Abstract
The potential risk of cablestayed archtruss damage is large and the damage is undetectable. The damage identification methods based on frequency domain have limitations such as limited data and complex theoretical methods. A damage identification method based on multinode timedomain data fusion was proposed to overcome these limitations. The timedomain data library was established by finite element analysis, and the timedomain data was preprocessed and augmented. Two CNNs models were established to identify the damage location and damage degree of cablestayed archtruss. The proposed method was verified by the analysis of a practical cablestayed archtruss scale model, and the recognition effect of the method on noisy data and noisefree data was studied respectively. The results showed that the CNN can effectively identify the damage degree and damage location of cablestayed archtruss structure with good robustness. CNN with Gaussian noise can accurately predict the damage degree of cablestayed archtruss. The prediction error of most elements is within 15%, which can meet the actual needs of engineering.
Keywords
Cablestayed archtruss; Damage identification; Convolutional neural networks; Timedomain data
1 INTRODUCTION
As a typical largespan spatial structure, cablestayed archtruss (CSAT) is widely used in largespan important public buildings such as convention centers and airports (Murthasmith, 1988Murthasmith, E. (1988). Alternate pathanalysis of spacetrusses for progressive collapse. Journal of Structural EngineeringASCE, 114(9), 19781999. doi:10.1061/(ASCE)07339445(1988)114:9(1978)
https://doi.org/10.1061/(ASCE)07339445(...
). However, CSAT is prone to damage in the service process and the damage is difficult to detect. If the structural damage cannot be found and processed in time, it will affect the normal use of the structure and even lead to structural damage, resulting in huge casualties and property losses. Therefore, it is of great practical significance to study the damage identification of CSAT during its whole building life cycle. Nowadays, the damage identification method based on frequency domain data is widely employed for structural damage identification. But it still has the limitations such as limited structural monitoring data and complex theoretical methods. When it is applied to the damage identification of complex longspan structures such as CSAT structures, a large amount of manpower and financial resources are required to process the monitoring data.
Deep learning (Zhang, Cheng, Qiu, Ji, & Ji, 2019Zhang, C., Cheng, L., Qiu, J. H., Ji, H. L., & Ji, J. Y. (2019). Structural damage detections based on a general vibration model identification approach. Mechanical Systems and Signal Processing, 123, 316332. doi:10.1016/j.ymssp.2019.01.020
https://doi.org/10.1016/j.ymssp.2019.01....
; Mu & Zeng, 2019Mu, R. H., & Zeng, X. Q. (2019). A Review of Deep Learning Research. Ksii Transactions on Internet and Information Systems, 13(4), 17381764. doi:10.3837/tiis.2019.04.001
https://doi.org/10.3837/tiis.2019.04.001...
) is based on big data and analyzed by computers, which has strong learning ability, good convergence and better stability. It provides a feasible way for feature location extraction in damage identification. Won et al (2021)Won, J., Park, J. W., Jang, S., Jin, K., & Kim, Y. (2021). Automated Structural Damage Identification Using Data Normalization and 1Dimensional Convolutional Neural Network. Applied SciencesBasel, 11(6). doi:10.3390/app11062610
https://doi.org/10.3390/app11062610...
proposed an automatic detection method of structural damage based on data normalization and CNN. The numerical simulation of simply supported beam model under random and traffic load excitations was carried out, showing that the damage location of the beam can be successfully detected. Fu et al (2021)Fu, L., Tang, Q. Z., Gao, P., Xin, J. Z., & Zhou, J. T. (2021). Damage Identification of LongSpan Bridges Using the Hybrid of Convolutional Neural Network and Long ShortTerm Memory Network. Algorithms, 14(6). doi:10.3390/a14060180
https://doi.org/10.3390/a14060180...
took advantage of the CNN highdimensional feature extraction and the time series modeling ability of longshort memory networks to identify the damage of longspan bridges. Taking a longspan suspension bridge as an example, the feasibility of its application in practical engineering was verified. Yang & Huang (2021)Yang, S. Q., & Huang, Y. (2021). Damage identification method of prestressed concrete beam bridge based on convolutional neural network. Neural Computing & Applications, 33(2), 535545. doi:10.1007/s0052102005052w
https://doi.org/10.1007/s0052102005052...
combined the flexibility curvature method and CNN, which can well identify the damage location and damage degree of the prestressed concrete beam bridge structure. Duan et al (2019)Duan, Y. F., Chen, Q. Y., Zhang, H. M., Yun, C. B., Wu, S. K., & Zhu, Q. (2019). CNNbased damage identification method of tiedarch bridge using spatialspectral information. Smart Structures and Systems, 23(5), 507520. doi:10.12989/sss.2019.23.5.507
https://doi.org/10.12989/sss.2019.23.5.5...
proposed an automated damage identification method of hanger cables in a tiedarch bridge using a CNN and simulated the multiple damage detection in the hangers. The results showed that the current CNN performed better under various damage states than the traditional neural network. Wang et al (2021)Wang, X. W., Zhang, X. N., & Shahzad, M. M. (2021). A novel structural damage identification scheme based on deep learning framework. Structures, 29, 15371549. doi:10.1016/j.istruc.2020.12.036
https://doi.org/10.1016/j.istruc.2020.12...
proposed a structural damage identification method based on IASCASCE SHM benchmark, which adaptively optimized the structural parameters of CNN model to ensure better performance and robustness of CNN. At present, the application scope of deep learning in structural damage is mainly concentrated in the damage monitoring of bridges, while less used in the damage identification of string truss structures. However, the application of deep learning in bridge damage monitoring also proves the feasibility of applying deep learning to structural damage identification.
Therefore, a CSAT damage identification method based on multinode timedomain data fusion is proposed in this paper. Two CNN models are established to identify the CSAT damage location and damage degree. The influence of noise on the accuracy of CSAT damage identification by CNN is studied. A CSAT model is selected to illustrate the establishment process of the method in detail to prove the damage identification effect and robustness of the method.
2 Overview of the steps for damage identification
Convolutional Neural Networks (CNN), also known as convolutional networks, is a multilayer neural networks based on deep supervised learning framework (Cha, Choi, & Buyukozturk, 2017Cha, Y. J., Choi, W., & Buyukozturk, O. (2017). Deep LearningBased Crack Damage Detection Using Convolutional Neural Networks. ComputerAided Civil and Infrastructure Engineering, 32(5), 361378. doi:10.1111/mice.12263
https://doi.org/10.1111/mice.12263...
; He, Zheng, Liao, & Chen, 2021He, H. X., Zheng, J. C., Liao, L. C., & Chen, Y. J. (2021). Damage identification based on convolutional neural network and recurrence graph for beam bridge. Structural Health Monitoringan International Journal, 20(4), 13921408. doi:10.1177/1475921720916928
https://doi.org/10.1177/1475921720916928...
) When the CNN is used to identify the damage, the acceleration time history signal measured by multiple sensors is input, and the final recognition result is obtained after data fusion and multilayer convolution kernel pooling feature extraction. Essentially, this method is a data layer fusion method (Krizhevsky, Sutskever, & Hinton, 2017Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017). ImageNet Classification with Deep Convolutional Neural Networks. Communications of the Acm, 60(6), 8490. doi:10.1145/3065386
https://doi.org/10.1145/3065386...
; Zhan, Lu, Xiang, & Wei, 2021Zhan, Y. L., Lu, S. J., Xiang, T. Y., & Wei, T. (2021). Application of convolutional neural network in random structural damage identification. Structures, 29, 570576. doi:10.1016/j.istruc.2020.11.056
https://doi.org/10.1016/j.istruc.2020.11...
). According to the fact that CSAT damage identification is essentially the same as deep learning, the flow chart of CSAT damage identification based on CNN is shown in Figure 1, which includes the following steps:

( 1 ) Establishment of timedomain database;

( 2 ) Data preprocessing and data augmentation ;

( 3 ) Construction of CNN ;

( 4 ) Training and testing of CNN.
3 Timedomain database and data processing
3.1 CSAT finite element model
The CSAT model shown in Figure 2 is selected for finite element analysis. The model is obtained by simplifying the actual roof structure of a railway station (Luo & Yu, 2013Luo, Y., & Yu, J. (2013). Design and Research of the LongSpan Truss String Structure for the Platform Canopy of Beijing North Station. China Railway Science, 34(1), 3542. (In Chinese)) by scaling. The total length of the model is 6 m, the rise height is 0.4 m, and the sag is 0.4 m. Only the three representative components of the upper rigid truss, the middle rigid brace member and the bottom flexible cable member in the CSAT structure are retained (Zeng, Zhou, Zhao, & Xu, 2016Zeng, B., Zhou, Z., Zhao, J., & Xu, Q. (2016). Damage identification analysis of truss string structure based on modal parameters. In Journal of Building Structures (Vol. 37, pp. 134138). (In Chinese)). Among them, the upper part of the structure is an inverted triangle threedimensional truss, five symmetrical circular steel pipe struts are evenly arranged in the middle part, the bottom part is arranged with wire rope cables, and 2 KN prestress is applied to the cables.
3.2 Construction of multinode timedomain database
In this paper, the structural damage is simulated by reducing the elastic modulus of the section. In real life, the degree of damage greater than 50% is easier to be identified, so this paper only considers the degree of damage within 50%. Four degrees of damage 0%, 30%, 40% and 50% were selected for parametric analysis. The external load acting on the structure is simulated by Gaussian random excitation. In order to simulate the limited environmental load acting on the actual project, the lowpass filter is selected to further deal with Gaussian random excitation. In the timehistory analysis, the Newmark method is selected to calculate the timehistory response of the structure without considering the effect of constant load. The load step is 2  11 s, and the load is 3 s. The number of acceleration time histories of each node is 1 × 6144. In this paper, the vertical acceleration timehistory data of 11 nodes in the bottom chord shown in Figure 3 are extracted to a sample database. Finally, the data amount obtained by each timehistory analysis of the structure is 11 × 6144.
To obtain higher prediction accuracy, a large amount of timedomain data is required to train CNN. Therefore, a large of time history analysis and calculations are carried out in this paper. Considering single damage each time, only one node of the upper chord is excited, so there are 48 calculated damage conditions under each Gaussian excitation (12 nondestructive and 36 damage at each position). In order to ensure the same number of samples for the four damage degrees, 15 different Gaussian excitations are used for time history analysis and calculation for each element under nondestructive working conditions, while 5 different Gaussian excitations are used for time history analysis and calculation for each element under the other three damage working conditions. Table 1 shows the consideration factors of damage conditions. Finally, the CSAT timedomain database with 2340 data sets and 1 × 6144 sample dimensions is obtained.
3.3 Data Preprocessing and data augmentation
The selected 211s load step in time history analysis leads to a large characteristic diagram, which affects the calculation efficiency and accuracy of convolution. In other words, it is detrimental to the overall training of the structure. Therefore, each group of data is downsampled by numerical analysis. After the raw data was downsampled, the sample size of each data changed from 11 × 6144 to 11 × 3072 in two dimensions and the size of timedomain data sample library was twice the original size. The downsampling operation reduces the sample size of each data while improves the sample size of the time domain database, which indirectly improves the training efficiency and training accuracy of CNN from two aspects.
Before using CNN for data analysis and processing, it is necessary to standardize the data. The standardized data is used as the input data of the network for feature extraction and classification. In this paper, the value range of acceleration sensor is unknown, so Zscore standardization method is selected to standardize the data.
Where D is the input sample data of the network, ${D}^{\mathrm{\text{'}}}$ is the input sample data after standardization, $\mu $ is the mean value of the input sample data, $\sigma $ is the standard deviation of the input sample data.
Noise is inevitable in the actual monitoring of CSAT structures. At present, the noise level of practical engineering is about 1% 2%. In order to analyze the CNN robustness, this paper adds 1% Gaussian noise to the standardized timedomain data (Lin, Nie, & Ma, 2017Lin, Y.Z., Nie, Z.H., & Ma, H.W. (2017). Structural Damage Detection with Automatic FeatureExtraction through Deep Learning. ComputerAided Civil and Infrastructure Engineering, 32(12), 10251046. doi:10.1111/mice.12313
https://doi.org/10.1111/mice.12313...
). The specific formula of Gaussian noise is as follows:
After the downsampling and data standardization steps, the size of data in the timedomain database is 4680. The size still belongs to the category of small data sets, so the data augmentation method is introduced (Lin, Nie, & Ma, 2017Lin, Y.Z., Nie, Z.H., & Ma, H.W. (2017). Structural Damage Detection with Automatic FeatureExtraction through Deep Learning. ComputerAided Civil and Infrastructure Engineering, 32(12), 10251046. doi:10.1111/mice.12313
https://doi.org/10.1111/mice.12313...
). 128 samples are randomly selected from the timedomain library to form a batch dataset for subsequent CNN training.
The data processing is completed through the steps of downsampling, data standardization, Gaussian noise introduction and data augmentation. The data samples are divided into 3263 training samples (about 70%), 949 test samples (about 20%) and 468 validation samples (about 10%). The test set, validation set, and training set data are completely independent without duplicate samples.
4 CNN Implementation
4.1 Construction of CNN
CSAT is a complex structure, so it is necessary to identify the CSAT damage location and the CSAT damage degree separately when studying the CSAT damage identification. The damage location is essentially a classification problem by analyzing the monitoring data, while the damage degree identification is essentially a data fitting problem by obtaining the damage degree of the damage interval according to the monitoring data. Due to the different characteristics of CSAT damage location recognition and damage degree recognition, two corresponding CNN models of damage location recognition and damage degree recognition were constructed respectively.
The learning curve was used to determine the value intervals of each parameter during the parameter adjustment process. Each parameter was adjusted one by one until the prediction model achieved the highest accuracy, and the specific values were shown in Table 2 and Table 3. Besides, in the final layer design of the fully connected layer, Softmax was selected by the damage location prediction model to predict the damage location (Table 2 and Figure 4). While the damage degree prediction model uses nonlinear activation functions to obtain the damage degree at different locations (Table 3).
4.2 Training and testing of CNN
The supervised learning algorithm is selected to train the CNN. Parameters such as learning rate and batch size are preset firstly during the training of CNN. Then appropriate parameters are selected for training through multiple debugging. The network training parameters selected in this paper are shown in Table 4.
In order to enhance the reliability of the prediction model, 10fold crossvalidation was performed during the training. The training process is divided into two stages, as shown in Figure 5. The input data are transmitted from low level to high level in turn to the forward propagation stage. The data enters the backward propagation stage when the prediction accuracy error is not within the allowable range. The error in the propagation is propagated from high level to low level. The training will not stop until the prediction accuracy meets the requirements and the confidence interval is [0.95,1].
The test process of CNN are as follows: After the network training is completed, the CNN training accuracy is tested with test samples without output value. If the prediction results of test samples do not meet the requirements, the CNN training parameters need to be adjusted and retrained.
5 Analysis of Damage Location Identification Results
In this section, 949 noisefree test samples and 949 noisy test samples are employed for damage location prediction model, which are trained by noisefree samples and noisy samples respectively. Then, their respective prediction results are obtained. Compared with the actual output, the convolution test accuracy is shown in Figure 6. It can be seen in Figure 6:

(1) The noisefree CNN prediction accuracy is 74.4%, which means that CNN can accurately identify the CSAT damage location.

(2) The noisefree CNN prediction accuracy is 74.4%, while the noisy CNN prediction accuracy is 77.6%. The noisy CNN prediction accuracy is slightly higher than that of the noisefree CNN. Adding noise in CNN is equivalent to increasing the number of training samples, so the accuracy is improved accordingly. The higher prediction accuracy exactly shows that CNN has good antinoise ability.
Figure 7(a) shows the prediction accuracy of noisefree CNN and noisy CNN for different position elements. From Figure 7(a), it can be seen that CNN has better damage prediction accuracy for each element of the bottom chord, which is more than 60%, and the noisefree CNN has the highest damage prediction accuracy for Element 9 of the bottom chord, which is 90.4%. The CNN with noise has the highest damage prediction accuracy of 97.3% for Element 11 of the bottom chord.
Figure 7 (b) shows the decline rate of the noisy CNN training accuracy compared with that of the noisefree CNN. When the noisy CNN is used to predict from Element 1 to Element 4, the accuracy is reduced and the maximum decline is 7.8%; the prediction accuracy of Element 5 to Element 12 is generally improved. The prediction accuracy of Element 6 is the largest, which is 18.3%. Although the structure is symmetrical, the accuracy of damage identification is different due to the difference in the constraint conditions of the left span and the right span. In general, the recognition effect of CNN with noise is ideal, and the CNN has good robustness.
Meanwhile, the tsne dimension reduction algorithm is used to classify 130 training data. Figure 8 intuitively shows that the data with the same feature are concentrated together while the data with different features are scattered, which reflects the strong feature extraction ability of CNN.
6 Analysis of Damage Degree Identification Results
Considering the randomness of the prediction of CNN, this paper takes the average value of the prediction results with the same actual damage location and damage degree to obtain the average accuracy of the CNN degree prediction. Figure9(a) compares the noisy CNN damage prediction results with the noisefree CNN damage prediction results under four damage conditions (0%, 30%, 40%, 50%) mentioned above, and Figure9(b) compares the CNN prediction errors based on two different kinds of data.
It is seen from Figure 9 that: (1) When the damage prediction is based on the CNN with noisefree data, the prediction error of the other elements is less than 15% except Element 4(16.63%). indicating that the CSAT damage identification is ideal; (2) When the CNN based on noise data is used to predict the damage, the prediction error of Element 3 and Element 8 is more than 15%, and the prediction error of other elements is less than 15%, which can also meet the actual needs in engineering; (3) The prediction effect of noisefree CNN is better than that of noisy CNN.
The average accuracy verifies the effectiveness of the CNN in identifying the damage degree. However, the average accuracy only analyzes the prediction of the damaged element by the network, which cannot reflect the prediction of the undamaged element. Therefore, this paper extracts the output layer data of the CNN, and selects three kinds of elements including the midspan element (Element 7) and the twoside span elements (Element 3 and Element 10) to analyze the specific prediction effect of the CNN on each element under the damage condition. The prediction effect of CNN on each element of the damage condition is shown in Figure 10.
Figure 10 shows that: (1) CNN can better predict the damage degree of each member element. In the prediction results of the two types of CNN, the predicted damage degree of nondamage elements is far less than that of damage elements, and the damage degree predicted by most nondamage elements is close to 0, which can be judged as nondamage. (2) Since the constraints of the left span (fixed hinge support) and the right span (sliding hinge support) are different, the damage prediction results of the left span Element 3 are different from the right span Element 10 at its symmetric position. (3) CNN has different damage identification accuracy for bar elements at different positions. The noisefree CNN of Figure 10 (a) (c) (e) show that the prediction accuracy of the leftspan Element 3 is the best, the prediction accuracy of the rightspan Element 10 is the second, while the prediction accuracy of the midspan Element 7 is the lowest. The noisy CNN of Figure 10 (b) (d) (f) show that the prediction accuracy of the midspan Element 7 is the best, the prediction accuracy of the right span Element 10 is the second, and the prediction accuracy of the left span Element 3 is the lowest.
7 Conclusion
In this paper, a fusion damage identification method based on CNN is proposed to identify the CSAT damage. Based on the two identification targets of CSAT damage location and damage degree, two CNN prediction models were established to predict the noisefree time domain data and the noisy time domain data respectively. The two prediction models were applied in the following way: the damage location prediction model output the damage location identification results, and then the damage degree prediction model output the damage degree identification results. The main conclusions are as follows:
(1) The damage location prediction model can accurately identify the damage location of CSAT. Moreover, the prediction accuracy of the damage location prediction model with noise is higher than that of the prediction model without noise, which also indicates that the damage location prediction model has good robustness.
(2) The damage degree prediction model without noise can effectively identify the damage degree of CSAT. And the damage degree prediction error of damage degree prediction model with noise is less than 15% for each CSAT unit, which can meet the needs of engineering practice.
(3) The fusion damage identification method of CSAT based on CNN is effective. CNN not only has good prediction effect on bar elements, but also has different damage identification accuracy for bar elements in different positions.
This paper mainly calculated and studied the single damage of CSAT. Considering that the CSAT is a complex structure with complex forces, further research can be conducted in the future on the case of multiple damages occurring simultaneously in CSAT.
Acknowledgments
The research presented in this paper were sponsored by the “National Key Research and Development Program of China” (2022YFC3801800) and “Key Program of the National Natural Science Foundation of China” (52038010).
References
 Murthasmith, E. (1988). Alternate pathanalysis of spacetrusses for progressive collapse. Journal of Structural EngineeringASCE, 114(9), 19781999. doi:10.1061/(ASCE)07339445(1988)114:9(1978)
» https://doi.org/10.1061/(ASCE)07339445(1988)114:9(1978)  Zhang, C., Cheng, L., Qiu, J. H., Ji, H. L., & Ji, J. Y. (2019). Structural damage detections based on a general vibration model identification approach. Mechanical Systems and Signal Processing, 123, 316332. doi:10.1016/j.ymssp.2019.01.020
» https://doi.org/10.1016/j.ymssp.2019.01.020  Mu, R. H., & Zeng, X. Q. (2019). A Review of Deep Learning Research. Ksii Transactions on Internet and Information Systems, 13(4), 17381764. doi:10.3837/tiis.2019.04.001
» https://doi.org/10.3837/tiis.2019.04.001  Won, J., Park, J. W., Jang, S., Jin, K., & Kim, Y. (2021). Automated Structural Damage Identification Using Data Normalization and 1Dimensional Convolutional Neural Network. Applied SciencesBasel, 11(6). doi:10.3390/app11062610
» https://doi.org/10.3390/app11062610  Fu, L., Tang, Q. Z., Gao, P., Xin, J. Z., & Zhou, J. T. (2021). Damage Identification of LongSpan Bridges Using the Hybrid of Convolutional Neural Network and Long ShortTerm Memory Network. Algorithms, 14(6). doi:10.3390/a14060180
» https://doi.org/10.3390/a14060180  Yang, S. Q., & Huang, Y. (2021). Damage identification method of prestressed concrete beam bridge based on convolutional neural network. Neural Computing & Applications, 33(2), 535545. doi:10.1007/s0052102005052w
» https://doi.org/10.1007/s0052102005052w  Duan, Y. F., Chen, Q. Y., Zhang, H. M., Yun, C. B., Wu, S. K., & Zhu, Q. (2019). CNNbased damage identification method of tiedarch bridge using spatialspectral information. Smart Structures and Systems, 23(5), 507520. doi:10.12989/sss.2019.23.5.507
» https://doi.org/10.12989/sss.2019.23.5.507  Wang, X. W., Zhang, X. N., & Shahzad, M. M. (2021). A novel structural damage identification scheme based on deep learning framework. Structures, 29, 15371549. doi:10.1016/j.istruc.2020.12.036
» https://doi.org/10.1016/j.istruc.2020.12.036  He, H. X., Zheng, J. C., Liao, L. C., & Chen, Y. J. (2021). Damage identification based on convolutional neural network and recurrence graph for beam bridge. Structural Health Monitoringan International Journal, 20(4), 13921408. doi:10.1177/1475921720916928
» https://doi.org/10.1177/1475921720916928  Cha, Y. J., Choi, W., & Buyukozturk, O. (2017). Deep LearningBased Crack Damage Detection Using Convolutional Neural Networks. ComputerAided Civil and Infrastructure Engineering, 32(5), 361378. doi:10.1111/mice.12263
» https://doi.org/10.1111/mice.12263  Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017). ImageNet Classification with Deep Convolutional Neural Networks. Communications of the Acm, 60(6), 8490. doi:10.1145/3065386
» https://doi.org/10.1145/3065386  Zhan, Y. L., Lu, S. J., Xiang, T. Y., & Wei, T. (2021). Application of convolutional neural network in random structural damage identification. Structures, 29, 570576. doi:10.1016/j.istruc.2020.11.056
» https://doi.org/10.1016/j.istruc.2020.11.056  Luo, Y., & Yu, J. (2013). Design and Research of the LongSpan Truss String Structure for the Platform Canopy of Beijing North Station. China Railway Science, 34(1), 3542. (In Chinese)
 Zeng, B., Zhou, Z., Zhao, J., & Xu, Q. (2016). Damage identification analysis of truss string structure based on modal parameters. In Journal of Building Structures (Vol. 37, pp. 134138). (In Chinese)
 Lin, Y.Z., Nie, Z.H., & Ma, H.W. (2017). Structural Damage Detection with Automatic FeatureExtraction through Deep Learning. ComputerAided Civil and Infrastructure Engineering, 32(12), 10251046. doi:10.1111/mice.12313
» https://doi.org/10.1111/mice.12313
Edited by

Editor: Pablo Andrés Muñoz Rojas
Publication Dates

Publication in this collection
13 Jan 2023 
Date of issue
2023
History

Received
30 July 2022 
Reviewed
24 Nov 2022 
Accepted
20 Dec 2022