esa-sceva/satcom-chunk-collection huggingface dataset:
# Research on Human-Robot Collaboration Method for Parallel Robots Oriented to Segment Docking
## 3 Control Design
### Fractional-Order Variable Damping Admittance Control
Specifically, for \(n=1\), the unitary Mittag-Leffler function is commonly utilized:  
\[E_{a_{1},b}(z_{1})=\sum\limits_{k=0}^{\infty}\frac{z_{k}^{1}}{\Gamma(b+ka_{1} )}\ a_{1},b>0,|z_{1}|<\infty \tag{10}\]  
The Laplace transform of the Mittag-Leffler function is given by the following equation:  
\[L\{t^{ak+\beta-1}E_{a,\beta}^{(k)}(\pm at^{a});s\}=\int_{0}^{\infty}e^{-st}t^ {ak+\beta-1}E_{a,\beta}^{(k)}(\pm at^{a})dt=\frac{k!s^{a-\beta}}{(s^{a}\mp a)^ {k+1}},Re(s)>|a|^{\frac{1}{2}} \tag{11}\]  
The Mittag-Leffler function can be used to describe the fractional-order differential equation presented above, and then, according to the Laplace transform of the Mittag-Leffler function, the following inverse transformation can be obtained:  
\[L^{-1}\{\frac{M_{D}s^{p-1}x_{e}(0)}{M_{D}s^{p}+K_{D}(\alpha)s^{q}};s\}=\frac{ M_{D}}{K_{D}(\alpha)}x_{e}(0)t^{q-p}E_{q-pA-p+1}(-\frac{M_{D}}{K_{D}( \alpha)}t^{q-p}) \tag{12}\]  
\[L^{-1}\{\frac{M_{D}s^{p}\dot{x}_{e}(0)}{M_{D}s^{p}+K_{D}(\alpha)s^{q}};s\}= \frac{M_{D}}{K_{D}(\alpha)}\dot{x}_{e}(0)t^{q-p+1}E_{q-pA-p+2}(-\frac{M_{D}}{K _{D}(\alpha)}t^{q-p}) \tag{13}\]\[L^{-1}\{\frac{K_{D}(\alpha)s^{q-1}x_{e}(0)}{M_{D}s^{p}+K_{D}(\alpha)s^{q}};s\}= \frac{K_{D}(\alpha)}{M_{D}}x_{e}(0)t^{p-q}E_{p-q,p-q+1}(-\frac{K_{D}(\alpha)}{M_ {D}}t^{p-q}) \tag{14}\]  
\[L^{-1}\{\frac{Q(s)}{M_{D}s^{p}+K_{D}(\alpha)s^{q}};s\}=Q_{i}*(\frac{1}{K_{D}( \alpha)}t^{q-1}E_{q-p,q}(-\frac{M_{D}}{K_{D}(\alpha)}t^{q-p})) \tag{15}\]  
Then, the analytical solution of the control system can be obtained using the above equations. \[ \begin{array}{l}x_{e}=\frac{M_{D}}{K_{D}(\alpha)}x_{e}(0)t^{q-p}E_{q-p,q-p+1} (-\frac{M_{D}}{K_{D}(\alpha)}t^{q-p})+\frac{M_{D}}{K_{D}(\alpha)}\dot{x}_{e}(0 )t^{q-p+1}E_{q-p,q-p+2}(-\frac{M_{D}}{K_{D}(\alpha)}t^{q-p})\\ +\frac{K_{D}(\alpha)}{M_{D}}x_{e}(0)t^{p-q}E_{p-q,p-q+1}(-\frac{K_{D}(\alpha)} {M_{D}}t^{p-q})+Q_{i}*(\frac{1}{K_{D}(\alpha)}t^{q-1}E_{q-p,q}(-\frac{M_{D}}{ K_{D}(\alpha)}t^{q-p}))\end{array}  \tag{16}\]  
Fractional-order variable damping admittance control introduces parameters \(\beta\) and \(\gamma\) compared to integer-order variable damping admittance control, allowing for better adjustment of the dynamic interactive behavior between the robot and interaction forces, and thus making the control strategy design more flexible. When the orders \(\beta\) and \(\gamma\) both take their minimum values, this becomes first-order damping control, and when the order \(\beta\) and \(\gamma\) both take their maximum values, this becomes second-order integer admittance. Thus, it is understood that, with decreasing orders, the fractional-order characteristics gradually diminish the inertial storage energy, while the energy-dissipation characteristics will take precedence. The specific orders of the controller can be determined based on this characteristic.
## 3 The Proposed Model
### Design of MHR-GOA Technique
The supremacy of FF is related to \(m+1\), in which \(m\) indicates the amount of CH contained from the system. Where \(F_{i}=(F_{i,1}(t),\ F_{i,2}(t)\ldots F_{i,m+1}(t))\) is the \(ith\) FF and the position \(F_{i,d},\forall_{1}1\leq\ i\leq\text{m}+1,\ \forall_{d}1\leq\ d\leq\text{m}+1\) defines next-hop for sending data to BS. It is possible to be extremely focused on discovering the ideal path from CH to SN. It may be achieved with the use of FF in a variety of sub-objectives, such as NDE, RE, and Euclidean distance, among other things [45]. In order to convey data, each subsequent hop obtains the data and transfers it to the BS server. As a result, the highest possible RE of the following hop is given first priority. Furthermore, for the main sub-objective of using RE, \(f1\) is enhanced as follows:  
\[f1=\sum_{i=1}^{\text{m}}E_{CHi} \tag{22}\]  
Euclidean distance may be defined as the distance between CH and the following hop, as well as the distance between CH and SN. When distances are kept to a minimum, the energy consumption rate is likewise decreased. The following purpose is to reduce the distance between CHs and SN as measured in the following manner:  
\[f2=\frac{1}{\sum_{i=1}^{\text{m}}\text{dis}(\text{CHi},\text{NH})+\text{dis}( \text{NH},\text{BS})} \tag{23}\]  
ND denotes the list of nodes in the next hops. If hop is composed of a small number of CH members, it consumes low energy in acquiring information from the nearby node and survives for a long period of time. Following that, the next-hop with a restricted node degree is notably picked. Finally, NDE is defined based on the degrees of node \(f3\),  
\[f3=\frac{1}{\Sigma_{i=1}^{m}I_{i}} \tag{24}\]  
As demonstrated in Equation (25), the weighted sum models are then processed for all sub-objectives and turned into a single objective model. Here \(\alpha_{1},\alpha_{2}\) & \(\alpha_{3}\) denotes the weight allocated to each sub objectives, where \(\alpha_{i}\varepsilon(0,1)\) and \(\alpha_{1}+\alpha_{2}+\alpha_{3}=1\). \[Fitness=\alpha_{1}(f1)+\alpha_{2}(f2)+\alpha_{3}(f3) \tag{25}\]
# Evaluating the Energy-Saving Potential of Solar Dedicated Ventilation Systems Based on ADRC
## 2 Photovoltaic and Solar Thermal System Combined with Dedicated Ventilation System
### Photovoltaic system  
For the photovoltaic system, the solar energy converts into electrical power by use of the solar panels. The direct current is supplied to the inverter by use of the direct current regulator, which also prevents battery reverse charging to the solar panels. In order to supply the alternating current power to the proposed solar dedicated ventilation system, the inverter converts direct current power into alternating current power. The control system and the batteries gain direct current power from solar panels. The standby power, which supplies electrical power directly and charges the batteries by using the battery charging system, should be provided in the proposed system to achieve stable running under the condition of a power shortage. The batteries store the power from night valley electricity and uses it in the peak power time to realize the peak shifting purpose. The voltage sensors V1 to V3 and current sensors A1 to A3 are applied to test and monitor the voltage and current of the photovoltaic system. The data from the voltage and current sensors are used to calculate the energy savings of the proposed system. The photovoltaic system is controlled by breakers K1 to K5 and contactors KM1 to KM5 and protected by fuses FU1 and FU2.
## 3 Results
### Long Time Stability of the Glucose Sensor  
To evaluate the stability, the SHPM-OS sensor was further tested using glucose titration at intervals. As shown in Figure 5a, when the glucose concentration increased from 0 to 20 mM, all of the response curves showed obvious ladder shape and great linearity. The relative sensitivity was defined as  
Figure 4: Response speed and anti-interference results of the SHPM-OS sensor. (**a**) current-time response of the SHPM-OS sensor to single high concentration (10 mM) injection of glucose into stirring phosphate buffer solution (PBS). (**b**) SHPM-OS sensor response to sequential glucose and common interferences. Concentrations of the additions in the measuring PBS include 4 mM glucose, 0.48-mM UA, 0.11-mM AA, 0.17-mM AP and 2-mM glucose.  
Figure 3: Performance comparison of NO-P, SGL-P and SHPM-OS sensors. The line in red is the response of the SHPM-OS sensor; the others are the SGL-P (blue) and NO-P sensor (black), respectively. (**a**) current response of three sensors versus glucose concentration. (**b**) linear fitting curves of three sensors. The fitting equation is displayed next to the corresponding line.  
the ratio of the present sensitivity to the initial sensitivity obtained at the beginning. The relative sensitivity of the SHPM-OS sensor remained at least 90% in the first 10 days (Figure 5b). Although the response slightly decreased after that, the relative sensitivity remained at approximately 78% of the original sensitivity on day 20 (Figure 5b), which is similar to the published data [10; 17; 20]. The results demonstrate that the SHPM-OS sensor could remain stabilization for a long time.
# Recent Progress on Irradiation-Induced Defect Engineering of Two-Dimensional 2H-MoS2 Few Layers
## 2 Charged Particle Irradiation
### Swift-Heavy Ion Irradiation
#### 2.1.2 Gallium Ion Irradiation  
[PERSON] et al. [98] deposited \(p\)-type mono-layered MoS\({}_{2}\) on \(c\)-sapphire substrates using CVD technique and irradiated the layers at 450 \({}^{\circ}\)C for 30 s at a low Ga flux beam (equivalent pressure: \(6\times 10^{8}\) torr) in ultra-high vacuum (UHV) conditions. Ga ions were produced from a plasma-assisted MBE system. Figure 4 shows the Raman spectra and X-ray photoelectron spectroscopy (XPS) spectra of Ga-irradiated MoS\({}_{2}\) mono-layers. Raman peaks, especially A\({}_{1g}\) mode, shifted after the Ga-irradiation. Mo-3\(d^{5/2}\) peaks shifted towards lower energies for Ga-irradiated samples relative to that of the pristine MoS\({}_{2}\) mono-layer. New Ga-2\(p^{1/2}\) and Ga-2\(p^{3/2}\) core levels were observed at 1117 eV and 1144 eV, respectively, revealing the incorporation of Ga into the MoS\({}_{2}\) layers. The Ga-irradiation reduced the value of binding energy of 0.2 eV. Room temperature photoluminescence (PL) spectroscopy indicated that the optical properties of the MoS\({}_{2}\) layers were changed.  
[PERSON] et al. [99] synthesized single-layer MoS\({}_{2}\) triangular-flakes via a halide-assisted powder vaporization method and transferred over holes. The suspending MoS\({}_{2}\) mono-layers were irradiated by Ga\({}^{+}\) ions in a focused ion beam (FIB). The Ga\({}^{+}\) ion dose varied from \(6.25\times 10^{12}\) ions/cm\({}^{2}\) to \(2.50\times 10^{13}\) ions/cm\({}^{2}\). Figure 5 shows high angle annular dark-field (HAADF) images of the MoS\({}_{2}\) mono-layers before and after Ga\({}^{+}\) ion irradiation for different doses: 0 (pristine), \(6.25\times 10^{12}\) ions/cm\({}^{2}\), \(8.16\times 10^{12}\) ions/cm\({}^{2}\), \(1.11\times 10^{13}\) ions/cm\({}^{2}\), \(1.60\times 10^{13}\) ions/cm\({}^{2}\), and \(2.50\times 10^{13}\) ions/cm\({}^{2}\). Statistical analysis showed that Ga\({}^{+}\) ion irradiation produced pores with average and maximum diameters of 0.5 nm and 1.0 nm. Within the irradiation dose range, the nanopore density increased with increasing doses. With increasing ion doses, nanopores started to merge, resulting in larger and irregularly shaped pores. For the lowest dose (\(6.25\times 10^{12}\) ions/cm\({}^{2}\)),  
Figure 4: (**a**) Raman spectra and (**b**) Mo-3\(d\) XPS of pristine- and Ga-irradiated mono-layered MoS\({}_{2}\) samples [98]. Reprinted with permission from Reference [98], with the permission of AIP Publishing.  
most of the atomic pores were single-molybdenum-based vacancies, while the amount of missing sulfur varied. With an increasing Ga\({}^{+}\) ion dose, the number of double-molybdenum-based vacancies increased, and some triple-molybdenum-based vacancies were also found. When the Ga\({}^{+}\) ion dose reached to \(2.50\times 10^{13}\) ions/cm\({}^{2}\), the density of larger pores (with diameter size \(>0.8\) nm) increased. Metal atomic vacancies were formed with sulfur vacancies while few topological defects and amorphous regions were observed.
# UAV-Assisted Caching Strategy Based on Content Cache Pricing in Vehicular Networks
## 4 RSU Caching Strategy Considering Content Cache Pricing
### Stackelberg Game for Joint Pricing and Cache Decision Optimization
#### 4.1.2 Stackelberg Game Model  
In this paper, the competitive relationship between the CP and the NO is modeled as a Stackelberg game, where the CP acts as a leader and the NO acts as a follower in response to the CP's actions. More specifically, CP first gives the rental price \(a\) and informs NO about it. The NO determines the amount of content it rents for each RSU and the optimal cache placement policy that maximizes its utility based on the lease price \(a\), the expected number of content requests, and the average content request probability. Thus, the Stackelberg game consists of two subproblems: the problem of how the leader (CP) determines the lease price to maximize its utility and the problem of how the follower (NO) conducts caching to maximize its utility.  
(1) The utility maximization problem of CP  
\[\begin{array}{rl}P1.1:&\max\limits_{a}\text{l}^{CP}=\sum\limits_{i=1}^{I}u_ {i}^{CP}\\ s.t.&(\text{C1})0\leq a\leq a_{\text{max}}\\ &(\text{C2})y^{R}\in(0,1)\end{array} \tag{27}\]  
where constraint (C1) indicates that the lease price does not exceed the maximum unit price set by the market and (C2) indicates that the cache decision indicator variable of the RSU takes the value of 0 or 1.  
(2) The utility maximization problem of NO  
\[\begin{array}{rl}P1.2:&\max\limits_{Y^{R}}\text{l}^{MNO}=\sum\limits_{i}^{I}u _{i}^{MNO}\\ s.t.&(\text{C2})y^{R}\in(0,1)\\ &(\text{C3})\sum\limits_{i=1}^{I}y_{m,i}^{R}s\leq CR,m\in\{l,r\}\end{array} \tag{28}\]  
where constraint (C3) indicates that the cached content data size cannot exceed the maximum cache capacity.  
The utility of the leader and the followers is optimal when the Stackelberg game reaches the equilibrium point; the lease price and cache decision corresponding to the equilibrium point are the optimal values. If any entity deviates from the equilibrium point, its own benefit will be reduced. According to the definition in [7], the equilibrium point of the Stackelberg game in this paper is defined as:  
Let \(a*\) denote the optimal solution of the utility maximization problem \(P1.1\) for CP and \(Y^{R}*\) denote the optimal solution of the utility maximization problem for NO given the optimal lease price \(a*\). For any \(\big{(}a,Y^{R}\big{)}\) in the feasible region, if the following conditions are satisfied:  
\[U^{CP}\Big{(}a*,Y^{R}*\Big{)}\geq U^{CP}\Big{(}a,Y^{R}*\Big{)} \tag{29}\]  
\[U^{MNO}\Big{(}a*,Y^{R}*\Big{)}\geq U^{MNO}\Big{(}a*,Y^{R}\Big{)} \tag{30}\]  
then \(\big{(}a*,Y^{R}*\big{)}\) is the equilibrium point of the proposed Stackelberg countermeasure.
## 4 Evaluation and Discussion
### Performance of Forecasting Based on Augmented and Original Dataset
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Original Data**} & \multicolumn{4}{c}{**Augmented Data**} \\ \cline{3-8}  & & **RMSE** & **MAE** & **R** & **RMSE** & **MAE** & **R** \\ \hline \multirow{8}{*}{Los Angeles} & SVM & 69.92 & 40.81 & 0.9348 & 68.56 & 40.12 & 0.9356 \\  & ANN & 63.18 & 36.88 & 0.9496 & 61.07 & 35.37 & 0.9538 \\  & LSTM & 57.16 & 36.82 & 0.9613 & 36.91 & 24.12 & 0.9695 \\  & CNN & 74.35 & 43.71 & 0.9221 & 48.84 & 29.52 & 0.9392 \\  & CNN-LSTM & 53.01 & 34.98 & 0.9672 & 29.68 & 17.73 & 0.9691 \\  & LSTM-CNN & 49.61 & 31.17 & 0.9701 & 25.97 & 17.31 & 0.9836 \\ \hline \multirow{8}{*}{San Diego} & SVM & 61.33 & 36.03 & 0.9552 & 60.39 & 35.47 & 0.9589 \\  & ANN & 59.56 & 36.91 & 0.9491 & 57.27 & 35.19 & 0.9501 \\ \cline{1-1}  & LSTM & 52.81 & 33.82 & 0.9675 & 33.28 & 22.08 & 0.9693 \\ \cline{1-1}  & CNN & 67.89 & 39.33 & 0.9398 & 44.23 & 26.57 & 0.9408 \\ \cline{1-1}  & CNN-LSTM & 44.98 & 29.96 & 0.9672 & 23.64 & 17.69 & 0.9687 \\ \cline{1-1}  & LSTM-CNN & 42.89 & 27.38 & 0.9701 & 22.26 & 15.36 & 0.9832 \\ \hline \multirow{8}{*}{San Francisco} & SVM & 84.38 & 51.64 & 0.9289 & 83.18 & 50.74 & 0.9313 \\ \cline{1-1}  & ANN & 77.12 & 46.83 & 0.9319 & 74.59 & 44.59 & 0.9361 \\ \cline{1-1}  & LSTM & 70.94 & 40.99 & 0.9587 & 43.23 & 26.18 & 0.9678 \\ \cline{1-1}  & CNN & 89.63 & 50.98 & 0.9004 & 58.74 & 33.53 & 0.9165 \\ \cline{1-1}  & CNN-LSTM & 61.08 & 37.91 & 0.9611 & 34.16 & 22.57 & 0.9699 \\ \cline{1-1}  & LSTM-CNN & 58.12 & 37.02 & 0.9673 & 29.14 & 21.46 & 0.9889 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The forecasting performance of proposed models utilizing augmented data generated by the GAN-CSVR model vs. original data for the three target locations. Figure 6: Comparison of improvement percentage for proposed models based on augmented and original data in terms of (**a**) RMSE (**b**) MAE. Figure 7: Compares the performance of proposed models utilizing augmented data over original data for three locations in terms of RMSE. Conclusively, the GAN-CSVR model demonstrates the power of deep learning along with the hybrid model that has been developed to augment datasets, in which the GAN-CSVR model is able to efficiently capture the intrinsic features from the time series data and generate new data identical to the original data. Furthermore, the proposed GAN-CSVR model can be generalizable to different geographical locations or longer times, such as (medium- and long-term periods) for forecasting models. However, the proposed approach can be recommended for use as a viable generative model to extend data sets in a variety of domains, including solar power data, electricity consumption data, load forecasting data, wind power data, rainfall data, and other practical engineering applications that are according to time series data.
## 2 Uncertainty Modeling
### Modeling the Load Demand Uncertainty  
The uncertainty of the load is usually modeled by the normal distribution with mean (\(\mu\)) and standard deviation (\(\sigma\)) [18]. In this paper, it is assumed that all the loads have constant PF, the same mean, and standard deviation. Therefore, for simplicity, a normal distribution is applied at the load level (\(\lambda\)) instead of applying in each load independently. The probability of each load level is shown by (\(\pi_{l}\)), and is calculated using Equation (1). The associated value of each load level is denoted by (\(\lambda_{l}\)), and can be obtained using Equation (2) [19]. It is worth mentioning that \(\lambda_{Min,l}\) and \(\lambda_{Max,l}\) are known as the minimum and maximum levels of the system loading at the \(l^{th}\) load level, respectively.  
\[\pi_{l}=\int_{\lambda_{Min,l}}^{\lambda_{Max,l}}\frac{1}{\sqrt{2\pi\sigma^{2} }}\exp{(-\frac{(\lambda-\mu)^{2}}{2\sigma^{2}})}d\lambda \tag{1}\]  
\[\lambda_{l}=\frac{1}{\pi_{l}}\int_{\lambda_{Min,l}}^{\lambda_{Max,l}}\lambda \frac{1}{\sqrt{2\pi\sigma^{2}}}\exp{(-\frac{(\lambda-\mu)^{2}}{2\sigma^{2}})}d\lambda \tag{2}\]
## 5 Experimental Results and Discussion
### A Comparison with Existing Methods  
The main contribution of the method proposed in this paper is to apply the inherent randomness characteristics of DC arcs to arc fault detection through an AR model-based method.  
Compared with the traditional methods, the proposed method has improved anti-interference capability with almost no increase in computational complexity. Therefore, it is suitable for cost-sensitive applications implemented by an industrial MCU (for instance, TMS320F28033). While compared to the AI-based method, the method in the paper needs significantly fewer computations to achieve nearly the same performance under interference conditions since it does not require big data.  
Comparative tests have been conducted on the TI RD195 evaluation board, an open-source solution available [19]. It can be seen from the test result (Figure 11) that the current changes due to the varying solar irradiation caused a nuisance trip to the RD195 evaluation board. However, the proposed method is immune to this interference. Table 5. summarizes the comparative analysis of the proposed method and other methods. It can be seen that the proposed method based on the AR model has a relatively small computation amount and strong anti-interference ability.  
Figure 10: The current and corresponding PSD analysis of the startup process of a PV system. (**a**) The current during the inverter starting; (**b**) The data partition of 50 ms in the startup process of the PV system; (**c**) The current and corresponding PSD analysis of the startup process of a PV system.
# Microscopic Simulation of Heterogeneous Traffic Flow on Multi-Lane Ring Roads and Highways
## 4 System Description
### Car-Following Models in SUMO
#### 4.2.3 CACC Vehicle Model  
CAVs are capable of accurately sensing their environment via V2I communication technology and can synchronize perception and share driving information through V2V communication technology. With V2V communication technology, CACC vehicles can obtain operating status data between vehicles and automatically adjust the distance between them based on the position and speed of the vehicle ahead. This helps to reduce traffic congestion, improve road usage efficiency, and prevent rear-end collisions and other potential hazards. Therefore, the CACC vehicle model is as follows:  
\[v(t+\Delta t)=v(t)+k_{\text{p}}e(t)+k_{\text{d}}\dot{e}(t) \tag{4}\]  
\[e(t)=d-s_{0}-l-\tau_{\text{c}}v(t) \tag{5}\]  
where \(v(t+\Delta t)\) is the speed of the vehicle at the time \((t+\Delta t)\), \(k_{\text{p}}\) and \(k_{\text{d}}\) are control gains, \(e(t)\) denotes the error term between the actual spacing and the desired spacing of the preceding and following vehicles. \(d\) is the headway between vehicles, and \(\tau_{\text{c}}\) is the desired time headway. The first-order Taylor expansion of Equations (4) and (5) yields the following acceleration equation:  
\[\dot{v}(t)=\frac{k_{\text{p}}(d-s_{0}-l-\tau_{\text{c}}v(t))+k_{\text{d}} \Delta v(t)}{k_{\text{d}}\tau_{\text{c}}+\Delta t} \tag{6}\]  
Based on the calibration of CACC vehicle data using real vehicles by the California Partners for Advanced Transportation Technology (PATH) team at UC Berkeley [48], these parameters were assigned the following values: \(k_{\text{p}}\) = 0.45 s\({}^{-1}\), \(k_{\text{d}}\) = 0.25 s\({}^{-1}\). In SUMO, the parameters \(k_{\text{p}}\) and \(k_{\text{d}}\) are represented by gapControl GainGap (the control gain determining the rate of positioning deviation) and gapControl GainGapDot (the control gain determining the rate of the positioning deviation derivative), respectively.
## 3 High-Dynamic Atmospheric Turbulence Compensation Algorithm
### Modeling Strategy
To handle this, we consider the contribution of each electrode on spots offsets as equal. Therefore, the \(k\)th calibration voltage vector is supposed to be designed as Equation (7)  
\[S_{full,k}= \begin{bmatrix}s_{j,k}^{2}\\ s_{j,k}\\ M\end{bmatrix}  \tag{7}\]  
Referring to the above complete second-order model, we build a model for FSM containing second-order terms, first-order terms, and constant terms. In addition, considering the fact that the reflective surface of FSM is continuous and flat with tough rigidity, such characteristics would cause FSM electrodes to have a fierce coupling effect and this becomes increasingly evident when the stroke of the wavefront corrector rises. Individually building models for a single electrode and executing a linear summation cannot completely capture the effect brought by the collaboration of the two electrodes thus producing modeling errors. Correspondingly, an application of coupling terms keeps the computational complexity bearable. Meanwhile, it would not pose unaffordable burdens on solving models. The following equation is our constructed model for FSM. \[offset_{i}=a_{i}\times s_{1}^{2}+b_{i}\times s_{2}^{2}+c_{i}\times s_{1}s_{2}+d _{i}\times s_{1}+e_{i}\times s_{2}+f_{i} \tag{8}\]  
where, \(a_{i}\), \(b_{i}\), \(c_{i}\), \(d_{i}\), \(e_{i}\), \(f_{i}\) indicate the model coefficients of the \(i\)th spots coordinate. \(s_{FSM,1}s_{FSM,2}\) are the called coupling terms with whom the reliability of the model bewriting the cooperation of the two electrodes is guaranteed.