esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussions  
### Model Geometry and Boundary Conditions  
The Tebessa-Morsoft alluvial aquifer system was conceptualized to develop a flow model in a steady state and in a transient regime using two different development scenarios.  
The aquifer was discretized into 70 \(\times\) 82 square meshes with 500 m sides. The model was made up of 1200 active meshes, i.e., an area of 600 km\({}^{2}\) (Figure 4).  
The piezometric map from May 2010 [33] was used as the reference piezometric state in the numerical model (Figure S2). This piezometric map was utilized as a top layer in the numerical model and for the calibration of the steady-state regime. However, the bedrock and the piezometric maps were exploited to calculate the saturated aquifer thickness map and to develop the aquifer geometry model.  
Using the Thornthwaite's method, the recharge rate was evaluated between 2 cm/year and 18 cm/year [33].  
Based on the pumping tests in twenty-two boreholes capturing the aquifer, the permeability values varied between 2 \(\times\) 10\({}^{-5}\) m/s and 3 \(\times\) 10\({}^{-4}\) m/s [36]. Moreover, the total porosity ranged between 28% and 80%.  
Hydrogeological conceptual models are collections of hypotheses describing the understanding of groundwater systems, and they are considered one of the major sources of uncertainty in groundwater flow and transport modeling. According to basic hydrogeological information, the following boundary conditions were set in the steady-state groundwater model. The aquifer was considered as unconfined with a heterogeneous layer. The entire study area received recharge by rainfall (flow boundary). The wadis of the region (El Ksob wadi, El kebir wadi and Chabro wadi) were defined as the second flow boundary. In some lateral boundaries, the boundaries were closed and considered watertight (no-flow boundary). Conversely, some boundaries were simulated as open flow boundaries, where hydraulic gradients allow flow across these boundaries (fractured limestones of the Maastrichtian and Turonian). The boundary conditions are given in Figure 4, and all the aquifer's parameters are shown in Table 2.  
Figure 4: Cell discretization and boundary conditions of the Tebessa-Morsoft alluvial aquifer model.  
Finally, the simulation was developed over a period of 20 years (period 2010-2030).
## 3 Establishment and Simulation of the Error Model
### Ray Tracing and Error Representation
#### 3.2.3 The Radial Motion Error along X Axis  
The output surface and incident surface of laser displacement sensor LDSI are defined in CS6. The output surface is expressed as x = 0. The light receiving plane of LDSI is x = \(L_{r}\). We can obtain the reflected light of the polyhedral prism from the output light of LDSI and the reflection matrix of the reflector.  
The coordinate \(\text{LDSX}(X_{LDSX},Y_{LDSX},Z_{LDSX})\) of the incident point of LDSI can be obtained from the reflected light of the polyhedral prism and the receiving surface of the LDSI. The coordinate \(\text{PHLX}(X_{PHLX},Y_{PHLX},Z_{PHLX})\) of the reflection point on the polyhedral prism can be obtained according to the incident light and the reflection surface. The measured value of the LDSI is expressed as \(\text{LX}_{lds}\). Using the spatial geometric relationship, \(\text{LX}_{lds}=\sqrt{X_{PHLS}^{6}+\left(Y_{PHLS}^{6}-K_{y}^{6}\right)^{2}+ \left(X_{PHLS}^{6}-K_{x}^{6}\right)^{2}}\). Because the values of \(Y_{PHLS}^{6}-K_{y}^{6}\) and \(X_{PHLS}^{6}-K_{x}^{6}\) are first order infinitesimal, \(\text{LX}_{lds}\approx X_{PHLS}^{6}\). Some system errors can be eliminated by reducing the initial value. Then, the radial motion error along the X axis is obtained:  
\[\begin{array}{c}\delta_{x}=\text{LX}_{lds}-\text{LX}_{lds(t-0)}-cos\theta \big{(}\delta_{xbc}+\left(K_{x}+K_{x}^{6}\right)\big{(}\varepsilon_{py}+ \varepsilon_{ybc}\big{)}\big{)}+sin\theta\big{(}\delta_{ybc}-\left(K_{x}+K_{ x}^{6}\right)\varepsilon_{xbc}\big{)}\\ +\delta_{xbc}+\left(K_{y}+K_{y}^{6}\right)\varepsilon_{pz(t-0)}+\left(K_{x}+K_ {y}^{6}\right)\varepsilon_{pz(t-0)}-\left(K_{y}+K_{y}^{6}\right)\varepsilon_ {pz}+\left(K_{y}+K_{y}^{6}\right)\varepsilon_{z}\\ -\left(K_{x}+K_{x}^{6}\right)\varepsilon_{y}\end{array} \tag{12}\]  
The main factors affecting the measurement of the radial motion error along the X axis include the following: installation errors \(\delta_{xbc}\), \(\delta_{ybc}\), \(\varepsilon_{xbc}\), and \(\varepsilon_{ybc}\); perpendicularity error \(\varepsilon_{py}\); working angle manufacturing error \(\varepsilon_{pz}\); the coordinates \(K_{y}+K_{y}^{6}\) and \(K_{z}+K_{z}^{6}\) of the light emission point in CS0. Where \(cos\theta\Big{(}\delta_{xbc}+\left(K_{x}+K_{z}^{6}\right)\Big{(}\varepsilon_{py}+ \varepsilon_{ybc}\Big{)}\Big{)}\), \(sin\theta\Big{(}\delta_{ybc}-\left(K_{z}+K_{z}^{6}\right)\varepsilon_{xbc}\Big{)}\), \(\delta_{xbc}\), \(\Big{(}K_{y}+K_{y}^{6}\Big{)}\varepsilon_{pz(t=0)}\), \(\big{(}K_{x}+K_{z}^{6}\big{)}\Big{(}\varepsilon_{py(t=0)}+\varepsilon_{ybc} \big{)}\) are con stants and can be compensated by triangular fitting, \(\left(K_{y}+K_{y}^{6}\right)\varepsilon_{pz}\) can be compensated by measuring the spatial coordinates of the LDS1 and the manufacturing errors of the polyhedral prism working surface. \(\varepsilon_{z}\) and \(\varepsilon_{y}\) in \(\left(K_{y}+K_{y}^{6}\right)\varepsilon_{z}-\left(K_{z}+K_{z}^{6}\right) \varepsilon_{y}\) can be calculated by the method mentioned above.
# FF-MR: A DoH-Encrypted DNS Covert Channel Detection Method Based on Feature Fusion
## 5 Experimental Evaluation
### Performance Evaluation
#### 5.3.1 t-SNE Feature Dimensionality Reduction and Visual Analysis  
Figure 8 shows the experimental results of the the normalized confusion matrix. We mainly focus on the detection results of encrypted DNS covert channels. As shown in the matrix, there was small amount of confusion in the classification of encrypted DNS covert channel traffic, i.e., malicious_DoH traffic generated by iodine, dnscat2, and dns2 tcp. To visually analyze the classification results, the test data were saved with the feature vectors learned by the MHA-Resnet before applying softmax, and we randomly selected 500 samples for each type of traffic, which were then reduced to two dimensions by t-SNE [41], as shown in Figure 9.  
The same category of traffic is aggregated into a cluster in Figure 9, and the distinction between traffic in different categories is obvious, in which there is a small amount of confusion for the identification of the three encrypted DNS covert channels due to the effect of data imbalance, verifying the experimental results of Figure 8. As shown in Table 3, after data preprocessing, the encrypted DNS covert channel traffic generated by the iodine and dnscat2 tools was much smaller than other forms of traffic, resulting in the inability of the data imbalance.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Substructure** & **Layer** & **Operation** & **Input** & **Output** \\ \hline \multirow{6}{*}{Residual neural Network} & Conv1D & One-dimensional convolution*4 & 1*1024 & 32*1024 \\  & ResLayer1 & One-dimensional convolution*4 & 32*1024 & 32*1024 \\  & ResLayer2 & One-dimensional convolution*4 & 32*1024 & 64*512 \\  & ResLayer3 & One-dimensional convolution*4 & 64*512 & 128*256 \\  & ResLayer4 & One-dimensional convolution*4 & 128*256 & 256*128 \\  & AvgPooling1D & Global average pooling & 256*128 & 256*1 \\ \hline \multirow{6}{*}{Multi-Head Attention mechanism} & Linear & linear transformation + Sigmoid word embedding calculate the attention weight matrix & 29*1 & 14*1 \\  & Embedding & & 14*1 & 14*128 \\  & Multi-Head Attention & Multi-Head activation weight matrix & (256 + 14)*128 & (256 + 14)*128 \\  & Feed Forward & & 12*1 & (256 + 14)*128 \\  & & Linear transformation Flatten the weighted fusion feature matrix & (256 + 14)*128 & 34,560*1 \\ \hline \multirow{6}{*}{MLP+softmax} & Linear & linear transformation + ReLU linear transformation linear transformation softmax & 34,560 + 256 & 200 \\  & Linear & Linear transformation softmax & 200 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Structural parameters in MHA-Resnet.  
Figure 8: Normalized confusion matrix.  
to learn the features to identify the above two categories of traffic. In general, this finding verifies that the FF-MR has a good feature extraction ability and performs well in detection and identification.
## 4 Communication Technologies for Seamless Connectivity in Smart Farming
### Availability and Challenges of Communication Technologies  
In smart farming, UAVs are deployed with mounted gateway to gather data from sensors and nodes spread over the farm areas. The UAVs can fly over obstacles such as trees in the wide farm areas. Various physical and systemic conditions of the agriculture, ranging from wide outdoor area to power life should be considered. In this case sending and receiving data should be carried out over a long distance with low power consumption. For this reason, we will focus on long-distance wireless connectivity challenges in agriculture and farm areas and decide to investigate the limitations of cellular networks and LPWAN (Sigfox, LoRa/LoRaWAN and NB-IoT) technologies [61].
## 5 Results  
### Comparative Analysis  
The validity of the longitudinal driving distance model was demonstrated by the PCA model test results. As demonstrated in the following section, SPSS was used to create a general linear regression equation for the standardized variables on the longitudinal driving distance of lane-changing behavior, which was then compared to the results of PCA to confirm the validity of the model.  
To begin, the R-square values of the two models were compared (see Table 8). The R-square result of the general linear regression model is slightly better than the PCA model. The model's fitting effect is influenced by the fact that some independent variables are abandoned in the process of PCA. The error of PCA estimation to the real value is smaller, which means a higher practical value. However, R-square and standard estimation error cannot comprehensively evaluate the model's fitting effect. It is therefore required to assess both the model's overall fitting degree and the significance test of independent variables.  
An integrity test was added to the general linear regression equation (as shown in Table 9). Its statistic \(F=97.7\
ot\in(0.345,\ 2.022)\), which passes the hypothesis test and means the general linear regression model equation generally fits well.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Non-Standardized Coefficient**} & \multicolumn{2}{c}{**Standardized**} & \multirow{2}{*}{**t**} & \multirow{2}{*}{**Sig.**} \\ \cline{2-2} \cline{5-6}  & **B** & **Standard Error** & & & \\ \hline (Constant) & 0.000 & 0.025 & & 0.000 & 1.000 \\ \(f_{1}\) & \(-0.032\) & 0.013 & \(-0.064\) & \(-3.336\) & 0.002 \\ \(f_{2}\) & 0.058 & 0.016 & 0.089 & 3.542 & 0.000 \\ \(f_{3}\) & 0.025 & 0.021 & 0.030 & 1.195 & 0.233 \\ \(f_{4}\) & 0.358 & 0.022 & 0.407 & 16.202 & 0.000 \\ \(f_{5}\) & \(-0.251\) & 0.023 & \(-0.270\) & \(-10.753\) & 0.000 \\ \(f_{6}\) & \(-0.142\) & 0.024 & \(-0.151\) & \(-6.014\) & 0.000 \\ \(f_{7}\) & 0.298 & 0.025 & 0.298 & 11.865 & 0.000 \\ \(f_{8}\) & 0.135 & 0.026 & 0.129 & 5.139 & 0.000 \\ \(f_{9}\) & 0.405 & 0.026 & 0.387 & 15.405 & 0.000 \\ \(f_{10}\) & \(-0.094\) & 0.028 & \(-0.084\) & \(-3.355\) & 0.001 \\ \(f_{11}\) & 0.519 & 0.031 & 0.428 & 17.015 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Principal component linear regression coefficient.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & \(R\) & \(R^{2}\) & **Adjusted \(R^{2}\)** & **Standard Estimation Error** \\ \hline PC Linear & & & \\ Regression & 0.849 & 0.720 & 0.713 & 0.536 \\ General Linear & & & \\ Regression & 0.895 & 0.801 & 0.793 & 59.399 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of \(R^{2}\) and standard estimation error of two models.  
In summary, the PCA regression model of longitudinal travel distance for lane changes is more practical than the general linear regression model and can estimate and predict the longitudinal driving distance for a series of indicators in the process of lane changes.
## 3 Ground Landing Station Design
### Landing Surface  
A non-actuated repositioning method is considered based on a sloped landing surface. Figure 5 shows the design divided into two parts: the bottom section is a base that matches the shape of the battery carriage receiver and the payload compartment attached to the UAV.  
The top section is a sloped surface, which extends the base shape; it measures 440 mm in length and 315 mm in height, giving a landing area of 0.14 m\({}^{2}\). The bottom part has four arms with a 12.7 mm (0.5 in) diameter, on its left and two on its right side; these arms hold securely the top part, which can be easily removed and replaced with a larger surface. The slope presents a 45\({}^{\circ}\) angle. At the top end of the slope, there is a flat surface where the UAV arms rest when docked.  
Figure 4: Battery storage design for UAV ground station: (**a**) circular battery array, and (**b**) mechanic base.  
Figure 5: Non-actuated landing surface design: (**a**) battery storage and (**b**) sloped landing surface.
## 3 Spectrum Management Issues
### Cognitive Radio
#### 3.2.5 Cluster Formation  
The authors in [124] have proposed a weight-based cluster formation scheme to overcome the clustering issues caused by node mobility and dynamic channel availability in the CR network. Furthermore, they have compared their designed protocol with competing protocols in the CR network. Subsequently, the developed algorithm produces better results than conventional protocols, especially in adverse conditions. Another cluster-based scheduling approach is proposed in [125]. The authors have proposed two scheduling approaches, i.e., Frame Intra Cluster Multichannel Scheduling algorithm denoted Frame-ICMS and the Slot Intra Cluster Multichannel Scheduling algorithm denoted Slot-ICMS. The performance is evaluated in terms of accurate and bad PU activity. It enables spatial reuse with noninterfering users, reduces delays, and saves energy.  
The above-discussed researches have been summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Approach** & **Methodology/Technique** & **Advantages** & **Limitation/Future Work** & **References** \\ \hline \multirow{8}{*}{Spectrum sensing} & A new Filter Bank Multicarrier & Efficient utilization of & \multirow{2}{*}{\
\begin{tabular}{c} Bio-inspired techniques \\ for more efficient \\ optimization approach \\ \end{tabular} } & \multirow{2}{*}{[116]} \\  & (FBMC) approach based on & & & \\  & the adjustment by using the & real-time Internet of & & \\  & non-linear fractional program & Things (IoT) & & \\  & and stationery KKT condition & applications & & \\ \cline{2-5}  & A group-based multi-channel & & & \\  & synchronized spectrum & & & \\  & sensing approach based on & & & \\  & Dynamic Multi-Channel Slot & & & \\  & Allocation (DMCSA) & & & \\  & algorithm & & & \\ \hline \multirow{8}{*}{Throughput enhancement} & It derives an optimal service & Better Quality of & \multirow{2}{*}{
\begin{tabular}{c} Queue length factor is \\ not considered \\ minimum sojourn time \\ \end{tabular} } & \multirow{2}{*}{[118]} \\  & rate for increasing the & & & \\  & performance of primary and & & & \\  & secondary users & & & \\ \cline{1-1} \cline{2-5}  & The undercover routing & & & \\ \cline{1-1} \cline{2-5}  & protocol, which consists of & & & \\ \cline{1-1} \cline{2-5}  & collaborative beamforming & & & \\ \cline{1-1} \cline{2-5}  & technique based on layer & & & \\ \cline{1-1} \cline{2-5}  & three routing & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the related work for CR.
## 3 Results and Discussion
\begin{table}
\begin{tabular}{l l c c c} \hline \hline \multirow{2}{*}{**Log/Type of Samples**} & **Position within** & \multicolumn{2}{c}{**Position over Tree Length**} & \multicolumn{1}{c}{**Cummulated Mean**} \\  & **Cross Section \({}^{*}\)** & **Lower Part** & **Upper Part** & **and STDEV** \\ \hline Log N\({}^{\circ}\) 1 & & & & \\ \hline \multirow{4}{*}{\begin{tabular}{l} Solid wood \\ (tangentially loaded) \\ \end{tabular} } & Core zone & 9490.00 \(\pm\) 933.92 & 11,011.33 \(\pm\) 721.69 & 10,250.67 \(\pm\) 827.81 \\ \cline{2-5}  & Middle zone & 11,480.83 \(\pm\) 922.26 & 10,787.67 \(\pm\) 1056.90 & 11,134.25 \(\pm\) 989.58 \\ \cline{2-5}  & Outer zone & 13,211.55 \(\pm\) 1167.09 & 13,021.41 \(\pm\) 1136.27 & 13,116.48 \(\pm\) 1151.68 \\ \cline{2-5}  & Mean and STDEV & 11,774.99 \(\pm\) 1719.06 & 11,725.93 \(\pm\) 1463.01 & 11,750.46 \(\pm\) 1591.04 \\ \hline \multirow{4}{*}{\begin{tabular}{l} Solid wood \\ (radially loaded) \\ \end{tabular} } & Core zone & 8612.17 \(\pm\) 728.33 & 8732.53 \(\pm\) 363.55 & 8672.35 \(\pm\) 518.98 \\ \cline{2-5}  & Middle zone & 9534.50 \(\pm\) 3721.91 & 10,629.95 \(\pm\) 527.30 & 10,082.23 \(\pm\) 953.13 \\ \cline{2-5}  & Outer zone & 12,414.60 \(\pm\) 974.53 & 12,165.43 \(\pm\) 773.24 & 12,290.02 \(\pm\) 848.76 \\ \cline{2-5}  & Mean and STDEV & 10,502.07 \(\pm\) 1872.56 & 10,864.66 \(\pm\) 1433.39 & 10,683.37 \(\pm\) 1648.84 \\ \hline Edge-bonded boards (at 45\({}^{\circ}\)) & Outer zone & 12,773.58 \(\pm\) 757.49 & 12,881.45 \(\pm\) 513.75 & 12,827.52 \(\pm\) 635.36 \\ \hline Log N\({}^{\circ}\) 2 & & & & \\ \hline \multirow{4}{*}{\
\begin{tabular}{l} Solid wood \\ (tangentially loaded) \\ \end{tabular} } & Core zone & 8521.33 \(\pm\) 656.18 & 8343.33 \(\pm\) 269.52 & 8432.33 \(\pm\) 462.85 \\ \cline{2-5}  & Middle zone & 9738.50 \(\pm\) 726.32 & 10,337.00 \(\pm\) 1459.98 & 10,037.75 \(\pm\) 1093.15 \\ \cline{2-5}  & Outer zone & 13,947.61 \(\pm\) 726.34 & 11,554.44 \(\pm\) 916.20 & 12,751.03 \(\pm\) 1477.61 \\ \cline{2-5}  & Mean and STDEV & 11,178.71 \(\pm\) 2425.11 & 10,425.20 \(\pm\) 1596.86 & 10,801.96 \(\pm\) 2010.99 \\ \hline \multirow{4}{*}{
\begin{tabular}{l} Solid wood \\ (radially loaded) \\ \end{tabular} } & Core zone & 8211.22 \(\pm\) 462.32 & 8897.74 \(\pm\) 640.04 & 8554.48 \(\pm\) 551.18 \\ \cline{2-5}  & Middle zone & 9722.33 \(\pm\) 931.89 & 10,130.42 \(\pm\) 488.50 & 9926.38 \(\pm\) 710.20 \\ \cline{2-5}  & Outer zone & 12,620.16 \(\pm\) 1395.89 & 11,424.44 \(\pm\) 812.06 & 12,022.30 \(\pm\) 1103.96 \\ \cline{2-5}  & Mean and STDEV & 10,579.24 \(\pm\) 2082.79 & 10,401.49 \(\pm\) 1159.21 & 10,490.37 \(\pm\) 1621.00 \\ \hline Edge-bonded boards (at 45\({}^{\circ}\)) & Outer zone & 12,258.38 \(\pm\) 844.76 & 12,374.44 \(\pm\) 1232.62 & 12,306.41 \(\pm\) 1004.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modulus of elasticity in static bending MOE\({}_{12}\) (in N/mm\({}^{2}\)) of solid and glued spruce samples. Figure 7: Variation tendency of density, MOE and MOR, over the cross section of the log, for the solid wood samples (represented with circles), compared to glued samples (represented with “x”).
## 3 Fundamentals of RF Energy Harvesting
### Principles of RF Energy Harvesting  
RFEH is based on the principle of capturing electromagnetic waves emitted from ambient RF sources, such as cellular networks, Wi-Fi routers, and broadcasting stations, and converting them into usable direct-current (DC) power. This process involves three fundamental stages: energy capture, conversion, and storage. In the first stage, a receiving antenna captures ambient RF waves from surrounding sources. These captured signals are then fed into a rectifier circuit (also known as a rectenna) that converts the alternating-current (AC) RF signals into DC voltage. Finally, the harvested energy is stored in an energy storage component, such as a battery or supercapacitor, ensuring a continuous and stable power supply for low-power electronic devices [13]. Figure 2 illustrates the RFEH process. The antenna collects RF signals from the environment and transfers them to the RF rectifier, which comprises a rectifying diode, a DC-pass filter, and a terminal load. The impedance matching network (IMN) plays a crucial role in ensuring maximum power transfer from the antenna to the rectifier [14]. The rectifying diode converts the RF signal into DC, while the DC-pass filter removes high-frequency harmonics to ensure a smooth DC output. The DC-pass capacitor filter further regulates the output impedance and enhances the stability of the generated DC power.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Category** & **Number of Articles** \\ \hline Single-band rectenna designs & 22 \\ Multi-band/multi-source energy harvesters & 20 \\ SWIPT-enabled systems & 18 \\ AI/ML-assisted energy optimization & 15 \\ Hybrid energy harvesting (RF + solar/etc.) & 12 \\ Biomedical applications & 10 \\ Smart cities/urban infrastructure & 13 \\ Industrial IoT/WSN & 22 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Categorization of selected RF energy-harvesting studies.  
The efficiency of RFEH is influenced by factors such as the strength and frequency of the ambient RF signals, the design and orientation of the antenna, the effectiveness of the rectifier circuit, proper impedance matching, variations in RF signal availability due to interference, distance from the source, and obstacles.
## 3 Approximate Analytical Solution of the Equations of Motion of the System
However, the traditional linear design TMD was designed based on ideal cases and did not take into account the nonlinear characteristics of the TMD. On the other hand, the NTMD designed using the nonlinear design method was closer to engineering reality and had more reliable stability than the TMD designed using the traditional linear design. The effect of the optimal nonlinear design NTMD on the vibration reduction of the structure is shown in Figure 15, where the amplitude of the primary structure in the steady-state phase was reduced by 71.47%. Figure 16 shows that the amplitude of the first-stage structure controlled by the ideal optimal linear design TMD was reduced by 75.43% in the steady-state phase, which is slightly better than that of the NTMD of optimal nonlinear design, but this is only the case where the TMD did not produce nonlinear characteristics. The comparison in Figure 13 shows that when the TMD produced nonlinear characteristics, the effectiveness of the linear optimal design parameters produced on the NTMD was greatly reduced. \[\alpha_{1}\Omega_{2}^{2}a_{2}+\frac{3}{4}\alpha_{1}\alpha_{2}\Omega_{2}^{2}a_{ 2}^{3}+\lambda_{1}\lambda_{2}a_{2}=f\sin b \tag{28}\]9 The frequency response curve of the primary structure (NTMD with nonlinear and linear design). \[\left\{\left[\frac{\left(3\alpha_{1}\alpha_{2}a_{2}^{3}\right)}{4}+ \alpha_{1}a_{2}\right]^{2}+\left[\frac{\left(3\lambda_{1}\alpha_{2}a_{2}^{3} \right)}{4}+\lambda_{1}a_{2}\right]^{2}\right\}\Omega_{2}^{4}+ \tag{29}\]0 The frequency response curve of primary structure (comparison of TMD and NTMD). \[\left\{\left[\frac{\left(3\alpha_{1}\alpha_{2}a_{2}^{3}\right)}{4}+ \alpha_{1}a_{2}\right]^{2}+\left[\frac{\left(3\lambda_{1}\alpha_{2}a_{2}^{3} \right)}{4}+\lambda_{1}a_{2}\right]^{2}\right\}\Omega_{2}^{4}+ \tag{29}\]1 Comparison of the time course curve of the primary structure with the optimal parameter design. In conclusion, the TMD optimization parameters obtained from traditional optimal linear design were only applicable to linear TMDs, and the optimization effect of TMDs decreased after nonlinear characteristics occurred during TMD usage. On the other hand, TMD optimization parameters obtained through nonlinear design had a good vibration reduction effect before and after the TMD produced nonlinear characteristics.