esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Quadrotor Dynamics Model and Problem Formulation
In addition, we define \(\dot{\mathbf{X}}_{3}=\mathbf{h}_{p}\) and \(\dot{\mathbf{X}}_{6}=\mathbf{h}_{\theta}\), with \(\mathbf{h}_{p}\) and \(\mathbf{h}_{\theta}\) representing the bounded derivative of the lumped disturbances and satisfying \(\parallel\mathbf{h}_{p}\parallel\leq H_{1}\) and \(\parallel\mathbf{h}_{\theta}\parallel\leq H_{2}\), where \(\parallel\bullet\parallel\) represents the 2-norm, and \(H_{1}\) and \(H_{2}\) are some positive numbers. For the sake of simplicity, let us present the following notations before moving forward. \(f_{2}(\mathbf{X}_{2})=-\mathbf{\Lambda_{1}}\mathbf{X}_{2}/m\), \(\mathbf{F}(\mathbf{X}_{4})=(\mathbf{B}_{1}u_{1}-\mathbf{G})/m\), \(f_{5}(\mathbf{X}_{5})=-\mathbf{J}^{-1}\mathbf{\Lambda_{2}}\mathbf{X}_{5}\), \(\mathbf{B}_{5}=\mathbf{J}^{-1}\mathbf{B}_{2}\)  
Here, note that \(\mathbf{F}\) becomes a virtual control vector to be designed later. Then, we can rewrite Equation (5) as  
\[ \begin{cases}\dot{X}_{1}=\mathbf{X}_{2}\\ \dot{X}_{2}=\mathbf{X}_{3}+f_{2}(\mathbf{X}_{2})+\mathbf{F}(\mathbf{X}_{4})\\ \dot{X}_{3}=\mathbf{h}_{p}\\ \dot{X}_{4}=\mathbf{X}_{5}\\ \dot{X}_{5}=\mathbf{X}_{6}+f_{5}(\mathbf{X}_{5})+\mathbf{B}_{5}\mathbf{U}_{2}\\ \dot{X}_{6}=\mathbf{h}_{\theta}\end{cases}  \tag{6}\]  
In the matrix form, system Equation (6) can be rewritten as  
\[\mathbf{X}=\mathbf{A}_{0}\mathbf{X}+\mathbf{\Phi}(\mathbf{X})+\mathbf{U}+\mathbf{\Delta} \tag{7}\]  
where, we use the following notations,  
\[\mathbf{X}= \begin{bmatrix}\mathbf{X}_{1}\\ \mathbf{X}_{2}\\ \mathbf{X}_{3}\\ \mathbf{X}_{4}\\ \mathbf{X}_{5}\\ \mathbf{X}_{6}\end{bmatrix} ,\mathbf{A}_{0}= \begin{bmatrix}\mathbf{0}&\mathbf{I}_{3}&\mathbf{0}&\bm {0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{I}_{3}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{I}_{3}&\mathbf{0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{I}_{3}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}&\mathbf{0}\end{bmatrix} ,\mathbf{\Phi}(\mathbf{X})= \begin{bmatrix} \mathbf{0}\\ \mathbf{f}_{2}(\mathbf{X}_{2})\\ \mathbf{0}\\ \mathbf{0}\\ \mathbf{f}_{5}(\mathbf{X}_{5})\\ \mathbf{0}\end{bmatrix} ,\mathbf{U}= \begin{bmatrix}\mathbf{0}\\ \mathbf{F}(\mathbf{X}_{5})\\ \mathbf{0}\\ \mathbf{0}\\ \mathbf{B}_{5}\mathbf{U}_{2}\\ \mathbf{0}\end{bmatrix} ,\mathbf{\Delta}= \begin{bmatrix}\mathbf{0}\\ \mathbf{0}\\ \mathbf{h}_{p}\\ \mathbf{0}\\ \mathbf{0}\\ \mathbf{h}_{\theta}\end{bmatrix} \]  
where \(\mathbf{I}_{3}\in\mathbb{R}^{3\times 3}\) stands for an identity matrix, and \(\mathbf{0}\) is a zero matrix or zero vector with proper dimensions. Now, the control goal is to design a robust backstepping trajectory tracking controller to steer the quadrotor to a given trajectory reference \(\mathbf{P}_{d}\) and a desired heading angle \(\psi_{d}\) using only the measurements of position and attitude, i.e., \(\mathbf{X}_{1}\) and \(\mathbf{X}_{4}\), despite the presence of both control input saturation and the lumped disturbances.
# Numerical Calculation of Slosh Dissipation
## 7 Conclusions  
The violent sloshing flow studied in this work presents several complexities. While the SPH results are promising in terms of comparison against experimental data, the two-phase results suggest that there are gas-liquid interactions in the flow leading to enhanced mixing, which is not captured in the single-phase approach. Conversely, the physical model adopted in the Elemental(r) solver is more rich, showing a more complex evolution of the gas-liquid interface compared to the single-phase model. However, the spatial resolution required for converged energy metrics seems to be significantly higher compared to the single-phase SPH model. This is clear when examining the dissipation components related to the viscous dissipation, including the sub-grid model. With the SPH solver, these dissipation components seem to remain bounded for the water test-cases and decreases for the oil test-cases with increasing resolution. Conversely, with the Elemental(r) solver, the energy dissipation is not yet fully converged with increasing mesh resolution.  
Figure 34: Time history of the vertical position of the fluid center of mass \(y_{G}(t)\) evaluated by the SPH-Flow and Elemental solvers in a 3D framework. (**Top**) water test-case. (**Bottom**) oil test-case.  
Figure 33: Time history of the vertical position of the fluid center of mass \(y_{G}(t)\) evaluated by the SPH-Flow and Elemental solvers in a 2D framework. The 2D results are given by an ensemble average of ten simulations. Error bars refer to the computed standard deviation. (**Top**) water test-case. (**Bottom**) oil test-case.  
For a future and further step of what is presented in this work, it would be interesting to extend the analysis using a two-phase SPH model, as well as conduct simulations with Elemental(r) at increased resolutions. Both these improvements, however, will require a large leap in computational resources.  
Conceptualization, A.C., A.G.M. and L.C.M.; methodology, A.G.M. and C.P.; software, A.C., A.G.M. and L.C.M.; validation, C.P., L.C.M. and A.G.M.; formal analysis, A.G.M. and A.C.; investigation, L.C.M. and C.P.; resources, A.C. and A.G.M.; data curation, C.P., L.C.M. and A.G.M.; writing--original draft preparation, L.C.M. and C.P.; writing--review and editing, A.C. and A.G.M.; visualization, C.P. and L.C.M.; supervision, A.G.M. and A.C.; project administration, A.C. and L.C.M.; funding acquisition, A.G.M. and A.C. All authors have read and agreed to the published version of the manuscript.  
The work was supported by the SLOWD project, which received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 815044.  
Not applicable.  
The SPH simulations were performed using HPC resources of the Centrale Nantes Supercomputing Centre on the cluster Liger. The authors acknowledge the Centre for High Performance Computing (CHPC), South Africa, for providing computational resources to this research project, specifically for the finite volume approach results with Elemental(r).  
The authors declare no conflict of interest.
## 2 Related Works  
### 3D Model Security  
Watermarking techniques for 3D models have been researched. 3D model watermarking methods focus on the frequency domain and geospatial domain [6; 7]. The key point of watermarking methods in the frequency domain is to embed watermark data into the spectrum coefficients of DFT, DWT, and DCT of a sequence of vertices or topologies, while the main concept of watermarking methods in the geospatial domain is based on modifying the value of vertices or geometric features such as length, area, or topology. Consequently, 3D model watermarking is not suitable for secured storage and transmission, as it fails to prevent attacks and illegal copying.  
Some techniques that secretly share the content of 3D models and encrypt 3D CAD models have been proposed. [PERSON] et al. [8] presented two methods that secretly transmit 3D models using Blakely, Thien, and Lin schemes. 3D models are separated into parts before they are shared, and users then reconstruct the 3D model from the shared parts of that model. However, this method is only for secured transmission. It is not an encryption method, and none of the 3D model is encrypted. [PERSON] et al. [9] proposed a method by which 3D objects are encrypted based on geometry-preserving. This algorithm encrypts 3D objects by permuting the vertices of a given 3D object and distorting their shape while preserving its intrinsic geometrical properties. However, it does not alter the entire content of a 3D object and is not sensitive to the various formats of 3D objects. Moreover, the reconstruction cannot fully restore the original 3D object from the encrypted 3D object. Furthermore, the security of this method is very low. [PERSON] et al. [10; 11; 12] proposed an encryption approach for 3D CAD models based on the geometric transformation of features of 3D CAD models. Here, a 3D CAD model is encrypted by randomization of the features of the 3D CAD model with an enhanced encryption transformation matrix. This method slightly changes the shape of 3D CAD models. Consequently, these methods do not achieve secured storage and transmission needed for 3D printing.
# Evaluation of Noise-Reduction Techniques for Gas-Turbine Test Stands: A Preliminary Analysis
## 3 Noise-Attenuation Assessment--Finite-Element Method
As observed in Figure 3b, the employed mesh contains quadratic elements, and it is partially structured in the regions adjacent to the baffles. For the porous domain, a structured mesh was generated using quadratic elements with an element size of 7 mm. For the 2D configuration presented in Figure 3b, 82,000 elements resulted as optimum. A 3D mesh with 5,760,000 elements was also generated for the first configuration of baffles to compare the 2D and 3D results and estimate the confidence in using the 2D simulation for time and computational saving. As in the case of 2D simulation, the same boundary conditions were applied for the 3D simulation. Figure 3 presents a comparative graph with radiated acoustic power resulting in a 2D simulation versus a 3D one. This comparative presentation was carried out to evaluate the similitude between them by taking into consideration the restriction introduced by a 2D concept as compared to a 3D one. Figure 4 highlights that the differences in radiated power outside of the test bench are similar, with small differences appearing at low and high frequencies. The acoustic pressure fields, as presented in Figure 5, are similar in 2D and 3D representations, so we can conclude that the 2D simulation is sufficiently accurate, as compared to the 3D one, and that it could be used as a good option to obtain correct results, by saving computational and time resources, especially when a flow-acoustic analysis is needed. The procedure for evaluating acoustic attenuation, both in numerical simulations and measurements, involves measuring the acoustic pressure at four points outside the test bench, which are positioned radially around the free end of the stand and then logarithmically averaging them. The first measured configuration is without an acoustic baffle inside the duct, resulting in an average sound pressure \(\overline{L_{p1}}\). This is followed by the introduction of baffles and subsequent measurement, resulting in an average sound pressure \(\overline{L_{p2}}\). The difference between the two average noise levels represents the acoustic attenuation (insertion loss--\(IL\)) in dB of the tested configuration  
\[IL=\overline{L_{p1}}-\overline{L_{p2}}\left[\mathrm{dB}\right] \tag{6}\]  
The main advantage of this numerical method is its ability to model complex attenuator shapes and incorporate various parameters of the mineral wool and perforated panels. However, the computational cost increases with model complexity. The primary disadvantage of this method is the significant computing resources required, particularly for 3D simulations. Additionally, the development of the CAD model and the computational grid can be time-consuming. Figure 4: Comparison of simulated radiated power, 2D and 3D results [dB].
# GPU Parallel Implementation for Real-Time Feature Extraction of Hyperspectral Images
## 5 Results and Discussion
### Parallel Implementation  
For the evaluation of the parallel acceleration effect, we give the implementation of three different versions of INAPC. One of them is our GPU parallel implementation based on CUDA (c++), the second is based on OpenCV (c++), and the last is based on the machine learning library PyTorch (python). In order to evaluate the real-time characteristic of our proposed method, different available methods are used to measure the execution time of programs. Using \(\mathit{clock}()\) in C++ language and \(\mathit{process\_time}()\) in python language to get the number of seconds used by CPU time, using chrono  
Figure 7: The false color composite image, the ground truth image, and the INAPC classification map of the three datasets. (**a**) Indian Pines; (**b**) Pavia University scene; (**c**) Salinas scene. package _chrono_ :: _steady_clock_ :: _now_() to measure the total execution time of the entire program, and using the CUDA event APIs to obtain the elapsed time of each kernel function of the GPU program. We give the calculation time of the three versions and the speedup factors for each function (the functions' number as stated in Table 1) in Table 6, where speedup1 is obtained from the OpenCV time divided by the CUDA time, and speedup2 represents the value of PyTorch time divided by CUDA time. In Table 6, the best results (minimum time) are highlighted in bold. It can be seen that the version of CUDA has an absolutely huge advantage in most calculations compared to the other two implementations, especially for the most time-consuming matrix multiplication and noise estimation. It is worth mentioning that PyTorch also has a good performance in matrix operations, and its efficiency of feature decomposition is remarkable, but it has enormous time overhead in noise estimation, because the noise estimation method is equivalent to the plenty of tensor operations in PyTorch, and CUDA only needs to specify the address of the threads in each block start from matrix pointer. Table 7 lists the run time of the whole INAPC algorithm on the different implementations, respectively. As shown in Table 7, we obtain different speedup factors with fixed parameters on the three HSI datasets. Because of the vast time cost of noise estimation, PyTorch has the largest run time, and our CUDA parallel implementation shows great superiority and stability. Comparing the results of the three datasets, we can see that as the spatial dimension of the hyperspectral data set is higher, the better the acceleration effect of our algorithm, which is also in line with the development of current hyperspectral data towards high spatial resolution. At the same time, we can see that our parallel
# Dark Type Dynamical Systems: The Integrability Algorithm and Applications +
## 2 Nonlinear Dynamical Systems and the Lax Type Representation
### Integrability Analysis: Dispersion Class Dynamical Dark Type Systems
#### 3.3.1 A First Dispersion Class Dynamical System
Then one obtains  
\[\sigma_{5}=\frac{1}{27}\partial^{-1}p_{t}-\frac{1}{81}u^{3}-\frac{1}{27}pu+ \frac{1}{9}(uu_{x})_{x}+\frac{2}{27}p_{xx}, \tag{103}\]  
which can be rewritten as  
\[\frac{1}{27}\partial^{-1}p_{t}-\frac{1}{81}u^{3}-\frac{1}{27}pu=\frac{1}{27}g[ u,p], \tag{104}\]  
or, equivalently, as  
\[p_{t}=g_{x}+u^{2}u_{x}+(pu)_{x} \tag{105}\]where an introduced mapping \(g:J(\mathbb{R}/\left\{2\pi\mathbb{Z}\right\};\mathbb{R}^{2})\rightarrow\mathbb{R}\) should be determined from the constraint \(\sigma_{6}=0\), that is  
\[\sigma_{6}=\left(-\frac{1}{9}uu_{xx}-\frac{1}{18}u_{x}^{2}-\frac{2}{27}up-\frac {1}{27}p_{xx}-\frac{2}{27}g\right)_{x}=0, \tag{106}\]  
reducing to the expression  
\[g=-\frac{3}{2}uu_{xx}-\frac{3}{4}u_{x}^{2}-\frac{1}{2}p_{xx}-pu. \tag{107}\]  
Based now on expressions (103), (106) and (107) we can calculate the next nontrivial conservation density  
\[ \begin{array}{l}\sigma_{7}=-\frac{1}{36}uu_{xxxx}-\frac{5}{36}u_{x}u_{xxx}- \frac{5}{36}u_{xx}^{2}+\frac{1}{18}u^{2}u_{xx}+\\ \\ +\frac{1}{12}uu_{x}^{2}+\frac{5}{54}p_{x}u_{x}-\frac{1}{36}p_{xxxx}+\frac{1}{1 8}up_{xx}-\frac{1}{324}u^{4}-\frac{1}{54}p^{2}\end{array}  \tag{108}\]  
and similarly all other ones, which prove to be compatible with the recurrent hierarchy (94). Summarizing calculations above, we can construct the next closed dynamical system  
\[ \begin{array}{l}u_{t}=(p+u_{xx})_{x}\\ p_{t}=(-\frac{3}{2}uu_{xx}-\frac{3}{4}u_{x}^{2}+\frac{1}{3}u^{3}-\frac{1}{2}p_ {xx})_{x}\end{array} \bigg{\}}=Q[u,p] \tag{109}\]  
on the functional manifold \(M_{u}\times M_{p}\), which also proves to be completely integrable, that we can easily check by means of the gradient-holonomic scheme, applied to the vector field (109). Moreover, we can combine the dynamical system (91) with that of (109) and obtain the joint completely integrable dynamical system  
\[\left. \begin{array}{l}v_{t}=-uv_{x}+v_{xxx}\\ u_{t}=(p+u_{xx})_{x}\\ p_{t}=(\frac{3}{2}uu_{xx}-\frac{3}{4}u_{x}^{2}+\frac{1}{3}u^{3}-\frac{1}{2}p_ {xx})_{x}\end{array} \right\}=K[v,u,p] \tag{110}\]  
on the extended functional manifold \(M_{v}\times M_{u}\times M_{p}\). The obtained above new integrability results subject to the combined dynamical system (110) can be formulated as the following theorem. Theorem 3.2: _The combined nonlinear dynamical system (110) presents a completely integrable dark type flow on the extended functional manifold \(M_{v}\times M_{u}\times M_{p}\), it is Lax type linearized and possesses an infinite number of suitably ordered conservation laws._
# Parameter Estimation and Error Calibration for Multi-Channel Beam-Steering SAR Systems
###### Abstract  
Multi-channel beam-steering synthetic aperture radar (multi-channel BS-SAR) can achieve high resolution and wide-swath observations by combining beam-steering technology and azimuth multi-channel technology. Various imaging algorithms have been proposed for multi-channel BS-SAR but the associated parameter estimation and error calibration have received little attention. This paper focuses on errors in the main parameters in multi-channel BS-SAR (the derotation rate and constant Doppler centroid) and phase inconsistency errors. These errors can significantly reduce image quality by causing coarser resolution, radiometric degradation, and appearance of ghost targets. Accurate derotation rate estimation is important to remove the spectrum aliasing caused by beam steering, and spectrum reconstruction for multi-channel sampling requires an accurate estimate of the constant Doppler centroid and phase inconsistency errors. The time shift and scaling effect of the derotation error on the azimuth spectrum are analyzed in this paper. A method to estimate the derotation rate is presented, based on time shifting, and integrated with estimation of the constant Doppler centroid. Since the Doppler histories of azimuth targets are space-variant in multi-channel BS-SAR, the conventional estimation methods of phase inconsistency errors do not work, and we present a novel method based on minimum entropy to estimate and correct these errors. Simulations validate the proposed error estimation methods.  
multi-channel; beam steering (BS); synthetic aperture radar (SAR); derotation rate; Doppler centroid; phase inconsistency errors +
Footnote †: journal:  
_Article_
## 7 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**SVC Accuracy (\%)**} & \multicolumn{3}{c}{**KNN Accuracy (\%)**} & \multicolumn{3}{c}{**RFC Accuracy (\%)**} \\ \hline \multirow{3}{*}{**Vowel**} & **Model** & **Model** & **Cross** & **Model** & **Model** & **Cross** & **Model** & **Model** & **Cross** \\  & **Training** & **Testing** & **Validation** & **Training** & **Testing** & **Validation** & **Training** & **Testing** & **Validation** \\ \hline \multirow{3}{*}{**Vowel**} & _/u_-_/ & 73.4 & 67.35 & 70.8 (\(\pm\)6) & 70.8 & 59.18 & 66.9 (\(\pm\)5) & 73.8 & 57.14 & 69.2 (\(\pm\)6) \\  & _/u_/ & **75.9** & **77.55** & **77.7 (\(\pm\)5)** & **73.2** & **69.39** & **68.7 (\(\pm\)6)** & **76.8** & **81.63** & **78.3 (\(\pm\)5)** \\  & _/l_/ & 75.9 & 67.35 & 68.3 (\(\pm\)5) & 72.4 & 55.1 & 67.4 (\(\pm\)6) & 72.2 & 63.27 & 68.6 (\(\pm\)7) \\  & _/u_/ & 69.7 & 69.39 & 68.7 (\(\pm\)6) & 65.9 & 59.18 & 67.5 (\(\pm\)6) & 70.8 & 69.39 & 70.8 (\(\pm\)6) \\ \hline \multirow{3}{*}{**Vowel**} & _/u_-_/ & **88.8** & **82.61** & **74.9 (\(\pm\)8)** & 66.5 & 60.87 & 63.7 (\(\pm\)7) & 82.4 & 78.26 & 76.3 (\(\pm\)8) \\  & _/l_/ & 78.2 & 69.57 & 73.5 (\(\pm\)9) & **73.5** & **69.56** & 67.6 (\(\pm\)9) & **85.3** & **82.61** & **82.3 (\(\pm\)7)** \\ \cline{1-1}  & _/l_/ & 74.1 & **82.61** & 70.2 (\(\pm\)8) & 71.2 & 43.48 & **68.4 (\(\pm\)9)** & 71.8 & 73.91 & 69.8 (\(\pm\)7) \\ \cline{1-1}  & _/h_/ & 81.2 & 65.22 & 72.4 (\(\pm\)7) & 68.2 & 65.22 & 66.1 (\(\pm\)6) & 78.2 & 73.91 & 72.5 (\(\pm\)8) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._  
**Funding:** This work was supported by the Slovak Research and Development Agency under the contract No. APVV-16-0211. **Conflicts of Interest:** The authors declare no conflict of interest.
## 3 Numerical Analysis
### Realization of Wide Impedance Bandwidth  
Our design attains wide impedance bandwidth by using multiple radiators that have adjacent resonances and similar radiation patterns (in our case, broadside radiation patterns). These radiators are the open prism and the feedlines.  
Figure 3: Square and octagonal ground cavity-backed radiating open prism antennas: (**a**) Differential reflection coefficient; (**b**) Realized gain and peak cross-polarization; (**c**) Aperture efficiency; (**d**) Cross-polarization ratio of OCROP for 1.1 GHz at all azimuth and elevation angles of interest; (**e**) 3D far-field co-polarized radiation pattern of the octagonal cavity-backed antenna at 1.1 GHz; (**f**) 3D far-field cross-polarized radiation pattern of the octagonal cavity-backed antenna at 1.1 GHz. (Black and red dots mark the lower and upper limits of the two \(\mathrm{S_{dd11}}\leq-10\) dB operating bands.).  
To demonstrate the resonance merging mechanism of this antenna, the differential reflection coefficients and input impedances of the antennas with and without the open prism are compared in Figure 4a,b. All other antenna dimensions remained constant, with \(L_{g}\) = 165 mm, \(H_{sw}\) = 80 mm, \(g\) = 11 mm, \(s\) = 3 mm, \(l\) = 53 mm, \(w\) = 30 mm, \(l^{\prime}\) = 1 mm, and \(w^{\prime}\) = 3.6 mm. As can be seen, the differential reflection coefficient for the antenna without the open prism (black dotted curve in Figure 4a) only has one notch, which is not very pronounced due to the antenna being poorly matched. However, this can be verified with the peak in the real part of the corresponding input impedance curve (black solid curve in Figure 4b). By adding the open prism, the antenna becomes well-matched. An extra notch in the reflection coefficient curve is introduced (red solid curve Figure 4a), which is also reflected by the extra bump in the real part of the input impedance curve (red solid curve Figure 4b). As the two notches are close together, they result in a merging effect, and a wide impedance bandwidth of 54.3% is created.
## 1 Measurement and Analysis of Local Humidity  
For this study, measurements of the local humidity of grounded aircraft (i.e., the humidity inside each structural bay of the aircraft) were carried out according to the previously reported method [23]. The test aircraft used in this study was a retired fighter parked on a parking apron, without the protection of a shelter. To make up for the limitation of a single aircraft model, 14 measurement points were fitted inside the aircraft to study the influences of bay size, location, and structure, as well as different weather conditions, on local humidity. To make up for the limitation of a single geographic location, measurements were performed across an entire year such that the aircraft experienced large variations in the external environmental conditions. Since the focus of this study is on exploring the relationship between the local humidity of the bays and the external environment, and since most aircraft have similar bay structures (the retired aircraft is a small aircraft however bays of large aircraft, especially large fighter planes, are divided into smaller spaces by bulkheads and ribs, therefore the partial cabin size of large aircraft is comparable to the bay of a retired aircraft), the conclusions of this study can be widely applied to other aircraft models across other geographical regions. When studying different aircraft models in different geographic locations, the bay classification system along with the humidity model proposed in this paper, with modification to certain parameters, could potentially be used.