esa-sceva/satcom-chunk-collection huggingface dataset:
# A Study of Forest Phenology Prediction Based on GRU Models
## 2 Method
### Phenological Evaluation Indicators  
#### 2.5.1. Region of Interest Selection  
The study selected the diagonal center points of different irrigation zones in preset points 1, 3, and 5 as regions of interest (ROI) as shown in Figure 3, with irrigation equipment located below. Images were processed using a custom algorithm developed in Python and executed in the PyCharm compiler (Version: PyCharm 2020.2.2). Due to varying lighting conditions, rain, snow, fog, and condensation on camera housing windows, the quality of the images occasionally suffered. To ensure objectivity of the results, no selective editing or manual enhancement was performed on any archived images, and no smoothing or filtering was applied to the resulting time series analysis. The mean brightness values  
Figure 2: Experimental equipment and installation site.  
(digital number, DN) of the R, G, and B bands in the image ROI were extracted using Equation (1). To mitigate the effects of variations in illumination on color balance, the mean brightness values of the R, G, and B bands were averaged on a daily basis using a 1-day time interval.  
\[\text{DN}_{\text{channel}}=(\text{sumDN})_{\text{channel}}/\text{N}_{\text{ channel}} \tag{1}\]  
DN represents the value of each wave band, \((\text{sumDN})_{\text{channel}}\) indicates the sum of all pixel brightness values of a certain band in the image, and \(\text{N}_{\text{channel}}\) indicates the number of pixels in the ROI.
# Path Planning for Laser Cladding Robot on Artificial Joint Surface Based on Topology Reconstruction
## 4 Generation of Laser Cladding Paths
### Determination of the Robot Position and Pose
\begin{split}& RPY(\gamma,\beta,\alpha)\\ &=\left[\begin{array}{ccc}\cos\alpha\cos\beta&\cos\alpha\sin\beta \sin\gamma-\sin\alpha\cos\gamma&\cos\alpha\sin\beta\cos\gamma+\sin\alpha\sin \gamma\\ \sin\alpha\cos\beta&\sin\alpha\sin\beta\sin\gamma+\cos\alpha\cos\gamma&\sin \alpha\sin\beta\cos\gamma-\cos\alpha\sin\gamma\\ -\sin\beta&\cos\beta\sin\gamma&\cos\beta\cos\gamma\end{array}\right]\end{split}  \tag{7}\]  
By comparing Equations (4) and (7), a set of equations for \(\alpha\), \(\beta\) and \(\gamma\) could be described:  
\[\left\{ \begin{array}{l}\cos\alpha\cos\beta=n_{x}\\ \sin\alpha\cos\beta=o_{x}\\ -\sin\beta=a_{x}\\ \cos\beta\sin\gamma=a_{y}\\ \cos\beta\cos\gamma=a_{z}\end{array} \right. \tag{8}\]  
Figure 11: Robot position and pose solution. Figure 12: RPY rotation angles: \(\alpha\) (Roll angle), \(\beta\) (Pitch angle) and \(\gamma\) (Yaw angle). By solving the equations, the expressions of \(\alpha\), \(\beta\) and \(\gamma\) could be obtained as follows:  
\[\left\{ \begin{array}{l}\alpha=A\tan 2(\alpha_{x},n_{x})\\ \beta=A\tan 2\Big{(}-a_{x},\sqrt{n_{x}^{2}+o_{x}^{2}}\Big{)}\\ \gamma=A\tan 2\Big{(}a_{y},a_{z}\Big{)}\end{array} \right. \tag{9}\]  
According to the calculation results of Equations (6) and (9), the final position and pose of the robot TCP could be expressed as \(P\) = [\(Px\;Py\;Pz\;\alpha\;\beta\;\gamma\)]. The robot positions and poses corresponding to all the interpolation points were obtained using the above method.
# Anomaly Detection Method Considering PLC Control Logic Structure for ICS Cyber Threat Detection
## 2 Background and Related Works
### Background  
A PLC is an embedded device in industrial control systems that controls field devices such as sensors, actuators, and motors. The PLC receives the current state from input devices such as sensors and switches, processes it through control logic, and controls output devices such as motors and valves [10]. A PLC operates based on control logic downloaded to its memory, which can be uploaded or downloaded via an EWS. It is an embedded device used in ICSs. A PLC consists of a power supply module, input/output modules, an operating system, memory, and a communication interface [11]. IEC 61131-3 standardized the PLC programming language for developing PLC control logic [12]. Table 1 shows the PLC control logic language specified in the standard.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Types of Programming Languages** & **Description** \\ \hline Ladder Diagram (LD) & A programming language written using ladder diagram symbols \\ Instruction List (IL) & Programming using one operator and one or more operands (like assembly language) \\ Structured Text (ST) & High-level programming languages like Basic, PASCAL, and C \\ Function Block Diagram (FBD) & Programming language using block diagrams \\ Sequential Function Chart (SFC) & A programming language like the format of a sequence diagram. \\ \hline \hline \end{tabular}
\end{table}
Table 1: IEC 61131-3 programming language.  
IL and ST are text-based languages, while LD, FBD, and SFC are graphical languages. However, both text and graphical formats are not suitable as inputs for anomaly detection models in control logic. Therefore, control logic must be embedded into a suitable format for model input.
# Effect of Laser Parameters on Optical Stealth Transmission System Performance
## 3 Optical Stealth Transmission System  
Based on the optical stealth carrier generator, the setup of optical stealth transmission system is shown in Figure 5a. The public channel has 4 wavelength multiplexed users with a wavelength spacing of 0.16 nm. In the public transmitter, the modulation format of public signal is nonreturn-to-zero (NRZ) and the bit rate is 10 Gbps. The multiplexed signals are transmitted over a 50-km single mode fiber (SMF) span. In the public receiver, the public signals are directly detected after dispersion compensation fiber and de-multiplexer. Through optical couplers, the stealth signal is sent to the public channel and separated from the public channel. Typically, a coded stealth signal is sent during a bit interval to represent 0 bits, and no energy is sent during a bit interval to represent 1 bits[4,9]. Therefore, there is a temporal energy fluctuation when the stealth signal is sent, which exposes the existence of the stealth signal. To avoid the power fluctuation in time domain under continuous 0 bits, a complemented encoding is proposed as shown in Figure 5b. The odd wavelength patterns are modulated by stealth data in the upper branch, while the even wavelength patterns are modulated by inverse stealth data in the lower branch. The insertion loss and time delay of the two branches are equal. In the stealth receiver, as shown in Figure 5c, the public signal and noise are suppressed by an optical filter. Then, the stealth signal is temporally compressed through DCF. The decoder matches the upper branch in the encoder. After decoding, the stealth signal is detected.  
Figure 4: The generated optical stealth carrier before and after encoding.  
Figure 3: The (**a**) bandwidth, (**b**) TNR, (**c**) FWHM changes along with the frequency and modulation current.
# Review of Fast Computation Methods for Finite-State Predictive Control of Multi-Phase Drives
## 2 MPC for Current Control of MPS
### Cost Function  
In a general MPC application, the CF incorporates various terms. The primary one constitutes a penalization of output variables from their references. Additional terms include penalization of control effort and other objectives. In FSMPC stator current control, typically, predicted control errors and VSI switching events are penalized in the following manner [22]:  
\[J(k+2)=\hat{e}_{\alpha-\beta}^{2}(k+2)+\lambda_{xy}\hat{e}_{x-y}^{2}(k+2)+ \lambda_{sc}\Delta S(k+1) \tag{6}\]  
where \(\Delta S(k+1)\) represents the number of switch transitions at the VSI when the configuration \(u(k)\) is changed to \(u(k+1)\). For single-vector approaches, the value of \(\Delta S(k+1)\) can be calculated as  
\[\Delta S(k+1)=\sum_{i=1}^{5}|u_{i}(k+1)-u_{i}(k)| \tag{7}\]  
With this cost function structure, the weighting factors (WFs) are the parameters \(\lambda_{xy}\) and \(\lambda_{sc}\). The first parameter emphasizes the reduction of \(x\)-\(y\) currents, while the second helps minimize the switching frequency.
## 3 Results
### Train Running Time Delay Decrease  
We utilised both multiple logistic regression and negative binomial regression models to explore the opportunity for train delay reduction whilst traversing segments with scheduled trackwork. Detailed summaries of these models are presented in Appendix A, specifically in Tables A3 and A4. The statistical significance of each coefficient was determined using the Wald chi-square test, providing a robust basis for our analysis.  
The outcomes of the multiple logistic regression model are summarised in Table 6. All coefficients are significant at the 0.1% level. The model indicates that trackwork is associated with a slight decrease in the likelihood of delay reduction (OR = 0.89). There is a notable increase in the probability of delay reduction for the quadruple track type (OR = 1.24). Among all train types, commuter trains exhibit an increased probability of delay reduction (OR = 1.30). If the train departs late, it is more likely to reduce delays (OR = 1.96). The time of day shows a minimal impact, with night-time operations slightly less likely to reduce delays (OR = 0.95).  
Table 7 presents the negative binomial regression model outcomes, examining the count of train running time delay decreases exceeding or equal to 1 min. The model indicates a slight reduction in the frequency of delay reductions in the presence of trackwork (IRR = 0.96). For track types, quadruple tracks correlate with a lower frequency of delay reduction (IRR = 0.78), while single tracks demonstrate a marginal increase (IRR = 1.05). In terms of train types, commuter trains are more likely to reduce delays (IRR = 1.15), in contrast to airport trains, which show a notable decrease (IRR = 0.37). Departure status is a significant predictor, with late departures more frequently reducing delays (IRR = 1.26) and similar trends observed for on-time departures (IRR = 1.18). The time of day does not have a statistically significant impact.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Coefficient** & \multicolumn{1}{c}{**Estimate**} & \multicolumn{1}{c}{**CI 95\%**} & \multicolumn{1}{c}{**Odds Ratio**} \\ \hline (Intercept) & -0.51 & [-0.51, -0.50] & 0.60 \\ \hline Trackwork (No = 0) & -0.12 & [-0.13, -0.11] & 0.89 \\ \hline Track type & Quadruple & 0.21 & [0.21, 0.22] & 1.24 \\ (Double = 0) & Single & 0.06 & [0.06, 0.07] & 1.07 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Multiple logistic regression model summary. Response variable: train running time delay decrease \(\geq\)1 min (1; 0).  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Coefficient** & \multicolumn{1}{c}{**Estimate**} & \multicolumn{1}{c}{**CI 95\%**} & \multicolumn{1}{c}{**IRR**} \\ \hline (Intercept) & -0.99 & [-1.00, -0.98] & 0.37 \\ \hline Trackwork (No = 0) & -0.04 & [-0.06, -0.02] & 0.96 \\ \hline Track type & Quadruple & -0.25 & [-0.27, -0.23] & 0.78 \\ (Double = 0) & Single & 0.05 & [0.04, 0.05] & 1.05 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Negative binomial regression model summary. Response variable: count of train running time delay decrease \(\geq\)1 min.
# Matching-Based Resource Allocation for Satellite-Ground Network
## 3 System Model  
In Figure 1, a cooperative satellite-ground network made up of GEO satellites, LEO satellites, IOP devices such as UAVs, PCs, and cars, as well as mobile users such as people living in remote places, is depicted. The user terminal uploads data to the LEO satellite, which then transmits it to the GEO satellite. During satellite-ground communication, the satellite directly establishes a satellite-ground link with the user terminal.
# Boundary-Aware Transformer for Optic Cup and Disc Segmentation in Fundus Images
## 1 Introduction
Geometry-aware Loss Function: Conventional Dice Loss and IoU Loss are effective for pixel-level accuracy but have limitations in improving boundary precision. This study introduces a Geometry-aware Loss by incorporating a normalized Hausdorff Distance to reduce boundary shape distortions and quantitatively correct structure-based errors.
## 4 Experiment and Result Analysis
### Battery Type Migration Analysis
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Group** & **Algorithms** & **MAE** & **MAX** & **RMSE** & **MAPE** \\ \hline C1 & CNN-TL & 0.0484 & 0.2127 & 0.0798 & 0.2894 \\  & AdaBoost & 0.0195 & 0.0551 & 0.0225 & 0.1440 \\  & RT-TradaBoost & 0.0187 & 0.0489 & 0.0223 & 0.0854 \\ \hline C2 & CNN-TL & 0.0464 & 0.1767 & 0.0712 & 0.2294 \\  & AdaBoost & 0.0217 & 0.0552 & 0.0251 & 0.1478 \\  & RT-TradaBoost & 0.0192 & 0.0384 & 0.0221 & 0.0870 \\ \hline C3 & CNN-TL & 0.0613 & 0.1987 & 0.0859 & 0.2773 \\  & AdaBoost & 0.0224 & 0.0357 & 0.0239 & 0.1036 \\  & RT-TradaBoost & 0.0188 & 0.0377 & 0.0211 & 0.0963 \\ \hline C4 & CNN-TL & 0.0521 & 0.2014 & 0.0797 & 0.2628 \\  & AdaBoost & 0.0204 & 0.0583 & 0.0249 & 0.0946 \\  & RT-TradaBoost & 0.0124 & 0.0361 & 0.0150 & 0.0733 \\ \hline C5 & CNN-TL & 0.0459 & 0.1685 & 0.0633 & 0.2326 \\  & AdaBoost & 0.0178 & 0.0427 & 0.0211 & 0.1074 \\  & RT-TradaBoost & 0.0154 & 0.0333 & 0.0185 & 0.0841 \\ \hline C6 & CNN-TL & 0.0491 & 0.1745 & 0.0713 & 0.2344 \\  & AdaBoost & 0.0193 & 0.0413 & 0.0223 & 0.0991 \\  & RT-TradaBoost & 0.0137 & 0.0396 & 0.0176 & 0.0424 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The evaluation criteria of the battery type migration on Group C.  
In addition, the color of the squares in Figures 12 and 13 highlights the large differences between the three models in the two evaluation criteria of MAX and MAPE. Therefore, on the Stanford-MIT-Toyota and Oxford datasets, the RT-TrAdaBoost method has an advantage in implementing aging information migration. Not only that but the operating conditions and temperatures of the two datasets are different. Therefore, under the joint action of multiple factors, the RUL prediction accuracy in the battery-type migration experiment is lower than that in the operating condition migration experiment, but the results still show that the model is effective. On the one hand, the utilization of historical battery data to migrate to a small sample of existing batteries for testing often encounters the challenge of being unable to match the battery type and charging conditions. The challenge has been effectively overcome in this experiment. On the other hand, the original  
Figure 13: The evaluation criteria of lithium-ion battery RUL prediction results. (**a**) Transfer g1c38 to Cell7. (**b**) Transfer g2c32 to Cell7. (**c**) Transfer g2c48 to Cell7. (**d**) Transfer g3c2 to Cell7. (**e**) Transfer g5c31 to Cell7. (**f**) Transfer g7c47 to Cell7. intention of choosing migration prediction is limited by the size of the battery data to be tested. This experiment still shows good predictive ability when the data scale ratio of the source domain and the target domain is set to nearly 17.4:1. In conclusion, the RT-TrAdaBoost method has a certain application value in RUL prediction.
## 3 Joint Huffman and LDPC Coding Enabled Free-Space Optical Communication  
### Experimental Setup  
Figure 4 shows the experimental setup for joint Huffman and LDPC coding enabled FSO communication system. In the transmitter, a 1550 nm CW light is generated as the optical carrier, and passes to an optical I/Q modulator. The PRBS signals are coded by Huffman procedure to the symbol sequences with alphabet sizes of 5 and 9 respectively [30]; or uniformly mapped to symbol sequences with alphabet sizes of 4 and 8, respectively. Then the GF(5), GF(3\({}^{2}\)) based nonbinary LDPC encoding is used, followed by mapping procedures from the coded sequences to 5-QAM and 9-QAM signals, respectively. Classical binary LDPC encoding is implemented for QPSK (or 4-QAM) and 8-QAM sequences. The used Huffman trees and the 5/9-QAM formats with corresponding bit labeling are provided (Figure 4(a1,a2,b1,b2)). When 12.5 G Baud electronic signals are generated, they drive the I/Q modulator. The optical signals are boosted by EDFA1, and filtered with an OTF. Then optical signals are separated by an optical coupler, decorrelated, and converted to OAM states 2 and \(-6\) by SLM1. The formed OAM modes are combined and centrally aligned by BS1. BS2 is used to separate the multiplexed OAM modes, and re-combined by the BS3. The optical signals in one optical path bounce off a mirror one time to generate the opposite OAM modes, i.e., OAM states \(-2\) and \(6\). The optical signals in the other path bounce off four times to keep the original mode states and decorrelate the carried optical signals. The desired SO between the two optical paths can be achieved by adjusting the BS3 position. In this setup, the limited SLM screen size restricts the SO freedom. To reduce the side effect-induced inter-mode crosstalk and mode power loss, OAM states \(2\) and \(-6\) are centrally aligned and transmitted in one optical path, while OAM states \(-2\) and \(6\) are combined and launched onto another optical path.  
The offset OAM beams are expanded by a BE, and then distorted in the designed turbulence emulator. The current turbulence emulator is designed according to the Rytov variance of 0.5. The distorted OAM beams are captured by a compressing telescope, demultiplexed by SLM4, and back-convert the target OAM mode to the Gaussian mode. The Gaussian beam is then coupled from free space into a fiber cable and pre-amplified by EDFA2. The ASE noise is loaded onto the signal in the 3-dB coupler, and later the out-of-band noise is removed by the OTF2. The optical signal is detected by a coherent receiver, and equalized by DSP signal recovery. The symbol log-likelihood ratio (LLR) estimation is executed before the GF(2)/GF(5)/GF(3\({}^{2}\)) based LDPC decoding procedures. Ultimately, BER values are calculated after LDPC decoding to determine system performance.
## 3 Methodology Research
### Artificial Neural Network (ANN)  
Artificial neural networks (ANNs), also known as neural networks, are predictive models built on simulating the functionality of the human brain and nervous system. They consist of input layers, hidden layers, and output layers [79]. ANNs have strong nonlinear processing capabilities, with landslide-influencing factors being the input neurons. Different neurons are interconnected through weights, and their weight calculation formula is as follows [80]:  
\[y_{i}=f\Big{(}\sum_{i}W_{ij}+b_{j}\Big{)}\]In the equation, \(\rm W_{ij}\) represents the weight value linking neuron i and neuron j; \(\rm b_{j}\) is the bias term; \(\rm f\) is the activation function. ANN models are applied to landslide susceptibility assessment, where the input layer consists of landslide evaluation factors, and the output layer represents the landslide susceptibility assessment results. Feature transformation is achieved by adding hidden layers [45].  
ANNs are nonlinear statistical models that are commonly used for regression and classification problems. Research has shown that applying artificial neural networks to landslide susceptibility assessment can effectively enhance the automatic identification capability of other geological hazards in different regions, achieving a correct identification rate of approximately 80% [81; 82; 83]. The backpropagation neural network (BPNN), which employs error backpropagation, is known for its excellent nonlinear mapping capability and has been introduced into landslide susceptibility assessment [64; 84].  
The BPNN algorithm is the most common and representative algorithm in artificial neural networks. It is a type of supervised learning method and utilizes the gradient descent algorithm to minimize the error function. Its objective is to minimize the difference between the target output values and the inferred output values of the output units. The specific process involves initializing the model's connection weights and biases with random values after constructing the model. Through adjusting the error function, the weights and biases are continuously updated in a backward manner, ultimately resulting in a model within the desired error range [85]. When conducting a landslide susceptibility assessment, the first step is to construct a BPNN model and obtain the final connection weight values. Then, the triggering factors are used as input data for the input layer. After the triggering factors are linearly combined and passed through the activation function, the output data of the hidden layer neurons are obtained. Subsequently, the output data of the hidden layer are linearly combined and passed through the activation function again to obtain the probability of landslide occurrence [39].  
The ANN [86] model exhibits strong nonlinear adaptive capabilities. It continuously updates itself when processing information and does not rely on external rules when handling variable relationships. Therefore, the ANN model has become an effective tool for landslide susceptibility assessment.
## 5 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Series** & **No.** & **Comp.** & **Porosity** & \(V_{p}/S_{p}\) & & \multicolumn{3}{c}{**TP**} & \multicolumn{3}{c}{**IP**} \\  & & & & \(\mathbf{\mu}\mathbf{\mu}\) & & \(\mathbf{\kappa_{LB}}\) & \(\mathbf{\kappa_{ML}}\) & \(\mathbf{\tau_{LB}}\) & \(\mathbf{\tau_{ML}}\) & \(\mathbf{\kappa_{LB}}\) & \(\mathbf{\kappa_{ML}}\) \\  & & **\%** & & \(\mathbf{\mu}\mathbf{\mu}\) & & & \(\mathbf{\mu}\mathbf{\mu}^{\mathbf{2}}\) & \(\mathbf{\mu}\mathbf{\mu}^{\mathbf{2}}\) & & \(\mathbf{\mu}\mathbf{\mu}^{\mathbf{2}}\) & \(\mathbf{\mu}\mathbf{\mu}^{\mathbf{2}}\) \\ \hline R2 & 1 & 6 & 0.688 & 7.12 & 1.22 & 1.26 & 6.01 & 8.18 & 1.01 & 18.20 \\  & 2 & 8 & 0.666 & 6.38 & 1.13 & 1.17 & 5.91 & 6.97 & 1.01 & 15.97 \\  & 3 & 11 & 0.678 & 6.72 & 1.15 & 1.28 & 6.07 & 7.03 & 1.01 & 16.31 \\  & 4 & 13 & 0.669 & 6.74 & 1.23 & 1.27 & 4.65 & 6.82 & 1.04 & 16.10 \\  & 5 & 16 & 0.669 & 6.74 & 1.11 & 1.35 & 6.98 & 6.25 & 1.05 & 16.09 \\  & 6 & 18 & 0.669 & 6.59 & 1.25 & 1.27 & 4.36 & 6.05 & 1.07 & 15.37 \\  & 7 & 19 & 0.680 & 6.05 & 1.12 & 1.26 & 5.49 & 5.91 & 1.07 & 14.09 \\  & 8 & 21 & 0.644 & 6.42 & 1.26 & 1.27 & 3.46 & 5.86 & 1.03 & 13.35 \\  & 9 & 24 & 0.640 & 6.41 & 1.27 & 1.27 & 3.23 & 5.12 & 1.02 & 12.25 \\  & 10 & 29 & 0.640 & 6.41 & 1.27 & 1.28 & 3.23 & 4.59 & 1.04 & 11.05 \\ \hline R3 & 1 & 7 & 0.685 & 7.61 & 1.18 & 1.13 & 7.46 & 7.65 & 1.08 & 16.23 \\  & 2 & 10 & 0.709 & 7.91 & 1.15 & 1.19 & 9.46 & 7.21 & 1.09 & 16.19 \\  & 3 & 11 & 0.669 & 7.02 & 1.20 & 1.13 & 5.39 & 6.94 & 1.07 & 15.08 \\  & 4 & 14 & 0.666 & 6.86 & 1.20 & 1.16 & 5.01 & 6.46 & 1.09 & 14.18 \\  & 5 & 18 & 0.678 & 6.91 & 1.18 & 1.20 & 5.68 & 6.08 & 1.08 & 14.13 \\  & 6 & 19 & 0.685 & 6.89 & 1.18 & 1.22 & 6.54 & 1.11 & 14.45 \\  & 7 & 24 & 0.597 & 4.61 & 1.08 & 5.15 & 1.04 & 10.79 \\  & 8 & 28 & 0.555 & 4.84 & 0.98 & 3.75 & 1.04 & 7.97 \\  & 9 & 30 & 0.570 & 6.69 & 1.19 & 3.80 & 1.12 & 7.38 \\  & 10 & 31 & 0.592 & 8.87 & 1.25 & 4.09 & 1.17 & 8.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The tortuosity and permeability of real data, predicted by the CNN, trained with fold no. 4. The series are annotated according to Section 2.5. The deviation in the KC trend in Figure 14 is in agreement with the observation that the LB simulations of these micro-structures failed more often than for the R2 series.
## 3 Design of Beam Steering and Adjustment Structure
### Analysis of Beam Adjustment Capability  
According to the design scheme of the beam steering and adjustment structure, the sub-light path piston error is controlled at 12 \(\upmu\)m and the tilt error is controlled at 1200 \(\upmu\)rad through the \"Three Screws for Pull and Three Screws for Push\" structure of the _FSM_ rough adjustment. The piston error and tilt error are then precisely adjusted by the _FSM_ piezoelectric ceramics. This section will simulate the correction of the piston error and tilt error of the system.  
Figure 11: Vibration analysis of the _FSM_ structure: (**a**) 7 th order vibration mode, (**b**) 1 st–10 th order mode natural frequency, (**c**) strain analysis of harmonic response in 7000 Hz, and (**d**) frequency–displacement curve of harmonic response.  
Figure 10: _FSM_ structure.