esa-sceva/satcom-chunk-collection huggingface dataset:
# Plant Electrical Signal Classification Based on Waveform Similarity
## 4 Results
### Classification Results of Deep Learning Method  
To make the length of all waveforms same, the 329 AP and non-AP waveforms were aligned at the peak points of these waveforms, then all waveforms are extended on the left and right of the peak.  
As similar to Section 4.4, two-thirds of the dataset were randomly selected to train the DBN, and one-third of data were for testing. The 10-fold cross validation was used to train the data.  
To get a better classification performance, we tried different network structure settings as shown in Table 9. For three hidden layers, the best performance is 77.4% which is corresponding to multiple optional parameter settings. For four hidden layers, the best performance is 77.4% too. By comparing different numbers of hidden layers and units, we got the highest accuracy of 77.4%.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Kernel Function** & \multicolumn{2}{l}{**Range of**} & \multicolumn{1}{l}{**Interval**} & \multicolumn{1}{l}{**Selected**} & \multicolumn{1}{l}{**Highest**} \\  & \multicolumn{1}{l}{**Parameters**} & \multicolumn{1}{l}{**Accuracy**} & \multicolumn{1}{l}{**Accuracy**} \\ \hline Quadratic kernel \(\left[\left(x_{i}\cdot x_{j}\right)+1\right]^{b}\) & \(b=2\) & \(0\) & \(b=2\) & 62.96\% \\ Polynomial kernel \(\left[\left(x_{i}\cdot x_{j}\right)+1\right]^{b}\) & \(b=3\) & \(0\) & \(b=3\) & 74.07\% \\ Gaussian Radial Basis Function \(\exp(-\frac{\left|x_{i}-x_{j}\right|^{2}}{2\sigma^{2}})\) & \(\sigma=\left[0.1,3\right]\) & \(0.1\) & \(\sigma=1.9\) & 77.59\% \\ Sigmoid kernel \(\tanh(\gamma\times(x_{i}-x_{j})+c)\) & \(\gamma=\left[0.1,5\right]\) & \(0.1\) & \(\gamma=0.1\)\(c=-0.3\) & 78.17\% \\ \hline \hline \end{tabular}
\end{table}
Table 8: Different kernel functions for classification.  
Figure 9: (a) First two principle components scatter plot; (b) First three principle components scatter plot.
# Best Relay Selection Strategy in Cooperative Spectrum Sharing Framework with Mobile-Based End User
## Appendix B Derivation of \({F_{{\gamma}_{R_{k}D}}}\)(\(\gamma\)/\({\gamma_{Sp}}\))  
To obtain the conditional CDF of the second hop, let \(Z=\left|h_{R_{k}D}\right|^{2}\). Hence,  
\[F_{{\gamma}_{R_{k}D}}(\gamma/Y_{Sp})=P_{r}\Bigg{(}\frac{Id_{2}Z}{\left|h_{R_{ k}P}\right|^{2}}\leq\gamma\Bigg{)}=P_{r}\Bigg{(}Z\leq\frac{\gamma|h_{R_{k}P}|^{2}}{ \bar{I}d_{2}}\Bigg{)}=\int_{0}^{\infty}\int_{0}^{z=\frac{\gamma t}{\bar{I}d_{ 2}}}f_{Z,\left|h_{R_{k}P}\right|^{2}}(z,t)dzdt \tag{14}\]  
It cannot be missed out that the fading coefficient channels \(\left|h_{R_{k}D}\right|^{2}\) and \(\left|h_{R_{k}P}\right|^{2}\) are independent. Thus, the joint PDF can be expressed as:  
\[f_{Z,\left|h_{R_{k}P}\right|^{2}}(z,t)=f_{Z}(z)f_{\left|h_{R_{k}P}\right|^{2} }(t) \tag{15}\]  
Therefore, the conditional CDF of the second hop, \(F_{{\gamma}_{R_{k}D}}(\gamma/Y_{Sp})\), can be written as follows:  
\[F_{{\gamma}_{R_{k}D}}(\gamma/Y_{Sp})=\int_{0}^{\infty}F_{Z}\bigg{(}\frac{ \gamma t}{\bar{I}d_{2}}\bigg{)}f_{\left|h_{R_{k}P}\right|^{2}}(t)dt \tag{16}\]  
Using the CDF given in Equation (6) and the PDF given in Equation (5), Equation (16) can be rewritten as follows:  
\[F_{{\gamma}_{R_{k}D}}(\gamma/Y_{Sp})=\int_{0}^{\infty}\Bigg{[}\frac{2F_{1}( m,m;1+m;1)}{m\beta(m,1-m)}-\frac{\Gamma(1-m)}{\beta(m,1-m)}\bigg{(}\frac{ \gamma t}{\bar{I}d_{2}}\bigg{)}^{\frac{m-1}{2}}e^{-\frac{\gamma t}{\bar{ \gamma}d_{2}}}W_{\frac{m-1}{2},\frac{\gamma t}{\bar{\gamma}d_{2}}}\Bigg{)} \bigg{]}\big{(}\lambda_{R_{k}}pe^{-\lambda_{k}p^{t}}\big{)}dt=I_{1}-I_{2} \tag{17}\]  
where  
\[I_{1}=\int_{0}^{\infty}\frac{2F_{1}(m,m;1+m;1)}{m\beta(m,1-m)}\Big{(}\lambda_ {R_{k}P}e^{-\lambda_{R_{k}P}t}\Big{)}dt=\frac{2F_{1}(m,m;1+m;1)}{m\beta(m,1-m)} \tag{18}\]and  
\[I_{2}=\frac{\Gamma(1-m)\lambda_{R_{k}P}}{\beta(m,1-m)}\left(\frac{\gamma}{\bar{ \gamma}Id_{2}}\right)^{\frac{m-1}{2}}\int_{0}^{\infty}t^{\frac{m-1}{2}}e^{-t \left(\frac{\gamma}{2\bar{\gamma}Id_{2}}+\lambda_{R_{k}P}\right)}W_{\frac{m-1}{2 },\frac{m}{2}}\left(\frac{\gamma t}{\bar{\gamma}Id_{2}}\right)dt \tag{115}\]  
Using Equation (7.621.3) [63] and after a few mathematical manipulations, \(I_{2}\) can be written as:  
\[I_{2}=m\lambda_{R_{k}P}\left(\frac{\gamma}{\bar{\gamma}Id_{2}}\right)^{m} \left(\frac{\gamma}{\bar{\gamma}Id_{2}}+\lambda_{R_{k}P}\right)^{-m-1}{}_{2}F_ {1}\left(m+1,1;2;\frac{1}{1+\frac{\gamma}{\lambda_{R_{k}P}\bar{\gamma}Id_{2}}}\right) \tag{116}\]  
Substituting Equations (114) and (116) into Equation (113), \(F_{\gamma R_{k}D}(\gamma/Y_{SP})\) can be obtained and expressed as follows:  
\[F_{\gamma_{R_{k}D}}(\gamma/Y_{SP})=\frac{2F_{1}(m,m;1+m;1)}{m\beta(m,1-m)}- \psi_{\tau_{k}p_{\tau}d_{\tau}}(\gamma) \tag{117}\]  
where \(\psi_{\tau_{k}p_{\tau}d_{\tau}}(\gamma)=I_{2}\).
# Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing
## 1 Introduction
So, the null hypothesis \(H_{0}\) is rejected or not at a certain significance level, comparing a fuzzy statistic \(\widetilde{U}\) constructed by a proper fuzzy estimator with fuzzy critical values \(\widetilde{CV}_{i}\), created using probabilistic concepts. In [30], this approach is generalized using fuzzy statistics produced by non asymptotic fuzzy estimators (see [31]) and a degree of rejection or acceptance of the null hypothesis. As it is proved in [32], the possibility distribution (see [2]) induced by confidence intervals around the mode is identical to the one obtained by the maximal specificity probability-possibility transformation. Based on this principle, we develop in this paper possibilistic fuzzy statistical tests of crisp hypotheses, which lead to a possibility of rejection or acceptance of the null hypothesis for cases in which both the hypothesis and the data are crisp, whereas the other fuzzy tests (for example, those of [12]) give crisp results when applied in such cases. This paper is organized as follows. The next section is concerned with classical hypotheses testing. In Section 3, we present the concept of fuzzy estimators and, also, find out that in the examples of [29; 33; 34; 35], the unbiased fuzzy estimator of the variance \(\widetilde{\sigma_{it}^{2}}\) introduced in [29] is not implemented as described there and propose its correct implementation. In Section 4, we develop possibilistic hypothesis tests for cases in which both the data and the hypotheses are crisp. In Sections 5-7, we present fuzzy hypothesis tests about the mean and the variance, and compare their results as well as the results of the respective tests developed in [29; 30] with those of crisp statistics (Examples 2 and 3).
## 3 JPRL-Based Joint Resource Allocation Approach
### P-MADDPG-Based Uplink Power Allocation
16: Store transition with bandwidth allocation \(\left(\mathcal{S}_{t},\mathcal{A}_{t}^{p},\mathcal{S}_{t+1},R_{t}\right)\) in \(\mathcal{D}1\). 17: Store transition \(\varphi\) with power allocation \(\left(\mathcal{S}_{t},\mathcal{A}_{t}^{p},\mathcal{S}_{t+1},R_{t},V_{t}^{ \varphi}\right)\) in \(\mathcal{D}2\). 18:if Both \(\mathcal{D}1\) and \(\mathcal{D}2\) are full then
19: Sample a mini-batch of transition from \(\mathcal{D}1\). 20: Sample a mini-batch of transition from \(\mathcal{D}2\) according to sample importance. 21: Compute the action-value function of MADDQN and P-MADDPQ according to Equations (9) and (14), respectively. 22: Update evaluated Q network of MADDQN by Equation (10). 23: Update actor online network by Equation (15). 24: Update critic online network by Equation (19). 25: Update the MADDQN and P-MADDPG networks by soft updating. 26:endif
27:endfor
```  
**Algorithm 1** JPRL method for joint bandwidth and power allocation  
For a mini-batch with \(D\) samples, directly traversing the experience buffer \(\mathcal{D}2\) for sampling requires \(D\) times, and the complexity is intolerable. To tackle this matter, a sum-tree frame is designed for \(\mathcal{D}2\), where the sample \(\varphi\) is stored with the sampling probability \(P_{t}^{\varphi}\). As shown in Figure 2, the structure is a binary tree with a root node at the top, and there are only two child nodes for each node of the upper level. For the leaf nodes at the bottom, the tuple \(\left(\mathcal{S}_{t},\mathcal{A}_{t}^{p},R_{t},\mathcal{S}_{t+1},V_{t}^{ \varphi}\right)\) of transition \(\varphi\) is stored with its probability according to Equation (16). Note that the value of each node is the sum of its child nodes' value. We divided the value of the root node (the sum of the probabilities of all samples) into \(D\) segments, which have an equal interval. In each interval, a random value, which is no more than the range of the interval generated to backtrack the leaf node from top to bottom. The specific backtracking rules are listed as follows, until the leaf node is selected, if the random value is less than or equal to the value of the left child node, and we continue backtracking from left child node; otherwise, we continue backtracking from the right child node and calculates the difference between this value and the value of the left child node as the basis for the next backtracking. Then, the critic and actor networks are updated by the selected transition samples. The proposed JPRL method is summarized in Algorithm 1.
## 2 Materials and Methods
### Data Pre-Processing and Feature Extraction
#### 2.2.2 Noise Reduction  
Signals data usually contain unwanted components resulting from sensor drift over time caused by the wearer's movements. To ensure accurate analysis, calibration adjustments and filtering techniques are commonly used. As a means of removing the noise of the captured data, a median filter with eleven taps was used [24]. The median filter effectively  
Figure 2: End-to-end workflow of setting up IMU sensors [38] on a human subject, synchronizing the sensors, capturing the data, and exporting them for detailed analysis.  
smooths data by replacing each data point with the median value of its surrounding points. This technique helps to reduce noise while preserving significant details and features within the dataset [40].
# A Linear Memory CTC-Based Algorithm for Text-to-Voice Alignment of Very Long Audio Recordings
## 4 Experiments and Results
### Reference Corpora
#### 4.2.1 Speech  
For speech, we manually annotated the audio recording of a whole chapter of a publicly available audiobook. We choose the chapter 10 of _The Problems of Philosophy_, by [PERSON] ([[https://librivox.org/the-problems-of-philosophy-by-bertrand-russell-2/](https://librivox.org/the-problems-of-philosophy-by-bertrand-russell-2/)]([https://librivox.org/the-problems-of-philosophy-by-bertrand-russell-2/](https://librivox.org/the-problems-of-philosophy-by-bertrand-russell-2/)) (accessed on 31 January 2023)). This audiobook does not belong to the Librispeech's list of books, and its reader does not belong to the Librispeech's list of readers either ([[https://www.openslr.org/resources/12/raw-metadata.tar.gz](https://www.openslr.org/resources/12/raw-metadata.tar.gz)]([https://www.openslr.org/resources/12/raw-metadata.tar.gz](https://www.openslr.org/resources/12/raw-metadata.tar.gz)) (accessed on 31 January 2023)). The chapter 10 contains exactly 100 sentences and 2672 words, and the corresponding audio has a duration of 21:05 (MM:SS). The other chapters were kept for our experiments (see below).  
We first removed from the audio the Librivox preamble with the title and copyright information. Then, we performed a first alignment of the audio with the available text with our algorithm, which we used as a starting point to manually and precisely align each word to the audio. During the alignment process, we corrected a few inconsistencies between the recording and the transcription, so that text and audio match exactly. The alignment was conducted by adjusting the markers for the start of each word. We used the spectrogram representation to precisely align the start of the words with the corresponding onsets. In the following, we will refer to this spoken voice reference corpus as \"Chapter 10\".
## 3 Problem Formulation
### Objective Function  
To obtain the optimal control performance under multiple operational conditions, four tests were designed to evaluate the proposed algorithm, as follows:  
1. Case 1: Step response from close to 2% opening
2. Case 2: Step response from close to 50% opening
3. Case 3: Step response from close to 80% opening
4. Case 4: Step response from 50% to 30% opening  
The ideal performance criteria are the closed-loop system settling time, overshoot, and steady-state error, which need to be included in the objective functions. Normally, in the single-objective optimization algorithm, the objective function can be defined as \(J=\int_{0}^{\infty}e^{2}(t)dt\), i.e., the Integral of the Squared Error (ISE). However, for a system with high static friction, if the single objective function were used a large overshoot could exist in the optimized closed-loop response with minimal steady-state error. Thus, an additional objective function related to the percentage of overshoot (PO) is added to the objective function to form a multiple-objective optimization problem. Based on the preceding discussion, the two objective functions are defined below in (10):  
\[\begin{split} J_{1}&=\frac{1}{k}\sum_{i=1}^{k}P \text{O}^{i}=\frac{1}{k}\sum_{i=1}^{k}\frac{|r_{\text{peak}}^{i}-s^{i}|}{s^{i}} \\ J_{2}&=\frac{1}{k}\sum_{i=1}^{k}\int_{0}^{t_{1}}( \frac{r^{i}(t)-s^{i}}{s^{i}})^{2}dt\end{split} \tag{10}\]  
where \(i\) represents the case number and the total number of cases is \(k=4\), while \(r(t)\), \(r_{peak}\), and \(s\) are the valve position, response peak, and settling time, respectively. Note that in this case the system percentage overshoot (PO) is associated with objective \(J_{1}\) and both the settling time and steady-state error are considered in \(J_{2}\).
# A Hierarchical Fusion SAR Image Change-Detection Method Based on HF-CRF Model
## 2 Materials and Methods
### Boundary Entropy Dynamic Fusion CRF Model
* Second, sliding window with fixed block size on two image blocks \({X_{l}}^{(i)}\) and \({X_{m}}^{(i)}\) with the same position on the sharpened images \(X_{L}\) and \(X_{M}\), respectively, and calculating them based on local information entropy, as shown in Equations (8) and (9), where sub-blocks \(Q_{l}\) and \(Q_{m}\) represent the image boundary entropy values on the \(i\)-th image block \({X_{l}}^{(i)}\) and \({X_{m}}^{(i)}\) corresponding to the modalities. \[Q_{l}=-\sum_{i}p(n)\times lnp(n)\] (8) \[Q_{m}=-\sum_{j}p(n)\times lnp(n)\] (9) \begin{table}
\begin{tabular}{l c c} \hline \hline  & \(S_{x}\) & \(S_{y}\) \\ \hline The Laplacian operator & \(\begin{bmatrix}0&-1&0\\ -1&4&-1\\ 0&-1&0\end{bmatrix}\) & \(\begin{bmatrix}-1&-1&-1\\ -1&8&-1\\ -1&-1&-1\\ -1&-1&-1\\ -1&0&1\end{bmatrix}\) \\ The Prewitt operator & \(\begin{bmatrix}-1&0&1\\ -1&0&1\\ -1&0&1\end{bmatrix}\) & \(\begin{bmatrix}-1&-1&-1\\ -1&8&-1\\ -1&-1&-1\\ -1&-1&-1\\ 0&0&0\\ -1&2&1\end{bmatrix}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the three image-sharpening operators. Figure 7: Difference images of two data sets and the entropy value of respective local information. (**a**) Berne difference image. (**b**) Information entropy of Berne data. (**c**) Ottawa difference image. (**d**) Information entropy of Ottawa data. * Third, the entropy ratio method is used to calculate the log-difference modal counterpart weights \(\alpha\) and the mean-difference modal weights \(\beta\) in the mixed pair-wise potential function. \[\alpha=\frac{Q_{m}}{Q_{l}+Q_{m}},\beta=\frac{Q_{m}}{Q_{l}+Q_{m}},\text{s.t. }\left\{ \begin{aligned} &\alpha\in[0,1]\\ &\beta\in[0,1]\\ &\alpha+\beta=1\end{aligned} \right.\] (10)  
Figure 9 shows the result plots of the D-DRUNet semantic segmentation network and the HF-CRF model for detection on the Ottawa dataset. By analyzing the detection results, it can be concluded that the dynamic fusion iterative structure CRF optimization significantly reduces the false detection phenomenon, with finer change boundaries. The improved CRF model uses a multimodal fusion method to achieve information complementarity between modes, and a more accurate change-detection region is obtained. Figure 8: Two dataset showing sharpening-processing difference boundary maps. (**a**) Original difference image of Berne data. (**b**) Sharpening results with the Laplacian operator. (**c**) Sharpening results with the Prewitt operator. (**d**) Sharpening results with the Sobel operator. (**e**) Original difference image of Ottawa data. (**f**) Sharpening results with the Laplacian operator. (**g**) Sharpening results with the Prewitt operator. (**h**) Sharpening results with the Sobel operator. Figure 9: Results of different methods on Ottawa data.
# AI Chatots for Mental Health: A Scoping Review of Effectiveness, Feasibility, and Applications
## 3 Results
### Preventive Care: Targeting Eating Disorders and HIV Prevention  
The utilization of AI chatbots in preventive health and well-being interventions has been explored in studies targeting eating disorder and HIV prevention. [PERSON] et al. [67] conducted a randomized controlled trial with 700 women at high risk for eating disorders to assess the efficacy of an AI chatbot named \"Tessa.\" The chatbot delivered a cognitive-behavioral intervention aimed at preventing eating disorders, and was employed as a standalone intervention. The results showed that the intervention group had significantly greater reductions in weight and shape concerns compared to the waitlist control group, with reduced odds of developing an eating disorder. However, challenges with engagement highlight the need for further strategies to maximize the impact of such interventions.  
[PERSON] et al. [68] shifted the focus to HIV prevention and testing, conducting a beta testing study with an AI chatbot prototype among men who have sex with men (MSM) in Malaysia. The AI chatbot was designed to be a complementary tool to existing HIV prevention and testing services, aiming to provide MSM with convenient and confidential access to information and services related to HIV self-testing, venue-based HIV testing, pre-exposure prophylaxis (PrEP), and mental health resources. The chatbot was found to be feasible and acceptable, with participants rating it highly on quality, satisfaction, intention to continue using, and willingness to refer it to others. Participants valued the chatbot's ability to provide information on HIV testing, and locating testing venues in a stigma-free way that protected privacy. However, participants suggested adding more mental health information and resources, as mental health issues were a major concern for MSM. Improving the conversational flow to seem more natural was also recommended. In general, the study supported the feasibility and acceptability of using an AI chatbot for HIV services among MSM in Malaysia if tailored to the local context and cultures.
## 2 Materials and Methods
### Model Accuracy Verification  
Before the application of a model, its accuracy should be verified to confirm the closeness to a real vehicle. A comparison testing was executed separately with the real prototype vehicle and the simulation model. We used the same driving and charging cycles for both the real prototype vehicle and the simulation model to characterize the battery performance and parameters changed during charging and discharging, and then we analyzed the variations between the real vehicle and the simulation model for evaluating the model reliability. A vehicle dynamometer was used for the real vehicle testing (Supplementary Figure S6). The driving condition and charging condition were set up for the comparison testing. Battery voltage, SOC, and current were recorded and analyzed to evaluate the matching degree between the model and reality, as shown in Supplementary Figure S7.  
The difference ratio between the model and reality is defined as  
\[\textit{Difference Ratio}=\sqrt{\frac{\int_{0}^{t}\left(\frac{Value_{ model}-Value_{vehicle}}{Value_{vehicle}}\right)^{2}}{t}}\;100\% \tag{15}\]  
Using Equation (15), the difference ratio between the simulation model and the real vehicle is summarized in Supplementary Table S1. It clearly shows that the simulation model has high accuracy with the real tested pack, thus proving that this model can be used to reliably predict the battery performance in real vehicle application to provide valuable research, optimization, and scaled-up fabrication information for LSBs.
# A Novel System of Mixed RF/FSO UAV Communication Based on MRR and RIS by Adopting Hybrid Modulation
## 4 Numerical Results and Discussion
Finally in Figure 10, we illustrate the average channel capacity of the end-to-end uplink and end-to-end downlink by varying the number \(N\) of RIS reflective elements under moderate turbulence and small pointing error. It can be seen that the channel capacity of the uplink is slightly lower than that of the downlink when RIS is not available, while the channel capacity of the uplink is greater than that of the downlink with RIS. This proves that RIS has a greater improvement effect on the uplink than on the downlink. Furthermore, when \(\overline{\gamma}_{1}=5\) dB and \(N=5\), the average channel capacity is \(6.49\) bits/s/Hz and \(5.98\) bits/s/Hz for the uplink and downlink, respectively, and \(1.71\) bits/s/Hz and \(1.66\) bits/s/Hz when RIS is not present. Furthermore, the performance improvement will be more pronounced as the value of \(N\) increases. Figure 10: Average channel capacity under different \(N\) when \(\alpha=4.0\), \(\beta=1.6\), \(\xi=10\), \(\overline{\gamma}_{2}=40\) dB, \(d=5.0\) km. Figure 9: Average BER under different FSO communication distance when \(\xi=10\), \(L=32\), \(N=10\).
# Simulation and Optimisation of Utility-Scale PV-Wind Systems with Pumped Hydro Storage
## 2 Modelling Approach
### Simulation
#### 2.1.5 Water Volume in the Reservoirs  
The water volumes (m\({}^{3}\)) in the upper and lower reservoirs at the next time step are calculated as  
\[V_{UR}(t+\Delta t) =V_{UR}(t)+(Q_{P}(t)-Q_{HT}(t))\cdot\Delta t+Q_{incomes\_UR}(t), \tag{24}\] \[V_{LR}(t+\Delta t) =V_{LR}(t)+(Q_{HT}(t)-Q_{P}(t))\cdot\Delta t+Q_{incomes\_LR}(t), \tag{25}\]  
where \(Q_{incomes\_UR}(t)\) and \(Q_{incomes\_LR}(t)\) (m\({}^{3}\)) represent the incoming water minus the outgoing water from the reservoir (apart from the pump and turbine flow) for the upper and lower reservoirs, respectively, which can be calculated based on the geographical features of the area, including losses caused by evaporation and seepage.  
The maximum stored energy depends on the maximum volume of the upper reservoir and static head, and it is given by  
\[E_{stored\_max}(\text{MWh})=\frac{V_{UR\_max}(\text{m}^{3})\rho\Big{(}\frac{ \text{kg}}{\text{m}^{3}}\Big{)}g\Big{(}\frac{\text{m}}{\text{s}^{2}}\Big{)}H _{TS\_are}(\text{m})}{3.6\cdot 10^{9}\Big{(}\frac{\text{MWh}}{\text{MWh}}\Big{)}}, \tag{26}\]  
where \(H_{TS\_are}\) represents the average static head in the turbine mode.  
\[H_{TS\_are}=H_{diff}+\frac{H_{UR\_max}}{2}+\frac{H_{LR\_max}}{2}. \tag{27}\]The duration of the upper reservoir (\(Duration\)) represents the time (h) at which the upper reservoir can supply the nominal flow of the turbine (PHS time of full-capacity operation in generation mode).  
\[Duration(\mathrm{h})=\frac{V_{UR\_max}\big{(}\mathrm{m}^{3}\big{)}-V_{UR\_min} \big{(}\mathrm{m}^{3}\big{)}}{3600\big{(}\frac{\mathrm{s}}{\mathrm{h}}\big{)}Q _{HT\_N}\Big{(}\frac{\mathrm{m}^{3}}{\mathrm{s}}\Big{)}}. \tag{28}\]