esa-sceva/satcom-chunk-collection huggingface dataset:
# BICM-ID with Physical Layer Network Coding in TWR Free Space Optical Communication Links +
## 2 System Description
### Channel Model
#### 2.2.1 Atmospheric Turbulence-Induced Fading  
Turbulence-induced signal fading is one of the main impairments affecting the operation of FSO systems. The distribution of the light intensity fading due to the weak turbulence can be described by a log-normal distribution as:  
\[p(h_{s})=\frac{\exp(\frac{(\ln(h_{s})+\sigma_{l}^{2}/2)^{2}}{2\sigma_{l}^{2}}) }{\sqrt{2\pi\sigma_{l}^{2}}h_{s}}, \tag{2}\]  
where \(\sigma_{l}^{2}\) is the scintillation index. For a weak turbulence regime, \(\sigma_{l}^{2}\) is found to be proportional to Rytov variance \(\sigma_{R}^{2}\), which can be calculated as shown in [3] by:  
\[\sigma_{R}=\sqrt{1.23\;\big{(}\frac{2\pi}{\lambda}\big{)}^{7/6}\;C_{n}^{2}\;L_ {d}^{11/6}}, \tag{3}\]  
where \(\lambda\) is the wavelength and \(L_{d}\) is the link distance between the transmitter and receiver points. Typically, the refractive index range value of \(C_{n}^{2}\) is from \(10^{-12}\) meters\({}^{-2/3}\) (m\({}^{-2/3}\)) for strong turbulence to \(10^{-17}\) m\({}^{-2/3}\) for weak turbulence. However, the gamma-gamma distribution is utilized to address both the large- and small-scale scintillations under moderate-to-strong scenarios, which can be written as:  
\[p(h_{s})=\frac{2\big{(}\alpha\beta\big{)}^{\frac{\alpha+\beta}{2}}\;h_{s}^{ \frac{\alpha+\beta}{2}-1}\;K_{\alpha-\beta}\big{(}2\sqrt{\alpha\;\beta\;h_{s} }\big{)}}{\Gamma(\alpha)\;\Gamma(\beta)}, \tag{4}\]  
where \(\Gamma(.)\) is the gamma function and \(K_{\alpha-\beta}(.)\) is the modified Bessel function of the second kind of order \(\alpha-\beta\). Parameters \(\alpha\) and \(\beta\) represent the effective number of large-scale and small-scale turbulence eddies, respectively. If the optical radiation at the receiver is assumed to be a plane wave,  
Figure 1: System model for two-way relay (TWR) with physical layer network coding (PNC).  
then the two parameters \(\alpha\) and \(\beta\) that characterize the irradiance fluctuation distribution are related to the atmospheric conditions by:  
\[\alpha= \bigg{(}\exp(\frac{0.49\;\sigma_{R}^{2}}{\big{(}1+1.11\;\sigma_{R}^{1 2/5}\big{)}^{7/6}})\bigg{)}^{-1} \tag{5}\] \[\beta= \bigg{(}\exp(\frac{0.51\;\sigma_{R}^{2}}{\big{(}1+0.69\;\sigma_{R} ^{12/5}\big{)}^{7/6}})\bigg{)}^{-1} \tag{6}\]
# Data-Aware Path Planning for Autonomous Vehicles Using Reinforcement Learning +
## 4 Experiments and Results
### Data Requirement Comparison  
In this experiment, we compared the performance of our trained agent when the data transfer requirement parameter is varied. This parameter denotes the amount of data that needs to be transferred before an agent reaches its destination.  
We choose to run this experiment on a short trip length for several compelling reasons. The short trip offers a more controlled environment with fewer confounding variables, allowing us to isolate and measure the direct impact of the data requirement parameter more accurately. Furthermore, these conditions simplify the decision-making process for  
Figure 8: Baseline comparisons for a long trip.  
Figure 7: Baseline comparisons for a medium-length trip.  
the reinforcement learning agent and allow for faster iterations of tests, thus providing a clearer analysis of how data requirements influence route selection.  
We can observe from Figure 9 that a lower data transfer requirement leads to a faster trip overall. This outcome aligns with our expectations, as the quicker the agent completes its data transfer, the sooner it can focus on completing the trip as fast as possible.
# Effect of MXene Nanosheet Sticking on Supercapacitor Device Performance
## 3 Factors Influencing Sticking in MXene Electrodes  
### Morphology and Size of MXene Flakes  
The morphology of MXene flakes primarily refers to their overall shape, including their aspect ratio, edges, and surface roughness. It has been observed that MXene flakes with irregular shapes, jagged edges, or high surface roughness tend to exhibit a higher propensity for sticking. The irregularities on the surface of MXene flakes provide more sites for inter-flake adhesion, leading to higher agglomeration.  
Ti\({}_{3}\)C\({}_{2}\) was obtained after etching of Ti\({}_{3}\)AlC\({}_{2}\) using hydrofluoric acid and lithium fluoride, and the interlayer gaps of the MXene nanosheets were investigated by transmission electron microscopy (TEM) [42]. Based on the image in Figure 1a, it is evident that the nanosheets exhibit nearly transparent properties, allowing for the visibility of individual layers (i.e., Ti and C layers) within a single Ti\({}_{3}\)C\({}_{2}\) sheet. Upon closer inspection in the higher magnification image (Figure 1b), it is estimated that the thickness of a single layer Ti\({}_{3}\)C\({}_{2}\) is approximately 1-2 nm. Given the observed layered morphological structure of MXene, it can be proposed as the \"lamella\" model.  
A study on interdigital micro-supercapacitors has investigated how the electrochemical properties of MXene vary with flake size [43]. The authors' findings reveal that nano-size MXene (200 nm) demonstrates greater ionic conductivity than its micron-size counterpart (1 \(\upmu\)m). Conversely, larger flake sizes exhibit higher electron conductivities. Consequently,the capacitance of micron-size MXene surpasses that of nano-size MXene (200 nm) due to the dominance of electron conductivities.
# Energy Efficient Routing in Wireless Sensor Networks: A Comprehensive Survey
## 3 Network Structure
### Hierarchical
#### 3.2.3 Fuzzy Logic Based
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Protocol** & **Advantages** & **Disadvantages** & **Scalability** & **Mobility** & **Routing** & **Robustness** \\ \hline FEERPP & Energy of routes is considered. Nodes & & & & & Routes are selected based & \\
[107] & sleep when idle. Data & Overhead is notable. & Good & None & & on residual energy, \\  & sleep when idle. Data & Overhead is notable. & & & & packets dropped and hop & \\  & losses are avoided. & & & & & count of each route. & \\  & It solves the hotspot & & & & & Nodes send data to the & \\  & problem and extends & It does not support & & & & cluster head, which & \\  & network lifetime. & coverage redundancy. & & & & forwards them to the BS & \\  & Network lifetime is & & & & & & via multi-hop & \\  & extended. The high & It lacks parameters for & & & & transmission. & \\  & energy nodes are & & & & & The cluster nodes send & \\  & preferably elected as & & & & & their data to the cluster & \\  & cluster heads. & & & & & head, which forwards & \\  & & Energy depletion is & & & & them to the BS via direct & \\ ECPF [110] & It has great network & & & & & Transmission. & \\  & lifetime. & & & & & Transmission. & \\  & & & & & & the cluster head, which & \\  & It is more energy & & & & & via multi-hop routing. & \\  & efficient than other & & & & & The cluster nodes send & \\  & protocols with fuzzy & & & & in dense networks. & & head, which forwards & \\  & logic approach. & & & & & them to the BS. & \\  & It extends network & & & & & The cluster nodes send & \\  & lifetime and provides & & & & & their data to the cluster & \\  & great stability. & & & & & head, which forwards & \\  & It improves network & & & & & them to the BS. & \\  & stability and & & & & & & \\  & uniformity of energy & & & & & \\  & and reduces energy & & & & & \\  & ingestion. & & & & & \\  & It provides good & & & & & \\  & credibility and energy & & & & & \\  & balancing. & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Synopsis of Hierarchical Protocols belonging to a Fuzzy Logic based subcategory.
## 5 Conclusions  
During this investigation, fibers were extracted manually and chemical-free from the Borassus fruit. Alkaline treatment or mererization was conducted on the natural fiber to improve its properties. The treatment might have introduced functional groups onto the fiber surface that interacted with water molecules in a specific way, leading to a linear dependence on relative humidity (RH).  
\begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Practical Implications**} & \multicolumn{1}{c}{**Theoretical Implications**} \\ \hline \hline
**DTR** & **DTR** \\ \hline Easy interpretability & Prone to overfitting \\ Handling numerical and categorical features without extensive & Inaccurate for complex relationships \\ preprocessing & Inadequate for continuous features \\ Quick development of the model and its training & Inadequate for continuous features \\ Best for categorical features & \\ Can identify the most important features & \\ Wide range applications & \\ \hline \hline
**GBR** & **GBR** \\ \hline Easy interpretability & Requires hyperparameter tuning \\ High accuracy on complex datasets & Reduce variance \\ Flexibility in handling various data types and non-linear & Ensemble of multiple trees thus hard to understand the internal \\ relationship & working \\ Less prone to overfitting & Accurate for complex nonlinear relationships \\ \hline \hline \multicolumn{1}{c}{**Examples of how the models can enhance decision-making**} \\ \hline \hline \end{tabular}
\end{table}
Table 5: Practical and theoretical implications of DTR and GBR.  
This research contributes to the understanding of BNF behavior, particularly its hygroscopic properties. By demonstrating the effectiveness of GBR and DTR models in predicting these properties, it offers a novel approach to characterizing natural fibers.  
The key findings of the investigation can be compiled as:  
* Borassus fruit fibers exhibit hysteresis in moisture absorption and desorption, influenced by their cellular structure.
* Alkaline treatment alters fiber morphology, leading to increased porosity and a more uniform diameter.
* GBR and DTR models accurately predict the hygroscopic properties of both treated and untreated fibers.
* GBR outperforms DTR in terms of model-fit metrics (R\({}^{2}\), MSE, RMSE, and MAE) The implications of the study can be summarized as follows:
* Practical Applications: The developed models can be used to optimize the production and application of Borassus fruit-based materials, leading to improved product performance and reduced costs.
* Research Advancement: The findings provide a foundation for further research into the relationship between fiber structure, chemical treatment, and hygroscopic behavior.
* Industry Impact: The study offers a potential alternative to traditional, time-consuming methods for characterizing fiber properties, contributing to the development of more sustainable and cost-effective materials.  
By accurately predicting hygroscopic properties, this research enables the development of BNF composites with enhanced dimensional stability and tailored properties for specific applications in the construction industry.
# MIDOM--A DICOM-Based Medical Image Communication System
## 2 Background
### Dicom  
Medical Imaging and Technology Alliance, a division of the National Electrical Manufacturers Association (NEMA), specifies the DICOM standard. It defines the communication and management of medical imaging information and related data. It establishes a set of protocols for network communication; commands' syntax and semantics for data exchange; file formats and folder structure for images and other information data storage; and information supplied for given DICOM standard. NEMA published version 1.0 of the DICOM in 1985, while it introduced the latest changes in 2019. DICOM standards led to high diagnostic criteria, such as:  
* Universal standard of digital medicine--for its data and image transmission and storage.
* High image quality--up to 16 bits monochrome images.
* Support for various image-acquisition parameters--much information about the image is also stored, such as size, orientation, and number of layers.
* Encoding of medical data--it defines more than 2000 standardized attributes, such as patients name, age, or diagnosis.
* Well described imaging devices--it precisely describes the device and its functionality.  
The structure of the DICOM is an object defined with standardized attributes--DICOM Information Object Definitions (IOD). It represents the patient's name, sex, height, name of the study, physician, and other similar attributes. There are 27 types of values, such as date, time, or age.  
The speed of changes in the DICOM standard may not follow the pace of changes in devices. Therefore, DICOM allows the use of the Private Data Dictionaries as reserved values that manufacturers may use for their internal use to overstep this limitation. The problem is that manufacturers are not required to publish their Private Data Dictionaries, and the data are not available to other medical devices.
## Appendix A  
### Stiffness Matrix of DCB Composite Specim in x-z Direction  
Assuming plane strain condition for DCB composite specimen (shown in Figures 4 and 5) in x-z direction:  
\[\varepsilon_{22}=0,\ \gamma_{12}=\gamma_{23}=0,\ \tau_{12}=\tau_{23}=0. \tag{11}\]  
Similar to plane stress assumption for unidirectional lamina in x-y direction, the strain-stress relationship and compliance matrix can be written as  
\[\left[\begin{array}{c}\varepsilon_{1}\\ \varepsilon_{3}\\ \gamma_{13}\end{array}\right]=\left[\begin{array}{ccc}S_{11}&S_{13}&0\\ S_{13}&S_{33}&0\\ 0&0&S_{55}\end{array}\right]\left[\begin{array}{c}\sigma_{1}\\ \sigma_{3}\\ \tau_{13}\end{array}\right]. \tag{12}\]  
Using uniaxial loading condition, the compliance matrix can be related to the engineering elastic constants of CFRP composite:  
(1) \(\sigma_{1}\
eq 0,\ \ \sigma_{3}=0,\ \ \tau_{13}=0\)  
\[\varepsilon_{1}=S_{11}\sigma_{1},\ \ \varepsilon_{3}=S_{13}\sigma_{1},\ \ \tau_{13}=0, \tag{13}\]  
\[E_{1}=\frac{\sigma_{1}}{\varepsilon_{1}}=\frac{\sigma_{1}}{S_{11}\sigma_{1}} =\frac{1}{S_{11}}, \tag{14}\]  
\[\
u_{13}=-\frac{\varepsilon_{3}}{\varepsilon_{1}}=-\frac{S_{13}\sigma_{1}}{S _{11}\sigma_{1}}=-\frac{S_{13}}{S_{11}}, \tag{15}\]  
\[S_{11}=\frac{1}{E_{1}}, \tag{16}\]  
\[S_{13}=-S_{11}\
u_{13}=-\frac{\
u_{13}}{E_{1}}. \tag{17}\]  
(2) \(\sigma_{3}\
eq 0,\ \ \sigma_{1}=0,\ \ \tau_{13}=0\)  
\[\varepsilon_{1}=S_{13}\sigma_{3},\ \ \varepsilon_{3}=S_{33}\sigma_{3},\ \ \gamma_{13}=0, \tag{18}\]  
\[E_{3}=\frac{\sigma_{3}}{\varepsilon_{3}}=\frac{\sigma_{3}}{S_{33}\sigma_{3}}= \frac{1}{S_{33}}, \tag{19}\]  
\[\
u_{31}=-\frac{\varepsilon_{1}}{\varepsilon_{3}}=-\frac{S_{13}\sigma_{3}}{S _{33}\sigma_{3}}=-\frac{S_{13}}{S_{33}}, \tag{20}\]  
\[S_{33}=\frac{1}{E_{3}}. \tag{21}\]  
(3) \(\tau_{13}\
eq 0,\sigma_{1}=0,\ \ \sigma_{3}=0\)  
\[\varepsilon_{1}=0,\ \ \varepsilon_{3}=0,\ \ \gamma_{13}=S_{55}\tau_{13}, \tag{22}\]  
\[G_{13}=\frac{\tau_{13}}{\gamma_{13}}\ =\frac{\tau_{13}}{S_{55}\tau_{13}}=\frac{1}{S _{55}}, \tag{23}\]  
\[S_{55}=\frac{1}{G_{13}}. \tag{24}\]  
The stiffness matrix of DCB composite specimen in x-z direction can be proposed by the inverse of compliance matrix,  
\[\left[\begin{array}{c}\sigma_{1}\\ \sigma_{3}\\ \tau_{13}\end{array}\right]=\left[\begin{array}{ccc}Q_{11}&Q_{13}&0\\ Q_{13}&Q_{33}&0\\ 0&0&Q_{55}\end{array}\right]\left[\begin{array}{c}\varepsilon_{1}\\ \varepsilon_{3}\\ \tau_{13}\end{array}\right], \tag{25}\]\[[Q]=[S]^{-1}=\left[\begin{array}{ccc}\frac{S_{33}}{S_{11}S_{33}-S_{13} ^{2}}&-\frac{S_{13}}{S_{11}S_{33}-S_{13}^{2}}&0\\ -\frac{S_{13}}{S_{11}S_{33}-S_{13}^{2}}&\frac{S_{11}}{S_{11}S_{33}-S_{13}^{2}}&0 \\ 0&0&\frac{1}{S_{55}}\end{array}\right], \tag{111}\]  
\[Q_{11}=\frac{S_{33}}{S_{11}S_{33}-S_{13}^{2}}=\frac{E_{1}}{1-v_{13}v_{31}}, \tag{112}\]  
\[Q_{13}=-\frac{S_{13}}{S_{11}S_{33}-S_{13}^{2}}=\frac{v_{13}E_{3}}{1-v_{13}v_{31}}, \tag{113}\]  
\[Q_{33}=\frac{S_{11}}{S_{11}S_{33}-S_{13}^{2}}=\frac{E_{3}}{1-v_{13}v_{31}}, \tag{114}\]  
\[Q_{55}=\frac{1}{S_{55}}=G_{13}. \tag{115}\]
## 5 Semantic Understanding of Concept Layer
### Object Semantics Based Method
#### 5.2.1 Target-Recognition-Based Method  
Geographic scenes involve the interaction of many objects in complex semantic patterns. According to the experience of human visual perception, images containing similar objects may represent the same geographic scene. When defining the category of the geographic scene, different objects have different importances in the scene. This prior knowledge provides ideas for the classification of geographic scenes.  
The method based on object recognition will identify the semantics of each object in the geographic scene and train the classifier for concept semantic understanding based on the semantic information of each object. Typical approaches include Object Bank [101], Latent Pyramidal Regions [102], Bag of Parts [103] and Latent Semantic Analysis [104] (Table 3). These approaches assume that a scene consists of a series of targets, and that by identifying and recognizing those targets with significant discrimination, the category of the scene can be inferred from the semantics of those targets [105]. In these approaches, the problem of semantic understanding of the concept layer is first transformed into the problem of target recognition, and then the geographic scene is represented by image blocks containing multiple targets. However, the errors caused by target recognition will further result in \"error propagation\", which will affect the semantic understanding of the geographic scene.
# Active Learning Strategy for Surrogate-Based Quantile Estimation of Field Function
## 2 Surrogate Model for Function with Mono-Dimensional Domain Random Field Output
### Gaussian Process
The negative log marginal likelihood is given by:  
\[L(\Theta|\mathcal{U}_{M},\mathcal{Y}_{M}) = \log(p(\mathbf{y}|\mathcal{U}_{M},\mathcal{Y}_{M},\Theta))\propto \log(|\mathbf{\hat{K}}_{MM}|)-\mathbf{y}^{T}\mathbf{\hat{K}}_{MM}^{-1}\mathbf{y} \tag{16}\]  
where all the kernel matrices implicitly depend on the hyperparameters \(\Theta\). Any gradient-based or gradient-free approaches optimization algorithms may be used to solve such minimization problem to determine the optimal hyperparameter values of the GP. In addition, a closed form of the constant mean function may be sometimes be found [6; 7; 8; 26; 27]. Once the GP has been trained, the prediction at a new unknown location \(\mathbf{u}^{*}\in\mathbb{R}^{d}\) is done by using the conditional properties of a multivariate normal distribution (Figure 1):  
\[p(y^{*}|\mathbf{u}^{*},\mathcal{U}_{M},\mathcal{Y}_{M},\Theta)=\mathcal{N} \Big{(}y^{*}|\xi_{\ell}^{*},s^{*2}\Big{)} \tag{17}\]where \(\underline{\xi}^{*^{*}},s*^{2}\) are the mean prediction and the associated variance. These terms are defined by:  
\[\underline{\xi}^{*} = \underline{\xi}(\mathbf{u}^{*})=m+\mathbf{k}_{\mathbf{u}^{*}}^{T} \Big{(}\mathbf{K}_{\mathrm{MM}}+\sigma^{2}\mathbf{I}\Big{)}^{-1}(\mathbf{y}- \mathbf{1}m) \tag{18}\] \[s^{*2} = \hat{s}^{2}(\mathbf{u}^{*})=k_{\mathbf{u}^{*},\mathbf{u}^{*}}- \mathbf{k}_{\mathbf{u}^{*}}^{T}\Big{(}\mathbf{K}_{\mathrm{MM}}+\sigma^{2} \mathbf{I}\Big{)}^{-1}\mathbf{k}_{\mathbf{u}^{*}} \tag{19}\]  
where \(k_{\mathbf{u}^{*},\mathbf{u}^{*}}=k(\mathbf{u}^{*},\mathbf{u}^{*})\) and \(\mathbf{k}_{\mathbf{u}^{*}}=\Big{[}k\Big{(}\mathbf{u}_{(i)},\mathbf{u}^{*} \Big{)}\Big{]}_{i=1,\ldots,M}\)  
An example of a 1D function and a GP built based on a dataset of \(M=4\) data is represented in Figure 1. The confidence region for the prediction results from the associated GP standard deviation \((\pm 38)\). At the observation locations the variance of the prediction is null if the data are not assumed noisy. The variance of the prediction grows as the distance from an existing data sample increases. GP surrogate model is appealing because it provides both the prediction of the model and its estimated uncertainty. This will be intensively used in the following of the paper to define an active learning strategy.
## 5 Discussion
In addition, comparisons among the spatial distributions of the regression coefficients for Pcp with the LAI, FVC and GPP GTWR models indicated that the area and intensity of the region of high Pcp coefficient values in northeastern China decreased from Period 1 to 2 (before and after 1991). Previous studies [96; 97] have reported that large areas of pasture and wetland were converted into agricultural land--especially paddy fields--in this region during this period. With significant increases in rice cultivation in this region, the extensive river runoff interception and groundwater extraction were conducted to meet the demands of irrigation [96], which probably resulted in the weakened relationship between Pcp and regional vegetation growth. In addition, the continuous conversion of pasture to paddy field in the Songnen Plain may be one of the reasons for the negative impact of pastures on LAI, FVC and GPP in the region. These results suggested that natural and anthropogenic factors jointly took effect and interacted with each other, affecting the vegetation regime of the ARB. The variations in the spatial patterns of the regression coefficients for the hydrological variables were generally more pronounced in time than those of the climatic factors, which is most likely attributable to more dramatic spatial-temporal changes in the hydrological processes. For example, the relationship between SW and GPP shifted from positive to negative in a large area of the southwestern part of the basin during Period 2 and Period 3 (before and after 2000). In addition, a significant increase in the range of positive SM coefficient values in the study area was found between Period 1 and Period 2 (before and after 1991). To some extent, the changes represent the increasingly apparent positive effect of SM runoff on vegetation growth in the study area during the period of 1982-1999. Comparing the distributions of regression coefficients for SURQ with different vegetation indexes, the smallest range of positive regression coefficients in the FVC model indicated that the relationship between surface runoff and vegetation productivity or vegetation vertical canopy distributions may be more positive than that with vegetation horizontal cover in the ARB. The impact of a single hydrological variable on the vegetation canopy structure and canopy function may vary in both direction (positive or negative) and intensity.
## 3 Damage Comparison with a Uniaxial Vibration Test
### Fatigue Damage of a Notched Simple Specim  
The measured acceleration data was obtained simultaneously during the uniaxial excitation, and the responses for the different spectral loading patterns are plotted in Figure 5. The sampling frequency of all measured signals was set for 8192 Hz, and the frequency range in Figure 4 was selected up to 2000 Hz because a majority of fatigue damage was accumulated at a resonance frequency of 1530 Hz. The first peak at approximately 290 Hz originated from the rigid mode of the notched simple specimen, which was shifted to 290 Hz from DC (direct current) by the clamped boundary condition. The second resonance at approximately 1530 Hz was shifted from 1162.7 Hz (see the modal test result in Table 1) for the same reason. Therefore, the shifted resonance frequencies, 290 Hz and 1530 Hz, are the most contributed responses during excitation as seen in Figure 4. The transformed acceleration data was used to count the fatigue damage using the formulations in Equations (5) and (7) for the three test modes illustrated in Figure 4. The coefficient \(c\) required in Equation (5) was set at \(-1/7\) based on a consideration of the suggested slope range of \(-1/3.5\) to \(-1/10\) in ISO 16750-3. Because the notched simple specimen was constructed of S45C (mild steel), \(b=-0.0806\) and \(S_{0}=664.5\) (MPa) were selected for the fatigue-related material properties used in Equation (7). The fatigue damage found in the vibration test of the notched simple specimen is summarized in Table 2. In addition, the test severity values of different spectral loading cases were compared using the damage ratio between the sine-on-random case and other single spectral pattern cases. These fatigue ratio results are summarized in Table 3 as percentages.  
Figure 4: Vibration test modes for three different spectral excitations (1 g = 9.8 m/s\({}^{2}\)): (**a**) random; (**b**) harmonic; (**a**) + (**b**) sine-on-random.