esa-sceva/satcom-chunk-collection huggingface dataset:
# Robustness Analysis for Multi-Agent Consensus Systems with Application to DC Motor Synchronization
## 3 DC Motor Speed Consensus Control  
The DC motor model employed in this work was presented in [13]  
\[\left(\frac{d}{dt}\omega_{I}\left(t\right)\right)\,J_{eq}+B_{eq,p}\,\omega_{I }\left(t\right)=A_{m}\,V_{m}(t) \tag{9}\]  
with  
\[B_{eq,p}=\frac{\eta_{g}K_{g}^{2}\eta_{m}k_{t}k_{m}+B_{eq}R_{m}}{R_{m}}\,\,,\,\,A _{m}=\frac{\eta_{g}K_{g}\eta_{m}k_{t}}{R_{m}}\]  
where \(J_{eq}=\eta_{g}K_{g}^{2}J_{m}+J_{I}\,\) and \(\,B_{eq}=\eta_{g}K_{g}^{2}B_{m}+B_{l}\). \(\omega_{I}\) is the motor angular velocity. Motor parameters employed in (9) are: \(R_{m}\) is the motor armature resistance, \(k_{m}\) is the motor back-emf constant, \(k_{t}\) is the motor current-torque constant, \(K_{g}\) is the gear ratio, \(\eta_{m}\) is the motor efficiency, \(\eta_{g}\) is the gearbox efficiency, \(J_{m}\) is the motor shaft moment of inertia, \(J_{l}\) is the load moment of inertia, \(B_{m}\) is the viscous friction on the motor shaft, and \(B_{l}\) is the viscous friction on the load shaft. The final model is obtained from (9)  
\[\dot{x}\left(t\right)\,=\alpha\,x\,\,\left(t\right)+\beta\,u\,\left(t\right) \tag{10}\]  
where \(x(t)=\omega_{I}(t)\), \(\alpha=-\frac{B_{eq,p}}{I_{eq}}\), \(\beta=\frac{A_{m}}{I_{eq}}\), and \(u(t)=V_{m}(t)\), which is designed to compensate the dynamics as follows:  
\[u\left(t\right)\,=\beta^{-1}(-\alpha\,x\,\,\left(t\right)+\bar{u}(t)) \tag{11}\]  
where \(\bar{u}(t)\) is the control law obtained in the following sections.  
Although multi-agent consensus control can be used to synchronize any number of DC motors, for simplicity, we illustrate the application of the consensus control on a three DC-motor system communicating over a network with cyclic topology.
## 5 Conclusions  
This paper proposes a short-term load forecasting method based on a VMD and GRU-TCN combined network, which effectively solves the problem of low accuracy of traditional forecasting models due to the high randomness and non-stationarity of original load data. The variational modal decomposition is used to decompose the noisy original load sequence data into intrinsic IMF modal components with different frequencies and amplitudes, which can effectively reduce the complexity of the original time-series data. The gated recurrent unit (GRU) and temporal convolutional network (TCN) are used to extract, train and predict the IMF modal components. The simulation results show that the combined method has a certain degree of improvement in the prediction accuracy compared with the single prediction model.  
However, there are some limitations of the proposed method in this paper. (1) The future work will focus on the coordination mechanism of the combined neural network. The forecasting results of different IMF models based on TCN and GRU will be linearly combined together for the result of electrical load forecasting, and the adaptive combined method will be a more suitable strategy. (2) From Table 3, which shows a comparison with the VMD-TCN method, the proposed model needs more time to obtain a better result. Thus, we will build a parallel computing framework for the proposed method in future work.  
Data curation, Y.L.; Formal analysis, T.Z.; Resources, Z.S.; Software, Y.H.; Writing--original draft, C.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by \"National Natural Science Foundation of China, grant number 51607057\", \"The Fundamental Research Funds for the Central Universities, grant number 2020B22514\"and \"The open funding of Jiangsu Key Laboratory of Power Transmission & Distribution Equipment Technology, grant number 2021 JSSPD07\".  
Not applicable.  
The authors declare no conflict of interest.
# Development of Heavy Metal Potentiostat for
## 2 Methodology
### Signal Generation and Processing  
The HMstat has been designed in such a way that it can perform two types of measurement. One is the measurement for performance tests, and the second is for heavy metal measurement. Three different types of signals were designed for the performance test, which were the constant potential, ramp potential, and square wave potential. For heavy metal measurement, a square wave anodic stripping voltammetry (SWASV) signal was designed. Basically, the SWASV signal is the incorporation of the constant, ramp, and square wave potential signal.  
These signals were generated and configured in the CSC using graphical programming language. The development of the graphical programs is depicted in the flowchart, as illustrated in Figure 3. Based on the figure, once the program has been turned on, the user must choose to perform the performance test or heavy metal measurement test. If the performance test is chosen, the user must set the performance test parameters and then, press the \"Start performance test\" button. The generated \(V_{ap}\) is applied to the PRCC by a mini system port (MSP) through analog output zero (AO0) and then, the performance test is implemented. At the same time, the data acquisition of \(V_{in(m)}\) and \(V_{out(m)}\) is to be done from the PRCC through MSP analog input zero (AI0) and one (AI1), respectively. Once the test is finished, the data are saved as xlsx file. In addition, the test can be aborted at any moment by pressing the \"Stop test\" button. Meanwhile, if heavy metal measurement is chosen, the user will undergo a similar sequence as done for the performance test.  
Figure 3: Flow chart of graphical program for signal generation (apply potential, \(V_{in}\)) and acquisition (measured input potential, \(V_{in(m)}\) and measured output potential, \(V_{out(m)}\)).
## 2 Materials and Methods
### Model Overview
\[\mathrm{sR_{10}}=\left\{ \begin{array}{c}1\\ \frac{\mathrm{GAL}}{\mathrm{GAL}_{\mathrm{max}}\times\mathrm{C_{s}}}\\ \end{array} \right. \tag{13}\]  
\[\mathrm{RUE}=0.28\times\mathrm{\ e}^{\frac{\mathrm{R_{eff}}}{\mathrm{R_{g}}} \times 1.54} \tag{14}\]  
\[\mathrm{fELUE}=\mathrm{RUE}\ \times\mathrm{ELUE} \tag{15}\]  
\[\mathrm{GPP}=\mathrm{APAR}\ \times\ \mathrm{F_{T}T_{a}}\times\mathrm{fELUE}\ \times\ \mathrm{sR_{10}} \tag{16}\]  
\(\mathrm{R_{eff}/R_{g}}\) is highly correlated with the \(\mathrm{R_{g}/R_{a}}\) where \(\mathrm{R_{eff}}\) is the diffuse fraction of the radiation, \(\mathrm{R_{a}}\) is the extra-terrestrial radiation and \(\mathrm{R_{g}}\) is the global radiation downwards. \(\mathrm{R_{eff}/R_{g}}\) is computed using the equations as suggested by [48]. Net Primary Productivity (NPP) is calculated as the difference between GPP and autotrophic respiration (\(\mathrm{R_{a}}\)) [13], estimated following [49]. This approach separates \(\mathrm{R_{a}}\) into two components--maintenance (\(\mathrm{R_{m}}\)) and growth (\(\mathrm{R_{g}}\)) respiration as shown in Equations (17)-(20) [25; 32]. \[\mathrm{Rm}=\mathrm{NPPpre}\ \times\mathrm{mR}\ \times\ \mathrm{sR_{10}} \tag{17}\]  
\[\mathrm{mR}\ =\mathrm{R_{10}}\times\ \mathrm{Q_{10}}\bigg{(}\frac{\mathrm{T_{a} }-10}{10}\bigg{)} \tag{18}\]  
\[\mathrm{Rg}=(1-\mathrm{Y_{G}})\times(\mathrm{GPP-Rm}) \tag{19}\]  
\[\mathrm{NPP}=\mathrm{GPP-(Rm+Rg)} \tag{20}\]  
Net ecosystem exchange (NEE) is computed as the difference between NPP and heterotrophic respiration (\(\mathrm{R_{h}}\)), calculated as follows  
\[\mathrm{Rh}=\mathrm{a}\times\mathrm{e}^{\mathrm{b}\ \times\mathrm{T_{s}}} \tag{21}\]  
\[\mathrm{NEE}=\mathrm{NPP-Rh} \tag{22}\]  
\[\mathrm{T_{s}}\]  
is the soil temperature. \(\mathrm{Reco}=\mathrm{Ra}+\mathrm{Rh}\) (23)  
Ecosystem respiration (\(\mathrm{R_{eco}}\)) is calculated as the sum of autotrophic (\(\mathrm{Ra}\)) and heterotrophic (\(\mathrm{Rh}\)) respiration. The list of all parameters employed in the model are outlined in the Supplementary Material Tables S1 and S2.
## 5 Discussion
### Implication for Tight Oil Recovery  
The pore structures have a crucial influence on the fluid-dynamic behavior of tight sandstone reservoirs by governing their storage space and flow capacity, thereby impacting the reservoir quality (e.g., porosity and permeability) and oil recovery [23]. The flow capacity is enhanced as the pore-throat size increases and pore-size distribution improves. Conversely, the complex micropore-microthroat networks and heterogeneity in tight oil reservoirs severely limit the fluid mobility, hydrocarbon accumulation, and enhancement of oil recovery [80]. In heterogeneous tight sandstones, identifying key fluid flow unitsthrough multi-scale and quantitative pore structure parameters can provide a scientific basis for methods such as precision hydraulic fracturing, chemical flooding, and nano-assisted flooding, thereby markedly improving oil recovery.  
The Type A pore structure provides low-resistance channels for fluids, significantly enhancing the permeability and oil productivity of the reservoirs. The coarse pores and wide throats create low capillary entry pressures and high absolute permeability, enabling an efficient hydrocarbon flow and typically higher initial production rates. The fluid mobility and oil recovery of the Type B pore structure show a moderate level. A balanced pore-throat geometry delivers moderate capillary pressures alongside reasonable connectivity, supporting both storage and flow properties that favor sustained oil recovery under conventional water flooding or a gas injection. In the Type C pore structure, although medium-sized throats can form flow channels, the reduced pore volumes limit the total storage and raise the heterogeneity, leading to increased residual oil saturation and requiring targeted displacement strategies to improve the tight oil recovery. The fluid-filling capacity is governed by capillary entry pressure: the lower the capillary pressure, the easier for fluid to fill. The coarse throats in the Type D pore structure markedly reduce the entry pressure. Therefore, despite exhibiting only medium pore sizes, the reservoirs display an excellent flow capacity and correspondingly enhanced tight oil production rates. The narrow throats in the Type E pore structure increase the capillary pressures, generating strong Jamin effects, which impedes the spontaneous imbibition [81]. Consequently, both water and oil flooding efficiencies are markedly reduced and oil recovery is correspondingly limited. The Type F pore structures are mainly composed of micro-nano pores, with narrow and dispersed throats, which are unfavorable for the migration and accumulation of oil and gas [82]. The combined fine-pore and fine-throat network almost blocks the conventional displacement flow. It is necessary to rely on high-pressure hydraulic fracturing or nano-modified displacement agents to improve connectivity and enhance oil recovery.
## 5 Correlations
#### Logarithmic model:  
\[Nu_{est}=-0.649939\ln Nb-0.261244\ln Nt-0.273526,\;\text{with}\;R^{2}=97.41\% \tag{18}\]  
and residual standard error \(0.0481435\)  
Equation (16) implies that an increase in both \(Nb\) and \(Nt\) leads to a decrease in \(Nu_{est}\). These results are consistent with our graphical results (see Figure 10a). However, the interactive and quadratic effects of \(Nb\) and \(Nt\) are favorable for \(Nu_{est}\) (see Equation (17)). Further, the quadratic model has a more precise fit for the Nusselt number than the linear and logarithmic models.  
This exercise was reiterated to present the models for \(Nu_{r}\) and \(Sh_{r}\) as a function of \(Nb\), \(Nt\), \(Ma\), and \(Q_{E}\). Now \(Nu_{r}\) and \(Sh_{r}\) are estimated for 1296 sets of values of \(Nb\), \(Nt\), \(Ma\), and \(Q_{E}\) in the range \(0.1\leq Nb\), \(Nt\leq 0.4\), \(0.1\leq Ma\leq 0.5\), and \(0\leq Q_{E}\leq 0.4\). The linear and quadratic regressions were performed on the outcome and recorded in Table 2.  
Table 2 shows that an increase in \(Nb\), \(Nt\), \(Q_{E}\), and \(Ma\) leads to an increase in \(Sh_{est}\). However, the interactive effects of \(Nb\) and \(Nt\) are favorable for \(Sh_{est}\). The Marangoni number is positively correlated to \(Nu_{est}\) and \(Sh_{est}\). Furthermore, the quadratic model has a more accurate fit to both \(Nu_{est}\) and \(Sh_{est}\) than the linear model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Correlations for \(Nu_{est}\)**} \\ \hline \multicolumn{2}{c}{**Type**} & \multicolumn{2}{c}{**Model**} \\ \hline \multirow{3}{*}{**Linear**} & \(1.945542 Ma-1.020937Q_{E}-1.960794 Nb-0.775818 Nt+0.975552\) \\ \cline{2-3}  & **Adjusted \(R^{2}\)** & \(90.9\%\) & **Residual Standard Error** \\ \hline \multirow{3}{*}{**Quadratic**} & \(3.517448 Nb^{2}+1.076601 Nt^{2}-0.191755Q_{E}^{2}\) \\  & \(-3.442968 Ma^{2}+3.372623 NbNt-1.801812 MaNt\) \\  & \(+2.075881 NbQ_{E}+1.817708 MaQ_{E}+4.098234 Ma\) \\  & \(-2.008518Q_{E}-4.977851 Nb-1.616731 Nt+1.2532640\) \\ \cline{2-3}  & **Adjusted \(R^{2}\)** & \(96.22\%\) & **Residual Standard Error** \\ \hline \multicolumn{3}{c}{**Correlations for \(Sh_{est}\)**} \\ \hline \multicolumn{3}{c}{**Type**} & \multicolumn{2}{c}{**Model**} \\ \hline \multirow{3}{*}{**Linear**} & \(4.741571 Ma+0.509317Q_{E}+1.206153 Nb+0.465005 Nt+1.509320\) \\  & **Adjusted \(R^{2}\)** & \(93.50\%\) & **Residual Standard Error** \\ \hline \multirow{3}{*}{**Quadratic**} & \(0.624259 Nt^{2}-8.412765 Nb^{2}-5.381747 Ma^{2}\) \\  & \(+0.172606Q_{E}^{2}+0.838207 NbNt-0.797004 MaNt\) \\ \cline{1-1}  & \(-3.985166 NbQ_{E}-1.503554 MaQ_{E}+8.470582 Ma\) \\ \cline{1-1}  & \(+1.887632Q_{E}+6.000017 Nb+0.182425 Nt+0.427243\) \\ \cline{1-1} \cline{2-3}  & **Adjusted \(R^{2}\)** & \(97.14\%\) & **Residual Standard Error** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Correlations for \(Nu_{est}\) and \(Sh_{est}\).
## 10 Conclusions and Future Work  
This paper proposes an integrated validation framework that combines digital twin, Software-in-the-Loop, and Hardware-in-the-Loop technologies, specifically tailored for automotive headlamp systems. The study contributes a layered architecture model, a structured requirement-to-validation traceability approach, and scenario-based validation examples that align with industry practices and standards.  
The framework emphasizes the transition from fragmented test stages to a unified validation pipeline that supports predictive, modular, and simulation-driven engineering. The use of conceptual validation chains and synthetic examples illustrates the practical relevance of the approach, even in the absence of physical prototyping.  
However, the study has several limitations. First, it does not include empirical implementation results or a full pilot case study. The validation scenarios are demonstrative, although grounded in realistic automotive challenges. Furthermore, the evaluation does not yet cover subjective metrics, such as visual comfort or real-time driver feedback, which are increasingly important in lighting system performance.  
Future research should focus on implementing the proposed framework within an industrial development project, allowing for quantitative performance assessment and real-world system integration. Additionally, research should explore the inclusion of human-in-the-loop simulations, cognitive feedback, and AI-assisted edge case generation. These extensions will help refine digital twin-based validation workflows into operationally relevant tools for both OEMs and regulatory stakeholders.  
**Author Contributions:** Conceptualization, G.B., P.N. and E.S.; methodology, G.B., P.N. and E.S.; software, G.B. and E.S.; validation, E.R.Z. and A.S.; formal analysis, G.B.; investigation, G.B., P.N. and E.S.; resources, G.B., P.N. and E.R.Z.; data curation, E.S.; writing--original draft preparation, G.B. and E.S.; writing--review and editing, G.B., P.N., E.R.Z., E.S., D.-D.L. and A.S.; visualization, D.-D.L.; supervision, D.-D.L.; project administration, A.S.; funding acquisition, A.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research paper was supported by the \"Boosting Ingenium for Excellence\" (BI4E) project, funded by the European Union's HORIZON-WIDERA-2021-ACCESS-05-01-European Excellence Initiative under the Grant Agreement No. 101071321.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflicts of interest.
## 5 Simulation Analysis
### Details and Results of the Third Simulation Condition  
Suppose that the extraction operation is the inverse process of the insertion. Then, an extraction simulation condition is designed based on the first simulation condition.  
The expected trajectory and output force are, respectively, designed as:  
\[\mathbf{X}_{d}=\left\{\begin{array}{ll}[\ 0\ \mathrm{rad},\ \ 2.604\ \mathrm{m},\ \ 0.1\ \mathrm{m},\ \ \ \mathrm{\pi rad}\ \ ]^{\mathrm{T}}&0\leq t<3\\ [\ 0\ \mathrm{rad},\ \ 2.604\ \mathrm{m},\ \ (0.16-0.02t)\ \mathrm{m},\ \ \mathrm{\pi rad}\ \ ]^{\mathrm{T}}&3\leq t<13\end{array}\right., \tag{43}\]  
\[\mathbf{F}_{\mathrm{td}}=\left\{\begin{array}{ll}[\ 0\ \mathrm{N}\cdot\mathrm{m},\ \ 0\ \mathrm{N},\ \ 0\ \mathrm{N},\ \ 0\ \mathrm{N}\cdot\mathrm{m}\ ]^{\mathrm{T}}&0\leq t<3\\ [\ 0\ \mathrm{N}\cdot\mathrm{m},\ \ 0\ \mathrm{N},\ \ (5(t-6))\ \mathrm{N},\ \ 0\ \mathrm{N}\cdot\mathrm{m}\ ]^{\mathrm{T}}&3\leq t<8\\ [\ 0\ \mathrm{N}\cdot\mathrm{m},\ \ 0\ \mathrm{N},\ \ 20\ \mathrm{N},\ \ 0\ \mathrm{N}\cdot\mathrm{m}]^{\mathrm{T}}&8\leq t<13 \end{array}\right., \tag{44}\]  
The setting of simulation parameters is consistent with that in Section 5.1 The results of extraction condition are shown in Figures 15-18. Different from the two previous working conditions, the trajectories shown in Figure 15b,c and Figure 17 belong to the manipulator end without the replaceable instrument.  
In Figure 15c, the manipulator end effector clamps the target and executes the extraction mission at 8 s. In addition, completes the extraction mission at 13 s with a setup of constant friction.  
Figure 16a-c are the joint tracking curve of space robot. The extracting operation is executed at 8 s. Taking t = 8 s as the central axis, it can be found that the joint trajectories at 3-8 s and 8-13 s are symmetrical. In addition, this is consistent with the setting in the extracting work condition.  
Figure 17 shows the XY two-dimensional trajectory of manipulator end without replaceable instruments. Figure 18 is the tracking curve of output force of the end.  
The same conclusions can be analyzed by the extraction comparison results in Section 5.3. These results of three simulating conditions consistently illustrate that the advantages of our proposed algorithm from multiple aspects. It is worth mentioning that the transient performance of PPC controller is much better than that of SMC controller.  
Figure 14: Output force of space robot end tracking curve of on-orbit insertion operation with friction change.  
Figure 16: Joint trajectory tracking curve of on-orbit extraction operation. (**a**) The joint \(O_{1}\). (**b**) The joint \(O_{2}\). (**c**) The joint \(O_{3}\).  
Figure 15: Space robot end trajectory tracking curve of on-orbit extraction operation. (**a**) The carrier attitude. (**b**) The X-direction position. (**c**) The Y-direction position. (**d**) The space robot end attitude.
## Appendix A  
In this appendix, it is shown that Equation (25) can be derived from Equation (88). For this purpose, first, two relationships need to be stated that follow from the following well-known _matrix inversion lemma_: Let \(\mathsf{A}\) denote an invertible square matrix of dimensions \((m\times m)\), let \(\mathsf{B}\) denote a matrix of dimensions \((m\times n)\), and let \(\mathsf{C}\) denote an invertible square matrix of dimensions \((n\times n)\); then, it holds true that  
\[\big{(}\mathsf{A}\pm\mathsf{B}\mathsf{C}\mathsf{B}^{\mathsf{T}}\big{)}^{-1}= \mathsf{A}^{-1}\mp\mathsf{A}^{-1}\mathsf{B}\big{(}\mathsf{C}^{-1}\pm\mathsf{B }^{\mathsf{T}}\mathsf{A}^{-1}\mathsf{B}\big{)}^{-1}\mathsf{B}^{\mathsf{T}} \mathsf{A}^{-1} \tag{10}\]  
and  
\[\big{(}\mathsf{A}\pm\mathsf{B}\mathsf{C}\mathsf{B}^{\mathsf{T}}\big{)}^{-1} \mathsf{B}\mathsf{C}=\mathsf{A}^{-1}\mathsf{B}\big{(}\mathsf{C}^{-1}\pm \mathsf{B}^{\mathsf{T}}\mathsf{A}^{-1}\mathsf{B}\big{)}^{-1}. \tag{11}\]  
After rearranging, Equation (88) consists of two terms, one containing \(\mathbf{\chi}_{t-1|t-1}\) and the other containing \(\mathbf{\mathsf{y}}_{t}\):  
\[ \begin{split}\mathbf{\chi}_{t|t}&=\big{(}\mathbf{\Omega}_{t} \mathsf{A}_{t}-C_{t}^{\mathsf{T}}\mathbf{\Sigma}_{t}^{\mathsf{T}}\mathbf{\Lambda}_{t} \big{)}\big{(}\mathsf{F}_{t-1|t-1}+\mathsf{A}_{t}^{\mathsf{T}}\mathbf{\Omega}_{t} \mathsf{A}_{t}\big{)}^{-1}\mathbf{\chi}_{t-1|t-1}\\ &\quad+\big{(}\big{(}C_{t}^{\mathsf{T}}\mathbf{\
abla}_{t}-\mathbf{ \Sigma}_{t}\big{)}+\big{(}\mathbf{\Omega}_{t}\mathsf{A}_{t}-C_{t}^{\mathsf{T}}\mathbf{ \Sigma}_{t}^{\mathsf{T}}\mathbf{\Lambda}_{t}\big{)}\big{(}\mathsf{F}_{t-1|t-1}+ \mathsf{A}_{t}^{\mathsf{T}}\mathbf{\Omega}_{t}\mathsf{A}_{t}\big{)}^{-1}\mathsf{A }_{t}^{\mathsf{T}}\mathbf{\Sigma}_{t}\big{)}\mathbf{y}_{t}.\end{split}  \tag{12}\]  
Equation (25) has the same structure:  
\[ \begin{split}\mathbf{\chi}_{t|t}&=\big{(}\mathsf{I}^{(m)} +\mathsf{G}_{t}^{\mathsf{T}}\mathbf{\Gamma}_{t}\mathsf{S}_{t}^{\mathsf{T}}\mathbf{ \Theta}_{t}\mathsf{A}_{t}\big{(}\mathsf{F}_{t-1|t-1}+\mathsf{A}_{t}^{\mathsf{T} }\mathbf{\Theta}_{t}\mathsf{A}_{t}\big{)}^{-1}\mathbf{\chi}_{t-1|t-1}\\ &\quad+\mathsf{G}_{t}^{\mathsf{T}}\mathbf{\Gamma}_{t}\mathbf{y}_{t}, \end{split}  \tag{13}\]  
so the coefficient matrices of these terms can be studied separately. Note that  
\[\mathbf{\Omega}_{t}=\mathbf{\Theta}_{t}+\mathbf{\Theta}_{t}\mathsf{S}_{t}\mathbf{\Psi}_{t} \mathsf{S}_{t}^{\mathsf{T}}\mathbf{\Theta}_{t}, \tag{14}\]  
where Equations (8), (9), and (10) have been used.
# A Multi-Resolution Approach to GAN-Based Speech Enhancement
## 4 Experimental Settings
### Evaluation Methods  
#### 4.3.1 Objective Evaluation  
The quality of the enhanced speech was evaluated using the following objective metrics:  
* PESQ: Perceptual evaluation of speech quality defined in the ITU-T P.862 standard [19] (from \(-0.5\) to \(4.5\)),
* STOI: Short-time objective intelligibility [20] (from 0 to 1),
* CSIG: Mean opinion score (MOS) prediction of the signal distortion attending only to the speech signal [39] (from 1 to 5),
* CBAK: MOS prediction of the intrusiveness of background noise [39] (from 1 to 5),
* COVID: MOS prediction of the overall effect [39] (from 1 to 5).