esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Algorithm
### System Model  
The problem of QoS routing and path allocation in an integrated TN-NTN network is modelled as a time-expanded minimum-cost multi-commodity flow. The overall network graph \(G(V,E,t)\) is composed of a set of domain sub-graphs, each belonging to a domain described by a unique identifier \(\mathfrak{d}\in\mathbb{N}\). Each sub-graph is time-variant \(G^{\mathfrak{d}}(V^{\mathfrak{d}},E^{\mathfrak{d}},t)\) in the NTN case (space and aerial strata) or time-invariant \(G^{\mathfrak{d}}(V^{\mathfrak{d}},E^{\mathfrak{d}})\) in the TN case. The graphs are constituted by sets of nodes and edges, i.e., \(V=[v_{1},v_{2},\ldots v_{j}]\) and \(E=[e_{12},e_{13},\ldots e_{ij}]\), with \(e_{ij}\) representing a bidirectional edge between vertices \(v_{i}\) and \(v_{j}\). Edge properties are described by a total of six features (\(F=\{f_{ij}|(v_{i},v_{j})\in E\}\in\mathbb{R}^{|E|\times m}\), \(m\)--dimensionality of features) that include total capacity \(c_{ij}\), total Guaranteed Flow Bit Rate (GFBR)--cf. [48], clause 5.7.2.5--allocated to flows \(b_{ij}^{\text{GFBR}}\), total Maximum Flow Bit Rate (MFBR)--cf. [48], clause 5.7.2.5--that can be consumed by flows \(b_{ij}^{\text{MFBR}}\), delay \(d_{ij}\), packet error rate \(\delta_{ij}\), link utilisation \(u_{ij}=b_{ij}^{\text{GFBR}}/c_{ij}\), indicating the fraction of capacity currently allocated to flows, and \(\zeta_{i}\)--the vector containing the share of flow types traversing the edge (one value per QoS class identifier). The nodes' features (\(X=\{x_{i}|v_{i}\in V\}\in\mathbb{R}^{|V|\times m}\)) correspond to the ones defined for edges, i.e., including node capacity (cf. Equation (1)), guaranteeing the maximum bandwidth allocated to flows traversing the node (cf. Equations (2) and (3)) and node utilisation (cf. Equation (4)). The edges incident to the vertex \(v_{i}\) are denoted with the \(E(v_{i})\) operator--i.e., \(E(v_{i})=\{e\in E:\exists v_{j}\in V,e=(v_{i},v_{j})\in E\}\). The delay and packet error rate are excluded from node features as they are both usually included in the link parameters due to measurement strategies that span over links and connecting switches egress/ingress ports [49]. The time consumed by switches on flow matching and forwarding is negligible and omitted. \[c_{v_{i}}=\!\!\!\!  
\[u_{v_{i}}=\frac{b_{v_{i}}^{\text{GFRR}}}{c_{v_{i}}} \tag{4}\]  
The edge metrics are used by SDNCs to calculate the overlay view for M-SDNC/M-QR. The corresponding overlay metrics and topology are denoted with a superscript \(\psi\). The metrics transformation takes into account only the BNs of the domain (\(V^{B}\subset V\)) so that M-SDNC sees the viable allocations between domain gateways. The bandwidth-related metrics between a pair of BNs, \(v_{i},v_{j}\in V^{B}\), are calculated using maximum flow (Ford-Fulkerson, Edmonds-Karp, Push-Relabel, etc.) and shortest path (e.g., Dijkstra) algorithms, denoted as \(maxflow\) and \(SP\), extending the concept [16].
# Physics-Informed Graph Neural Networks for Attack Path Prediction
## 2 Materials and Methods
### Path Prediction Training
#### 2.5.1 Data Loss  
Since the target prediction matrix is highly sparse, the data loss incorporates a masking strategy to mitigate the class imbalance. Without masking, the network tends to learn parameters that predict \(\hat{Y}_{ij}=0,\forall\,ij\in Y\), which minimizes the loss but does not predict meaningful path structures.  
We define the masking mechanism in \(\mathcal{L}_{\text{data}}\) such that a subset of negative label entries (\(Y_{ij}=0\)) is randomly sampled within the target adjacency matrix \(Y\) while all positive labels (\(Y_{ij}\
eq 0\)) are retained. Let \(\mathcal{M}_{ij}\) denote this mask for an entry \(Y_{ij}\), defined as follows:  
\[\mathcal{M}_{ij}=\begin{cases}1,&\text{if }Y_{ij}\
eq 0\\ 1,&\text{if }Y_{ij}=0\text{ and }u_{i}<w_{c},\quad u_{i}\sim\text{Uniform}(0,1)\\ 0,&\text{otherwise}\end{cases} \tag{3}\]  
where \(w_{c}\) is the masking coefficient that determines the fraction of \(Y_{ij}=0\) values included in the loss computation. We set \(w_{c}\) to a small value to force the network to focus on edges composing the attack path. We also introduce a weighting mechanism. Let \(w_{p}\) be the weighting coefficient for type-II errors, defined as follows:  
\[w_{p}=\frac{|Y_{ij}=1|}{|Y_{ij}=0|}\cdot w_{s} \tag{4}\]  
where \(|Y_{ij}=1|\) and \(|Y_{ij}=0|\) denote the number of positive and negative entries, respectively. Since \(w_{p}\) is typically large, we introduce a scaling factor \(w_{s}\), set to \(10^{-3}\). We then define \(\gamma=\frac{1}{w_{p}}\) as the weighting coefficient for positive labels. With the mask \(\mathcal{M}\) and weight coefficient \(\gamma\) defined, the weighted binary cross entropy (WBCE) loss is:  
\[\mathcal{L}_{\text{wbce}}(\hat{Y}_{ij},Y_{ij})=-\big{(}Y_{ij}\log(\hat{Y}_{ij })+(1-Y_{ij})\gamma\log(1-\hat{Y}_{ij})\big{)} \tag{5}\]  
Averaging over the unmasked elements for training samples in batch size \(N\), the data loss is thus computed as follows:  
\[\mathcal{L}_{\text{data}}=\frac{1}{N}\sum_{n=1}^{N}\cdot\left(\frac{1}{| \mathcal{M}|}\sum_{ij}-\mathcal{M}_{ij}\cdot\big{[}Y_{ij}\log\big{(}\hat{Y}_{ ij}\big{)}+\big{(}1-Y_{ij}\big{)}\cdot\gamma\log\big{(}1-\hat{Y}_{ij} \big{)}\big{]}\right) \tag{6}\]  
This formulation ensures that the loss focuses on the most relevant edges while preventing the model from collapsing to a trivial all-zeros prediction.
## 3 Model Formulation and Scheme Design
### Improved Clustering Algorithm
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Descriptions** \\ \hline DCP & The points directly above each cluster head are data collection points (DCP) \\ ILEACH & Improved cluster head selection algorithm based on LEACH \\ TGA & Improved genetic algorithm based on TLBO \\ DCMDR & Dual Channel Multiple Data Rate \\ DR & Data Rate \\ \(dF_{i}\) & The average distance factor of neighbor nodes \\ \(NF_{i}\) & The number of nodes covered factor \\ \(EF_{i}\) & The remaining energy factor \\ \(DF_{i}\) & The distance factor from the node to the UAV take-off point \\ \(L\) & Path length of UAV traversing cluster head \\ \(x_{ij}\) & Binary variable, if UAV goes to cluster head \(j\) after arriving at cluster head \(i\), \(x_{ij}=1\), \\  & otherwise is 0 \\ \(d_{ij}\) & Distance from cluster head \(i\) to \(j\) \\ \(f(m_{j})\) & Fitness function \\ \(T_{F}\) & The teaching factor, which determines the degree to which the average value is changed, typically 1 or 2, \\ \(rand\) & A random vector, each element of which is a random number in the range of \([0,1]\). \\ \(R(i,j)\) & The correlation formula between cluster head \(i\) and \(j\) \\ \(\sigma\) & Current solution \\ \(\sigma^{\prime}\) & Updated solution \\ \(v\) & The UAV’s flight speed \\ \(m\) & The data rate obtained from ACK \\ \(b\) & The data size stored by the cluster head \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptions of the main notations. The node chooses to join the cluster that has received the cluster head information late, if it receives more than one cluster head information. \[t_{c}(i)=\alpha\times e^{-\theta_{i}} \tag{1}\]  
\[\theta_{i}=100\times[\omega_{1}\cdot dF_{i}+\omega_{2}\cdot NF_{i}+\omega_{3} \cdot EF_{i}+\omega_{4}\cdot DF_{i}] \tag{2}\]  
\[d(i)=\frac{\sum\limits_{j-Ne(i)}d(i,j)}{Nu(i)} \tag{3}\]  
In the above formulas, \(\alpha\) is the proportional coefficient that determines the delay size; \(d(i,j)\) denotes the distance between any two nodes \(i\) and \(j\). When \(d(i,j)\leq R_{c}\), node \(j\) is called the neighbor node of \(i\). \(R_{c}\) is the effective broadcast radius of node \(i\), the set of neighbor nodes of node \(i\) is represented by \(Ne(i)\); \(\omega_{1}\), \(\omega_{2}\), \(\omega_{3}\), \(\omega_{4}\) is the weight assigned to each metric, respectively, and \(\omega_{1}+\omega_{2}+\omega_{3}+\omega_{4}=1\).
# Chin Morphology in Relation to the Skeletal Pattern, Age, Gender, and Ethnicity
###### Abstract  
Chin morphology is visually impactful and significantly influences harmonious facial appearance. Therefore, it is important to know the morphological characteristics of the chin in relation to gender and skeletal pattern when performing an orthodontic and surgical orthognathic treatment. This study aimed to examine the relationship between chin size, skeletal pattern, age, gender, and ethnicity. In this study, cone-beam computed tomography images of 208 participants (males: 90, females: 118; 63 Koreans and 145 Egyptians), aged 18 years and older, were used to evaluate the size of the chin in linear dimension, volume, and skeletal pattern. The larger the vertical skeletal pattern, the larger the chin volume and the smaller the width (\(p<0.01\)). In the anteroposterior skeletal pattern, Class III showed a larger volume than that of Class II and Class I (\(p<0.01\)). There was no significant association between age and any of the chin-related measurements. Regarding gender, all measurements of chins were larger for men than for women (\(p<0.01\)). In terms of ethnicity, Koreans had larger chin volumes than Egyptians \(p<0.01\)). Chin volume was related to population, sex, anteroposterior skeletal pattern, and vertical skeletal pattern, indicating the combined effects of various factors.  
chin; skeletal pattern; cone-beam computed tomography +
Footnote †: journal: Medical Imaging
# Use Electroencephalogram Entropy as an Indicator to Detect Stress-Induced Sleep Alteration
## 4 Discussion
### The EEG Spectrum after Footshock  
Spectrum is a common way for analyzing the power as a function of frequency. The spectrum between the control and footh shock group did not show extensive changes. If we focus on the x-axis (time), the spectrum demonstrates the alterations mostly occurred during the first 2 h of the light period; the power of delta band (0.5-4 Hz) was attenuated in NREM sleep, theta power (4-12 Hz) during REM sleep was increased, and gamma power (25-30 Hz) in wakefulness was also increased. If we focus on the y-axis (frequency) of each stage, the footh shock enhanced theta power in NREM sleep, although delta power is the predominant frequency during NREM sleep. Since the type-1 (6-12 Hz) and type-2 (4-9 Hz) [10; 31] theta bands contain an overlap frequency (6-9 Hz) in rats, we can hardly differentiate which type(s) of theta band(s) was (were) mainly affected without pharmacological approaches. However, we noticed the enhanced theta was very likely the type-1 since it contained 9 to 12 Hz frequencies as we demonstrated in Figure 2C. Regarding to REM sleep, Figure 2F demonstrated the increases of type-1 and type-2 theta rhythms, and they mainly occurred during the first 2 h of sleep. Studies depicts that type-1 theta rhythm was correlated to movement and exploration [32] and type-2 theta oscillation was observed during a predator presence [10; 31]. Regarding to the wakefulness, slow gamma (25-30 Hz) power was increased after footh shock. Slow gamma is known to be generated when rats are retrieving memories [33]. Taken the presence of theta and gamma oscillations together, we proposed that the aversive memories from footshock cause sleep disturbances during the subsequent light period. This phenomenon may link to the occurrence of nightmare in ASD and PTSD patients [14]. However, this hypothesis needs to be further investigated in the future.
## 2 Materials and Methods
### Experimental Setup and Design
#### 2.1.1 Identification of Relevant Control Element Parameters
Either the test person saw only a bar graph with the current positioning value (refer to Figure 2, top right) or a bar graph with the current rate of change in the positioning value (refer to Figure 2, top left). For both control elements, we investigated whether **haptic** or **acoustic feedback** as well as the **visualization of the hand** influenced the operation of the control elements. For example, if the participant activated the joystick, the hand grasping the joystick was visualized in VR. If there was no visualization, the participant saw only the joystick and its deflection. If the value changed, the participant heard a click and/or felt the vibration of the controller. It was investigated whether the design of the **VR environment** influenced the operation and especially the subjective evaluation of the control elements. In addition, the influence of the design of the VR controller on the operation was investigated. Valve Index controllers (+) have integrated sensors to detect hand and finger positions. This enables the control elements to be \"grasped\" similarly to reality. For HTC Vive (-) controllers, interaction is performed by moving the controller close to the control element and press  
Figure 2: Experimental setups with different factor levels. **Top left**: Visual feedback on the rate of change. **Top right**: Horizontal joystick. **Bottom left**: A 20 mm rotary control with knurling. **Bottom right**: An 80 mm rotary control with knob and 45\({}^{\circ}\) inclination. ing the \"trigger button\" on its back. Images of the controllers used can be found in the Supplementary Material (refer to Figure S1). The various control elements and the virtual environments were created in the Unity 2020.2.3f1 development environment (Unity Technologies, San Francisco, CA, USA) and coded in C# (Microsoft Corporation, Redmond, WA, USA). Visualization was performed using the Valve Index HMD (Valve Corporation, Bellevue, WA, USA) and a PC with an i7 processor and a GeForce GTX 1070 graphics card (NVIDIA Inc., Santa Clara, CA, USA). Figure 2 shows examples of the different factor characteristics listed in Table 2.
## 4 Case Study and Applications
### A Classification Problem: Binary Prediction of Smoker Status Using Bio-Signals
#### 4.3.2 Odds Ratio Calculation  
The odds ratio (OR) is a statistical measure employed to quantify the strength of the association between two events. It enables the comparison of the odds of the event occurring in one group with the odds of the event occurring in the other group. The OR is calculated using the following equation:  
\[OR\ =\ \frac{Odds\ in\ favor\ of\ event\ in\ Group\ 2}{Odds\ in\ favor\ of\ event\ in\ Group\ 1} \tag{3}\]  
The odds ratio should be interpreted according to three ranges of values: OR == 1, indicating the absence of association between exposure and outcome; OR \(>1\), which indicates a positive association between exposure and outcome; and OR \(<1\), which indicates a negative association between exposure and outcome.  
The principal findings of Table 7, which presents odds ratio values, are as follows: (1) Individuals with elevated sugar and relaxation indices are more prone to smoking than those with low indices. (2) There is a correlation between smoking and higher body weight. (3) There is a notable elevation in triglycerides (a type of blood fat) and haemoglobin, accompanied by a considerable reduction in HDL. (4) Furthermore a decrease in LDL and an increase in serum creatinine, a waste product present in the blood, is observed, albeit to  
\begin{table}
\begin{tabular}{l c c} \hline
**Variable** & **Chi-Squared Value** & \(p\)**-Value** \\ \hline Height & 35,178.19 & 0.0 \\ \hline Weight & 20,419.24 & 0.0 \\ \hline Waist & 10,849.84 & 0.0 \\ \hline Eyesight (left) & 2819.29 & 0.0 \\ \hline Eyesight (right) & 3432.92 & 0.0 \\ \hline Hearing (left) & 232.12 & \(2.06\times 10^{-52}\) \\ \hline Hearing (right) & 215.86 & \(7.25\times 10^{-49}\) \\ \hline Systolic & 1090.97 & 3.31e\(-\)236 \\ \hline Relaxation & 1875.90 & 0.0 \\ \hline Fasting blood sugar & 2089.03 & 0.0 \\ \hline Cholesterol & 1215.51 & \(3.16\times 10^{-263}\) \\ \hline Triglyceride & 18,319.41 & 0.0 \\ \hline HDL & 10,973.96 & 0.0 \\ \hline LDL & 1067.00 & \(5.24\times 10^{-231}\) \\ \hline Hemoglobin & 34,114.14 & 0.0 \\ \hline Urine protein & 165.31 & \(7.82\times 10^{-38}\) \\ \hline Serum creatinine & 13,429.07 & 0.0 \\ \hline AST & 725.64 & \(5.77\times 10^{-157}\) \\ \hline ALT & 7484.18 & 0.0 \\ \hline Gtp & 26,874.75 & 0.0 \\ \hline Dental caries & 1810.41 & 0.0 \\ \hline \end{tabular}
\end{table}
Table 6: Chi-squared tests for each variable.  
a lesser extent. (5) Additionally, a significant increase in alanine aminotransferase (ALT) is evident, which is an enzyme predominantly located in the liver. An excess of ALT in the bloodstream may indicate damage to liver cells.
## 3 Experimental Results and Analysis
### Dynamic Strength Criterion  
3.4.1. Mohr-Coulomb Strength Criterion  
The Mohr-Coulomb strength criterion, equivalent to the third strength theory, posits that material failure occurs when the maximum shear stress at any point reaches the material's shear strength. This criterion incorporates two parameters: the internal friction angle and cohesion. The shear strength of rock comprises cohesive forces and internal friction on the failure surface, expressed as  
\[\tau=\sigma_{\rm n}{\rm tan}\ \varphi+{\rm c} \tag{3}\]  
Figure 11: The macroscopic failure morphology of granite specimens with different strain rates and confining pressures.  
where \(\tau\) denotes shear stress, \(\sigma_{\rm n}\) represents normal stress, \(\varphi\) is the internal friction angle, and c indicates cohesion.  
Under conventional triaxial loading, normal stress (\(\sigma_{\rm n}\)) and shear stress (\(\tau\)) can be derived from principal stresses (\(\sigma_{1}\) and \(\sigma_{3}\)):  
\[\sigma_{\rm n}=\frac{1}{2}(\sigma_{1}+\sigma_{3})+\frac{1}{2}(\sigma_{1}- \sigma_{3})\text{cos}\,2\beta \tag{4}\]  
\[\tau=\frac{1}{2}(\sigma_{1}-\sigma_{3})\text{sin}\,2\beta \tag{5}\]  
Here, \(\beta\) represents the angle between the fracture plane and the lateral specimen surface (Figure 12).  
Combining Equations (3)-(5) yields the critical stress condition for arbitrary \(\beta\)[36]:  
\[\sigma_{1}=\frac{2\text{c}+\sigma_{3}\{\text{sin}\,(2\beta)+\text{tan}\,\varphi 1-\text{cos}(2\beta)\}}{\text{sin}(2\beta)-\text{tan}\,\varphi 1+\text{cos}(2\beta)} \tag{6}\]  
The geometric relationship between \(\beta\) and \(\varphi\) (Figure 13) gives  
\[2\beta=\frac{\pi}{2}+\varphi \tag{7}\]  
Figure 12: Force on rock fracture surface under conventional triaxial loading.  
Figure 13: Mohr stress circle and Mohr–Coulomb strength criterion.  
Substituting Equation (7) into Equation (6) simplifies to  
\[\sigma_{1}=2\text{c}\cdot\frac{\cos\varphi}{1-\sin\varphi}+\frac{1+\sin\varphi}{1 -\sin\varphi}.\sigma_{3} \tag{8}\]  
Letting the first term in Equation (8) be A and the coefficient of \(\sigma_{3}\) be B, the Mohr-Coulomb parameters are derived as  
\[\text{A}=2\text{c}\cdot\frac{\cos\varphi}{1-\sin\varphi} \tag{9}\]  
\[\text{B}=\frac{1+\sin\varphi}{1-\sin\varphi} \tag{10}\]
## 4 Communication Frame  
There is a wide range of communication protocols available, all of which have some drawbacks in terms of requirements. The industry partner (airport) pays attention to a constant response time (round trip time = time from query to received response). This results in the polling method and the requirement of a 20 ms round trip time for 50 MU responses per second. This in turn results in the minimum number of bytes in the data frame.  
An important part of a mobile device response frame is its ID and GPS coordinates. The simplest form of GPS encoding is a standard NMEA format read directly from the GPS receiver, such as a GGA frame:  
$GPGGA,100639.000,**5014.8289,N,01850.0039,E,1,6,1.92,107.8,M,42.2,M,,**5A with encoded location \(\mathbf{50^{\circ}14.8289^{\prime}}\) N, \(\mathbf{18^{\circ}50.0039^{\prime}}\) E. Direct retransmission results in the shortest encoding/decoding time and requires at least 19 ASCII characters (bytes), e.g., \"**50148289N018500039E**\"--not counting start/end of frame/line characters. Note that the encoding is accomplished by the MU's low-power microcontroller and may increase the response time. However, 19 bytes is still too much for our time-limited communication.  
The above frame can be shortened without precision loss using coding with _signed 32-bit integer_ representation. The hemisphere (N-S or E-W) is encoded by sign and each pair of ASCII characters is encoded into a single byte. Four bytes with a sign (_int32_) represent a single coordinate, e.g.:  
\[50^{\circ}14.8289^{\prime}\ \mathrm{N}\rightarrow+[50\ \mathrm{d}]\ [14\ \mathrm{d}]\ [82\ \mathrm{d}]\ [89\ \mathrm{d}]\rightarrow+[32\ \mathrm{h}]\ [0\ \mathrm{Eh}]\ [52\ \mathrm{h}]\]  
where \(d\) means decimal, \(h\) is the hexadecimal representation, and sign \"+\" encodes northern hemisphere (N). The example above assumes NBC (Natural Binary Coding), which is usually not true for real hardware representation, but well supported on the standard compiler level (e.g., C/C++) and simplifies programming. The total number of required bytes to transmit full position (coordinates) is 8. Detailed information about designed custom data frames can be found in [18].  
\begin{table}
\begin{tabular}{c c c c} \hline
**Module** & **Antenna** & **Cold Start [s]** & **\(\mathcal{N}\) of Sats.** \\ \hline mod\_5 & Internal (half sphere) & 194 & 4 \\ mod\_3 & & 131 & 6 \\ mod\_4 & & 378 & 4 \\ mod\_2 & & 195 & 3 \\ \hline mod\_5 & Internal (open sky) & 90 & - \\ mod\_4 & & 40 & - \\ mod\_7 & & 75 & - \\ mod\_8 & & 70 & - \\ \hline mod\_5 & Microstrip & 691 & 4 \\ mod\_4 & & 226 & 4 \\ mod\_2 & & 1377 & 3 \\ \hline mod\_5 & External & 92 & 4 \\ mod\_4 & & 357 & 3 \\ mod\_1 & & 35 & 5 \\ \hline \end{tabular}
\end{table}
Table 10: Time-to-fix time (cold start).
## 1 Introduction
[PERSON] [23] replaced the traditional rigid fixed end with a flexible cantilever beam, which is beneficial for the piezoelectric energy harvester system to realize the large-amplitude motion, and the output voltage can be increased by 22.58%. [PERSON] [24] proposed a magnetically coupled piezoelectric energy trap with the addition of an auxiliary beam and developed a centralized parametric model that broadened the operating bandwidth of the piezoelectric energy trap by 66.7% and improved the energy harvesting efficiency by 35% compared to that before the magnet was introduced. [PERSON] [25] developed a piezoelectric energy harvester with two fixed magnets. This research showed that the operating frequency can be adjusted to between 22 and 32 Hz with suitable magnet spacing. [PERSON] [26] added a small magnet based on the traditional bistable piezoelectric energy harvester. The simulation results show that the reduction in the system potential barrier height can enable the piezoelectric energy harvester to operate at a lower excitation level. A large response output is achieved under excitation conditions. Compared with the non-magnetic piezoelectric energy harvester, the bistable piezoelectric energy harvester with the introduction of magnetic coupling has superior output performance. The above-mentioned scholars have found that changing the number of magnets and the spacing of magnets can affect the distribution of potential wells in the system. Based on the research of the research group [27], we found that there is an optimal distance between the magnets in the BPEH system, and under this condition, the system performance will be the best. Is there any way to further improve the performance of the bistable piezoelectric energy harvester? This paper proposes an IBPEH to broaden the operating frequency bandwidth and enhance the response output of the bistable piezoelectric energy harvester. In Section 2, the structural models of BPEH and IBPEH are given, the restoring force of the composite beam is fitted, the magnetic force on magnet A is calculated by the magnetic dipole theory, and the lumped parameter model of the IBPEH system is established. In Section 3, based on the control variable method, the nonlinear equations are solved by the Newton-Raphson iteration method, and the optimal positions of the magnets C and D are obtained, the vibration characteristics of the BPEH and IBPEH systems are analyzed by numerical simulation, and the output performance of the system under different excitation frequencies and excitation amplitudes is compared. In Section 4, an experiment is designed to verify the correctness of the theoretical analysis. The conclusion follows in Section 5.