esa-sceva/satcom-chunk-collection huggingface dataset:
## Appendix A
### A1 Processing
#### a.1.1 Image Segmentation  
The goal of segmentation is to divide an image into parts or regions; the division into parts is based on the characteristics of the pixels in the image. For example, one way to find regions in an image is to look for sharp discontinuities in the pixel values, which indicates the presence of edges [41]. Segmentation algorithms have two basic properties; an algorithm can be based on one of these basic properties of the gray level values, the discontinuity or the similarity between the gray levels of neighboring pixels [42]. Discontinuity divides the image based on abrupt gray level changes for a single point, line, and edge detection. Similarity divides the image based on finding areas having similar values according to predetermined criteria such as regional growth and thresholding [43; 44].  
To process the algorithm in Python that was created in the late 1980s by [PERSON] at the Center for Mathematics and Informatics in the Netherlands, the OTSU threshold is used, which eliminates the result of over-segmentation due to noise or any other irregularity in the image, and it is implemented with OpenCV. OpenCV is a free computer vision library originally developed by Intel in January 1999. Figure 14 shows the output of the image transformed by the threshold operation where the noise it contains in each stage of the transformation is observed. To remove any white noise in the image, it is possible to use morphological closure and bring the object to the foreground. Image segmentation is a fundamental process in image recognition, both for image compression and the study of its content. This is based on the partition of the image into separate regions that correspond to representations of different objects; in this work, these objects are numbers. With segmentation or thresholding, when capturing the image of a number, it is divided into regions based on intensity values; these allow an object to be identified or extracted from its background based on the distribution of gray levels or the texture of the image of the number.  
In the figure after image segmentation, the objects present in the background, where the slate is located, have been separated. In addition to other objects, it is possible to create spots using the blackboard or even other unwanted images within the ID to be captured by the camera focus. Therefore, by applying segmentation, it is possible to identify which pixels belong to which elements of a photograph. For this purpose, using OTSU, it is possible to find a rough estimate of the objects in the image; subsequently, small sections of white noise are removed. In the lower-left frame, the results of the process are presented, and in the lower-right frame, the objects are dilated, ensuring that any background regions are part of the background and not noise.
## 3 Description of the Obtained Results: Processing and Interpretation
The coordinates of the radiation stations and the distance from the measuring systems are presented in Table 3.  
Based on the calculation results from Table 4, we can see a good agreement of the values of seismoacoustic energy densities at stations 2 and 3 with the first experiment. However, there are differences at stations No. 1 and No. 4, which we discuss below. Usually, in our experiments, to quantify the transformation of energy from hydroacoustic to seismoacoustic, we measure the vertical distribution of the pressure field along the signal propagation path at several points. In the experiment, described in [15], such a measurement was made at a point at a depth of 37 m, 335 m from the radiator, and the energy density calculated from the obtained values was 0.176 J/m\({}^{2}\). Of course, this value is an order of magnitude larger than the values obtained in this work, but it confirms our earlier conclusions that the energy (energy density) propagates from the place of radiation at each station to the laser strainmeter according to the spherical law or close to it.
# An Algorithm for the Fisher Information Matrix of a VARMAX Process
## 2 The Fisher Information Matrix of VARMAX Processes  
Using (2) for all \(t\in\mathbb{Z}\) enables us to determine the residual \(\varepsilon_{t}(\vartheta)\) which depends on the parameter vector, \(\vartheta\). Under the above assumptions, the asymptotic Fisher information matrix, \(\mathcal{F}(\vartheta)\), is defined by the following \((l\times l)\) matrix, which does not depend on \(t\):  
\[\mathcal{F}(\vartheta)=\mathbb{E}\Bigg{\{}\left(\frac{\partial\varepsilon_{t }(\vartheta)}{\partial\vartheta^{T}}\right)^{T}\!\Sigma^{-1}\!\left(\frac{ \partial\varepsilon_{t}(\vartheta)}{\partial\vartheta^{T}}\right)\Bigg{\}} \tag{5}\]  
where the \((n\times l)\) matrix \(\partial(\cdot)/\partial\vartheta^{T}\) is the derivative with respect to \(\vartheta^{T}\). That derivative is computed in [19], using the Kronecker product \(\otimes\), to obtain:\[\begin{array}{ll}\frac{\partial\epsilon_{t}}{\partial\theta^{T}}&=\{[(A^{-1}(z)C(z )x_{t})^{T}+(A^{-1}(z)B(z)\epsilon_{t})^{T}]\otimes B^{-1}(z)\}\frac{\partial \operatorname{vec}A(z)}{\partial\theta^{T}}\\ \\ &\quad\quad-\{x_{t}^{T}\otimes B^{-1}(z)\}\frac{\partial\operatorname{vec}C(z )}{\partial\theta^{T}}-(\epsilon_{t}^{T}\otimes B^{-1}(z))\frac{\partial \operatorname{vec}B(z)}{\partial\theta^{T}}.\end{array} \tag{6}\]  
For each positive integer \(k\), denote \(u_{k}(z)=(1,z,z^{2},\ldots,z^{k-1})^{T}\). Let us define:  
\[\mathcal{G}(z)=\left(\begin{array}{c}u_{p}(z)\otimes A^{-1}(z)(-B(z))\\ O_{rm\times n}\\ u_{q}(z)\otimes I_{n}\end{array}\right),\quad\mathcal{K}(z)=\left(\begin{array} []{c}u_{p}(z)\otimes A^{-1}(z)(-C(z))\\ u_{r}(z)\otimes I_{n}\\ O_{qn\times m}\end{array}\right). \tag{7}\]  
Let \(\sigma(z)=B^{-T}(z)\Sigma^{-1}B^{-1}(z^{-1})\) and the square matrices of dimension \((p+q)n+rm\)  
\[\mathcal{P}(z):=\mathcal{G}(z)\Sigma\mathcal{G}^{*}(z)\text{ and }\mathcal{Q}(z):= \mathcal{K}(z)R_{x}(z)\mathcal{K}^{*}(z), \tag{8}\]  
using the Hermitian spectral density matrix, \(R_{x}(z)\), defined in (4). Then, as shown in [19] (for the special case where \(m=n\)), the Fisher information matrix is given by:  
\[\mathcal{F}(\theta)=\frac{1}{2\pi i}\oint_{|z|=1}(\mathcal{P}(z)\otimes \sigma(z))\frac{dz}{z}+\frac{1}{2\pi i}\oint_{|z|=1}(\mathcal{Q}(z)\otimes \sigma(z))\frac{dz}{z}. \tag{9}\]  
The integrals are counter-clockwise. It is easy to check that the result in (Proposition 2.1, [19]) is valid even if \(m\
eq n\) and \(C(0)\) is not the identity matrix. The main changes are in (7) but also in the middle block of (Equations (18)-(20), [19]) where \(I_{n^{2}}\) has to be replaced by \(I_{mn}\). Note that the subsequent sections of [19] are not valid if \(m\
eq n\).
## 3 System Model  
The system model of the IHS network for emergency communications is depicted in this section. When a disaster occurs, an emergency communication system will be established, as shown in Figure 1, which consists of three parts, _i.e._, space segment, near space segment and ground segment. The details of the three segments are described in the following subsections.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Notation** & **Description** & **Notation** & **Description** \\ \hline \(C_{i}\) & The channel \(i\) & \(n_{i}\) & The path loss exponents of the channel \(i\) \\ \(G_{r}\) & The receive antenna gain & \(k_{i}\) & The Rician factor of send-receive (S-R) channel \\ \(G_{s}\) & The transmit antenna gain & \(d_{i}\) & The send-receive (S-R) distances \\ \(R_{b}\) & The data rate & \(\upalpha\) & The mean channel power gain \\ \(\rho_{e}\) & The bit error rate & \(E_{b}\) & The energy of per bit \\ \(\uppsi\) & The longitude & \(\upphi\) & The latitude \\ \(P_{s}\) & The transmission power & \(\Delta\left(\cdot\right)\) & The gradient operator \\ \(E\) & The energy consumption & \(v_{i}^{opt.}\) & The optimal transmission path of the \(i\)-th terminal \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations.  
Figure 1: System model of the integrated high altitude platform (HAP)/satellite (IHS) network for emergency scenarios.
## 4 Deep Learning-Based Minimum Timeline Cover
### Iterative Algorithm
#### 4.5.1 Algorithm Description  
The algorithm takes the initial intervals from the DL model and iteratively adjusts them to cover all temporal edges. For each uncovered edge, it decides which node's interval to adjust based on the minimal increase in the total sum-span \(S(\mathcal{T})\).  
Given a temporal graph \(G=(V,E)\), an activity interval \(I_{u}=[s_{u},e_{u}]\), the total sum-span of all activity intervals \(S(\mathcal{T})=\sum_{u\in V}(e_{u}-s_{u})\) and a set of uncovered edges \(U=\{(u,v,t)\in E\mid t\
ot\in I_{u}\wedge t\
ot\in I_{v}\}\), the algorithm performs the following steps:  
1. Initialization: Copy the initial intervals \(\mathcal{T}\) and initialize the uncovered edges in set \(U\).
2. Edge Checking: For each edge \((u,v,t)\in E\), check if \(t\in I_{u}\) or \(t\in I_{v}\). If not, add the edge to \(U\).
3. Interval Adjustment: For each edge \((u,v,t)\in U\), calculate the minimal increase required to adjust \(I_{u}\) and \(I_{v}\) to include \(t\).
4. Update Intervals: Adjust the interval of the node with the minimal increase to include \(t\).
5. Iteration: Repeat steps 3 and 4 until all edges in \(U\) are covered.
6. Output: Return the adjusted intervals \(\mathcal{T}\) that now cover all edges in \(E\).  
The algorithm is detailed in Algorithm 1.
## 3 Results

Table 2: Descriptive statistics (mean \(\pm\) standard deviation, median, Q1 and Q3) and Friedman test values for all variables (time of first fixations, number of fixations, and total time of fixations) for the sample (n = 18). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{**Conditions**} & \multirow{2}{*}{**Mean \(\pm\) SD**} & \multirow{2}{*}{**Median**} & \multicolumn{2}{c}{**Percentiles**} & \multicolumn{1}{c}{**Friedman Test**} \\ \cline{5-6}  & & & & **Q1** & **Q3** & \(p\) \\ \hline \multirow{6}{*}{Accuracy} & B1 & 2.08 \(\pm\) 1.08 & 2.00 & 1.00 & 3.00 & \\ \cline{2-6}  & B2 & 1.70 \(\pm\) 0.86 & 2.00 & 1.00 & 2.00 & \\ \cline{2-6}  & B3 & 1.66 \(\pm\) 0.84 & 2.00 & 1.00 & 2.00 & \\ \cline{2-6}  & B4 & 1.76 \(\pm\) 0.82 & 2.00 & 1.00 & 2.00 & \\ \cline{2-6}  & N1 & 2.22 \(\pm\) 1.15 & 2.00 & 1.00 & 3.00 & \\ \cline{2-6}  & N2 & 1.75 \(\pm\) 0.91 & 2.00 & 1.00 & 2.00 & \\ \cline{2-6}  & N3 & 1.63 \(\pm\) 0.83 & 1.00 & 1.00 & 2.00 & \\ \cline{2-6}  & N4 & 1.65 \(\pm\) 0.82 & 2.00 & 1.00 & 2.00 & \\ \cline{2-6}  & O2 & 1.52 \(\pm\) 0.72 & 1.00 & 1.00 & 2.00 & \\ \cline{2-6}  & O3 & 1.60 \(\pm\) 0.80 & 1.00 & 1.00 & 2.00 & \\ \cline{2-6}  & O4 & 1.52 \(\pm\) 0.78 & 1.00 & 1.00 & 2.00 & \\ \hline \multirow{6}{*}{Total duration of fixations (ms)} & B1 & 707.41 \(\pm\) 345.45 & 701.00 & 480.00 & 941.75 & \\ \cline{2-6}  & B2 & 532.64 \(\pm\) 322.164 & 480.00 & 340.00 & 681.00 & \\ \cline{2-6}  & B3 & 568.98 \(\pm\) 302.932 & 520.00 & 330.50 & 761.00 & \\ \cline{2-6}  & B4 & 550.79 \(\pm\) 302.73 & 501.00 & 335.25 & 681.00 & \\ \cline{2-6}  & N1 & 763.44 \(\pm\) 418.70 & 741.00 & 460.00 & 680.50 & \\ \cline{2-6}  & N2 & 519.83 \(\pm\) 307.19 & 461.00 & 301.00 & 680.50 & \\ \cline{2-6}  & N3 & 546.09 \(\pm\) 305.52 & 481.00 & 320.00 & 721.00 & \\ \cline{2-6}  & N4 & 488.55 \(\pm\) 250.44 & 461.00 & 320.00 & 641.00 & \\ \cline{2-6}  & O2 & 498.51 \(\pm\) 323.81 & 421.00 & 300.00 & 661.00 & \\ \cline{2-6}  & O3 & 506.61 \(\pm\) 268.73 & 491.00 & 281.00 & 666.00 & \\ \cline{2-6}  & O4 & 481.70 \(\pm\) 265.11 & 420.50 & 301.00 & 641.00 & \\ \hline \hline \end{tabular} Legend: B1—baseline in position 1; B2—baseline in position 2; B3—baseline in position 3; B4—baseline in position 4; N1—simulated gym audience noise in position 1; N2—simulated gym audience noise in position 2; N3—simulated gym audience noise in position 3; N4—simulated gym audience noise in position 4; O2—opposition in position 2; O3—opposition in position 3; O4—opposition in position 4.  
\end{table} 
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{**Conditions**} & \multirow{2}{*}{**Mean \(\pm\) SD**} & \multirow{2}{*}{**Median**} & \multicolumn{2}{c}{**Percentiles**} \\ \cline{5-6}  & & & **Q1** & **Q3** \\ \hline \multirow{6}{*}{Accuracy} & B1 & 2.57 \(\pm\) 1.39 & 3.00 & 1.00 & 4.00 \\ \cline{2-6}  & B2 & 1.78 \(\pm\) 1.37 & 1.00 & 1.00 & 3.00 \\ \cline{2-6}  & B3 & 2.12 \(\pm\) 1.46 & 1.00 & 1.00 & 4.00 \\ \cline{2-6}  & B4 & 1.84 \(\pm\) 1.40 & 1.00 & 1.00 & 4.00 \\ \cline{2-6}  & N1 & 2.62 \(\pm\) 1.44 & 3.00
## 2 Configuration
### Lossless to Lossy Medium: Air to Muscle Tissue  
First, a simple two-layer approach is considered here with the Tx placed in a lossless medium, air (\(\epsilon_{r}=1\) and \(\sigma=0\) S/m), at a distance of 1 m from the muscle tissue medium, which has a thickness of 0.2 m, as shown in Figure 1. The Tx in air is a free space half-wavelength dipole antenna made of perfect electric conductors (PEC) as designed in [2], and having a length of \(\lambda\)/2 = 0.0612 m, where \(\lambda\) is the wavelength in air at 2.45 GHz. The Rx is an insulated dipole antenna where the dipole arms are PEC surrounded with an insulation made of polytetrafluoroethylene (\(\epsilon_{r}=2.07\) and \(\sigma=0\) S/m). The insulation is 2.5 mm in thickness. The Rx is placed in the lossy medium of human muscle tissue. Dipole antennas (length, \(\ell_{1}\) = 3.9 cm) are used for this study, as they are the best understood antennas in free space and have a simple structure [7]. The reason for the Tx being placed at 1 m from the muscle tissue layer is so that a plane wave is obtained when the waves reach the muscle tissue layer. We begin the PL modeling using plane waves, hence this requirement. Both of the layers are infinite in extent in the direction perpendicular to the propagation direction.
## 3 Main Results
** First, Equation (40) is derived by the definition of \(\hat{\mathbf{z}}_{ik|k-1}^{*}\), and according to the definition of \(\mathbf{P}_{ik|k-1}^{zz}\), we have  
\[\mathbf{P}_{ik|k}^{\eta\eta}=\frac{(v_{2}-2)\Big{(}v_{2}+\big{(}\Delta_{k}^{*} \big{)}^{2}\Big{)}}{v_{2}(v_{2}+m-2)}\Big{(}\Xi_{k}-\mathbf{K}_{k}^{\eta}\mathbf{P}_{ k|k-1}^{\eta\eta}\Big{(}\mathbf{K}_{k}^{\eta}\Big{)}^{\mathsf{T}}\Big{)} \tag{31}\]2 \[\mathbf{P}_{ik|k}^{\eta\eta}=\frac{(v_{2}-2)\Big{(}v_{2}+\big{(}\Delta_{k}^{*} \big{)}^{2}\Big{)}}{v_{2}(v_{2}+m-2)}\Big{(}\Xi_{k}-\mathbf{K}_{k}^{\eta}\mathbf{P}_{ k|k-1}^{\eta\eta}\Big{(}\mathbf{K}_{k}^{\eta}\Big{)}^{\mathsf{T}}\Big{)} \tag{31}\]3 \[\mathbf{P}_{ik|k}^{\eta\eta}=\frac{(v_{2}-2)\Big{(}v_{2}+\big{(}\Delta_{k}^{*} \big{)}^{2}\Big{)}}{v_{2}(v_{2}+m-2)}\Big{(}\Xi_{k}-\mathbf{K}_{k}^{\eta}\mathbf{P}_{ k|k-1}^{\eta\eta}\Big{(}\mathbf{K}_{k}^{\eta}\Big{)}^{\mathsf{T}}\Big{)} \tag{31}\]4Then, the definition of \(\hat{\mathbf{z}}_{k-1|k-1}^{*}\) and \(P_{k-1|k-1}^{zz}\) is as follows:  
\[\mathbf{P}_{ik|k}^{\eta\eta}=\frac{(v_{2}-2)\Big{(}v_{2}+\big{(}\Delta_{k}^{*} \big{)}^{2}\Big{)}}{v_{2}(v_{2}+m-2)}\Big{(}\Xi_{k}-\mathbf{K}_{k}^{\eta}\mathbf{P}_{ k|k-1}^{\eta\eta}\Big{(}\mathbf{K}_{k}^{\eta}\Big{)}^{\mathsf{T}}\Big{)} \tag{31}\]5  
\[\mathbf{P}_{ik|k}^{\eta\eta}=\frac{(v_{2}-2)\Big{(}v_{2}+\big{(}\Delta_{k}^{*} \big{)}^{2}\Big{)}}{v_{2}(v_{2}+m-2)}\Big{(}\Xi_{k}-\mathbf{K}_{k}^{\eta}\mathbf{P}_{ k|k-1}^{\eta\eta}\Big{(}\mathbf{K}_{k}^{\eta}\Big{)}^{\mathsf{T}}\Big{)} \tag{31}\]6  
Using the Student's t integral to approximate \(p\Big{(}\mathbf{x}_{k-1}^{a}|\mathbf{Y}_{k-1}^{*}\Big{)}\) with the known \(\hat{\mathbf{x}}_{k-1|k-1}^{a}\) and \(\mathbf{P}_{k-1|k-1}^{a}\), we can obtain Equations (37) and (38). Second, according to Equation (10), \(\overline{\mathbf{y}}_{k|k-1}\) can be written as follows:  
\[\mathbf{P}_{ik|k}^{\eta\eta}=\frac{(v_{2}-2)\Big{(}v_{2}+\big{(}\Delta_{k}^{*} \big{)}^{2}\Big{)}}{v_{2}(v_{2}+m-2)}\Big{(}\Xi_{k}-\mathbf{K}_{k}^{\eta}\mathbf{P}_{ k|k-1}^{\eta\eta}\Big{(}\mathbf{K}_{k}^{\eta}\Big{)}^{\mathsf{T}}\Big{)} \tag{31}\]7  
Then, by substituting Equation (45) to the definition of \(\mathbf{P}_{k|k-1}^{yy}\) and \(\mathbf{P}_{k|k-1}^{yy}=E\Big{[}\eta_{k}\overline{\mathbf{y}}_{k|k-1}|\mathbf{Y}_{k-1}^{*} \Big{]}\) we can get Equations (35) and (36). Finally, \(\hat{\mathbf{\eta}}_{k|k}\) and \(\mathbf{P}_{k|k}^{\eta\eta}\) can be derived a by similar method as \(\hat{\mathbf{x}}_{k|k}\) and \(\mathbf{P}_{k|k}\) by Equation (30) and (31). \(\Box\)  
**Theorem 3**. : _Given \(\hat{\mathbf{x}}_{k-1|k-1}^{a}\) and \(\mathbf{P}_{k-1|k-1}^{a}\), the posterior estimation of the augmented state \(\hat{\mathbf{x}}_{k|k}^{a}\) and the covariance \(\mathbf{P}_{k|k}^{a}\) are given as follows:_  
\[\hat{\mathbf{x}}_{k|k}^{a}=\left[ \begin{array}{cc}\hat{\mathbf{x}}_{k|k}\\ \hat{\mathbf{\eta}}_{k|k}\end{array} \right] \tag{46}\]  
\[\mathbf{P}_{k|k}^{a}=\left[ \begin{array}{cc}\mathbf{P}_{k|k}&\mathbf{P}_{k|k}^{\eta\eta} \\ \Big{(}\mathbf{P}_{k|k}^{\eta\eta}\Big{)}^{\mathsf{T}}&\mathbf{P}_{k|k}^{\eta\eta} \end{array}
## 3 Full-Scale Experiments on a Real Train and Proposition of Behavioural Laws
### Electrical Behavioural Law at 230 Hz and 2300 Hz  
Interestingly, the nonlinear behaviour and hysteresis phenomenon observed at a reduced scale, as shown in Section 2 (Figure 5), were also witnessed in the railway site tests under real conditions, as one can see in Figures 6 and 7. One can note that the nonlinearity is slightly less pronounced compared to the 6 A curves pictured in Figure 5, since the track circuit only allowed a current of 2 A to flow. The voltage current characteristics in this real case are therefore in between those obtained with the laboratory bench. Consequently, it was deemed interesting to investigate which behavioural law could fit those data to serve as a model for railway engineers.  
For each frequency and intensity, a nonlinear regression of \(U=f(I)\) was performed over several periods, containing around 2 million points. It was found empirically that the tension-current curves could be satisfyingly approximated by the following nonlinear law:  
\[U=a\;exp(bI)+c\;exp(dI) \tag{1}\]  
Figure 6: Comparison between the experimental results (**left**) for \(I=3\)A and the proposed nonlinear model (**right**) for the \(U=f(I)\) characteristics at \(f=230\) Hz (**above**) and \(f=2300\) Hz (**below**).  
where \(a\), \(b\), \(c\), and \(d\) are the regression parameters, while \(U\) and \(I\) are the contact tension and the current through the contact, respectively. The nonlinear regression was carried out using the nonlinear least-squares solver function in MATLAB (R2022b).  
In practice, it was found that \(c\cong-a\) and \(d\cong-b\); consequently, (1) can be simplified as follows:  
\[U=2a\ \text{sinh}(bI) \tag{2}\]  
Figure 6 shows how, at low frequencies (230 Hz and 2300 Hz), the nonlinear model proposed in (2) accurately fits the experimental \(U=f(I)\) series. The estimated coefficients \(a\) and \(b\) are given in Table 1. The experimental series chosen in this example exhibit very similar behaviour to those in Figure 3.
## 3 Results and Discussion
### Optimistic Scenario  
In positive conditions of the political environment, the \(SEM_{f}\) indicator reaches the highest value--up to 100%--and the lowest value of 20% (Figure 5). This situation may occur in the case of the dynamic development of renewable energy sources due to a favorable energy policy, as indicated by the high level of demand for rare earth elements. Due to this, even in conditions of high demand for primary energy, the \(SEM_{f}\) indicator does not reach 0%.  
The political factor was also taken into account in the research presented in the literature [26; 35; 36]. The results confirmed that political factors have a major impact on the level of energy security. However, only the energy security index value was calculated. The authors created alternative scenarios for Poland's energy security index: pessimistic, optimistic, and the most probable, depending on the conditions of the political environment, instead of relying on measurements obtained by quantitative and statistical methods [37; 38; 39], which are currently dominant in the literature. This is especially important in a rapidly changing, turbulent market and political environment.  
Figure 5: Dependence of the demand for primary energy (\(ZEP\)) and rare earth elements (\(ZREE\)) on the energy security index of Poland in the situation of favorable legal status. Source: own study. blue—lowest indicator value, red—highest indicator value.
# A PID Parameter Tuning Method Based on the Improved QUATRE Algorithm
## 5 Experiment Analysis  
### Analysis of Algorithm Experimental Results  
In this paper, three algorithms were selected for testing: first, the improved QUATRE algorithm where \(N\_\text{min}=4\); \(N\_ini=\text{round}[25\log(D)\sqrt{D}]\); the dimension is 30; and \(F=0.7\). The second and third were PSO and QUATRE, where: the population number is 100; the number of iterations is 3000; and the dimension is 30. \(c_{1}=c_{2}=2\), \(w=0.6\) in PSO. \(F=0.7\). in QUATRE. The abscissa is \(nfe/100\), the ordinate is the fitness value, and the absolute error by time (ITAE) performance index is taken as the fitness function. The implicit test of the test function of CEC2013 was adopted, and the experimental results are shown in Figures 2-5.  
Figure 4: Rastrigrin function.  
Figure 3: Rotated Griewank function.  
Figure 2: Rotated Schaffer’s F7 function.  
In the rotated Schaffer's function, the algorithm began to flatten before 500 generations, and the convergence speed of the three algorithms was not much different. However, the improved QUATRE algorithm determines that the optimal solution is smaller, i.e., that the value of convergence is smaller; so under the same conditions, the optimization accuracy is higher, and the performance in this function is superior. In the rotated Griewank function, the optimization results of the improved algorithm and the standard QUATRE algorithm are evidently better than that of the PSO algorithm, and the optimization accuracy is improved. In the Rastrigin function and the Schwefel function, the optimization accuracy of the improved algorithm is improved by several orders of magnitude, and a very good fitness value is obtained.  
From the test function results--compared with the standard QUATRE algorithm and particle swarm optimization algorithm--in terms of optimization accuracy, it can be concluded from the curves of these test functions that the improved algorithm has been greatly improved, with convergence and smaller values. This was also due to the improvement of our strategies. When the particles start searching, they pay attention to the perception of the whole search space, and take into account the search development ability of the particles in the future. The result is that the particles can be closer to each other when searching. It is close to finding the solution we need. The performance of the algorithm has been enhanced. In the convergence rate of the algorithm, the improved algorithm is not good enough in some functions. The experimental results verify the feasibility and effectiveness of the improved QUATRE algorithm.