esa-sceva/satcom-chunk-collection huggingface dataset:
# A Sparse Autoencoder-Based Unsupervised Scheme for Pump Fault Detection and Isolation
## 3 Experimental Data Description  
High-pressure injection pumps are widely used in the oil and petrochemical industry for oil transportation, lift and injection. Centrifugal pumps are the most common pump type. They are typically operated under high rotating speed, high pressure, and high loading conditions and thus are likely subjected to performance degradations.  
The pumps are used to move fluid through mechanical actions. To be specific, the pump's impeller rotates within the housing, reduces pressure at the inlet, and creates a vacuum. This motion then drives fluid to the outside of the pump's housing, which increases the pressure high enough to send it outside the discharge [40].  
The working conditions of the pump is linked to its mechanical action and controlling methods. According to its mechanical action, several methods have been applied to control the pump to meet the end users' requirements. The most common include throttling control, the rotational speed control, and using a sequence circuit [41]. These controlling methods adjust the flow, pressure or shaft speed of a pump to achieve expected performance. Consequently, in this paper, the flow, pressure and speed  
Figure 3: Receiver operating characteristics (ROC) curve and area under the ROC curve (AUC) value.  
are used to evaluate the pump's working conditions. The training data are selected under the same working condition as the test data.  
The data used in this paper were obtained from a multivariate condition monitoring system mounted on a high-pressure injection pump in an oil and petrochemical industry. The measurement variables are listed in Table 1. The data cover the period from 18 September 2012 to 08 September 2017, captured at a sampling rate of one sample per hour.  
In practice, the raw data from monitoring system cannot be directly used, as it often contains erroneous data or missing data due to communication system failure, sensors faults, maintenance or repair actions, etc. In order to filter out the errors in training data, the following rules are applied for data pre-processing:  
* Filter out all missing values;
* Filter out downtime data, where speed is less than 10 rpm;
* Filter out all data vectors where one or more parameters have a value higher/lower than a predefined threshold (viewed as erroneous data). This step aims to delete downtime data and erroneous data due to sensor fault. In this paper, the threshold values were decided based on the manufacturer specifications. For example, all measurements with a discharge pressure lower than 130 bar or greater than 250 bar were filtered out. After this process, there might still exist some outliers in the training data. The influence of such outliers was further eliminated by setting reference fault detection thresholds in training process of both SAE and the PCA models using Equation (7).
## 4 Case Study: The Northeast Part of the Slovenian Transmission System  
The northeast part of the Slovenian transmission system is discussed, as shown in Figure 10. An individual substation (SS) was modeled by a TR 110 kV/X, an aggregated constant load, and an aggregated PV unit with the discussed FFC concepts. Furthermore, two BES units with the discussed FFC concepts and two hydropower plants (HPPs) were also considered in the network, along with five different aggregated network supplies. The main data of all discussed SSs are given in Table 3. Maximal load \(P_{\text{L,max}}\) was calculated according to the measurements for a period of three months during the summer, considering only the day-time. Furthermore, according to realistic plans, the PV and BES units' capacity \(P_{\text{IIDG,n}}\) will increase approximately up to four times by 2030. All PVs and BESs were assumed to operate with their maximal capacity expected by 2030, except the PVs in SSs Sobota and Mackovci and BES in Kidricevo.  
Numerous short-circuit analyses were performed for different fault types and locations on different 110-kV lines. The faults were accepted at a simulation time of 0.3 s, while at 0.42 s, the faulted line was disconnected. Three states were observed, i.e., normal operation (State 1), fault (State 2), and disconnection of the faulted line (State 3). Only two cases are presented, with the most indicative results.  
Figure 8: Distance protection operation in radial topology for different fault types on the C-D line at 20% from bus C (**a**), and at 80% from bus C (**b**), where SSCan = 12 MVA (the dotted arrow line indicates disconnection at the side C).  
Figure 9: Distance protection operation in radial topology for different fault types on the C-D line at 20% from bus D, where SSCan = 1500 MVA (the dotted arrow line indicates disconnection at the side C).
# Characterization of the Intelligibility of
## 2 Materials and Methods
### Intelligibility Measures  
In order to assess specific sets of spoken VCVs in the five languages in light of the three aforementioned criteria (in Section 1.2) for use in multilingual settings, the intelligibility of spoken VCVs in speech-shaped noise was estimated as a function of the SNR by using the STOI measure [33], an objective measure of speech intelligibility that has been shown to generate accurate predictions in various languages [33; 38; 39]. Even though the recognition of intervocalic consonants, such as the VCV stimuli used here, is less influenced by the subject's native language than that of words and sentences, there is an intrinsic linguistic perceptual factor that does not allow subjects to determine whether a language is more intelligible than another one [40]. An objective intelligibility measure, such as the STOI used here, can help address differences in intelligibility between speech materials in different languages. The STOI is an intrusive measure of speech intelligibility based on a correlation coefficient between the temporal envelopes of the time-aligned reference (i.e., the VCV spoken stimulus, with an average duration of about 1 s) and the processed speech signal (VCV plus noise) in short-time overlapped segments of 386 ms [33]. To evaluate the influence of noise on the STOI estimates, the mean STOI was computed in this study by averaging over 100 simulations with different noise realizations. For each VCV recording, the STOI for the 3 AFC task was computed as a function of the SNR in the range \(-12\) to \(+6\) dB in 2 dB steps to cover most of the dynamic range of stimuli, as shown by our earlier experimental data [12; 21; 22].  
The accuracy of the STOI estimates of VCV intelligibility in the five languages was validated using psychometric estimates from previously conducted experimental subjective tests [15; 16] in a 3 AFC speech recognition task. The three alternatives followed a  
Figure 1: Outline of the study methodology.  
maximal opposition criterion: the two wrong alternatives differ from the spoken stimulus in manner, voicing, and place of articulation (for example, ata, ava, ama) (details are reported in: [12; 21; 22]) and subjects had to select their response among the three alternatives displayed on a touch-sensitive screen. Subjective data were collected from a sample of young, normal-hearing native listeners for each language. The sample size ranged from 20 to 25 participants across the five languages. The 12 VCVs used in this study were presented in each of the five languages, except ama and ana in Portuguese, which were not used in the original experiment. The sets of VCVs in each language were presented monaurally, one ear at a time, at SNRs ranging from \(-10\) to \(+6\) dB in 2 dB steps. At each SNR, VCVs were presented 20 times in a randomized sequence of 2160 stimuli per ear (12 VCVs \(\times\) 20 presentations \(\times\) 9 SNRs) for an approximate session duration of 45 min, and the intelligibility of each VCV as a function of SNR was estimated as the average percentage of correct responses at each SNR.
# Optimizing the Use of RTKLIB for Smartphone-Based GNSS Measurements
## 2 Strategies
### Kinematic Solution Algorithm
\right] \tag{10}\]  
\[\mathbf{R}=diag\Big{(}\mathbf{D}\mathbf{R}_{\mathbf{\phi,1}}\mathbf{D}^{T}\mathbf{D}\mathbf{R}_{\mathbf{\phi,5 }}\mathbf{D}^{T}\mathbf{D}\mathbf{R}_{\mathbf{P,1}}\mathbf{D}^{T}\mathbf{D}\mathbf{R}_{\mathbf{P,5}}\mathbf{D}^{T} \Big{)} \tag{11}\]  
\[\mathbf{h}_{\mathbf{\phi,i}}=\left[ \begin{array}{ccc}\rho_{rb}^{12}+\lambda_{i} \big{(}B_{rb}^{1}-B_{rb}^{2}\big{)}\\ \rho_{rb}^{13}+\lambda_{i}\big{(}B_{rb}^{1}-B_{rb}^{3}\big{)}\\ \ldots\\ \rho_{rb}^{1m}+\lambda_{i}\big{(}B_{rb}^{1}-B_{rb}^{m}\big{)}\end{array} \right] \mathbf{h}_{\mathbf{P,i}}=\left[ \begin{array}{c}\rho_{rb}^{12}\\ \rho_{rb}^{13}\\ \ldots\\ \rho_{rb}^{1m}\end{array} \right] \tag{12}\]  
\[\mathbf{D}=\left[ \begin{array}{cccc}1&-1&0&\cdots&0\\ 1&0&-1&\cdots&0\\ &\vdots&&\ddots&\vdots\\ 1&0&0&\cdots&-1\end{array} \right]\mathbf{E}=\left[\mathbf{e}_{r}^{1},\mathbf{e}_{r}^{2}, \ldots,\mathbf{e}_{r}^{m}\right]^{T} \tag{13}\]  
\[\mathbf{R}_{\mathbf{\phi,i}}=diag\Big{(}2\sigma_{\mathbf{\phi,i}}^{1\ 2}\,2\sigma_{\mathbf{\phi,i}}^{2\ 2}\,\ldots,2\sigma_{\mathbf{\phi,i}}^{m\ 2}\Big{)}\mathbf{R}_{\mathbf{P,i}}=diag\Big{(}2\sigma_{\mathbf{\phi,i}}^{1\ 2}\,2\sigma_{\mathbf{\phi,i}}^{2\ 2}\,\ldots,2\sigma_{\mathbf{\phi,i}}^{m\ 2}\Big{)} \tag{14}\]  
where \(\mathbf{e}\) is the light of sight (LOS) vector between the satellite and the receiver, \(\sigma\) is the standard deviation of the pseudorange and carrier phase measurement error for each satellite. For the time update of the EKF, the positioning mode is kinematic and the receiver dynamics are turned on. Therefore, the state transition matrix and the system noise covariance matrix are defined as below. \[\mathbf{F}_{k}^{k+1}=\left[ \begin{array}{cccc}\mathbf{I}_{3\times 3}&\mathbf{I}_{3\times 3} \tau_{r}&\mathbf{I}_{3\times 3}\frac{\tau_{r}^{2}}{2}\\ 0&\mathbf{I}_{3\times 3}&\mathbf{I}_{3\times 3}\tau_{r}\\ 0&0&\mathbf{I}_{3\times 3}\\ &&&\mathbf{I}_{(2m-2)\times(2m-2)}\end{array} \right] \tag{15}\]  
\[Q_{k}^{k+1}=diag\Big{(}\mathbf{0}_{3\times 3},\mathbf{0}_{3\times 3},\mathbf{Q}_{a},\mathbf{0 }_{(2m-2)\times(2m-2)}\Big{)} \tag{16}\]  
\[\mathbf{Q}_{a}=\mathbf{E}_{r}^{T}diag\Big{(}\sigma_{ae}^{2}\tau_{r},\sigma_{an}^{2} \tau_{r},\sigma_{au}^{2}\tau_{r}\Big{)}\mathbf{E}_{r} \tag{17}\]  
\[\tau_{r}=t_{k+1}-t_{k} \tag{18}\]  
where \(\tau_{r}\) is the receiver sampling interval in seconds between epochs \(k\) and \(k+1\), and \((\sigma_{ae},\sigma_{an},\sigma_{au})\) are the east, north, and up components of the receiver acceleration system process noise.
## 4 The Proposed Model
### Evidential Deep Learning Module
#### 4.3.2. Evidential Deep Learning for Regression  
In the case of regression tasks, EDL adopts a slightly different approach. Given a dataset \(D=\{\,x_{i},y_{i}\}_{i=1}^{N}\), where the labels \(y_{i}\) are assumed to follow a Gaussian distribution with unknown parameters \(\left\{\mu,\sigma^{2}\right\}\), to estimate model uncertainty, the evidential model places a prior distribution on the parameters \(\left\{\mu,\sigma^{2}\right\}\). Specifically, the mean \(\mu\) follows a Gaussian distribution, while its variance \(\sigma^{2}\) follows an inverse gamma distribution. These resulting higher-order distributions, also known as evidence distributions, can be represented using the Gaussian conjugate prior to normal-inverse-gamma (NIG) distribution \(p\left(\mu,\sigma^{2}|\mathbf{m}\right)\), where the parameters \(\mathbf{m}=\left\{\gamma,v,\alpha,\beta\right\}\).  
\[\begin{array}{c}(y_{1},y_{2},\ldots,y_{N})\sim\mathcal{N}\left(\mu,\sigma^ {2}\right)\\ \mu\sim\mathcal{N}\left(\gamma,\sigma^{2}v^{-1}\right)\sigma^{2}\sim\Gamma^{- 1}(\alpha,\beta)\end{array} \tag{9}\]  
where \(\Gamma(\cdot)\) represents the gamma function, \(\gamma\in R,v>0,\alpha>1,\beta>0\).  
In the regression task, the model outputs four values per target through the evidential layer, corresponding to \(\left\{\gamma,v,\alpha,\beta\right\}\). From these values, we can obtain the predicted value \(\gamma\) and uncertainty \(\frac{\beta}{v(\alpha-1)}\).  
According to Bayesian probability theory, we can obtain the likelihood of the observed predicted targets by marginalizing the parameters of the Gaussian distribution. Additionally, leveraging the properties of the NIG distribution, we derive the following marginal likelihood:  
\[p(y_{i}\mid\mathbf{m})=\int_{\sigma^{2}=0}^{\sigma^{2}=\infty}\int_{\mu=-\infty}^{ \mu=\infty}\ p\left(y_{i}\mid\mu,\sigma^{2}\right)p\left(\mu,\sigma^{2}\mid \mathbf{m}\right)d\mu d\sigma^{2} \tag{10}\]  
where \(y_{i}\) represents the ADAS-cog13 cognitive score of the \(i\)-th sample.  
To learn the model parameters, the training process involves minimizing the negative log marginal likelihood (NLL) loss. The NLL loss function is defined as follows:  
\[\mathcal{L}_{i}^{NLL}=-log(p(y_{i}\mid\mathbf{m})) \tag{11}\]  
In addition, we also introduce a regularization term \(\mathcal{L}_{i}^{R}\) to minimize evidence on errors. The regularization term \(\mathcal{L}_{i}^{R}\) is defined as follows:  
\[\mathcal{L}_{i}^{R}=|y_{i}-\mathbb{E}[\mu_{i}]|\cdot\Phi=|y_{i}-\gamma|\cdot(2 v+\alpha) \tag{12}\]  
where \(\Phi=2v+\alpha\) represents the total evidence. This regularization term serves to penalize errors in model predictions, and the magnitude of this penalty is directly proportional to the total evidence.  
In conclusion, for the regression problem, the overall loss function for the \(i\)-th sample can be defined as follows:  
\[\mathcal{L}_{i}^{r}=\mathcal{L}_{i}^{NLL}+\lambda_{r}\mathcal{L}_{i}^{R} \tag{13}\]  
where \(\lambda_{r}\) is a hyperparameter to adjust regularization.
# On Training Data Selection in Condition Monitoring Applications--Case Azimuth Thrusters
## 2 Materials and Methods
### Description of Data
#### 2.2.1 Thruster and Measurements  
The data for this study come from a UUC 455 thruster manufactured by Kongsberg Maritime Finland Oy. The data were collected during a campaign during April-May 2021 on 'Pioneering Spirit', the largest construction vessel in the world. Figure 3 presents a drawing of the thruster model with the main components of interest highlighted. The data from the piezoelectric accelerometer located next to the pinion shaft support bearing and gear were selected for analysis. The sampling rate varied based on the shaft speed. During one shaft revolution, 512 acceleration values were measured and the length of the complete time series in a sample was 16,384 values. Samples were collected roughly at 5-min intervals.
# Numerical Validation of the Radiative Model for the Solar Cadaster Developed for Greater Geneva
## 5 Conclusions  
The solar cadaster has proven its ability to provide accurate results in terms of the level of irradiance on both roofs and vertical facades. Indeed, the results predicted by the new version of the solar cadaster developed for Greater Geneva are in good accordance with those predicted by ENVI-met and DIVA-for-Rhino.  
Regarding the concordance of the results, the non-shaded horizontal surfaces match almost perfectly. This is not the case for the shaded facades and vertical facades, but the results are very satisfactory. The differences observed between the tools come from the differences between the models in terms of diffuse radiation, the evaluation of reflections, or shading.  
Finally, the solar cadaster provides precise results at a low spatial resolution while keeping the computation time low. It ranges from a few hours for the solar cadaster and DIVA-for-Rhino to a few days for ENVI-met. It can therefore be used on a large scale and can prove to be a reliable tool for promoting and intensifying the use of solar energy on the scale of Greater Geneva. However, work is in progress to improve the modeling of reflected components and, thus, the reliability of the tool for more complex geometries.  
**Author Contributions:** Conceptualization, B.G., M.T., G.D., C.M. and S.G.-J.; Methodology, B.G., M.T. and G.D.; Software, V.G. and G.D.; Resources, G.D.; Writing--original draft preparation, B.G.; Writing--review and editing, B.G, M.T., K.B., E.P., S.G.-J., C.M. and G.D.; Visualization, B.G.; Supervision, C.M. and G.D.; Funding acquisition, C.M. and G.D.; All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by EU-INTERREG V France-Suisse program (G2-SOLAIRE Ref: 4610), and received support by the French National Research Agency, through Investments for Future Program (ref. ANR-18-EURE-0016--Solar Academy).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that supports the findings of this study are available from the corresponding autho upon reasonable request.  
**Acknowledgments:** The authors would like to thank the INTERREG V Suisse-France program for providing financial support for conducting this study in the framework of the G2 Solar project, which aims to extend the solar cadaster to Greater Geneva and intensify solar energy production at this level. This work was supported by the French National Research Agency through the Investments for Future Program (ref. ANR-18-EURE-0016--Solar Academy). The research units LOCIE and FRESBE are members of the INES Solar Academy Research Center.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
# Efficient Massive MIMO Detection for M-QAM Symbols
## 2 Preliminaries
### MMSE Detector  
To reduce the complexity, the MMSE detector relaxes the constellation constraints \(\mathbf{s}\in\mathcal{A}^{K_{t}}\) to \(\mathbf{s}\in\mathbb{C}^{K_{t}}\) and adds a regularization term to the Equation (2) as follows:  
\[\mathbf{\hat{s}}_{\text{mmse}}=\arg\min_{\mathbf{s}\in\mathbb{C}^{K_{t}}} \Bigl{\{}\|\mathbf{y}-\mathbf{R}\mathbf{s}\|^{2}+\mu||L\mathbf{s}||^{2}\Bigr{\}}, \tag{3}\]  
with regularization operator \(L\) and regularization parameter \(\mu>0\). By setting \(L=\mathbf{I}\) and \(\mu=\sigma^{2}\), the solution to (3) is given by  
\[\mathbf{\hat{s}}_{\text{mmse}}=(\mathbf{R}+\sigma^{2}\mathbf{I})^{-1}\mathbf{y}. \tag{4}\]The iterative Tikhonov regularization technique helps to obtain a more accurate solution. By applying this technique to Equation (3), we can obtain a sequence of constrained optimizations.  
\[\mathbf{s}^{(\mathrm{v})}=\arg\min_{\mathbf{s}\in\mathcal{C}^{k_{t}}}\|(\mathbf{y}+\sigma^{2} \mathbf{s}^{(\mathrm{v}-1)})-\mathbf{\mathrm{R}}\mathbf{s}\|^{2}+\sigma^{2}||\mathbf{I}\mathbf{s}||^ {2} \tag{5}\]  
The solution of the \(v\)th iteration to Equation (5) can be considered as an unconstrained solution to the following equation:  
\[\mathbf{s}^{(\mathrm{v})}_{\text{Iterated mmse}}=(\mathbf{\mathrm{R}}+\sigma^{2}\mathbf{ \mathrm{I}})^{-1}(\mathbf{\mathrm{y}}+\sigma^{2}\mathbf{s}^{(\mathrm{v}-1)}) \tag{6}\]  
Although the MMSE approach has been demonstrated to be efficient for small-scale MIMO systems (e.g., at most eight antennas in LTE-A), it requires matrix inverse operation. In massive MIMO systems with hundreds of antennas, the matrix inverse operation has a prohibitively large complexity of \(\mathcal{O}(K_{t}^{3})\) (and \(\mathcal{O}((V-1)K_{t}^{3})\) for iterated MMSE) [13].
## 2 Materials and Methods
### Theoretical Principal
#### 2.3.4 Energy Aspects of The Indirect Solar Convective Drying System  
The total consumption of energy (kWh) by the drying system was calculated using Equation (9) [45]:  
\[E_{t}=(A.v.\rho_{a}.C_{a}.\Delta T.D_{t})+E_{mec} \tag{9}\]  
where \(E_{t}\): The total energy consumption (kWh), \(A\):tray surface area (m\({}^{2}\)), \(v\): velocity of air (m/s), \(\rho_{a}\): density of air (kg/m\({}^{2}\)), \(C_{a}\): air specific heat (kJ/kg \({}^{\circ}\)C), \(\Delta T\): the difference between ambient and hot air temperatures (\({}^{\circ}\)C), \(D_{t}\): total drying time (h), and \(\rho_{\text{a}}\) refers to the power (kW).  
The specific heat capacity parameters of both the inlet air [46] and the power [47] were computed using Equations (10) and (11):  
\[\rho_{a}=\frac{101.325}{0.287\times T} \tag{10}\]  
\[C_{a}=1.04841-\frac{3.83719\times T}{10^{4}}+\frac{9.45378\times T^{2}}{10^{7 }}-\frac{5.49031\times T^{3}}{10^{10}}+\frac{7.92981\times T^{4}}{10^{14}} \tag{11}\]  
The mechanical energy (E\({}_{\text{mec}}\)) used per each experiment is measured via an electric energy meter. It is the total energy used by both auxiliary heater and fan.  
The specific thermal energy (kWh/kg) required to remove one kilogram of mass of water from the product was calculated by using Equation (12) [48]:  
\[SEC=\frac{E_{t}}{m_{w}} \tag{12}\]  
where: \(m_{w}\) is the quantity of water evaporated (kg). It is computed using Equation (13) [48]:  
\[m_{w}=\frac{W_{0}\left(Y_{0}-Y_{f}\right)}{100-Y_{f}} \tag{13}\]  
where: \(W_{0}\) is the mass of the initial sample (kg), \(Y_{0}\) and \(Y_{f}\) are the initial (t = 0) and final moisture content (% d.b).  
The energy efficiency was calculated (Equation (14)) as the ratio of the water evaporation energy and the total energy used [49].  
\[n_{e}=\frac{Q_{w}}{E_{t}} \tag{14}\]  
where \(Q_{w}\) represents the water evaporation energy (kWh).  
Since fruit samples have a higher water content, Equation (15) was used to calculate evaporation energy.  
\[Q_{w}=h_{fg}\times m_{w} \tag{15}\]  
where \(h_{fg}\) is the latent heat of vaporization (kJ/kg). It is a function of the air temperature (T abs) and is calculated using the following formulas [46].  
\[h_{fg}=2.503\times 106-2.386\times 103\times(T_{abs}-273.16)273.16<T_{abs}(K)<338.72 \tag{16}\]  
\[h_{fg}=\left(7.33\times 1012-1.60\times 107\times T^{2}_{abs}\right)^{0.5}338.72<T_{abs}(K)<533.16 \tag{17}\]
# A Novel Embedding Model for Knowledge Graph Entity Alignment Based on Graph Neural Networks
## 3 Proposed Framework  
### Problem Definition  
As a type of graph structure, in a knowledge graph entities are represented as nodes and the relations between entities are represented as edges. However, the symbolic features of triples make processing difficult. Obtaining more effective entity embedding representations has become a major challenge in entity alignment tasks. For generality, this paper uses uppercase letters to represent sets and lowercase letters to represent vectors. Let \(G=(E,R,P,V,T)\) represent a knowledge graph, where \(E\) represents the set of all entities; \(R\) represents the set of relationship predicates; \(P\) represents the set of property predicates; \(V\) represents the set of property values; and \(T\) represents the set of triples that relate entities and their properties. \(T=T_{r}\cup\ T_{p}\), where \(T_{r}\) represents relationship triples \((h,r,t)\) in the knowledge graph--where \(h\) stands for head entity, \(t\) stands for tail entity, and \(r\) stands for relationship (predicate) between them--\(T_{p}\) represents property triples \((e,p,v)\)--where \(e\) stands for entity, \(p\) stands for property name, and \(v\) stands for property value. Entity alignment endeavors to unearth the corresponding entities across divergent knowledge graphs.  
Given two knowledge graphs, \(G_{1}=(E_{1},R_{1},P_{1},V_{1},T_{1})\) and \(G_{2}=(E_{2},R_{2},P_{2},V_{2},T_{2})\), we aim to discover \((e_{1},\ e_{2})\), where \(e_{1}\in E_{1},\ e_{2}\in E_{2}\), and \(e_{1}\equiv e_{2}\), indicating that \(e_{1}\) and \(e_{2}\) denote the identical real-world entity, with \({}^{\prime}\equiv\) \" indicating an equivalence relation. We employ an embedding-based model to assign a continuous representation to every element of two types of triples \((h,r,t)\) and \((e,p,v)\), represented in bold font \((\mathbf{h},\mathbf{r},\mathbf{t})\), \((\mathbf{e},\mathbf{p},\mathbf{v})\).