esa-sceva/satcom-chunk-collection huggingface dataset:
# Numerical Modeling of Scholte Wave in Acoustic-Elastic Coupled TTI Anisotropic Media
## Appendix B stability condition
\begin{bmatrix}D_{11}&D_{44}&D_{55}&2D_{15}\\ D_{44}&D_{22}&D_{66}&2D_{46}\\ D_{55}&D_{66}&D_{33}&2D_{35}\\ \frac{D_{11}+D_{22}+D_{13}}{3}&\frac{D_{12}+D_{23}+D_{23}}{3}&\frac{D_{13}+D_{ 33}+D_{33}}{3}&\frac{2(D_{15}+D_{25}+D_{35})}{3}\\ \frac{2D_{11}-\tilde{D}_{12}-D_{13}}{3}&0&0&\frac{2D_{15}-\tilde{D}_{35}-D_{35} }{3}\\ 0&\frac{2D_{22}-D_{12}-D_{23}}{3}&0&0\\ 0&0&\frac{2D_{33}-D_{33}-D_{13}}{3}&\frac{2D_{35}-D_{35}}{3}\\ D_{44}&D_{44}&0&\frac{1}{3}&\frac{2}{3}\\ D_{55}&0&D_{55}&D_{15}+D_{35}\\ 0&D_{66}&D_{66}&D_{46}\end{bmatrix}  \tag{106}\]  
where \(k_{x},k_{y},k_{z}\) are operators corresponding to \(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z}\) in the frequency-wave number domain, respectively, and \(D_{ij}\) is the element of the elastic coefficient matrix of TTI medium. According to stability conditions [24; 44]:  
\[0\leq\frac{\Delta t^{2}}{4}\lambda_{i}\leq 1. \tag{101}\]  
By comparison, it can be found that \(\lambda_{i}\) (i = 4, 5, 6, 7, 8, 9, 10) is always less than any one of \(\lambda_{1},\lambda_{2},\lambda_{3}\). Combined with the inverse time-frequency transformation, thus:  
\[0\leq\frac{\Delta t^{2}}{\rho}\Big{(}D_{11}\Delta x^{2}+D_{44}\Delta y^{2}+D_{ 55}\Delta z^{2}+2D_{15}\Delta x\Delta z\Big{)}\Bigg{[}\sum_{n=1}^{\text{N}}|a_{ n}|\Bigg{]}^{2}\leq 1, \tag{102}\]  
\[0\leq\frac{\Delta t^{2}}{\rho}\Big{(}D_{44}\Delta x^{2}+D_{22}\Delta y^{2}+D_{ 66}\Delta z^{2}+2D_{46}\Delta x\Delta z\Big{)}\Bigg{[}\sum_{n=1}^{\text{N}}|a_{ n}|\Bigg{]}^{2}\leq 1, \tag{103}\]  
\[0\leq\frac{\Delta t^{2}}{\rho}\Big{(}D_{55}\Delta x^{2}+D_{66}\Delta y^{2}+D_{ 33}\Delta z^{2}+2D_{35}\Delta x\Delta z\Big{)}\Bigg{[}\sum_{n=1}^{\text{N}}|a_ {n}|\Bigg{]}^{2}\leq 1. \tag{104}\]  
Therefore, the stability conditions of the 3D TTI acoustic-elastic coupled equation in 2 nd-order of time and 2N-order of space in x, y, and z directions are as follows:  
\[\Delta t\sqrt{\frac{D_{11}\Delta x^{2}+D_{44}\Delta y^{2}+D_{55}\Delta z^{2}+2 D_{15}\Delta x\Delta z}{\rho}}\leq\frac{1}{\sum_{n=1}^{\text{N}}|a_{n}|}, \tag{105}\]  
\[\Delta t\sqrt{\frac{D_{44}\Delta x^{2}+D_{22}\Delta y^{2}+D_{66}\Delta z^{2}+2 D_{46}\Delta x\Delta z}{\rho}}\leq\frac{1}{\sum_{n=1}^{\text{N}}|a_{n}|}, \tag{106}\]  
\[\Delta t\sqrt{\frac{D_{55}\Delta x^{2}+D_{66}\Delta y^{2}+D_{33}\Delta z^{2}+2 D_{35}\Delta x\Delta z}{\rho}}\leq\frac{1}{\sum_{n=1}^{\text{N}}|a_{n}|}. \tag{107}\]  
Setting \(\Delta x=\Delta y=\Delta z=h\), the stability condition is simplified as:  
\[\sqrt{5}\frac{\Delta t}{h}\sqrt{\frac{S}{\rho}}\leq\frac{1}{\sum_{n=1}^{\text {N}}|a_{n}|}, \tag{108}\]  
\[\text{where }S=\max\{D_{11},D_{22},D_{33},D_{44},D_{55},D_{66},D_{15},D_{35},D_{46}\}.\]
# A Goal-Oriented Evaluation Methodology for Privacy-Preserving Process Mining
## 4 Case Study
### Data Preprocessing  
Transforming the event logs into model-ready feature vectors is the most important step. To carry out this process, under each category, event logs were preprocessed to construct their feature vector according to the algorithmic model's requirements.  
For group-based anonymization models such as \(k\)-anonymity, \(l\)-diversity, and \(t\)-closeness, after setting activity names as the sensitive attribute, the rest of the attributes were used as quasi-identifiers for the models run. However, some event logs, especially timestamp attributes were preprocessed to be converted into a common format since some of them include differences. AnonyPy tool has a preserver component which is responsible for auto-preprocessing the feature vectors internally.  
For the privacy-preserving machine learning models, skelam's preprocess library was utilized to create their feature vectors. By converting timestamp attributes to strings initially, we applied the LabelEncoder technique to transform ordinal string values into numeric integers. Moreover, for unsupervised learning as DP-k-Means, training set features were standardized by scaling to unit variance to ensure their equal contribution to distance-based model performance.  
More sophisticated PPPM models use their internal techniques to represent the event log features in order to preserve the sequential order between the instances. The two state-of-the-art approaches are _prefix-tree encoding_ and _trace variant encoding_. The prefix-tree encoding method characterizes each trace as an ordered sequence of activities and systematically encodes all trace prefixes within a hierarchical tree structure (i.e,.Trie). Each node is associated with a distinct activity, and every path extending from the root to a given node delineates a prefix of a trace. Alternatively, trace-variant encoding categorizes traces based on their precise sequences of activities, thereby discerning distinct execution patterns, referred to as variants. Each variant is represented as either a vector or a categorical identifier, enabling the simplification of log complexity while supporting variant-based analytical and comparative evaluations.
# A Speed Tracking Method for Autonomous Driving via ADRC with Extended State Observer
## 5 Autonomous Driving Vehicle Configuration and Road Experiments Results
### Stepped Speed Test  
This experiment used a stepped set speed profile to assess the continuous acceleration and braking ability of the controller. The set speeds were 15, 25, 18, and 10 km/h. The vehicle traveled for 80 s at each speed. Figure 18 shows the speed tracking. The sample points with a tracking error within \(\pm\)0.5 km/h accounted for 98.02% of the total sample points, and the points with an absolute value of error \(>\)0.6 km/h appeared at the moments the speed step changed. The MFC-ADRC controller used an ESO to obtain observed values of state variables and disturbances, and Figure 19 shows the observation results. This ability to use observations of disturbances and state variables is the key to actively correcting for disturbances under different uncertainties.  
Figure 19: Observations made by extended state observer.  
Figure 18: Longitudinal velocity tracking results with stepped set speeds.
# Improving Juvenile Age Estimation Based on Facial Landmark Points and Gravity Moment
## 5 Experimentation
### Datasets and Evaluation  
FG-NET consists of 1002 facial photographs from 82 individuals with ages ranging from 0 to 69 years. Although the number seems small, there are at least 12 age-separated images per person, and a substantial majority of the images are younger faces within the 0-40 age group. We collected images from ages 0 to 34 years to constitute our dataset. Since the FG-NET contains only 1002 faces, it could not be divided into the typical 80-20, train-test strategy. Therefore, we adopted the leave-one-person-out (LOPO) cross-validation strategy. In order to train our model, the dataset was divided into the various age classes, such that each class had approximately the same number of samples. This strategy maintained balance in the dataset. The training was first conducted on the entire set with ages ranging from 0-34 years to obtain a large reference matrix. Since the focus is on juveniles,we reduced the set to reflect ages 0-17 years, as depicted in Figure 3. Consequently, we utilized the new dataset to construct a new reference matrix.  
To validate the performance of our scheme, the Mean Absolute Error (MAE) was used to indicate the effectiveness of our proposal. MAE is expressed as:  
\[MAE=\frac{1}{N}\sum_{i=1}^{N}|Ag_{1}-Ag_{0}| \tag{13}\]  
where \(N\) is the total number of test data, \(Ag_{0}\) the actual age and \(Ag_{1}\) is the estimated age.  
Additionally, we investigated the accuracy by another metric known as the Cumulative Score (CS) expressed as follows.  
\[CS=\frac{N_{e\leqslant th}}{N}\cdot 100\% \tag{14}\]  
where \(N\) is the total number of test images and \(N_{e\leqslant th}\) is the number of test images whose absolute error is less than \(th\).
# Methods for Aggregation and Remuneration of Distributed Energy Resources
## 5 Results
### Scheduling of Resources  
In this subsection, the results of the scheduling are addressed, taking into account the energy scheduled for the several types of resources considered, for each period. In this way, results are shown in Figure 4.  
The scheduling results show a large penetration of distributed generation, with a certain level of demand response utilization, namely, through load reduction and curtailment programs. Also, regarding the shifting of consumption, results show that certain periods are more convenient to consume energy than others, namely, the optimization shows that consumption in the right (hours 1 to 3) has been reduced in order to be consumed, in its majority, along the day taking advantage of the available photovoltaic energy.  
The energy losses are also accounted, being summed to the initial consumption values, according to the load shifting made, as shown in Figure 5.  
In this way, the aggregator obtains the cost minimization through the use of distributed resources, with a focus on distributed generation, but using demand flexibility to adjust consumption according to the context of available production-side resources. The optimization run time is 55 min for the proposed case study, obtaining a total cost of 64.56 m.u. for the aggregator. This shows that currently, the optimization is not suitable to be applied in closer to real-time problems, i.e., the aggregator must have enough time to obtain the solution and deal with other issues regarding the implementation of resources and market participation.  
Figure 4: Results of the scheduling of resources.  
Figure 5: Consumption and losses detail.  
The complexity of the problem increases significantly when considering that the aggregator is responsible for the technical verification of the network, i.e., the solution presented by it regarding the scheduling of resources must be in accordance with technical limits of the physical network. In this way, the equations of AC power flow make the optimization problem become included in the class of mixed-integer non-linear programming (MINLP), which increases significantly the complexity, and consequently requires a higher computation time. In real applications, the entities (transmission system operators, distribution system operators, balance responsible parties, aggregators) that manage the physical operation of the network are not keen on using AC power flow calculations due to the issues referred to above (computation time and complexity), for which results may be needed with more time in advance. Instead they commonly use DC power flow calculation, allowing some simplifications regarding its implementation when compared with the AC. The choice of using AC power flow in this paper is based on the consideration of day-head planning by the aggregator and the dimension of the network being relatively small. Thus, the computation time and the complexity of the problem can be solved in useful time, taking into consideration the planning horizon and network considered.
## 4 Experiments
### Ablation Experiments  
To further analyze the effectiveness of the key components in STGNN, we conduct ablation experiments to evaluate three variants of our model on two datasets:  
STGNN-noSM: It removes the total spatial modeling module to investigate the benefits of modeling the spatial dependencies of the passenger flow network.  
Figure 6: Network configuration analysis. These four figures demonstrate the impact of different model dimensions and attention head numbers on RMSE and MAE, respectively.  
STGNN-noDAG: It removes the dynamic global attention network to investigate the utility of dynamic spatial correlation strength impact between global node pairs rather than relying solely on static topological relationships.  
STGNN-noLSA: It replaces the locality-aware sparse attention block with a traditional attention block to investigate the usefulness of considering various contextual information.  
Except for the variances, all the variant models share identical settings. Figure 7 shows the performance of the three variants on our simulation dataset and the Hangzhou dataset. We can easily observe that the changes in RMSE and MAE are almost consistent across different datasets. By comparing STGNN-noSM and STGNN, no doubt that modeling the spatial dependences plays a positive role in multi-step metro station passenger flow prediction and verifies the effectiveness of the spatial modeling module. STGNN-noDAG, which only uses GCN for spatial modeling, yields inferior performance compared to STGNN but is slightly better than STGNN-noSM. This result indicates the significance of the dynamic global spatial relationship between global node pairs. Moreover, the superior performance of STGNN compared to STGNN-noLSA demonstrates the effectiveness of modeling local trends by employing multi-head self-attention for long-term passenger flow forecasting.
## 2 Experimental Approaches
### Experimental Method and Procedure
The conditions for basic analysis are shown in Figure 2. Light scattering refers to the phenomenon in which reflection, refraction,  
Figure 1: (**a**) Photograph and (**b**) schematics of test duct and light scattering chamber (LSC). and diffraction interact in a complex manner [31]; Figure 2a illustrates the scattering as well as the absorption of incident light by smoke particles. The amount of light scattered by the smoke particles is proportional to the amount of radiated light, and may be affected by their size and refractive index as well as the wavelength of the light. According to the basic theory of light scattering, when light reaches the smoke particles, scattering occurs in all directions. Representative of this phenomenon are forms called Rayleigh scattering and Mie scattering. Rayleigh scattering occurs when the size of the scattering particles is smaller than the wavelength of light (e.g., very small water droplets, nitrogen, and oxygen) [32], and Mie scattering occurs when the particle size is similar to or larger than the wavelength of light. Thus, the characteristics of the scattered light vary according to the interaction between wavelength and particle size. As shown in Figure 2b, scattering that occurs in the same direction as the incident light is called forward scattering, and scattering that occurs in the opposite direction is called backward scattering. As the particle size increases, forward scattering becomes more active, and the intensity of light scattered in the light propagation direction increases [33]. To consider this phenomenon in the analysis, the area was divided into two regions--those where forward scattering and backward scattering mainly occur--for the purpose of analyzing the difference between the distributions of scattered light according to the smoke particles introduced into the LSC. For reference, the photocell installed at an angle of \(0^{\circ}\) serves to transmit the light that is not absorbed or scattered, and the photocell at \(90^{\circ}\) can be included in both forward and backward scattering.
# A Multi-Objective Hybrid BESSA Optimization Scheme for Parameter Extraction from PV Modules
## 6 Parameter-Setting of the Optimization Technique
The application of such metaheuristic techniques has also been observed in crack detection for cantilever beams [42]. _Analysis and Appraisal of Exploitation Capability (\(f_{1}(y)\)-\(f_{7}(y)\))_  
The unimodal functions ascertain and evaluate the exploitation capability of an optimization technique. These unimodal functions are tabulated in Table 1.  
To appraise the exploitation capability of the proposed BESSA Technique, it is tested on seven unimodal functions, i.e., \(f_{1}(y)\)-\(f_{7}(y)\), as presented in [9]. The results are depicted in Table 2. These unimodal functions are characterized by having single global optima. The statistical outcomes of the BESSA, original BES, CamWOA, and the other 10 algorithms presented in [9] are also tabulated. It was observed that the Hybrid BESSA produced better results and was able to find global optima for all of the unimodal functions as compared to the BES, CamWOA, and other techniques mentioned in [9]. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Functions** & **Range** & \(f_{min}\) \\ \hline \(f_{1}(p)=\sum\limits_{i=1}^{n}p_{i}^{2}\) & \([-100,100]^{10}\) & 0 \\ \(f_{2}(p)=\sum\limits_{i=1}^{n}|p_{i}|+\prod\limits_{i=1}^{n}p_{i}\) & \([-10,10]^{10}\) & 0 \\ \(f_{3}(p)=\sum\limits_{i=1}^{n}\left(\sum\limits_{i=1}^{i}p_{i}\right)^{2}\) & \([-100,100]^{10}\) & 0 \\ \(f_{4}(p)=max_{i}[\{p_{i}|,1\leq i\leq n\}]\) & \([-100,100]^{10}\) & 0 \\ \(f_{5}(p)=\sum\limits_{i=1}^{n-1}\left[100(p_{i+1}-p_{i}^{2})^{2}+(p_{i}-1)^{2}\right]\) & \([-30,30]^{10}\) & 0 \\ \(f_{6}(p)=\sum\limits_{i=1}^{n-1}[(p_{i}+0.5)]^{2}\) & \([-100,100]^{10}\) & 0 \\ \(f_{7}(p)=\sum\limits_{i=1}^{n}ip_{i}^{4}+random[0,1)\) & \([-1.28,1.28]^{10}\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Unimodal benchmark functions. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{2}{c}{**BESSA**} & \multicolumn{2}{c}{**BES**} & \multicolumn{2}{c}{**CamWOA**} & \multicolumn{2}{c}{**WOA**} \\ \cline{2-9}  & **Avg. ** & **Std. Dev** & **Avg. ** & **Std. Dev** & **Avg. ** & **Std. Dev** & **Avg. ** & **Std. Dev** \\ \hline \(f_{1}(p)\) & 0 & 0 & 0 & 0 & 0 & 0 & \(1.4\times 10^{-16}\) & 0 \\ \(f_{2}(p)\) & 0 & 0 & 0 & 0 & \(2.1\times 10^{-3}\) & 0 & \(5.3\times 10^{-17}\) & \(2.3\times 10^{-16}\) \\ \(f_{3}(p)\) & 0 & 0 & 0 & 0 & 0 & 0 & 0.10019 & 0.23771 \\ \(f_{4}(p)\) & 0 & 0 & 0 & 0 & \(4.5\times 10^{-36}\) & 0 & 0.00054 & 0.00024 \\ \(f_{5}(p)\) & \(5.91\times 10^{-13}\) & \(0.027\times 10^{-16}\) & \(23.52\times 10^{-13}\) & \(0.12\times 10^{-16}\) & \(6.8177\) & 0.602 & 4.7626 & 0.346 \\ \(f_{6}(p)\) & 0 & 0 & 0 & 0.001415 & 0.000982 & \(7.03\times 10^{-7}\) & \(6.62\times 10^{-7}\) \\ \hline \multirow{2}{*}{**Function**} & \multicolumn{2}{c}{**WCMFO**} & \multicolumn{2}{c}{**ABC**} & \multicolumn{2}{c}{**PSOGSA**} & \multicolumn{2}{c}{**CS**} \\ \cline{2-9}  & **Avg. ** & **Std. Dev** & **Avg. ** & **Std. Dev** & **Avg. ** & **Std. Dev** & **Avg. ** & **Std.
# Optimal Design and Experiment of Manipulator for Camellia Pollen Picking
## 3 Optimal Design of the Manipulator for Camelia Pollen Picking  
### Simplified Processing of Picking Space  
The working space of the robot is determined by the primary linkage system. The primary linkage system consists of three degrees of freedom determined by the base, the big arm, and the forearm. The structural parameters of the exact pollen-picking manipulator are mainly determined by the geometric length and rotation range of the main connecting rod. The size is as small as possible for meeting the requirements of the working area. The forearm adopts a parallel mechanism to ensure the final angle of the moving platform.  
After the new camellia forest is uniformly reshaped, the target picking space is the upper half of the globe, and the diameter of the globe is \(r=1500\) mm. To preserve the vigor of the camellia tree after pollen picking, only the pollen within the height range of \(2/3\) from the top in the upper hemisphere area are picked. Considering the width of the machine-plowing road and the requirements of the camellia-pollen-picking operation, the camellia-pollen-picking manipulator is placed on the multi-functional pollen platform with a height of \(1\)m, and the camellia flowers in the target picking area are distributed \(800\)-\(1600\) mm from the center of the robot vehicle. The height is \(2000\)-\(3000\) mm, and the depth is \(-300\)-\(300\) mm when the pollen-picking robot travels along the plowing road in  
Figure 2: Three-dimensional model of the pollen-picking robot.  
the east-west direction. The front view of the pollen-picking robot and the target picking area is shown in Figure 3.  
The picking area is an incomplete globe, and the target picking area is now simplified [20; 21; 22; 23; 24]. The working space of the manipulator end effector is enlarged to form a cube containing the picking area. The length of the cube is \(w=3000\) mm, the height is \(h=1000\) mm, and the width is \(b=500\) mm.  
As shown in the simplified working-space diagram in Figure 4, the cube is marked by the red area. The problem of satisfying the cube \(w\times h\times m\) can be regarded as the problem of satisfying \(b\times h\) in the vertical plane (\(xoz\)), and then using the rotation degree of freedom of the big arm to rotate the corresponding angle \(\varphi_{1}\). In this way, the entire red cube can be covered, and the two blue arcs are the nearest and farthest trajectories of the manipulator's end. According to the geometric relationship, the minimum angle \(\varphi_{1}\) of the rotation of the big arm should satisfy:  
\[\varphi_{1}\geq\arctan\frac{\mathrm{w}/2}{\left(2300-1500\right)+\mathrm{b}} \tag{2}\]  
\[\mathrm{r}_{1}=2300-1500=800\text{ mm} \tag{3}\]  
\[\mathrm{r}_{2}=\sqrt{\left(\mathrm{w}/2\right)^{2}-\left(2300-1500+500\right) ^{2}} \tag{4}\]  
Substitute into the calculation, and we can obtain  
\[\varphi_{1}\geq 50^{\lx@math@degree},\mathrm{r}_{1}=800\text{ mm},\mathrm{r}_{2}=1985\text{ mm}\]
## 5 Deep Neural Network Framework
### Evaluation of Proposed DNN Models
#### 5.1.2 Estimation of Bracing Force (\(F_{br}\))  
Figure 12 shows comparisons of the training and validation loss with respect to MSE between predicted and FEA values. Based on the comparisons, the DNN models require at least 100 epochs for all cases of the number of neurons for reasonable estimations from Figure 12. Furthermore, the predicted \(F_{br}\) of the test sets were also compared using various performance criteria, as summarized in Table 10. The DNN model with five hidden layers, 50 neurons, and 100 epochs (H5N50E100) shows the best prediction results, based on the comparisons. In this model, the performance values in terms of the coefficient of determination are 0.997 and the minimum values for RMSE, MSE, and MAE, respectively.  
Figure 11: Comparisons of predicted minimum bracing moments (\(M_{br,min}\)) of training and validation data sets: (**a**) training data and (**b**) test data.  
Figure 10: Comparisons of predicted maximum bracing moments (\(M_{br,max}\)) of training and validation data sets: (**a**) training data and (**b**) test data.  
Figure 12: Comparisons of training and validation loss of bracing forces (\(F_{br}\)): (**a**) 3-50-200; (**b**) 3-100-200; (**c**) 3-200-200; (**d**) 4-50-200; (**e**) 4-100-200; (**f**) 4-200-200; (**g**) 5-50-200; (**h**) 5-100-200; and (**i**) 5-200-200 (in which 3-50-200 means a DNN model with 3 hidden layers, 50 neurons for each hidden layer, and 200 epochs).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Hidden Layers** & \multirow{2}{*}{**Neurons**} & **Epochs** & \(\mathbf{R^{2}}\) & **RMSE** & **MSE** & **MAE** \\ \hline H3N50E100 & 3 & 50 & 100 & 0.997 & 30.2 & 910.4 & 19.0 \\ H3N50E200 & 3 & 50 & 200 & 0.95 & 109.6 & 12,004.7 & 76.2 \\ H3N100E100 & 3 & 100 & 100 & 0.99 & 48.9 & 2388.8 & 33.1 \\ H3N100E200 & 3 & 100 & 200 & 0.991 & 56.7 & 3211.6 & 39.1 \\ H3N200E100 & 3 & 200 & 100 & 0.996 & 32.3 & 1043.4 & 20.6 \\ H3N200E200 & 3 & 200 & 200 & 0.995 & 34.8 & 1212.5 & 22.8 \\ H4N50E100 & 4 & 50 & 100 & 0.996 & 33.4 & 1116.5 & 19.3 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Accuracy of DNN models for \(F_{br}\) using various performance criteria.  
Figure 13 compares the predicted bracing forces (\(F_{br}\)) with the FEA results, which served as training and validation data in this study. For all cases, the prediction values show good correlations with the FEA results. Based on the FEA results, the magnitude of the bracing forces is relatively low compared to the bracing moments, as the maximum bracing force acting on the bracing elements is 3421.2 N, as seen in Table 6. Although the bracing forces are relatively small compared to the bracing moments, a more accurate prediction may be possible if we use the bracing force prediction model derived from this study.