esa-sceva/satcom-chunk-collection huggingface dataset:
## Materials and Methods
### Image Segmentation and Feature Extraction
#### 2.3.2 Grabcut Algorithm  
Grabcut is a graph-based segmentation method, which is an improvement to the Graphcut algorithm [28]. The Grabcut algorithm is based on the Red-Green-Blue (RGB) three-channel mixed Gaussian model. It only needs to confirm the foreground and background in the image to complete the segmentation between the foreground and background. The Otsu algorithm can calculate the edge of the infrared image and determine the foreground in the image, that is, the detection target. Using the coordinate range of the target in the binary map calculated by the Otsu algorithm as the foreground input in the Grabcut algorithm, the original image can be segmented. The Grabcut algorithm needs to manually circle the foreground target, and it can cover a small amount of background information within the range.  
The Grabcut algorithm uses a Gaussian mixture model to build a data model for the background and foreground regions. Assuming that there are \(N\) pixels in the figure, the points selected in the frame are first regarded as the target pixel Pt belongs to the foreground Gaussian mixture model, and the points outside the frame are regarded as the background pixel \(P_{b}\) belongs to the background Gaussian mixture model, calculated for each pixel The Gaussian components corresponding to other pixels are stored in the vector k = (\(k_{1}\), \(k_{2}\),..., \(k_{N}\)), and each pixel corresponds to a unique Gaussian component. When the pixel belongs to the front scene spot, let = 0; when the pixel belongs to the background spot, let = 1, the algorithm continues to iterate until the energy E reaches the minimum to obtain the current segmentation boundary.
## 6 Storage Capacity Estimation: A Review  
This section provides a review of the storage capacity estimation of Lithuanian saline aquifers using numerical modeling [28]. This approach takes into consideration the inherent uncertainties in determining petrophysical reservoir properties, applying the uncertainty principle. Three distinct cases are defined: the mid case utilizes properties from the published literature [7], the low case assumes values 10% below the mid case, and the high case assigns values 30% higher than the mid case. These parameters are detailed in Table 8.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Syderai**} & \multicolumn{4}{c}{**Vaskai**} \\ \hline  & **Low** & **Mid** & **High** & **Low** & **Mid** & **High** \\ \hline Porosity & 0.144 & 0.16 & 0.208 & 0.207 & 0.23 & 0.299 \\ Perm X & 360 & 400 & 520 & 252 & 280 & 364 \\ Perm Y & 360 & 400 & 520 & 252 & 280 & 364 \\ Perm Z & 119.7 & 133 & 172.9 & 84 & 93.33 & 121.33 \\ Thickness & 51.3 & 57 & 74.1 & 51.3 & 57 & 74.1 \\ NTG & 0.675 & 0.75 & 0.975 & 0.45 & 0.5 & 0.65 \\ AREA & 23.4 & 26 & 33.8 & 11.07 & 12.3 & 15.99 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Uncertainty ranges used for storage capacity estimation for the Syderai and Vaskai saline aquifers of Lithuania.  
Figure 13: Porosity vs permeability plots comparing sub-volumes at 22 \(\upmu\)m and 8 \(\upmu\)m with laboratory values for samples S3 (**left**) and V4 (**right**).  
The injection process is conducted through five interconnected wells (Figure 14), with the injections constrained by the bottom hole pressure. Injection continues until a pressure differential of 80 bars is maintained between the reservoir and the well. Mechanistic models were developed to facilitate numerical simulations, covering various combinations of parameters. Consequently, a total of three simulations were conducted for each of the saline aquifers. The numerical simulations were executed using tNavigator, employing the CO2 SOL modeling option, which accounts for CO\({}_{2}\) solubility. The results yield a range of storage capacity estimates, spanning from the low-case to the high-case values, shown in Table 9[27; 28].  
The results suggest that the saline aquifers exhibit the capability to store CO\({}_{2}\) within a considerable capacity range. The total capacity spans from a minimum estimate of 79 Mt to a maximum of 338 Mt. In other words, these saline aquifers have the potential to sequester CO\({}_{2}\) within this broad range, providing a substantial reservoir for carbon storage initiatives.  
However, there are risks and challenges associated with the long-term storage of CO\({}_{2}\), including the risk of leakage, the creation of cracks and fractures due to changes in mechanical properties during injection, and the impacts of the injection and storage process on the integrity of the caprock [27; 28].
## 3 Results and Discussion
This indicates that thermal modification leads to a stronger SCM structure formed, and due to reduced porosity and pore size, to a decrease in the moisture sorption from the environment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Mechanically Activated** & **Thermo-Modified Mechanically** \\  & **SCM Mixed with Water** & **Activated SCM Mixed with Water** \\ \hline Specific surface, m\({}^{2}\)/kg & 50,789 & 1005 \\ Porosity, cm\({}^{3}\)/g & \(4.52\times 10^{-2}\) & \(8.75\times 10^{-4}\) \\ Pore diameter, nm & Less than 472 & Less than 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: SCM specific surface area, porosity, and pore size. Figure 3: Thermal analysis of samples: 1—mechanically activated SCM; 2—mechanically activated SCM mixed with water; 3—mechanically activated and thermo-modified (850 \({}^{\circ}\)C) SCM.
# Tunable Coloring via Post-Thermal Annealing of Laser-Processed Metal Surface
## Materials and Methods  
### Laser Coloring and Thermal Treatment  
High purity titanium (Ti GR1) plates are mechanically polished as the substrates. Twenty samples are prepared, of which two serve as reference substrates (Ref). The sample surfaces are oxidized by Ytterbium nanosecond pulsed fiber laser across an area 10 mm x 10 mm in the ambient air. The laser source model is IPG YLP-R-0.3-A1-60-18 with pulse duration \(\sim\)1 ns. The beam quality is in TEM00 mode (1.08). A galvanometer is used for scanning. The focal length is 160 mm with beam spot size at 30 \(\upmu\)m. The scanning pattern is straight-line scanning in a defined direction. The laser wavelength is 1.064 \(\upmu\)m, operating at 300 kHz repetition rate with 1 ns pulse width. The fluence is calculated as pulse energy (J) divided by spot area (cm\({}^{2}\)). The scanning speed, hatch density, and laser fluence are set as 38 mm/s, 0.005 mm, and 2.5 J/cm\({}^{2}\) to produce oxide layer 1 (OL1); and 60 mm/s, 0.007 mm, and 2.5 J/cm\({}^{2}\) to produce oxide layer 2 (OL2). Thermal annealing is then conducted by a hotplate in the air. Both annealing temperature and time are varied. Annealing is performed at temperatures of 300, 400, and 500 \({}^{\circ}\)C, for durations of 0.5 h, 1.0 h, and 1.5 h. This leads to 9 different experimental groups for each oxidized Ti substrate (i.e., 20 in total including the two reference groups). For ease of reference, the Ti substrate with OL1 annealed at 300 \({}^{\circ}\)C for 0.5 h is hereafter referred to as \(\mathrm{OL1}_{300^{\circ}\mathrm{C},0.5h}\).
## 3 Results and Discussion
### Cytotoxicity and Biocompatibility  
Figure 7A shows the results of the MTT assay and cell morphology observations, which indicate that CMSC had little toxicity in HeLa cells with all concentrations tested. The morphology of HeLa cells was not affected by treatment with CMSC and, therefore, cell proliferation was not inhibited by the CMSC synthesized. The biocompatibility of the CMSC was seen in Figure 7B where the HEK (Human Embryonic Kidney)-Neuroblastoma cells were cultured for 48 h and observed. The morphology of the cells was not affected when compared with positive controls either. The negative control was used as a reference for morphological changes in the cells in the presence of a toxic substance. This indicates that cell proliferation in the presence of CMSC proves that it is bio-nontoxic as it did not negatively influence cellular growth showing a promising potential application as a biomaterial.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{8}{c}{**Average Value**} \\ \cline{2-7}  & \(\mathbf{L_{0}}\)* & \(\mathbf{a_{0}}\)* & \(\mathbf{b_{0}}\)* & \(\mathbf{L}\)* & \(\mathbf{a}\)* & \(\mathbf{b}\)* & \(\Delta\)E \\ \hline
1 & - & - & - & 89.40 & 0.93 & 13.30 & 0.1068 \\
2 & - & - & - & 89.43 & 0.94 & 13.22 & 0.1581 \\
3 & - & - & - & 89.43 & 0.93 & 13.37 & 0.0510 \\ Commercial CMC & 89.48 & 0.94 & 13.37 & - & - & - & - \\ \hline \hline \end{tabular}  
* Each sample represents average of 3 determinations (\(n=3\)).  
\end{table}
Table 6: Color of CMSC DS 0.6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{1}{c}{**Concentration of**} & \multicolumn{1}{c}{**Concentration**} & \multicolumn{1}{c}{**Concentration of**} & \multicolumn{1}{c}{**Concentration of**} & \multicolumn{1}{c}{**Concentration**} \\  & \multicolumn{1}{c}{**Na (ppb)**} & \multicolumn{1}{c}{**of Al (ppb)**} & \multicolumn{1}{c}{**of Mg (ppb)**} & \multicolumn{1}{c}{**K (ppb)**} & \multicolumn{1}{c}{**of Ca (ppb)**} \\ \hline Average & 14,540.00 \(\pm\) 141.42 & 12.35 \(\pm\) 6.81 & 18.08 \(\pm\) 12.78 & 1125.80 \(\pm\) 212.41 & 25.70 \(\pm\) 3.42 \\ \hline \hline \end{tabular}  
* Each sample represents average of 3 determinations \(\pm\) s.d.  
\end{table}
Table 5: Elements present in CMSC.
## Appendix B
\begin{array}{ll}I_{1}&=\frac{p_{\textit{case1}}\times 2{A_{M}}^{2}{D_{R}}^{2} {I_{V_{1}-PD}}e\frac{-c_{\varepsilon}{D_{R}}}{\xi}}{L_{w}\xi^{4}\left(I_{V_{1 }-M,1,case1}\right)^{2}}\int_{\delta_{1}}^{\delta_{2}}\left(1-\cos 2\delta \right)^{1+2/\varepsilon}d\delta\\ &=\frac{p_{\textit{case1}}\times 2{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}}e \frac{-c_{\varepsilon}{D_{R}}}{\xi}}{L_{w}\xi^{4}\left(I_{V_{1}-M,1,case1} \right)^{2}}\left\{Beta\left[\frac{4I_{V_{1}-PD}}{L_{w}}^{2}+4I_{V_{1}-PD}^{2},3\right.\frac{1}{2}+\frac{2}{\varepsilon},\frac{1}{2}\right]-Beta\left[\frac{ I_{V_{1}-PD}}{L_{w}}^{2}}\frac{3}{2}+\frac{2}{\varepsilon},\frac{1}{2}\right] \Bigg{\}},\end{array} \] (A12)  
and\[I_{2} =\frac{p_{cas2}\times 2{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{ \frac{-c_{E}D_{R}}{\xi}}}{(L_{w}-2v_{w})\xi^{4}\big{(}I_{V_{1}-M,1,cas2}I_{M-PD,1, case2}\big{)}^{2}}\int_{\theta_{1}}^{\theta_{2}}{(1-\cos 2\theta)^{1+2/\varepsilon}d\theta} \tag{13}\] \[=\frac{p_{cas2}\times 2{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{ \frac{-c_{E}D_{R}}{\xi}}}{(L_{w}-2v_{w})\xi^{4}\big{(}I_{V_{1}-M,1,cas2}I_{M-PD, 1,case2}\big{)}^{2}}\] \[\times\Bigg{\{}Beta\Bigg{[}\frac{4I_{V_{1}-PD}^{2}}{(3L_{w}-2v_{w} )^{2}+4I_{V_{1}-PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon},\frac{1}{2}\Bigg{]} -Beta\Bigg{[}\frac{I_{V_{1}-PD}^{2}}{L_{w}^{2}+I_{V_{1}-PD}^{2}},\frac{3}{2}+ \frac{2}{\varepsilon},\frac{1}{2}\Bigg{]}\Bigg{\}}.\]  
Therefore, the average path loss of the NLOS link formed by \(M\) from Tx1 is as follows:  
\[h_{NLOS\_M,1}^{PL\_ap} =\frac{{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{\frac{-c_{E}D_{R}}{ \xi}}}{(L_{w}-v_{w})\xi^{4}}\Bigg{\{}\frac{\bigg{\{}Beta\Bigg{[}\frac{4I_{V_{1} -PD}^{2}}{L_{w}^{2}+4I_{V_{1}-PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon}, \frac{1}{2}\Bigg{]}-Beta\Bigg{[}\frac{I_{V_{1}-PD}^{2}}{L_{w}^{2}+I_{V_{1}- PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon},\frac{1}{2}\Bigg{]}\Bigg{\}}}}{ \big{(}I_{V_{1}-M,1,cas2}I_{M-PD,1,cas2}\big{)}^{2}} \tag{14}\] \[+\frac{\bigg{\{}Beta\Bigg{[}\frac{4I_{V_{1}-PD}^{2}}{(3L_{w}-2v_{w })^{2}+4I_{V_{1}-PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon},\frac{1}{2}\Bigg{]} -Beta\Bigg{[}\frac{I_{V_{1}-PD}^{2}}{L_{w}^{2}+I_{V_{1}-PD}^{2}},\frac{3}{2} +\frac{2}{\varepsilon},\frac{1}{2}\Bigg{]}\Bigg{\}}}{\big{(}I_{V_{1}-M,1, cas2}I_{M-PD,1,cas2}\big{)}^{2}}\Bigg{\}}.\]  
It should be noted that Tx1 and Tx2 are not symmetrical in forming the NLOS link by \(M\).
# Chaotic Pulse-Shaping Filter Based on Root-Raised-Cosine Division
###### Abstract  
Chaotic baseband wireless communication system (CBWCS) suffers bit error rate (BER) degradation due to their intrinsic intersymbol interference (ISI). To this end, an ISI-free chaotic filter based on root-raised-cosine (RRC) division is constructed to generate a chaotic signal. A wireless communication system using this chaotic signal as a baseband waveform is proposed. The chaotic property is proved by the corresponding new hybrid dynamical system with topological conjugation to symbolic sequences and a positive Lyapunov exponent. Simulation results show that under a single-path channel and multi-path channel, the proposed method outperforms CBWCS in both BER performance and computational complexity.  
chaotic filter; wireless communication; ISI; dynamical system; Lyapunov exponent +
Footnote †: journal:  
0023
# An Authentication Method for AMBTC Compressed Images Using Dual Embedding Strategies
## 4 Experimental Results
### The Performance of the Proposed Method
We observe that under the same threshold, the larger the ratio of smooth blocks, the higher the PSNR, implying that the proposed method is more effective. The reason is that the differences of quantized values of smooth blocks are close to each other, thus the error caused by flipping bits of bitmaps is also small. For example, Lena, Jet, Tiffany, Splash and House contain more than 40% smooth blocks, and the PSNR of these images can reach more than 42 dB. However, the PSNR of Baboon is the lowest (41.04 dB), which is due to the fact that it has only 6.99% smooth blocks. PSNR is a metric to measure an embedding method, and higher PSNR means that the embedding method is more effective. In these 8 test images, the PSNRs of all images are higher than 41 dB, implying the effectiveness of our method. The following experiment demonstrates the detectability of the proposed method. The marked codes of Lena are tampered such that the tampered decompressed image shows a daisy on [PERSON]'s hat, as shown in Figure 5a. Figure 5b shows the tampered region indicated by black blocks, while Figure 5c,d present the coarse and refined detection results of Figure 5a. An image contains a total of \((512\times 512)/(4\times 4)=16384\) blocks, and this \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Image** & **Number of Smooth Blocks** & **Ratio of Smooth Blocks** & **PSNR** \\ \hline Lena & 8695 & 53.07\% & 42.49 \\ \hline Jet & 9758 & 59.56\% & 43.31 \\ \hline Baboon & 1146 & 6.99\% & 41.04 \\ \hline Tiffany & 9518 & 58.09\% & 42.78 \\ \hline Sailboat & 3638 & 22.20\% & 41.64 \\ \hline Splash & 11,820 & 72.14\% & 43.33 \\ \hline Peppers & 5524 & 33.71\% & 41.91 \\ \hline House & 6616 & 40.38\% & 42.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The relation between the ratio of smooth blocks and the PSNR of images. Figure 4: The plot of threshold \(T\) versus PSNR for various test images. experiment tampers with 2176 blocks with a tampering rate of 13.28%. Figure 5c shows that a few scattered blocks are not detected in the coarse detection. Nevertheless, those undetected blocks can be detected in the refined detection, as shown in Figure 5d.
###### Abstract
However, it remains the optimal solution for serving fixed-size periodic traffic, provided that the reservation periodicity aligns with the traffic generation period;
* Conversely, the performance of the DS scheme remains independent of PDB requirements, making it most effective for handling both fixed- and variable-size aperiodic traffic under low or average density conditions;
* Although the DS scheme performs better than SB-SPS in aperiodic traffic scenarios, its effectiveness diminishes as traffic density increases due to the random selection of transmission resources, leading to higher collision probabilities;
* The SEAC strategy consistently outperforms both SB-SPS and DS schemes, particularly in aperiodic traffic scenarios, by improving reliability, reducing collisions, and enhancing resource utilization.
# Rapid Prototyping of Multi-Functional Battery Energy Storage System Applications
## 5 Proof-of-Concept Evaluation
### Framework Prototype and Validation Example
#### 5.1.3 Control Mechanism  
The CEI 0-21 standard specifies a frequency-dependent active power limitation for DER connected into the low-voltage grid [48]. Guidelines defined in that standard are fulfilled in the FW mode. In that sense, FW commands the active power of the battery to balance the frequency of the grid as stated in Equation (5). The resulted active power value \(P_{ref}^{FW}\) is restricted to technical limitations of the battery (i.e., SoC and active power limits) as indicated in Equation (6). SelfC controls the BESS to assure that no energy from the grid is taken. To achieve that a PI controller is designed by following Equation (7), the resulted active power value \(P_{ref}^{SelfC}\) is also restricted by Equation (6):  
\[\Delta P_{ref}^{FW}=\alpha\Delta F_{grid}, \tag{5}\]  
\[SoC^{min}<SoC<SoC^{max},\quad P_{bat}^{min}<P_{bat}<P_{bat}^{max}, \tag{6}\]  
\[e=P_{grid}^{ref}-P_{grid},\quad P_{grid}^{ref}=0,\quad P_{ref}^{SelfC}=K_{p}e+ K_{i}\int_{0}^{t}e(\tau)d\tau. \tag{7}\]  
The specification, design and proof-of-concept of CEMS are deployed under EMSOnto, and these steps are addressed in the following.
# Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications
## 5 Simulation Results
### Performance of the Msg3 PR Scheme  
In this subsection, we present the analysis (Anal.) and simulation (Sim.) results of the Msg3 PR scheme when the network is in a steady-state. Because the steady-state analysis model defined in Section 4 can be obtained when \(N\) is determined, the simulations also performed with fixed \(N\). Therefore, we generate static new arrival at each RACH to converge the total arrival to \(N\). Moreover, the locations of newly arrived devices are determined by the uniform distribution.  
The simulation model assumes a steady-state condition. In other words, the number of arrivals and the distribution of the trial and the ramping number of devices converge.  
We show RA throughput performance in terms of \(PRS\), \(N_{max}\), and the number of preambles in an RACH, \(V\). Furthermore, the connection failure probability analysis and the average energy consumption analysis according to \(PRS\) change are additionally performed to further analyze the performance of Msg3 PR scheme. The performance metrics used in the study are defined as follows.  
The RA throughput performance is evaluated in terms of \(PRS\), \(N_{max}\), and the number of preambles in a RACH, \(V\). Furthermore, analyses of the connection failure probability and the average energy consumption according to \(PRS\) change are additionally performed to further analyze the performance of the Msg3 PR scheme. Note that we use the same parameters relative to energy consumption model as in Table 2 in the simulation. The performance metrics used in the study are defined as follows:  
* RA throughput (Anal.)--Equation (18). (Sim.) \[E[S|N]=\frac{\textit{Total}\,\#\,\textit{of}\,\textit{R}\,\textit{A}\,\textit{ Success}\,\textit{Devices}}{N\times\textit{SimNumber}},\]
* Connection failure probability (Anal.)--Equation (25). (Sim.) \[\mathbb{P}_{\textit{CF}|N}=\frac{\textit{Total}\,\#\,\textit{of}\,\textit{Connection}\, \textit{Failed}\,\textit{Devices}}{\textit{Total}\,\#\,\textit{of}\,\textit{R}\, \textit{A}\,\textit{Completed}\,\textit{Devices}},\]
* Average energy consumption (Anal.)--Equation (30). (Sim.) \[E[W|N]=\frac{\textit{Total}\,\textit{E}.\textit{C}\,\textit{of}\,\textit{R}\, \textit{A}\,\textit{Completed}\,\textit{Devices}}{\textit{Total}\,\#\,\textit{of}\, \textit{R}\,\textit{A}\,\textit{Completed}\,\textit{Devices}}.\]  
In each figure, the analysis results are displayed as lines, and the simulation results are displayed as markings if we performed both an analysis and a simulation.
# Progressive Collapse Performance of Prefabricated Step-Terrace Frame Structures in Mountain Cities
## 4 Analysis of Progressive Collapse Performance of Prefabricated Step-Terrace Frame Structures
#### 4.1.1 Structural Design Parameters and the Design of Working Conditions  
The seismic fortification intensity is 7 degrees (0.15 g), the site category is Class II, the design earthquake group is Group I, and the ground roughness is Class B. The beams and columns adopt C30 concrete, the longitudinal reinforcement is HRB400, the stirrup is HPB300, and the angle steel is Q90. The total number of stories of the reinforced concrete structure is 7, the floor height is 3.6 m, the total height including the dropped stories is 25.2 m, the section size of the column is 600 mm \(\times\) 600 mm, the section size of the beam is 250 mm \(\times\) 600 mm, and the thickness of the floor is 120 mm. The floor live load is 2.0 kN/m\({}^{2}\), the floor dead load is 3.5 kN/m\({}^{2}\), the accessible roof dead load is 5.5 kN/m\({}^{2}\), the accessible roof live load is 2.0 kN/m\({}^{2}\), the beam line load is 8.5 kN/m, the roof parquet line load is 3.0 kN/m, and the basic wind pressure is 0.4 kN/m\({}^{2}\).  
Considering that the moment transfer capacity of the joints with the connection method of the exposed corbel-dowel bar-angle steel plate is limited and is between rigid connection and hinged connection, in this paper, when performing structural design calculations in PKPM V1.4.1.3 software, two calculation models are considered:  
1. Rigid connection form of beams and columns. The frame beam and the frame column are completely rigidly connected. The joint area transmits both shear force and bending moment, and the bearing capacity is equivalent to that of the cast-in-place structure.  
Figure 16: Comparison between simulation and experiment of the prefabricated substructure.  
2. Hinged connection form. In this connection method, the frame column is reliably connected, and its performance is comparable to that of an integral cast-in-place column. The prefabricated frame beam and the prefabricated frame column adopt a hinged form at the beam end. The joint area only transmits shear force and does not transmit bending moment. According to the reinforcement schemes of the two calculation models and considering this semirigid connection, the final reinforcement scheme satisfies the two structural forms. Using PKPM design software, the prefabricated structures of C1K2, C2K2, C3K2, and the prefabricated plain flat frame structure (C0K0) model were established. Based on this series of prefabricated step-terrace frame structures with different dropped story numbers, this section will study the differences in the progressive collapse performance under six working conditions. The six working conditions, from working condition 1 to working condition 6, are the dismantled structure columns A, B, C, D, E, and F, respectively. The elevations of the four prefabricated step-terrace frame structures are shown in Figure 17.
## 4 Analysis of the Simulation Signal
### Evaluation Indicators  
To compare the noise reduction effect of these three methods, the percentage of signal energy after noise reduction to the original signal energy (\(ESN\)) and the root mean square error (\(RMSE\)) are used as noise reduction evaluation indicators. \(ESN\) is defined as follows:  
\[ESN=\frac{E^{\prime}}{E}. \tag{27}\]  
where \(E\) is the total energy of the original signal and \(E^{\prime}\) is the energy of the signal after noise reduction. The \(RMSE\) can be defined as follows:  
\[RMSE=\sqrt{\frac{1}{N}\Big{(}f(t)-f(t)^{\prime}\Big{)}^{2}}. \tag{28}\]  
The results of EMD, EVMD, and FCI-VMD denoising evaluation indicators for signals with different SNRs are shown in Table 2. It is generally believed that the smaller the \(RMSE\) and the larger the ESN are, the closer the denoised signal is to the real signal. Compared with EMD and EVMD, after denoising the noisy analog AE signal with the FCI-VMD method, the signal retains a higher proportion of energy, and the RMSE is also smaller. This shows that at different noise levels, FCI-VMD is better than EMD and EVMD in processing AE signals.