{\sigma\phi }{\alpha_{\infty}\rho_{0}\omega}\sqrt{1+j\frac{4\alpha_{\infty}^{2}\rho_{0} \omega\eta}{\sigma^{2}\phi^{2}\Lambda^{2}}}\Bigg{]} \tag{11}\]  
\[K(\omega)=\frac{\gamma P_{0}}{\phi}\Bigg{[}\gamma-\frac{\gamma-1}{1-j\frac{8 \eta}{\omega_{\rm{P}}\rho_{\rm{T}}\Lambda^{2}}\sqrt{1+j\frac{\omega\rho_{0}P_ {\rm{T}}\Lambda^{2}}{16\eta}}}\Bigg{]}^{-1} \tag{12}\]  
Here,  
\[\Lambda=\frac{1}{b}(\frac{8\alpha_{\infty}\eta}{\sigma\phi})^{\frac{1}{2}}, \Lambda^{\prime}=\frac{1}{b^{\prime}}(\frac{8\alpha_{\infty}\eta}{\sigma\phi} )^{\frac{1}{2}} \tag{13}\]  
where \(\alpha_{\infty}\) is the curvature factor, \(\sigma\) is the flow resistance, \(\phi\) is the porosity of the porous material, \(\eta\) is the dynamic viscosity of air, \(\gamma\) is the specific heat capacity ratio of air, \(P_{0}\) is the static pressure of air, \(P_{r}\) is the Prandtl number of air, \(b\) is the cross-sectional shape factor of the pores, \(b^{\prime}\) is the scale factor of the pores, and \(\Lambda\) and \(\Lambda^{\prime}\) are the viscous and thermal characteristic lengths, respectively.  
The porous material used in this study was melamine sponge, which is an open-cell porous foam acoustic material with an excellent sound absorption performance and is widely used in aircraft adiabatic insulation materials, payload racks, and the mufflers of the International Space Station. It has a good suppression effect on cabin noise, and its relevant parameters are listed in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & \(\sigma\) (**N**\(\cdot\)**s**\(\cdot\)**m-4)** & \(\phi\) & \(\alpha_{\infty}\) & \(\Lambda\) (\(\mu\)m) & \(\Lambda^{\prime}\) (\(\mu\)m) \\ \hline
**Numerical value** & 10,500 & 0.995 & 1.0059 & 240 & 470 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of melamine sponge.  
The transfer matrix of the MPP+Porous structure is:  
\[\Pi_{b}=MP=\begin{bmatrix}\Pi_{11}&\Pi_{12}\\ \Pi_{21}&\Pi_{22}\end{bmatrix} \tag{14}\]  
The absorption coefficient can be obtained by substituting the values into Equations (5)-(7).
## 4 Experimental Verification
### Results Analysis
After applying the algorithm in this study and analyzing the data using the five-axis four-linkage trajectory, a total of 597,861 sampling points were obtained, out of which 68,294 points were found to be out of tolerance, accounting for 11.42% of the total sampling points. This mainly manifested at the root of the blade and splitter blade. Figure 11: Analysis results of (**a**) 3D IPW for five-axis five-linkage, (**b**) deviation gauge for five-axis five-linkage, (**c**) 3D IPW for five-axis four-linkage, (**d**) deviation gauge for five-axis four-linkage. Based on the analysis presented above, two key observations can be made regarding the proposed interpolation algorithm. Firstly, it enables the transformation from five-axis five-linkage machining to five-axis four-linkage machining. Secondly, the algorithm demonstrates superior machining accuracy in surface machining operations where the tool axis vector changes minimally. However, when the tool axis vector undergoes significant changes, the machining accuracy of the algorithm may experience a relative decline.