extfieldsofstudy:
Physics
Environmental Science

text:
Analysis and improvement measures of defective coal gangue fired brick

According to the phenomenon of the accident of defective products of finished bricks, combined with fuzzy mathematics and fault tree analysis theory, the causes of the accident are studied. Firstly, the downward method is used to analysis the structure of fault tree and the influence degree of each basic event on the defective top event of finished brick is sorted. Secondly, the trigonometric fuzzy function is used to normalize the probability value of the basic event collected and the probability value of the basic event without statistical data obtained by the expert scoring. The importance of the processed triangular fuzzy probability is quantitatively analyzed and compared and the main factors affecting the top event are obtained. Finally, specific and targeted suggestions are put forward according to the factors causing the top event.

Introduction
As a new modern wall material, coal gangue fired brick is widely concerned by people. Using coal gangue as the raw material for producing sintered brick can not only reduce the damage of coal gangue to the environment but also solve the problem of using a lot of land for brick making, realizing " No coal is used to burn bricks and soil is not used to make bricks ". Many coal companies rely on their own companies to build coal gangue brick factories nearby, hoping to consume coal gangue and bring more benefits to the company. However, due to the immaturity of technology and management defects, defective products will appear in the process of producing sintered bricks. Defective products will not only affect the quality level of the assessed product, but also affect the sales of the product.

Overview of coal gangue fired brick
Coal gangue fired porous brick and hollow brick are new energy-saving wall materials. Through the analysis of the chemical composition of coal gangue, it is found that the coal gangue fired brick can completely replace the solid brick made of clay, which greatly reduces the environmental damage. Coal gangue brick not only saves land space, but also consumes mine waste [1]. It is a low-carbon building material which is conducive to environmental protection. Gangue brick has a broad market, it has unique performance advantages: (1) Good fireproof, sound insulation and dimensional stability (2) Low energy consumption, excellent quality (3) Increase the use area of building (1) According to the calculation, there are 14 minimum cut sets in the defective products of gangue bricks, which indicates that there are 14 ways to cause defective products.

4.1.2.
solving the structural importance of fault tree. According to the minimum cut set of fault tree, the importance of each event structure is judged. The cut set is the smallest: According to the formula , the structural importance coefficient of the basic event is solved as follows: According to the above basic events, the order of structural importance is as follows: According to the order of structure importance, it can be concluded that the cooling is too fast, the aging is not enough, and the emergency fire has the greatest impact on the defective products of fired bricks. Therefore, it is necessary to strengthen the control and management of these events [4].

normalization of basic time probability.
4.2.1.1 data processing with exact statistical data. According to the collected data, the basic events of probability statistics are as follows: x2, x3, x5, x8, x10, x11, x15, x18 The basic events without statistics are: x1, x4, x6, x7, x9, x12, x13, x14, x16, x17 Basic events with accurate probability and statistics: x2, x3, x5, x8, x10, x11, x15, x18 the probability values are: q2=0.0049, q3=0.0002, q5=0.00035, q8=0.0065, q10=0.00017, q11=0.0098, q15=0.077, q18=0.0082. Affected by external conditions, these seemingly accurate data still have fluctuation range. In order to describe more accurately, three experienced experts are asked to score and give the fluctuation range [5]. The triangular fuzzy probability ̃= ( , , ) is obtained by normalizing the fluctuation value and its precise value, where a is the lower limit of the fluctuation value scored by the expert, and b is the upper limit of the fluctuation value scored by the expert. As shown in Table 2.  is taken as the m, and the standard deviation is taken as σ. It is assumed that the evaluation value follows the normal distribution [6]. According to the 3σ principle, the possibility of the value of the evaluation value in the interval is 99.7%. Therefore, = = 3 ,it is required to normalize the data without exact statistics, and the data obtained is shown in Table 3.

importance analysis of basic events.
The influence degree of top event by basic event can be described by fuzzy importance and the fuzzy importance of basic event is positively correlated with the impact on the system, so improving the event with higher fuzzy importance can effectively improve the system reliability. In this paper, triangular fuzzy numbers are selected, When A 1 ,A 2 represents the area of two small triangles respectively,Suppose there is a point Z , so that the two parts of the area under the fuzzy curve can be divided equally through the boundary of the point, Then this point Z is the median of triangular fuzzy number, and the value of point Z can be calculated according to the following formula: The evaluation method is as follows: The first case: for those with exact statistical data, it can be obtained according to formula (12), (13). The second case: if there is no exact statistical data, the median is determined by the score of experts, which is obtained by equation (14).
According to the above formula, the fuzzy probability of each basic event is calculated: Therefore, the fuzzy importance of basic event X i is ranked as follows: According to the ranking of the above fuzzy importance, it can be seen that the chemical composition content does not meet the requirements of the standard brick, the lubrication is not normal, the particle grading is unreasonable, the equipment is not matched, and the aging is not sufficient, to strengthen the control of these factors, we can effectively reduce the occurrence of defective product accidents [7]. Among them, insufficient aging is very high in the analysis of structural importance and fuzzy importance, that is to say, it has a great impact on the top event, so it is necessary to focus on monitoring this basic event in the normal production process.

raw material crushing
The ball mill is installed in the raw material crushing system to overcome the hard and hard to break material on the screen by hammer. The returned material is ground into powder by ball mill and added into the raw material, and the raw material particles after ball milling are no longer angular, which increases the plasticity of raw material; A stone remover is added at the entrance of raw materials to prevent iron nails, iron sheets, welding rod heads, large stones, broken mixer cutters, etc. from entering the extruder, increasing the wear of bearings.
Due to the high moisture content of coal gangue discharged from underground coal mine or washing plant, it is easy to stick and block crushing, crushing and screening equipment, so it is necessary to store gangue in advance to reduce the moisture content of raw materials. Reasonable control of particle gradation, particle composition ratio are: particle size less than 0.05mm content of 33%~52%; particle size of 0.05mm~1.3mm content of 22%~66%; particle size of 1.3mm~2mm content of less than 30%, to ensure reasonable particle gradation, through the control of particle size to reduce the damage caused by limestone particles [8]. Reasonable aging can improve the plasticity of raw materials and the strength 8 of green bodies. Therefore, it is necessary to ensure that the aging time is more than 3 days. The temperature should be kept above 10 ℃ and the moisture content should be controlled at 11%~13%.

brick forming stage
The air content should be controlled at 10%~12% (volume ratio) before brick forming. When excess air is found, vacuum pump should be used to extract air before molding. The formed brick is mainly composed of raw materials, air and water. The cracks can be eliminated by mixing evenly with a mixer to keep the slurry homogenized.
In order to prevent the core frame from cracking, the extruder head and mouth adopt the structure of equal speed extrusion with low stress, and the length of the die is controlled within 0.6~0.7 times of the first section of cutter. The head and mouth of the machine should be equipped with lubrication structure to reduce the resistance during extrusion, so as to solve the problem of speed difference of mud stick, and save about 20% of electric energy. Since the cost of electric energy accounts for a large proportion in the production cost, this method should be paid attention to. When the surface of the core head is too rough or there are impurities which lead to fish scale in the hole, the surface of the core head should be polished, the design scheme should be optimized, the molding moisture should be increased and the impurities should be removed [9].

product firing
Because the drying speed and shrinkage speed of the green body are always fast outside and slow inside, the shrinkage should be controlled less than the elastic coefficient (1%~2%) of the slurry to prevent the occurrence of network cracks. The air supply temperature is not easy to be too high during drying and should be controlled between 105 ℃ and 130 ℃. Because the hollow brick wall is thin, the rib is thin, the strength is low, the crack resistance is weak, and it is not resistant to high temperature. Therefore, the hot air temperature of the air inlet of the artificial drying chamber should be 30%~50% lower than that of drying solid brick under the same conditions.
The strength of hollow brick is low, and it is easy to collapse due to moisture. Therefore, it is necessary to check the moisture discharge hole frequently, discharge the moisture with relative humidity greater than 95% in time, improve the baking level, fully preheat the body, slowly dehydrate, and steadily raise the temperature, so as to avoid moisture absorption collapse. In order to prevent hairy cracks, the cooling should be slow after high-temperature roasting, the fire eye cover should be kept closed in the negative pressure area, and the kiln door should not be opened too early or too close [10]. The temperature of kiln car table should not be too high. Refractory materials with good thermal insulation effect should be used on the table surface. The length of empty car line should be extended and the cooling time should be increased.

Conclusion
With the continuous development of China's gangue brick industry and policy guidance, the use of coal gangue to produce sintered brick has attracted more and more attention. In this paper, the fuzzy fault tree analysis method is used to analyze the accidents that lead to the defective products of finished coal gangue bricks in the production process. Through effective measures to reduce the occurrence rate of defective products accidents, in order to reduce the comprehensive cost of gangue bricks, it provides reference data for the future brick industry and promotes the circular development of enterprise economy.


An in-depth performance analysis of the oversampling techniques for high-class imbalanced dataset

Article history: Received 23 December 2020 Revised 13 February 2021 Accepted 18 February 2021 Available online 28 February 2021 Class imbalance occurs when the distribution of classes between the majority and the minority classes is not the same. The data on imbalanced classes may vary from mild to severe. The effect of highclass imbalance may affect the overall classification accuracy since the model is most likely to predict most of the data that fall within the majority class. Such a model will give biased results, and the performance predictions for the minority class often have no impact on the model. The use of the oversampling technique is one way to deal with high-class imbalance, but only a few are used to solve data imbalance. This study aims for an in-depth performance analysis of the oversampling techniques to address the high-class imbalance problem. The addition of the oversampling technique will balance each class’s data to provide unbiased evaluation results in modeling. We compared the performance of Random Oversampling (ROS), ADASYN, SMOTE, and Borderline-SMOTE techniques. All oversampling techniques will be combined with machine learning methods such as Random Forest, Logistic Regression, and k-Nearest Neighbor (KNN). The test results show that Random Forest with Borderline-SMOTE gives the best value with an accuracy value of 0.9997, 0.9474 precision, 0.8571 recall, 0.9000 F1-score, 0.9388 ROCAUC, and 0.8581 PRAUC of the overall oversampling technique.

Introduction
Class imbalance occurs when the distribution of classes between the majority and the minority classes is not equal. In real-world applications, the class imbalance may vary from minor to severe [1]. The dataset can be said to be unbalanced if each class is not represented in a balanced manner. The majority class consists of a large portion of the dataset, while the minority class consists of a small portion of the dataset, which is often the object to be modeled. The consequence of high-class imbalance will impact the classification's overall performance when the model is most likely to predict most of the data falling within the majority class. This model will yield biased results, and the performance predictions for the minority class frequently have little impact on the model. The research conducted by He and Garcia [2] explains that unbalanced data can be seen based on the majority and minority class ratios ranging from 100:1 to 10,000:1. The creation of a model using a high level of imbalance is considered challenging by experts due to the complexity of the processing of balancing data [3].
There are two methods commonly used in modeling data imbalances, namely supervised and semi-supervised [4]. The model will estimate based on the dataset's existing sample to be classified in the supervised approach. Several algorithms can be used, such as Random Forest (RF) [4,5], K-Nearest Neighbors (KNN) [6,7], and Support Vector Machine (SVM) [8,9]. In the semi-supervised approach, data classification will be identified using label and unlabeled data in the dataset. One of the algorithms included in the semi-supervised approach is K-Means [10,11]. Modeling in the high-class data imbalance is important because not all models can provide the actual classification. The unbalanced characteristics of the dataset will result in bias in the model so that a process at the data level is required, such as resampling minority data.
Resampling is a process that tries to balance the distribution of data between minority data and majority data. There are two groups in resampling, namely under-sampling and oversampling. Undersampling is a way to remove or reduce existing samples in the data majority, and oversampling tries to flatten data distribution by duplicating minority data. Oversampling is the focus of this research because all data in the dataset is crucial to be modeled by machine learning.
Currently, the state-of-the-art oversampling technique developed by Chawla [12] is Synthetic Minority Oversampling Technique (SMOTE). This method produces a sample based on the closest rivalry by duplicating it along the lines between minority classes. There are several developments in the oversampling technique method based on the SMOTE method. Each method development has its characteristics, such as Borderline-SMOTE [13], which focuses on duplication on the margins of the minority class, and Adaptive Synthetic Sampling Approach for Imbalanced Learning (ADASYN) [14], which calculates based on the density of minority data. Even though many oversampling techniques have been developed, only a few have been applied to high-class data imbalances.
Many imbalanced datasets can be accessed publicly, such as wine quality [15], cancer diagnosis [16], and credit card fraud detection [17]. The wine quality dataset contains data for classifying the quality of red wine based on wine quality classes. This dataset has 1,599 data with the percentage ratio of minority/majority data of 3.31%/96.69%, which indicates that only about 53 minority data are available in this dataset. Furthermore, cancer diagnosis data contains data to classify whether the patient has cancer or not. This dataset has a total of 1,056 data with a minority/majority data percentage ratio of 18.09%/81.9%, which indicates that there are about 191 minority data that can be modeled. The last dataset is the credit card fraud dataset, which contains data to detect credit card fraud. This dataset's total data is 284,807, with a percentage ratio of the minority/majority data of 0.17%/99.83%. The ratio data shown in the credit card fraud dataset indicates that this dataset experiences a high-class imbalanced dataset with a minority data of 492 from the existing data population. The credit card fraud dataset will be selected in this study because it has the characteristics of a high-class imbalanced dataset.
Several studies use this high-class data imbalance dataset, such as Makki [18], which performed fraud detection using several machine learning models, namely Support Vector Machine and Artificial Neural Network with random oversampling technique. Meng [19] used a combination of XGBoost with oversampling and under-sampling techniques to detect credit card fraud. The obtained result is that the SMOTE technique gives a better score than the under-sampling technique. Almhaithawi [20] used several machine learning methods such as Logistic Regression, Random Forest, and XGBoost by calculating the cost-sensitive Minimum Bayes Risk, which is balanced using SMOTE, which shows good results. Awoyemi [21] used a hybrid technique of under-sampling and oversampling to solve the data imbalance problem. Several machine learning methods used in this test, namely Naïve Bayes, K-NN, and Logistic Regression, showed quite good results. However, all of the above studies use SMOTE as the main oversampling, and a few use other oversampling techniques to solve the problem of high-class data imbalance.
This study aims for an in-depth performance analysis of the oversampling techniques to address the high-class imbalance problem. We compare the performance of Random Oversampling (ROS), ADASYN, SMOTE, and Borderline-SMOTE techniques. All oversampling techniques are combined with machine learning methods such as Random Forest, Logistic Regression, and K-NN. Utilizing the oversampling technique will balance each class's data to provide unbiased evaluation results in modeling. Each characteristic of the oversampling technique has its respective advantages, which will be explained in this study.

Research diagram system
Fig. 1 shows the diagram system used in this study. The initial workflow in the system model is to split up the data using the hold-out method so that it becomes two parts, namely training set, and test set. In the training set, oversampling techniques are used to increase the number of minority class so that when a model fitting is carried out, a balanced dataset can be obtained.  • Random oversampling method (ROS) performs duplication by selecting a random set of minority classes for random data replication [22]. Because the sampling process is carried out randomly, random oversampling has a disadvantage, namely that it requires a long training time, and there is the possibility of overfitting. • SMOTE duplicates data by measuring the similarity between neighboring minority class samples [12]. Each data will be reproduced based on the nearest neighbor line. • Borderline-SMOTE duplicates data by making the closest neighbor line to the sample data on the margins of the minority class [13]. Duplication on this border will strengthen the difference between the minority and majority class. • ADASYN calculates the density distribution in minority classes before duplicating data based on the criteria obtained when calculating class density [14]. This approach helps to focus on the midpoint of the minority class area depending on the dataset.

Description of the dataset
The dataset used in this study is obtained from European cardholder transactions for two days in September 2013 [17]. The dataset is collected by two research teams from Worldline and Libre Brussels University. The dataset contains 30 attributes containing transaction time, number of transactions, and 28 other attributes labeled V1 to V28 through the transformation results using Principal Component Analysis (PCA). This transformation is performed to hide sensitive attribute data from the user. Fig. 3 shows the distribution of the minority and majority classes. There were 284,807 transactions with a positive fraud class percentage of 0.17% and a negative fraud class of 99.83% of the total transactions. Credit card transactions contain numeric and categorical data so that this combination will be processed to detect credit card fraud.

Evaluation metrics
There are four basic metrics used for the evaluation of this study, namely the number of true positive (TP), false positive (FP), false negative (FN), and true negative (TN). TP and TN is the number of samples from the test set that are classified correctly and incorrectly, respectively. In contrast, FN and TP represent the number of samples from the test set, classified incorrectly as negative and positive. A commonly used evaluation metric uses accuracy to get the ratio of how many samples of data were correctly classified. The accuracy is shown in Eq. 1. The information provided by accuracy is sometimes useless when measuring how reliable a model using imbalanced data is. So, in this case, we can measure it using the evaluation metric F1-score. F1-score evaluation requires two metric evaluations: precision and recall, which can be seen in Eq. 2 and Eq. 3.
The F1-score will balance the two metrics so that they are harmonious with each other through Eq. 4. An evaluation called Area Under the Receiver Operating Characteristic Curve (ROC-AUC) is needed to find out how well the model can differentiate between positive and negative classes (ROC-AUC), which is shown in Eq. 5. In the context of an imbalance, the ROC AUC evaluation data sometimes provide misleading information so that an evaluation metric called Precision-Recall Curve (PRAUC) is used.

Results and Discussion
Four oversampling techniques are carried out depending on the formal diagram scheme being used: ROS, SMOTE, Borderline-SMOTE, and ADASYN. Three machine learning methods are employed to determine the best candidate to solve credit card fraud, namely Random Forest, Logistic Regression, and K-NN.
(1) Table 1 shows the classification accuracy, precision, recall, F1-score, ROC-AUC, and PRAUC of the four oversampling techniques on the credit card fraud dataset. In the use of raw data, the results are shown to be very good. However, this is the main problem because the data's composition is highly unbalanced, resulting in a bias in the classification model. The oversampling technique is needed to increase the number of minority classes in data imbalances [23].   The precision value determines how many relevant predictive values were correctly predicted. The best score is Borderline-SMOTE, with a result of 09474. Interestingly, when observing the model, Random Forest's results give the highest average precision compared to other models because Random Forest uses bagging approach in the decision tree process to provide lower variance [24].
The next metric is recall, which determines how many the actual predictive value of the data. ADASYN held the best score with a result of 0.9286. ADASYN has the advantage of calculating the density of data distribution so that the results of the duplication data provided can be focused on one particular area and strengthen the results of recall evaluation.
Precision and recall have mutually dependent characteristics, which are called trade-offs. Through this, the F1-score plays an important role in knowing the alignment between the precision and recall values by calculating the average value for each evaluation value from the precision and recall metrics. The best F1 score is Borderline-SMOTE, with a score of 0.9000. This high result indicates that Borderline-SMOTE provides the most balanced results compared to other oversampling values because the resulting data duplication is on the margins of the minority data to strengthen the differentiating value between the minority class and the majority class. Furthermore, the ROC-AUC value will determine how well the machine learning model distinguishes between negative and positive classes. Among all the oversampling techniques in this study, the highest result is obtained by ROS with a value of 0.9822. It can be seen in Fig. 4 that the combination of machine learning and oversampling techniques can distinguish negative and positive classes with satisfactory results with a value range of 0.93-0.98. Even though the ROC-AUC result is relatively high, there is still a possibility that the results presented could be misleading when using a highly unbalanced dataset. Therefore, PRAUC is used to find out the reliability of the resulting classification model. PR-AUC identifies how well the average precision is generated at each threshold result of the recall. The best result is ROS, with a score of 0.8603, beating all other competitors in the oversampling techniques. According to Fig. 5, it can be seen that the K-NN gives results between 0.58-0.82, which shows that this model is not reliable for credit card fraud cases. Furthermore, the Logistic Regression results show that the value between 0.74-0.76, giving an unreliable average result. In Table 1, the precision results generated by Logistic Regression are terrible. Finally, Random Forest yields a result value between 0.84-0.86, which shows that this model is reliable for credit card fraud cases.

Conclusion
The effect of high-class imbalance can affect the overall classification performance. The machine learning model will predict most of the data included in the majority class so that the evaluation of the evaluation results gives biased results. Results without using oversampling give high evaluation results indicating bias in the model. Bias in the model occurs because the prediction model for the minority class has no impact on the model so that an oversampling technique is needed to avoid bias in the results of the model evaluation. In this study, the oversampling technique can avoid bias in the overall evaluation results. The test results of the oversampling technique on the imbalance of credit card fraud data gave quite good results with an accuracy of above 0.89. However, the accuracy results sometimes give misleading results, so that the evaluation of other metrics are needed, such as precision, recall, F1score, ROC-AUC, and PRAUC. Borderline-SMOTE gave the best results with an average PRAUC of 0.8131. Borderline-SMOTE achieves the highest results because it duplicates the margins of the minority data so that it strengthens the difference between the minority and majority class data. ROS obtained the second position with an average PRAUC result of 0.7961. This result is obtained by duplicating based on minority data and randomly. Even though it has a high result, ROS's biggest drawback is that there is little variation in the duplicated data due to the duplication of data based on the original data. SMOTE gives an average PRAUC result of 0.7307. SMOTE duplicates data based on the closest neighbor to minority data so that the characteristics of SMOTE are sensitive to outliers, which can result in minority data being duplicated into the majority data area. Finally, ADASYN with an average PRAUC result of 0.7189. ADASYN works by duplicating data based on the density of the data distribution for the minority class. The more scattered the minority data, the higher possibility of resulting one sample data of minority class.
The best machine learning model is generated by Random Forest with an average accuracy value of 0.9996, precision of 0.9121, recall of 0.8541, F1-score of 0.8819, ROC-AUC of 0.9448, and PRAUC of 0.8513. The Random Forest has a characteristic of being more resistant to overfitting, usually when minority data are accidentally duplicated into the majority data area. Interestingly, Logistic Regression gives poor precision results with an average value of 0.0486. Poor precision results from Logistic Regression affects the resulting F1 score because there is a trade-off between precision and recall. The best combination of oversampling and machine learning method is Borderline-SMOTE with Random Forest with 0.9997 accuracy, 0.9474 precision, 0.8571 recall, 0.9000 F1 score, 0.9388 ROC-AUC, and 0.8581 PRAUC. Through the results of this test, it can be seen that the oversampling technique can provide actual results from data imbalances and can avoid bias in the entire machine learning model. Selecting the right oversampling technique is critical to do in order to maximize the evaluation results of the predictive model.

Declaration of Competing Interest
We declare that we have no conflict of interests.


extfieldsofstudy:
Computer Science
Medicine

text:
Algorithms for Delivery of Data by Drones in an Isolated Area Divided into Squares

Drones are frequently used for the delivery of materials or other goods, and to facilitate the capture and transmission of data. Moreover, drone networks have gained significant interest in a number of scenarios, such as in quarantined or isolated areas, following technical damage due to a disaster, or in non-urbanized areas without communication infrastructure. In this context, we propose a network of drones that are able to fly on a map covered by regular polygons, with a well-established mobility schedule, to carry and transfer data. Two means exist to equidistantly cover an area with points, namely, grouping the points into equilateral triangles or squares. In this study, a network of drones that fly in an aerial area divided into squares was proposed and investigated. This network was compared with the case in which the area is divided into equilateral triangles. The cost of the square drone network was lower than that of the triangular network with the same cell length, but the efficiency factors were better for the latter. Two situations related to increasing the drone autonomy using drone charging or battery changing stations were analyzed. This study proposed a Delay Tolerant Network (DTN) to optimize the transmission of data. Multiple simulation studies based on experimental flight tests were performed using the proposed algorithm versus five traditional DTN methods. A light Wi-Fi Arduino development board was used for the data transfer between drones and stations using delivery protocols. The efficiency of data transmission using single-copy and multiple-copy algorithms was analyzed. Simulation results showed a better performance of the proposed Time-Dependent Drone (TD-Drone) Dijkstra algorithm compared with the Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery routing protocols.

Introduction
Delay tolerant networks (DTNs) allow communication in environments in which frequent transmission discontinuities are present [1][2][3][4]. They have applications in numerous fields, such as space communication networks [1][2][3], smart cities [5], intelligent transport networks, rural networks, environmental monitoring networks, and vehicle networks [4,6]. Within DTNs, message transmission is based on the store-carry-forward paradigm [7,8]. Devices update their communication routes based on the topological changes of the network, and the mobility of the devices plays an important role [9][10][11].
The role of routing [12][13][14] in DTNs is to find the best path to send data through the network to reach the destination. The routing strategies used by DTNs are classified based on criteria such as connection type between nodes, the time at which the path for messages is established, the amount of information held by the nodes about the network, and the number of copies of a message that a node sends.
Algorithms containing different amounts of DTN information are proposed for investigation in [14]. It has been shown that the performances of these algorithms gradually increase, depending on the amount of information about the network they use. Based on the number of copies of a message, single-copy algorithms (forward based) and multiplecopy algorithms (flood based) have been investigated [15,16]. The Direct Delivery algorithm only sends the message to the destination node, and is suitable for both small-and high-mobility networks, in which the probability of meeting between the nodes is high. Comparisons between classical flood-based protocols, such as Epidemic [17], Spray and Wait [18], PRoPHET [19], and MaxProp [20], were undertaken in [15]. Maximum flow with the static approach in buffer-limited delay tolerant networks was investigated in [21,22].
In public transport networks, the connection type between nodes is based on a wellknown schedule and well-defined routes. A DTN composed of pedestrians and cyclists equipped with smart devices was investigated using routing protocols in an Opportunistic Network Environment (ONE) [23]. The MaxProp protocol yielded the best results in terms of delivery probability and average latency. DTN communications in the network storage depend on the store-carry-forward mechanism. A DTN system applied in a communication network on a railway line was found to reduce the message delivery time by 20%, depending on the schedule of trains [8]. In [24], an algorithm to search for the shortest safe path on the network with a time-dependent and edge-length danger factor was proposed. This work is suitable for the optimization of heavy trucks carrying inflammable materials, poison gas, or explosive cargo, and traveling within a city. Based on the simulation in ONE software, the Scheduling-Probabilistic Routing Protocol using History of Encounters and Transitivity (PROPHET) improves the delivery rate and optimizes the delivery delay with low overhead in DTNs for IoT applications [25].
Drone flight path planning can be categorized as off-line planning, on-line planning, or cooperative planning [37,38]. The relatively short flight distance of drones due to their limited battery energy [39] can be extended using drone networks.
Flight simulations using a topological map of hexagons, in which each hexagon contains one drone, have shown the potential for application in indoor rescue missions [36]. In [40], coverage path planning with UAVs was studied, addressing simple geometric flight patterns, such as back-and-forth and spiral, and more complex grid-based solutions considering full and partial information about the area of interest. The area was divided into squares and a drone was flown from a square to another. Parcel delivery missions using a drone were simulated based on heuristic flight path planning (HFPP) and other routing algorithms [28]. The results showed that HFPP delivers up to 33% more data packets compared with Encounter-Based Routing and Epidemic routing protocols.
Vehicular ad hoc networks (VANETs), which are a type of mobile ad hoc network (MANET), can be used in an intelligent transport system. VANETs allow the mobile vehicles to establish three main categories of communication: vehicle to vehicle, vehicle to infrastructure, and infrastructure to infrastructure. A specific application of VANET applied to a drone network allows messages to be sent via wireless links [32]. A bio-inspired coordination protocol for a drone flying ad-hoc network (FANET) used for agriculture applications [30] has been used in an ad hoc simulator for a preliminary analysis of the feasibility of drone network design. The performance of the branch and bound searchbased mode selection (BBS-MS) for drone-based air-to-ground wireless networks was investigated in [31].
In this study, we investigated six routing algorithms in a network of drones with a mobility schedule to ensure communication between isolated areas or in areas with technical damage. We then qualitatively compared the algorithms. The major contributions of this study are as follows:

•
The proposed drone network is independent of the Internet, and is of the DTN type. • A topological map as a collection of regular polygons (squares) was proposed.
• A time-dependent variant of Dijkstra's algorithm, which determines the fastest route by taking into account the time when the message reaches the node and the time allocated for data transfer, was developed for the proposed network. • Five classical algorithms for DTN networks were adapted and tested for the proposed network.

•
Simulations based on flight tests were performed to analyze the efficiency of the data transmission. The results obtained by the single-copy and multiple-copy algorithms were compared, in the case of buffer limited capacity. • Practical application of this work is to facilitate the transmission of information in regions quarantined due to an infectious outbreak, such as COVID-19 pandemic, in regions with technical damage due to a disaster, and in non-urbanized areas without electricity access or communication infrastructure.
The remainder of the paper is organized as follows. In Section 2, a drone network architecture based on the mission profile, and drone sensing and communication, are proposed. Then, the algorithms and protocols for the delivery of data using drones are proposed, described, and analyzed. In Section 3, simulation results are summarized and discussed. Finally, conclusions and possible future work are presented in Section 4.

Drone Network Architecture and Communication
A network map is essential for both drone flight control and simultaneous localization and mission tasks. As noted in [36], three forms of map generation exist: metric, topological, and hybrid maps. A metric map is represented as a grid, geometric, or feature map. Topological maps are represented by graphs comprised of nodes and edges, where nodes represent places, and the edges represent the paths between the nodes [36]. A hybrid map consists of small metric map locations in nodes. These nodes are connected by edges, which are the paths between the metric maps [36]. In this work, a topological map was proposed.
The 2D network surface is intended to be covered with equidistantly distributed points. These points form regular polygons covering the 2D surface. Below, we prove that the only possible means of covering the 2D surface in this manner is by using equilateral triangles or squares. First, we prove the following lemma: Lemma 1. There are 3 ways to cover a 2D surface using regular polygons: equilateral triangles, squares, or regular hexagons.
Proof of Lemma 1. The sum of the degrees of the angles of a polygon with n vertices (n ≥ 3) is 180 • · (n − 2). Each angle of a regular polygon has [360 • · (n − 2)]/n degrees. If a point of the surface is a vertex of a polygon, then it is a vertex for m polygons (m ≥ 3) around this point ( Figure 1). Thus, at such a point we have: It results that 2 · n/(n − 2) = 2 + 4/(n − 2) is an integer value greater or equal to 3. This implies that n − 2 is a divisor of 4 and, because n ≥ 3, it follows that n − 2 is one of the values 1, 2, or 4, which is equivalent to the fact that n is 3, 4, or 6, and m is 6, 4 or, respectively, 3. This means that the 2D surface can only be covered with equilateral triangles, squares, or regular hexagons. Theorem 1. There are two ways to equidistantly cover a 2D surface with points.
Proof of Theorem 1. Using the result from Lemma 1 and the fact that the points are considered equidistant on the 2D surface, it follows that there are only two ways to cover It results that is an integer value greater or equal to 3. This implies that n − 2 is a divisor of 4 and, because n ≥ 3, it follows that n − 2 is one of the values 1, 2, or 4, which is equivalent to the fact that n is 3, 4, or 6, and m is 6, 4 or, respectively, 3. This means that the 2D surface can only be covered with equilateral triangles, squares, or regular hexagons.

Theorem 1.
There are two ways to equidistantly cover a 2D surface with points.
Proof of Theorem 1. Using the result from Lemma 1 and the fact that the points are considered equidistant on the 2D surface, it follows that there are only two ways to cover the 2D surface: with equilateral triangles or with squares, because using regular hexagons is impossible (the vertices of the hexagons are not equidistantly positioned). □ A network to cover a surface with hexagon cells containing three equilateral triangles was proposed in [41]. In the current paper, a network is proposed to cover a similar surface with square cells containing two operational squares ( Figure 2). Each operational cell is covered by a drone. A battery charging/changing dock, which is shared by two drones, is placed in the center of each cell. The docks are able to automatically change/recharge drones, without manual intervention, allowing fully autonomous drone management. The mission profile of each drone consists of several phases or steps: engines start, take off, climb at the cruise altitude, cruise, hovering and data exchange, descent, landing, and engines shut-down. The cruise phase of the flight mission profile consists of four segments ( Figure 3). Charging or changing the drone battery is a necessary step at the end of the flight mission. A network to cover a surface with hexagon cells containing three equilateral triangles was proposed in [41]. In the current paper, a network is proposed to cover a similar surface with square cells containing two operational squares ( Figure 2). Each operational cell is covered by a drone. A battery charging/changing dock, which is shared by two drones, is placed in the center of each cell. The docks are able to automatically change/recharge drones, without manual intervention, allowing fully autonomous drone management. The mission profile of each drone consists of several phases or steps: engines start, take off, climb at the cruise altitude, cruise, hovering and data exchange, descent, landing, and engines shut-down. The cruise phase of the flight mission profile consists of four segments ( Figure 3). Charging or changing the drone battery is a necessary step at the end of the flight mission.     A drone with a quadcopter configuration [42], i.e., a DJI Mavic 2 Pro (DJI, Shenzhen, China) with a size of 214 × 91 × 84 mm (length × width × height), and takeoff weight of 905 g, was considered in this study. The performance characteristics of this drone are presented in Table 1 [43]. All of the drones of the proposed squares network operate in a pre-programmed manner. The drone network communicates with data exchange points via wireless links. The endurance of drones can be improved using various methods, such as changing the battery [44,45], charging the battery via wires [46,47], wireless recharging [48], solar cells [49,50], laser-beam in-flight recharging [49,51], and tethered drones [49]. An average time of 90 min is needed to fully charge an empty battery. An automated means of charging a battery via a wire can be performed using a charging platform installed on the ground and a drone retrofit-kit mounted on the drone [46,47]. Thus, the landing gear of the drone is connected by touch with the charging platform after the drone lands, and A drone with a quadcopter configuration [42], i.e., a DJI Mavic 2 Pro (DJI, Shenzhen, China) with a size of 214 × 91 × 84 mm (length × width × height), and takeoff weight of 905 g, was considered in this study. The performance characteristics of this drone are presented in Table 1 [43]. All of the drones of the proposed squares network operate in a pre-programmed manner. The drone network communicates with data exchange points via wireless links. The endurance of drones can be improved using various methods, such as changing the battery [44,45], charging the battery via wires [46,47], wireless recharging [48], solar cells [49,50], laser-beam in-flight recharging [49,51], and tethered drones [49]. An average time of 90 min is needed to fully charge an empty battery. An automated means of charging a battery via a wire can be performed using a charging platform installed on the ground and a drone retrofit-kit mounted on the drone [46,47]. Thus, the landing gear of the drone is connected by touch with the charging platform after the drone lands, and charging starts automatically. The main disadvantage of this system is that the drone is locked on the ground during the charging of the battery.
An automatic battery changing and recharging system was investigated in [44]. The battery is automatically recharged after it is changed at the station. The electricity needed at each station is able to be provided by a solar panel that charges a battery located at the station. The changing time depends on the efficiency of the changing mechanism, and varies between 15 s [44] and 60 s [45]. In the current study, a maximum changing time before the drone is ready to take off of 60 s was considered.
Four flight tests were performed based on the square-shaped flight mission in the Brasov area of Romania. The flight tests were performed at a temperature of 2 • C, humidity of 69%, and wind speed of 3.5 km/h. A Samsung S9 smartphone device, on which DJI Go 4 app software (DJI, Shenzhen, China) was installed, connected to a DJI remote controller, was used to program the flight mission segments and to remotely control the drone ( Figure 4). A flight altitude of 30 m was chosen [52] and the cruise flight distance of each drone was 12,000 m.
Four flight tests were performed based on the square-shaped flight mission in the Brasov area of Romania. The flight tests were performed at a temperature of 2 °C, humidity of 69%, and wind speed of 3.5 km/h. A Samsung S9 smartphone device, on which DJI Go 4 app software (DJI, Shenzhen, China) was installed, connected to a DJI remote controller, was used to program the flight mission segments and to remotely control the drone ( Figure 4). A flight altitude of 30 m was chosen [52] and the cruise flight distance of each drone was 12,000 m.  (Table 2). Moreover, the average calculated cruise speed of the drone obtained from the flight tests was 12.93 m/s. The percentage of the remaining drone battery obtained at the end of the flight mission was 16% for the rectangular cell. The charging time for the drone battery was 79 min. A safety multiplier of 1.1 was applied to obtain the considered charging time, and the resulting time was used in the simulations. Thus, 87 charging minutes were considered for the rectangular cell flight. The average values of the flight times for each segment were used as input parameters for the simulation of the drone networks in the DTN algorithms.
Eight high-resolution and two infrared sensors were used on the DJI Mavic 2 Pro. These sensors enabled omnidirectional obstacle sensing, to determine the relative speed and distance between the drone and the object, and to ensure good stability in forward  (Table 2). Moreover, the average calculated cruise speed of the drone obtained from the flight tests was 12.93 m/s. The percentage of the remaining drone battery obtained at the end of the flight mission was 16% for the rectangular cell. The charging time for the drone battery was 79 min. A safety multiplier of 1.1 was applied to obtain the considered charging time, and the resulting time was used in the simulations. Thus, 87 charging minutes were considered for the rectangular cell flight. The average values of the flight times for each segment were used as input parameters for the simulation of the drone networks in the DTN algorithms.
Eight high-resolution and two infrared sensors were used on the DJI Mavic 2 Pro. These sensors enabled omnidirectional obstacle sensing, to determine the relative speed and distance between the drone and the object, and to ensure good stability in forward and hovering flight. Left, right, up, down, forward, and backward obstacle sensing were used.
A NodeMCU Lua Wi-Fi, V3, ESP-12E, CP2102 Wi-Fi Arduino development board (Espressif Systems, Shanghai, China) was used for the data transfer between the drones and the stations. The main characteristics of the NodeMCU are shown in Table 3. The data were stored on a micro-SD card. The Wi-Fi board and micro-SD card module are very lightweight and have very low power consumption. The experimental layout, consisting of the NodeMCU Lua Wi-Fi board and the micro-SD card module mounted on a breadboard, is shown in Figure 5a. Arduino code was used to program the Wi-Fi boards.  (Figure 5b) for the Wi-Fi boards was designed using the SolidWorks version 2016 software (Dassault Systèmes, Waltham, MA, USA), and then 3D printed using material extrusion technology from PLA (BCN3D Technologies, Barcelona, Spain) on a BCN3D Sigma R19 printer (BCN3D Technologies, Barcelona, Spain). The Wi-Fi board, micro-SD module, SD card, connection wires, and power cable weighed a total of 21.8 g, thus representing an increase of 2.4% in the total weight of the drone.

Algorithms and Protocols for Delivery of Data Using Drones
The DTN was modeled with a graph having fixed and mobile nodes. There are no connections between the fixed nodes, so there is no possibility of direct data transmission because the considered distance between the nearest two nodes is 3000 m. Network connections are provided by mobile nodes (drones), but their condition is not always the same; they have periods when they are active and periods when they are inactive. This means that there is not always an end-to-end path available between any two nodes in the graph. The Wi-Fi board, micro-SD module, SD card, connection wires, and power cable weighed a total of 21.8 g, thus representing an increase of 2.4% in the total weight of the drone.

Algorithms and Protocols for Delivery of Data Using Drones
The DTN was modeled with a graph having fixed and mobile nodes. There are no connections between the fixed nodes, so there is no possibility of direct data transmission because the considered distance between the nearest two nodes is 3000 m. Network connections are provided by mobile nodes (drones), but their condition is not always the same; they have periods when they are active and periods when they are inactive. This means that there is not always an end-to-end path available between any two nodes in the graph.
We tested five well-known routing algorithms for DTNs (Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery [54]), and a newly proposed TD-Drone Dijkstra approach, on the square-shaped network shown in Figure 6. We performed tests on the network by choosing random sources and random destinations that could be located on any node (marked as a gray circle or a gray rectangle). We considered the drones worked each day from 7:00 a.m. to 6:00 p.m. and the messages may leave a source node between 7:00 a.m. and 5:00 p.m. We considered 1000 messages randomly sent within this interval of time.
Epidemic is the basic form of a flood-based routing protocol: when two nodes meet, they identify the packages that the other node has and transfer the packages that it does not have. At the end of the process, the two nodes have the same content in the buffer. This process is repeated each time two nodes come into contact. When a node has a copy of a message, it waits to meet the destination. In this case, the resource consumption is high but, in a high mobility network, the delay of message transmission is small. In the current network configuration, the algorithm produces poor results due to the low number of contacts between nodes.
Spray and Wait is an algorithm with two phases, one for sending messages (spray) and one to wait for the contact with the destination node (wait). This algorithm circulates in two variants-standard and binary-depending on the number of spread copies of the message. It acts in the same manner as Epidemic, with an important difference: the number of spread copies is constant. The spray phase of the standard approach consists of spraying L copies of the message by the source node itself. The spray phase of the binary approach consists of spraying half of the number of copies to a meeting node. In this case, not only does the source spray messages, but also every node that has more than one copy. The nodes that have only one copy enter the wait phase. This algorithm has the disadvantage that nodes must keep track of other nodes' movement, but the advantage is that the level of flooding is limited. tests on the network by choosing random sources and random destinations that could be located on any node (marked as a gray circle or a gray rectangle). We considered the drones worked each day from 7:00 a.m. to 6:00 p.m. and the messages may leave a source node between 7:00 a.m. and 5:00 p.m. We considered 1000 messages randomly sent within this interval of time.
Epidemic is the basic form of a flood-based routing protocol: when two nodes meet, they identify the packages that the other node has and transfer the packages that it does not have. At the end of the process, the two nodes have the same content in the buffer. This process is repeated each time two nodes come into contact. When a node has a copy of a message, it waits to meet the destination. In this case, the resource consumption is high but, in a high mobility network, the delay of message transmission is small. In the current network configuration, the algorithm produces poor results due to the low number of contacts between nodes. Spray and Wait is an algorithm with two phases, one for sending messages (spray) and one to wait for the contact with the destination node (wait). This algorithm circulates in two variants-standard and binary-depending on the number of spread copies of the message. It acts in the same manner as Epidemic, with an important difference: the number of spread copies is constant. The spray phase of the standard approach consists of spraying L copies of the message by the source node itself. The spray phase of the binary approach consists of spraying half of the number of copies to a meeting node. In this case, not only does the source spray messages, but also every node that has more than one copy. The nodes that have only one copy enter the wait phase. This algorithm has the disadvantage that nodes must keep track of other nodes' movement, but the advantage is that the level of flooding is limited.
PRoPHET is similar to Epidemic, with the exception that it uses information from the buffer of the other node to update its predictability vector. Each node calculates the predictability of the message delivery and sends the message onward only if the contact node has higher predictability than its own. The disadvantage of this approach is the relationship between the overhead ratio and the number of nodes-as the number of PRoPHET is similar to Epidemic, with the exception that it uses information from the buffer of the other node to update its predictability vector. Each node calculates the predictability of the message delivery and sends the message onward only if the contact node has higher predictability than its own. The disadvantage of this approach is the relationship between the overhead ratio and the number of nodes-as the number of nodes increases, the overhead ratio increases [15]. This protocol is known for the complexity of its forwarding strategy. Thus, it consumes a significant quantity of resources to process and store historical values. This approach is feasible for networks with high computation and infrastructure capabilities.
MaxProp is an algorithm based on prioritizing packet transmission and discarding. The packets in the queue are divided into two categories: those below the "n" hop threshold (up to that point), and those above this threshold. Newer packages that have not traveled too much are considered a priority and the guarantee that they will reach their destination is considered to be high. This algorithm also requires high computation and infrastructure capabilities. This protocol has low performance when nodes have small buffer sizes because of the adaptive threshold calculation, but gives better performance with a larger buffer size. It has a so-called slow start problem, because, in the case of a big network, it may take a very long time before each node receives the delivery predictability of other nodes because of the disconnecting nature of the networks, as shown in [20].
MaxDelivery [54] is an algorithm based on prioritizing message delivery using an appropriate buffer management strategy that consists of a forwarding, dropping, and buffer-cleaning mechanism.
Next, we propose our time-dependent Dijkstra algorithm to find a route between two nodes in our drone network. Dijkstra's algorithm is used to find the shortest path connecting two nodes in a network [55]. Our routing problem can be modeled using a time-dependent oriented network [56] defined as follows.

Definition 1. A triple G = (V, A, f) is called a time-dependent oriented network
, where V is a set of vertices, A ⊆ V × V is a set of arcs, and f is the time dependency function defined on each arc, f: A × T → T, T ⊆ R+ is called the time set and when moving on the arc a = (u, v) ∈ A from node u to node v, f(a, t) ∈ T is the moment of arrival at node v if node u is left at the moment t ∈ T. Of course, f(a, t) > t, for each arc a ∈ A and for any moment t ∈ T.
In our problem, V is the equidistantly distributed set of 2D points, A is the set of connections between these points ensured by drones, and T = {0, 1, 2, . . . } is the set of counting seconds in a day. The value of f(a, t) must be computed as quickly as possible. Thus, for each arc a = (u, v), the arrival moments of drones at node v are maintained in order to enable a binary search to be undertaken when f(a, t) is calculated at arc a and time t. The arrival moments of drones for all arcs are pre-calculated (once before starting to use the algorithm) because an exact schedule of drones is known based on each drone's starting second in a day, its travel on each arc, its data transfer at nodes, and its wireless charge/battery change time.
For a given source node s ∈ V, the function dists: V × T → N is introduced, where dists(u, ts) is the distance in seconds from s to u starting from the moment ts, i.e., it is the minimum number of seconds needed to go from node s to node u ∈ V on the arcs of A if source s is left at moment ts. Of course, dists(s, ts) = 0 for every ts ∈ T. If node u is not reachable (accessible) from s, then dists(u, ts) = +∞. For a given destination node d, our problem is to determine dists(d, ts) at a given time ts. The pseudo-code for the time-dependent Dijkstra algorithm is presented in Figure 7. Q is a priority queue. This means that, at any moment, the nodes from Q are sorted in ascending order according to their distance in seconds from s. At the end of the algorithm, if destination d was reached, the values kept in the so-called predecessor vector p are used to determine the route from s to d. If a node v was reached, then this was done Q is a priority queue. This means that, at any moment, the nodes from Q are sorted in ascending order according to their distance in seconds from s. At the end of the algorithm, if destination d was reached, the values kept in the so-called predecessor vector p are used to determine the route from s to d. If a node v was reached, then this was done using the arc (p(v), v), where node p(v) is called the predecessor of v. After the time-dependent Dijkstra algorithm is executed using the staring moment ts, the route from s to d (if it exists, i.e., dists(d) < +∞) is determined using the algorithm presented in Figure 8. Because the nodes of the route are found by the above algorithm in inverse order (from d to s), the route must be reversed at the end. For each data file that has to be delivered, a "json" file is attached that stores all of the information needed to transfer the file from the source to the destination: delivery type (Dijkstra, Epidemic etc.); file information (name, size, time-to-leave); route information (node codes: stations and drones); etc. The json files that store message information for the algorithms Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery implemented in the ONE environment are similar to those considered in [41]. Each route starts and ends with a station id. Each station id (except for the destination) is followed by a drone id, and each drone id is followed by a station id. When a drone arrives at a station, a transfer is initiated between the drone and the station. The drone transfers to the station all of the files that have the station's id in the attached json files. After the drone transfer to the station is completed, the station transfers to the drone all of the files that have the drone's id in the json file.
The range of the Wi-Fi boards was tested. The connections between the boards and file transfer were performed at a distance of up to 85 m with no obstacles in between. In Figure 9, the console output of the Wi-Fi board is presented. The following steps are executed: setup (upload speed is set to 115,200, MAC address is obtained), the connection between two Wi-Fi boards is established, the file transfer is performed, and, finally, the Wi-Fi boards are disconnected. For each data file that has to be delivered, a "json" file is attached that stores all of the information needed to transfer the file from the source to the destination: delivery type (Dijkstra, Epidemic etc.); file information (name, size, time-to-leave); route information (node codes: stations and drones); etc. The json files that store message information for the algorithms Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery implemented in the ONE environment are similar to those considered in [41]. Each route starts and ends with a station id. Each station id (except for the destination) is followed by a drone id, and each drone id is followed by a station id. When a drone arrives at a station, a transfer is initiated between the drone and the station. The drone transfers to the station all of the files that have the station's id in the attached json files. After the drone transfer to the station is completed, the station transfers to the drone all of the files that have the drone's id in the json file.
The range of the Wi-Fi boards was tested. The connections between the boards and file transfer were performed at a distance of up to 85 m with no obstacles in between. In Figure 9, the console output of the Wi-Fi board is presented. The following steps are executed: setup (upload speed is set to 115,200, MAC address is obtained), the connection between two Wi-Fi boards is established, the file transfer is performed, and, finally, the Wi-Fi boards are disconnected.
In our model, when transferring files, the drone hovers over the station at a height of 30 m, which is significantly less than the maximum distance obtained in range tests. The transfer speed, including writing on and reading from the SD card, was also tested at a distance of 30 m. An average of 5.81 Mbps was obtained, which means that a file of 10 MB was transferred in 13.77 s. Sensors 2021, 21, x FOR PEER REVIEW 12 of 21 In our model, when transferring files, the drone hovers over the station at a height of 30 m, which is significantly less than the maximum distance obtained in range tests. The transfer speed, including writing on and reading from the SD card, was also tested at a distance of 30 m. An average of 5.81 Mbps was obtained, which means that a file of 10 MB was transferred in 13.77 s.

Simulation Results and Discussion
The proposed network of drones can be applied in various scenarios, such as in remote quarantined or isolated areas, following technical damage due to a disaster (e.g., an earthquake), or in non-urbanized areas without electricity access or communication infrastructure. For instance, a remote quarantined zone (e.g., due to the COVID-19 pandemic), in which buildings are separated by a safe distance, is considered. In this scenario, each building may be a house in which patients are isolated, a warehouse storing food or drugs, a laboratory in which medical tests are performed for patients, or a location at which doctors are working (isolated from patients). Data packages (medical images, tests, results, prescriptions from doctors, etc.) must be sent between these build-

Simulation Results and Discussion
The proposed network of drones can be applied in various scenarios, such as in remote quarantined or isolated areas, following technical damage due to a disaster (e.g., an earthquake), or in non-urbanized areas without electricity access or communication infrastructure. For instance, a remote quarantined zone (e.g., due to the COVID-19 pandemic), in which buildings are separated by a safe distance, is considered. In this scenario, each building may be a house in which patients are isolated, a warehouse storing food or drugs, a laboratory in which medical tests are performed for patients, or a location at which doctors are working (isolated from patients). Data packages (medical images, tests, results, prescriptions from doctors, etc.) must be sent between these buildings. The communication between these buildings can be achieved by drones organized in a square-shaped network.
To validate the proposed method, simulations were performed using the drone network maps as a collection of squares. Most of the simulations were performed using the Java-based simulator ONE and its provided facilities, using an ASUS ROG GL752VW-T4015D laptop with Intel ® Core™ i7-6700HQ 2.60GHz processor (Asus, Taipei City, Tai-wan), and 8 GB of RAM. The routing protocols used for the simulation within the ONE simulator were Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery.
The following main steps were used for implementation of the ONE scenarios. The first step consists of defining the map (Figure 10) in wkt file format, in which the coordinates of all the points on the map, including points that establish the route of each drone, are defined. The initializations of the algorithms that define the mobility of drones consist of establishing the initial positions of drones and the recharging/changing points, associating each drone with a recharger/changing point, establishing the stationary points for data transfer, and defining the route of each drone. The final step is the establishment of the simulation parameters, as shown in Table 4. The time parameters, such as the travel autonomy time, the hovering time for the transfer points, and the parking time at the charging or changing points, were established based on the experimental flight tests of the DJI Mavic 2 Pro drone.  The proposed time-dependent Dijkstra variant was implemented in Visual C++ 2017 programming language. The application has about 1100 lines of C++ source code.
The application written in C++ was executed for each of the two considered situations: squares with battery charging, and squares with battery changing. For each case,  The proposed time-dependent Dijkstra variant was implemented in Visual C++ 2017 programming language. The application has about 1100 lines of C++ source code.
The application written in C++ was executed for each of the two considered situations: squares with battery charging, and squares with battery changing. For each case, the same 1000 route simulations considered in the ONE experiments were executed.
The delivery rate and latency metrics were used to measure the performance of all six routing protocols analyzed in this paper. The delivery rate is determined as a ratio between the number of delivered messages and the number of created messages. The latency is the average time needed for a message to reach the destination starting from the source (departure node).
Detailed results of the comparison between changing the battery and charging the battery cases are presented in Table 5. The results obtained in this paper by simulation were compared with those obtained in [41]. In the case of the squares network and battery changing, the values of the delivery rate were within the range of 0.166 to 0.646 for the routing protocols Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery. The best delivery rate was 0.954 for the TD-Drone Dijkstra protocol ( Figure 11). The worst result in terms of latency was obtained for MaxDelivery, and TD-Drone Dijkstra's average latency was the best, as expected ( Figure 12).
The delivery rate in the case of drone battery charging was between 0.135 and 0.143 for the routing protocols Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery. The maximum delivery rate was 0.54 and was obtained for the TD-Drone Dijkstra protocol. These low values were obtained because of the large delay due to the battery charge. The worst results for latency were obtained for PRoPHET and Epidemic, and TD-Drone Dijkstra's latency was also the best. and Wait, PRoPHET, MaxProp, and MaxDelivery. The best delivery rate was 0.954 for the TD-Drone Dijkstra protocol ( Figure 11). The worst result in terms of latency was obtained for MaxDelivery, and TD-Drone Dijkstra's average latency was the best, as expected ( Figure 12). The delivery rate in the case of drone battery charging was between 0.135 and 0.143 for the routing protocols Epidemic, Spray and Wait, PRoPHET, MaxProp, and MaxDelivery. The maximum delivery rate was 0.54 and was obtained for the TD-Drone Dijkstra protocol. These low values were obtained because of the large delay due to the battery charge. The worst results for latency were obtained for PRoPHET and Epidemic, and TD-Drone Dijkstra's latency was also the best.  The comparison between average latencies was performed on the routes where the delivery was successful for all of the algorithms (66 routes for the case of battery change and 64 routes in the case of battery recharge). Figure 11. Delivery rate in the squares drone network.
The comparison between average latencies was performed on the routes where the delivery was successful for all of the algorithms (66 routes for the case of battery change and 64 routes in the case of battery recharge). The best delivery rate in all cases was given by the TD-Drone Dijkstra algorithm because its buffer load was the lowest (the data was loaded only in the stations and drones belonging to the calculated route). The latency in the case of Dijkstra's algorithm was high because it can deliver most of the packages. Generally, the other algorithms can de- The best delivery rate in all cases was given by the TD-Drone Dijkstra algorithm because its buffer load was the lowest (the data was loaded only in the stations and drones belonging to the calculated route). The latency in the case of Dijkstra's algorithm was high because it can deliver most of the packages. Generally, the other algorithms can deliver only on the shorter distances due to buffer restrictions. It is known that Dijkstra's algorithm results in the shortest path, and, therefore, the best latency.
The delivery rate was better for the triangles drone network (Figures 13 and 14), with the exception of the Spray and Wait algorithm in the battery changing case. For PRoPHET, Max Prop, and TD-Drone Dijkstra in the battery charging case, the latency was significantly better.
Latency in the case of changing the battery in the triangles drone network was generally better (Figure 15), with the exception of Spray and Wait, and in the case of Max Delivery a significantly better latency was obtained. In the case of battery charging (Figure 16), latency was better in the triangles drone network for three algorithms (Epidemic, Max Delivery, and TD-Drone Dijkstra), and, for the other three algorithms, the latency was better in the squares drone network. liver only on the shorter distances due to buffer restrictions. It is known that Dijkstra's algorithm results in the shortest path, and, therefore, the best latency. The delivery rate was better for the triangles drone network (Figures 13 and 14), with the exception of the Spray and Wait algorithm in the battery changing case. For PRoPHET, Max Prop, and TD-Drone Dijkstra in the battery charging case, the latency was significantly better.
Latency in the case of changing the battery in the triangles drone network was generally better (Figure 15), with the exception of Spray and Wait, and in the case of Max Delivery a significantly better latency was obtained. In the case of battery charging (Figure 16), latency was better in the triangles drone network for three algorithms (Epidemic, Max Delivery, and TD-Drone Dijkstra), and, for the other three algorithms, the latency was better in the squares drone network.     In essence, the delivery rate was considerably better for the triangles drone networks, and latency was generally better for the triangles case. The significant disadvantage of the triangles drone network is that double the number of drones is needed to cover approximately the same surface, and double the number of loading/changing stations is required, although the total number of fixed communication stations is similar (63 vs. 65).  In essence, the delivery rate was considerably better for the triangles drone networks, and latency was generally better for the triangles case. The significant disadvantage of the triangles drone network is that double the number of drones is needed to cover approximately the same surface, and double the number of loading/changing stations is required, although the total number of fixed communication stations is similar (63 vs. 65). In essence, the delivery rate was considerably better for the triangles drone networks, and latency was generally better for the triangles case. The significant disadvantage of the triangles drone network is that double the number of drones is needed to cover approximately the same surface, and double the number of loading/changing stations is required, although the total number of fixed communication stations is similar (63 vs. 65).
Epidemic, Spray and Wait, PRoPHET, and MaxProp are classic algorithms used for DTN. However, in our case, as shown, the time-dependent Dijkstra algorithm adaptation can be successfully used because since the flight timetables are known. There are numerous advantages of the TD-Drone Dijkstra algorithm: an exact and optimum route is a priori calculated, ensuring the fastest time of delivery from departure to destination if the route exists; a message is not unnecessarily sent in the network if no route exists from departure to destination; multiple copies of the messages are not unnecessarily spread through drone and station buffers, resulting in unnecessary overloading of the buffers; and, finally, the rate of delivery success is maximized. The drawback of the TD-Drone Dijkstra algorithm is that the route is calculated using the information about the operating drones and stations at the moment of route calculation and, if a drone or a station from the route is down on this route, the message does not reach the destination. All the routes passing through the station or drone that is down are compromised until the fault is detected. Moreover, this problem reappears when the drone/station is fixed until the moment this information is updated. However, the chance of this problem occurring is low and, if it appears, it may be fixed in time following the repair of the drone/station or when the current status of the network is updated. Using the example of the Spray and Wait or Epidemic algorithms presented in this paper, any message has the chance to reach the destination even if drones or stations are down because a copy of the message is spread in the network.

Conclusions and Future Work
This paper presents a novel method of communication in quarantined or isolated areas, or areas with technical damage, using networks of drones that fly based on a wellestablished mission plan and schedule, on 2D surfaces covered by squares. Two situations of drone battery management-charging and battery changing stations-were investigated.
A network of square cells with two drones in each cell was proposed to cover a geographical area. The drone network was simulated based on input data from experimental flight tests of a quadcopter using six routing algorithms.
A TD-Drone Dijkstra algorithm (single-copy algorithm) and multiple-copies algorithms were proposed to simulate a Delay Tolerant Network of drones. Results showed a delivery rate ranging from 0.166 to 0.954 in the drone network with battery changing, and from 0.135 to 0.540 in the drone network with battery charging. The best latency of 0.43 h for a drone network with battery changing was obtained using the TD-Drone Dijkstra algorithm. Thus, the best results were obtained for the TD-Drone Dijkstra algorithm, which was able to deliver most of the data packages in the shortest time.
The traditional DTN algorithms, such as Epidemic, Spray and Wait, and MaxProp, produced lower results due to the small number of contacts between nodes, and a low number of message exchanges. The fastest communication was established for the drone squares network with battery changing. It was found that the battery change scenario led to an increase in the delivery rate of 76% compared to the battery charge scenario.
It was found that the battery change scenario led to an increase in the delivery rate of 200% compared to the battery charge scenario.
The fastest communication was found for the drone triangular network with battery charging, and for the drone square network with battery changing. However, the drone square network is considerably cheaper than the drone triangular network. Thus, if cost is not an issue, the triangle network of drones may be implemented because better performances can be achieved. However, if there is a budget constraint, then the square network type is more suitable.
In future work, we will aim to apply this network of drones to parcel delivery during emergencies in remote quarantined zones.


Research on Optimization of Distributed Node Location Algorithm in Wireless Sensor Networks

This paper studies the related theories of wireless sensor networks, and an improved DV-Hop algorithm is proposed, which used to estimate the distance error mainly based on the error of average per hop distance, unknown nodes and anchor nodes in traditional algorithm. Through the simulation analysis, it can be found that compared with the traditional Location algorithm of DV-Hop and other improved algorithm, the improved algorithm proposed in this paper can reduce the location error and improve the location accuracy when the proportion of the anchor nodes is moderate and the communication radius is small, and this algorithm is suitable for the low power and wide range wireless sensor network environment.

The WSNs randomly distribute its nodes in the monitoring zone, and the collection, processing and transmission of information are implemented for the perceived objects, which includes sensor node, task management node and sink node. The nodes in sensor are randomly broadcast, and its functions include generating and transmitting monitored data, and transmitting the data to the surrounding sensor nodes after a simple local processing, and the information is transmitted to the sink node by using the way of multi-hop. Each sensor node can acquire, process and transmit monitored data.

Topology Structure
Nodes in wireless sensor network are broadcast randomly, cluster-based topology structure and planebased topology structure form the node topology.

2.2.1.
Cluster-based topology structure. In wireless network, the nodes can be categorized into different clusters, each of which is formed from a cluster head and several members. All of the cluster members transfer the collected data to the head; the sink node receives the data through multi-hop or directly after the cluster head completes a simple data fusion [3]. Cluster head is responsible for large amounts of communication and computation, and it requires more energy consumption. In general, every sensor node in each cluster takes as the cluster head in turn.

2.2.2.
Plane-based topology structure. Plane-based topology structure can be divided into networkbased planar topology and chain-based planar topology. In network-based planar topology, the network structure formed by nodes, and the sensor nodes only exchange data with neighbour nodes, and finally converge to sink nodes, as shown in Figure 1 (a). This topology can still maintain the life of the whole network when some nodes died [4]. In chain-based planar topology, the unknown nodes form several links for sink node to receive information. In the link, the closer distance between sensor node and sink node means larger and more important data transmission. Their neighbours need to reconstitute the link to transmit data, and as shown in Figure 1

Improvement for the Location Algorithm
Although the location algorithm of DV-Hop has the benefits of good scalability and low complexity, location accuracy of it is low. Based on Location algorithm of DV-Hop, the mean per hop distance for the anchor node is improved in this paper firstly. During the calculation process, the anchor nodes selected based to a certain standard, and take the distance between each anchor nodes as the weight to reduce the introduction error [5]. Secondly, for unknown nodes, this paper improves the selection process of the average distance of per hop. Since there are different hops number from the unknown node to the anchor node, different schemes are chosen to obtain the mean distance of per hop for the unknown node. We use the mean hop scope to reduce the error when we get the estimation of the distance from unknown nodes to anchor nodes. Degree of collinearity theory refers to the minimum value in the high line of the three-edge of a triangle consisting of three anchor nodes. As the research shows, if the anchor nodes are collinear or almost collinear, the mean distance for one hop has the minimum error. This section reduces the error in calculating process of mean hop distance of for the anchor node is reduced by screening and weighted. Among the anchor nodes, when the unknown nodes have poor degree of collinearity, using the ratio, which is the actual distance for anchor nodes to minimum hops to calculate average per hop distance will introduce error. For this problem, the method adopted in document is that use the correction coefficient to correct after getting the mean distance per hop between anchor nodes [6]. The coefficient is calculated from the actual distance for the anchor node; ratio of estimate distance difference to hops, which has a certain effect. The methods in this section include first eliminating the anchor nodes that will introduce large errors, and then weighting the anchor nodes [7].
For the rectangular distribution area, the maximum ideal hop k is defined as: (1) (d1, d2, d3 and d4 represent the distance from anchor node i to four vertices of rectangular distribution ranges) In ideal situation, the average distance between hops is close to the communication radius. When the minimum hops the anchor, the node will receive from the other anchor nodes is beyond the maximum ideal hops in the range of node distribution, it will show the degree of collinearity between the anchor nodes is lower in this path and it is removed.
After eliminating the anchor nodes with the poor degree of collinearity, using the method of weighted processing to obtain average jump distance of anchor node i. Definition: (dij means the real distance from anchor nodes i to j； R means the communication radius； hopsij represents the minimum hops from anchor nodes i to j) When the anchor node i is involved for the calculation of the hops' mean distance of nchor node j whose weight is: (m denotes the anchor nodes' number participating in calculating the average distance of hops for the anchor node i) The hops' mean distance for the anchor node i is as follows:

Mean distance for the unknown nodes per hop.
In the selection of the mean hops for these unknown nodes, when the anchor node and the unknown node are at 1 hop, the algorithm of IDV-Hop will directly select the anchor node's average hops, otherwise, the average hops for all anchor nodes should be chosen, so that the division is too general. In algorithm of MDV-Hop, when the hops between the unknown node and the anchor node is smaller than the value of the threshold M, the mean value of the hops' average distance of these anchor nodes is chosen as the hops' mean distance for the unknown nodes, and this strategy increases the computational complexity for the unknown node and anchor node in the 1 hop range. This section presents an improvement for the unknown nodes' average hop distance based on MDV-Hop and IDV-Hop [8]. When the anchor and the unknown node are in the 1 hop range, unknown node directly selects the nearest anchor node hops' mean distance as its mean hop distance. When the minimum hop of unknown node and anchor node is between in the 1~M hops, it takes the mean value of the all anchor nodes' mean hop distance within M hop as mean hop distance. When the minimum hop for the unknown node and anchor node is outside the M hop, and the global mean hop distance is taken [9]. The mean distance of hops for the unknown node K is: (m represents anchor nodes' number in the M hops range around the unknown node k.; n represents the anchor nodes' number in the entire WSN) The threshold M is: (A represents the area that the entire wireless sensor network covered; Ln represents anchor nodes' average number needed for each unknown node location; Tn represents the total nodes' number; Lp represents the anchor nodes' proportion; Hmax represents the maximum number of minimum hops between anchor and unknown nodes) In the case of satisfying the location of all unknown nodes, M selects the minimum value to participate in the operation. When the nodes were distributed unevenly, threshold M needs to be selected slightly larger to meet the coverage of the entire network. The parameter p (the value is between 0-1) is used to adjust the lower limit of the threshold M. If the proportion of anchor nodes is large, a smaller p value can be selected to raise the lower limit. Conversely, if the proportion of anchor nodes is large small, large P values can be selected to reduce the lower limit.
According to the formula (5), in different cases, unknown nodes will select different mean hops distance according to the anchor nodes minimum hops, which overcomes the error caused by simply leveraging the nearest anchor node's mean hops of in the traditional DV-Hop algorithm, and when the unknown node and the anchor node within 1 hop range, it guarantees the average hop distance's accuracy.

The estimated distance calculation based on the average hop scope.
When the nodes' density of near the anchor and the unknown node differs, the difference between the mean distance of hops of the two is larger, and simply using the mean unknown nodes' hop distance to get the calculation distance will lead to large errors. In this section, the average hop scope is claimed. After getting the mean hop distance for the anchor nodes and the unknown nodes mean hop distance, when calculating the distance between the unknown and the anchor nodes, half of hop number near the unknown node leverages the unknown hop mean distance to get the distance, and the other half uses the anchor nodes mean hop distance [10]. The calculation process is: Hopsize hops Hopsize hops = × + × (7) (Hopsizei represents the anchor node i mean hop distance; Hopsizek represents the average hop distance for the unknown node k) And satisfies:

Analysis of Average Location Error
Each experiment was done 100 times, the mean value of which is used as the ultimate result to compare how the anchor nodes' proportion for the impacts on the location error when the communication radius R is set to be 30m. The result is shown in Figure.3. The location error for the 6 three algorithms are compared at different ratio of anchor nodes. With the anchor nodes' proportion adding, the three algorithms' location errors are decreasing. When the proportion for the anchor nodes becomes small, and in the WSN area the anchor nodes are not evenly distributed and have large randomness. Most of the unknown nodes in IDV-Hop and MDV-Hop algorithm choose the global average distance of hops as their own hop distance. and the improved algorithm in this section has a significant effect through the double segmentation of 1 hop and threshold M. When the anchor node's proportion is at 15%~30%, the location effect of threshold M in MDV-Hop algorithm performs better compared with that of simple 1 hop segmentation in IDV-Hop algorithm, and the algorithm is separately processed on the basis of the threshold, and the effect is better. When the proportion for the anchor nodes is more than 30%, the location error does not decrease obviously with the increase of anchor node. The improved algorithm in this section is better than other algorithms.

Figure 3. Comparison of location error under different communication radius
If the communication radius increases, the location errors of all algorithms are reduced. If the communication radius is less than 25m, the distance of 1 hop is small. In the comparison for the algorithm that was improved in this paper, more unknown nodes in IDV-Hop and MDV-Hop algorithm choose the global mean distance of hops as their own hop distance, which leads to the accumulation of errors. If the communication radius is greater than 28m, the anchor nodes obtain the average distance of hops and get better results after screening and weighting, while the average distance of hops scope further reduces the error. In comparison with other improved algorithms, the proposed algorithm was improved has the advantages of different levels.

Fluctuation Analysis of Location Error
When it has totally 100 nodes and 30m communication radius, and 20% nodes are the anchor nodes, every unknown node's location error is depicted in Figure.   section is relatively stable. In order to more clearly compare the differences of fluctuation, the variance is used to represent the data in this paper. The variance of node location error of each algorithm in 100 times experiments shows in Figure.5. The larger the variance is, the greater the error fluctuation of the unknown node location is. Simply comparing the average location error can't fully explain the algorithm's advantages and disadvantages. When the variance is very large and the average location error is very small, for some unknown nodes, their error in the location process is far greater than the average location error, which is unfavourable to the practical application.

Conclusion
The improved the traditional location algorithm of DV-Hop is proposed in this paper. Firstly, when calculating the anchor node's average hop distance, the anchor nodes are screened and weighted, and the anchor nodes that are likely to introduce relatively large errors are eliminated to get the improvement for the accuracy of anchor node mean distance of hops. Secondly, when the calculation of the mean distance of hops between unknown nodes, different selection schemes are adopted for different unknown nodes. Based on the hops of the nearest anchor and unknown node, average hops of anchor node, mean hops of anchor node within the range of M hop or global average hops are selected as its own hop distance. Finally, when the calculation for the distance from anchor node to unknown node, different mean distance of hops to participate in operation will be chosen based on the mean distance of hops scope. When the anchor nodes have the moderate proportion and small communication radius, the algorithm can increase the location accuracy and decrease the location error, which can be widely applicable to the wireless sensor network environment with low power and wide range.