Vehicle tailgating or simply tailgating is a hazardous driving habit. Tailgating occurs when a vehicle moves very close behind another one while not leaving adequate separation distance in case the vehicle in front stops unexpectedly; this separation distance is technically called “Assured Clear Distance Ahead” (ACDA) or Safe Driving Distance. Advancements in Intelligent Transportation Systems (ITS) and the Internet of Vehicles (IoV) have made it of tremendous significance to have an intelligent approach for connected vehicles to avoid tailgating; this paper proposes a new Internet of Vehicles (IoV) based technique that enables connected vehicles to determine ACDA or Safe Driving Distance and Safe Driving Speed to avoid a forward collision. The technique assumes two cases: In the first case, the vehicle has Autonomous Emergency Braking (AEB) system, while in the second case, the vehicle has no AEB. Safe Driving Distance and Safe Driving Speed are calculated under several variables. Experimental results show that Safe Driving Distance and Safe Driving Speed depend on several parameters such as weight of the vehicle, tires status, length of the vehicle, speed of the vehicle, type of road  and the weather condition (clear or foggy). The study found that the technique is effective in calculating Safe Driving Distance, thereby resulting in forward collision avoidance by connected vehicles and maximizing road utilization by dynamically enforcing the minimum required safe separating gap as a function of the current values of the affecting parameters, including the speed of the surrounding vehicles, the road condition, and the weather condition. Road traffic accidents kill approximately 1.3 million people each year, according to the World Health Organization (WHO), prompting the United Nations General Assembly (UNGA) to set an ambitious target of halving the casualties of road traffic accidents worldwide between now and 2030. One of the primary causes of traffic accidents is tailgating—tailgating consists in having a vehicle following another vehicle too close to brake safely if the followed vehicle stops unexpectedly, as shown in (a)Forward collision due to tailgating.(b)Traffic optimization: leaving too much gap between two connected vehicles will result in poor utilization of the roads and highways and consequently create unnecessary traffic on crowded roads.(c)Over speeding (for the following vehicle) and under speeding (for the followed vehicle) on a busy highway.To avoid tailgating, there is a need for a smart technique based on Intelligent Transportation System (ITS) and Internet of Vehicles (IoV) ,5,6,7,8 The determination of ACDA by classical means is unsuitable for Intelligent Transportation Systems (ITS), smart cities, and smart roads . ACDA deIoV technology ,5,6,7,8,In IoV, an intelligent vehicle (V) has an On-Board Unit (OBU) which extends the vehicle’s onboard computer’s capabilities. The simplicity of conversion of a non-IoV vehicle to an IoV vehicle can be done by incorporating the OBU into a non-IoV vehicle; this simplicity of converting a non-IoV vehicle into an IoV vehicle makes the deployment and the transition toward the next generation ITS easy.IoV and Connected Vehicles (CV) consist of several entities ,24,25. TIoV is a promising technology enabling the deployment and development of endless practical applications in smart cities ,29,30,31In this paper, we are setting to find the Ideal Safe Driving Distance  based on IoV for the avoidance of forward collision due to tailgating so that other researchers and automobile manufacturers can use this research as a background for developing applications that require the knowledge of the ideal gap between two vehicles. The knowledge can also be used to assess safe driving or detect safe driving violations.(1)We studied the different measurement techniques that can be used to measure in real time the Assured Clear Distance Ahead (ACDA) in the IoV environment and autonomous vehicles.(2)We have studied in detail all the factors affecting the Stopping Distance by studying the braking dynamics in the IoV and the autonomous vehicles.(3)We conducted a complete study considering all the parameters affecting the safe following distance and speed as the current speed of the followed vehicle, the speed of the following vehicle, the separation distance, the deceleration, the driver reaction time, road conditions , the weather conditions , the mass of the vehicles, the braking force, the tires state, etc.(4)Studying the effect of using the Autonomous Emergency Braking (AEB) system that exists in some vehicles and is a must in autonomous vehicles. In other words, we studied the case when the rear vehicle auto-brake in case of emergency, hence eliminating the driver’s reaction time, especially in foggy weather or bad visibility conditions, hence maximizing the road efficiency and decreasing the trip time.(5)Studying the case when the followed vehicle instantly stops and the effect of the safe driving distance and the safe following speed. In other words, we studied the effect of the sudden stop of the followed vehicle on the safe driving distance and speed for the different conditions.(6)We formulated how to use the IoV emergency safety message to exchange the related parameters between the followed and the following vehicles so that each vehicle on the road can calculate the ideal safe following distance and speed according to the current conditions .We can summarize the contributions of this paper as follow:The rest of the paper is organized as follows. In Several previous works tackled safe driving distance determination. In , a distaThe study presented in  providesSimulation and reinforcement learning to determine the safe driving distance as a function of the speed of the following vehicle and the separation gap only was given in . A similIn , the autThe authors of  proposedUnlike the time-headway and traditional braking models, a new safety indicator called time gap interval for safe following distance (TGFD) is proposed in , which iBased on reinforcement learning, a model of velocity control during automobile following is developed . A rewarTo explain the microscopic car-following behavior of RVs (Regular Vehicles) and AVs (Autonomous Vehicles) , offers The maximum distance of the highway ahead visible to the motorist is referred to as the available sight distance (ASD) is examined in . Road geLastly, in , the stuAssured Clear Distance Ahead (ACDA) is the separation between the followed vehicle and the following vehicle that will not cause a crash if the followed vehicle stops unexpectedly; this section provides state-of-the-art techniques and technologies used to measure or estimate the separation distance between the followed and the following vehicles.Intelligent vehicles are typically equipped with different types of distance measurement sensors, as shown in Several approaches for measuring the distance between the current vehicle and the front vehicle using stereo vision cameras are proposed in ,40,45,52Given that each vehicle in IoV knows its absolute real-time location, the distance between any two vehicles could be calculated as follows. First, each vehicle periodically broadcasts its current location while it is moving. Each vehicle receives the broadcast locations of all surrounding vehicles. The vehicle can use GNSS or RTK to calculate its moving direction (heading angle) and broadcast this information. Thus, any vehicle can know which vehicles are moving in the same lane and direction. The vehicle calculates the distance to all vehicles that are in the same lane and then selects the shortest distance of the vehicles that are moving ahead. Thus, the vehicle can know the distance to the followed vehicle. In tunnels and city centers where the GNSS signals are not received, several other localization techniques are used, such as the received signal strength from different radio sources  ,58,59.It is essential to understand the braking dynamics to be able to estimate the safe driving speed and the safe driving separation distance or ACDA. In this section, we present the Stopping Distance (SD) affecting parameters and the braking dynamics. As shown in rding to , if the V is the vehicle speed, f) for different road types/conditions; it can be seen that Asphalt (Dry) has the highest adhesive coefficient (f = 0.9) whereas Icy road has the lowest adhesive coefficient (f = 0.1). There is also a 10% decrease in the adhesive coefficient of Asphalt (Dry), Pavement (Dry), Asphalt (wet), and Pavement (wet), respectively. An increase in adhesive coefficient results in a sharp decrease in braking distance, as shown in Equation (1).The braking time The tire state significantly affects the braking distance. The extra stopping distance in meters on snowy roads compared to dry asphalt roads for different speeds is presented in CASE A: The stopping distance of a vehicle traveling on dry asphalt road at different speeds as reaction distance plus braking distance. At a low speed , the reaction distance is doubled when the braking distance 8 m (independent of the type of road), and the braking distance is 4 m. The braking distance becomes higher at high speed (braking distance = 84 m compared to a reaction distance of 39 m at 140 km/h).CASE B: On a snowy road, the stopping distance is longer mainly due to the longer braking distance. At 20 km/h, for example, the braking distance is 58.5% of the stopping distance (7.9 m), and at higher speed, for example, at 140 km/h, the braking distance is 90.8% of the stopping distance (385 m).CASE C: The same phenomenon is observed on icy roads. The braking distance at 20 km/h is 73.7% (15.7 m) of the stopping distance and at a higher speed of 140 km/h, the braking distance is 95.2% of the stopping distance.In In the previous section, we presented the stopping dynamics when the driver of one vehicle perceives danger and decides to stop. We assumed that the vehicle was moving with a constant speed and then constant deceleration until it stops completely. However, vehicles are moving normally at approximately the same speed. If two vehicles realize the same danger at the same time and start barking at the same time, they will not collide as they will stop at the same time, maintaining the same gap while they brake. If we consider the stopping distance presented in the previous section as the minimum safe driving distance or Assured Clear Distance Ahead (ACDA), this will reduce road utilization efficiency and hence create many traffic management and optimization problems. Without IoV technology, it is not possible to objectively obtain ACDA for each vehicle as a function of the speed of the two vehicles, the tire states, the road type and condition, the weather condition, etc. In this section, we aim to calculate the sufficient ACDA dynamically, taking into account all affecting parameters when the two vehicles are moving at different speeds and decelerate with different decelerations.d, between them at a specific time We show in When the front vehicle B starts braking, the rear vehicle A will not brake instantly, it will continue at its current speed during the thinking and the reaction times  = D + Braking Distance of A (followed vehicle), neglecting the reaction time of A.Stopping distance of f and For any given initial distance between the two vehicles, AmaxV) and the initial gap between the vehicles assuming the reaction time of the driver of 1 s are shown in We have calculated the maximum speed of the following vehicle for different speeds of the followed vehicle given an initial gap. In the case of dry asphalt, which is the ideal condition, the maximum speed of vehicle A  system that brakes the vehicle autonomously in the case of perceived danger without any intervention from the driver. Connected vehicles may have this system, while autonomous vehicles must have this system.In the case when the vehicle can brake instantly when it receives an Imminent-Danger message from any of the vehicles in front of it using V2V, then the driver reaction time of the following vehicle is zero or In such a case, the maximum driving speed of the following vehicle will be increased, and the minimum safe driving distance given the speed of the two vehicles will decrease. Similarly, we calculated the minimum safe driving distance for different speeds of both the following and the followed vehicle in the case when the following vehicle is dotted with an Autonomous Emergency Braking (AEB) system , in the case of a sudden crash with a stopped vehicle, for example, or in any other critical situation. If ACDA is calculated according to what has been described in the previous subsections, the following vehicle will collide with the followed vehicle. Thus, it is essential to consider this case when calculating the ACDA.Assuming that vehicle B stops suddenly with zero stopping distance. Thus, setting In the case when the following vehicle does not have an AEB system:In the case when the following vehicle has an AEB system  is applied to stop a moving car with a mass of 1500 Kg, it will decelerate at only 1 m/s2. When the car’s mass is doubled and the same braking force is applied, the car is now slowing down at half rate. The car with double mass will take twice as long to come to a complete halt.In this section, we present the effect of the mass of the vehicle on the braking distance. From Newton’s Second Law of motion, the force  is the product of mass and acceleration . The braking distance of a vehicle increases proportionally with its mass. Assume a force of 1500 N is applied by the brakes to stop a moving car with a mass of 750 Kg, the car will decelerate at 2 m/sThe braking distance (m) and mass of the vehicle (Kg) are described in The speed of the vehicle (m) and the braking distance (m) at different masses of the vehicle (Kg) are presented as shown in The effect of braking force in the determination of braking distance is discussed in this section. For a moving vehicle to come to rest, there must be work done sufficient to remove all its kinetic energy. Work done = Kinetic Energy, where work done is the work needed (in Joule) to remove all vehicle’s kinetic energy.2 measured in Joule, and the work done is the product of braking force and distance. Thus:Kinetic Energy = 0·5 × mass × velocityTherefore, for a fixed maximum braking force, the braking distance is proportional to the square of the vehicle’s speed. In In this paper, we thoroughly studied the minimum safe driving separation distance or the Assured Clear Distance Ahead (ACDA) that must be used to avoid forward collisions. We have presented the braking and the stopping distance as well as the braking dynamics that are essential to understand the minimum required separation gap to avoid the collision. We have discussed all factors that affect the ACDA, namely, the speed of both vehicles, the initial separation distance, the tire state, the weather condition, the road condition, and the vehicle’s mass. Furthermore, we have presented the necessary equations required to calculate that distance. In addition, we have devised and analyzed the maximum speed of the following vehicle to avoid the collision given the speed of the followed vehicle and the current separation distance for all studied factors that affect the stopping distance.Moreover, both ACDA and the maximum safe driving speed equations and analysis were presented in the case when the followed vehicle suddenly stops. The study was complemented by the case when the following vehicle is equipped with Autonomous Emergency Braking (AEB) system. Finally, we have presented the required braking force as a function of the vehicle mass for different speeds and braking distances. We have presented the traditional and smart distance measurement techniques between the followed and the following vehicles that can be used in connected and autonomous vehicles. The presented analytical results are essential for connected vehicles and self-driving vehicles to avoid collisions and maximize road utilization, and hence reduce traffic problems. One important advantage of this study is using vehicle-to-vehicle communication of IoV; both vehicles know the factors affecting the ACDA and the maximum allowed safe speeds, and they exchange them; thus, each can calculate them in real-time.The future directions of this study are to use the proposed calculations of ACDA and the safe following driving speed to detect automatically and autonomously tailgating violations using IoV. We are currently exploring this research direction.


Software reliability is prioritised as the most critical quality attribute. Reliability prediction models participate in the prevention of software failures which can cause vital events and disastrous consequences in safety-critical applications or even in businesses. Predicting reliability during design allows software developers to avoid potential design problems, which can otherwise result in reconstructing an entire system when discovered at later stages of the software development life-cycle. Several reliability models have been built to predict reliability during software development. However, several issues still exist in these models. Current models suffer from a scalability issue referred to as the modeling of large systems. The scalability solutions usually come at a high computational cost, requiring solutions. Secondly, consideration of the nature of concurrent applications in reliability prediction is another issue. We propose a reliability prediction model that enhances scalability by introducing a system-level scenario synthesis mechanism that mitigates complexity. Additionally, the proposed model supports modeling of the nature of concurrent applications through adaption of formal statistical distribution toward scenario combination. The proposed model was evaluated using sensors-based case studies. The experimental results show the effectiveness of the proposed model from the view of computational cost reduction compared to similar models. This reduction is the main parameter for scalability enhancement. In addition, the presented work can enable system developers to know up to which load their system will be reliable via observation of the reliability value in several running scenarios. As reliance on software applications is growing, software reliability analysis is unavoidable. Software reliability is defined as the probability that reveals the capability of a system to perform a required service or function correctly (failure-free) in a certain environment, over a particular time ,2. A faiDepending on the reliability measurement lifecycle, the measures can be taken early in development, or later in the testing or post-deployment ,4,5. TheThe main goal of design-time reliability models is to predict the reliability of software based on information related to the software architecture made out of components. Key potential benefits that may be obtained from using architectural design artifacts as input for the reliability model can enable comparing of different architecture options or design alternatives. In addition, studying the sensitivity of complete application reliability to the reliabilities of components and identifying critical components and scenarios. Furthermore, this kind of model assists with a better understanding of the reliability requirements and how they relate to the architectural design.Software behavior models that are derived from requirement specifications ,10,11,12Most reliability models that lack scalability rely directly on Markov notation (state machine specifications) as their primary modeling notation and give no details on how the states are derived. Moving to Markov provides a mathematical formula to calculate reliability. However, this can lead to a state-space explosion problem . In the s-TS), which was introduced in [s-TSs helps in describing scenarios of a system compactly and concisely, leading to fewer scenarios. The s-TS in our previous work [The first part of this paper shows a strategy for scalable scenario modeling and reliability calculations. It adapts our previous scenario description language named scalable triggered scenario fScj=s-TS can participate in discovering inconsistencies related to component interactions. These inconsistencies cause errors such as a signature mismatch of interfaces and pre- and post-conditions. The definition and categorization of the errors caused by these inconsistencies are beyond this paper. More details of such errors can be found in [The scenarios described by found in . In the found in  and the found in , the coms-TS, the operation invoked for each specific component’s interaction can be determined exactly. Therefore, going back to Equation ,,3), we cEquation  can be rEquation  below bas-TS is producing branching scenarios. Therefore, branching scenarios are expected   4) are tj is depicted as the probability of there not being a failure; thus, the reliability of scenario j can be calculated as follows:The reliability of the scenario s-TS scenario specification, where each component instance participates in the scenario represented by an FSM, it is time to calculate the scenario’s reliability. Firstly, the component’s failure probabilities are calculated using the expected failure values of the operations invoked by the components as inputs to Equation , a car departing a terminal (scenario 2) and a car approaching a terminal (scenario 3). Assume the occurrence probabilities of these three scenarios Equation  and the pn assumption.The values of shown in  will be j is represented as N trials (refers to the number of active instances of the scenario) for independent events. Each has an occurrence probability p (mapped to the failure probability of scenarios). Using the probability of failure of the scenario jjThe reliability of the scenario combination can be calculated based on the definition of the system failure . The deffinition , NFIj isEquation  and the Equation  as inputEquation , the PRsyk, and K is the total number of the combinations.ns value  a reduction of the number of state machines (Ss) within the state machine itself. The proposed model achieved a medium number of The proposed model introduced a new system-level scenario description language named s-TS, through the development of open-source tools. s-TS can be used independently as a modeling tool. Furthermore, we plan to add the proposed reliability prediction model as part of the tool to make the model available to public users and enrich the evaluation results.A multinomial statistical distribution was adopted in the proposed model for scenario combinations to calculate system reliability. This adaptation allows us to represent the nature of concurrent software applications wherein the number of scenarios running simultaneously is unknown. Therefore, software architects can increase or decrease the number of running scenarios in reliability calculations to know under what load the system will be reliable. In our future work, we plan to perform user studies to evaluate the usability and practical utility of the introduced scenario description language,


F-statistic, and mutual information (MI). The features are then ordered according to this combination. In the second stage, the modified wrapper-based sequential forward selection is utilized to discover the optimal feature subset, using ML models such as support vector machine (SVM), decision tree (DT), random forest (RF), and K-nearest neighbor (KNN) classifiers. To examine the proposed algorithm, many tests have been carried out on four cancerous microarray datasets, employing in the process 10-fold cross-validation and hyperparameter tuning. The performance of the algorithm is evaluated by calculating the diagnostic accuracy. The results indicate that for the leukemia dataset, both SVM and KNN models register the highest accuracy at 100% using only 5 features. For the ovarian cancer dataset, the SVM model achieves the highest accuracy at 100% using only 6 features. For the small round blue cell tumor (SRBCT) dataset, the SVM model also achieves the highest accuracy at 100% using only 8 features. For the lung cancer dataset, the SVM model also achieves the highest accuracy at 99.57% using 19 features. By comparing with other algorithms, the results obtained from the proposed algorithm are superior in terms of the number of selected features and diagnostic accuracy.Cancer is a deadly disease that occurs due to rapid and uncontrolled cell growth. In this article, a machine learning (ML) algorithm is proposed to diagnose different cancer diseases from big data. The algorithm comprises a two-stage hybrid feature selection. In the first stage, an overall ranker is initiated to combine the results of three filter-based feature evaluation methods, namely, chi-squared,  DNA microarray is a modern biological research technology for gene expression analysis. It has the ability to measure the expression levels of thousands of genes, during important biological operations . TherefoThe microarray data have some specific characteristics. That is, there are a high dimensionality and a small number of samples. As such, the analysis of microarray data is considered a difficult task . Since mDR techniques can be classified into two main approaches: feature extraction and feature selection. The feature extraction approach aims to construct the features into a new feature space with lower dimensionality. Actually, the newly constructed features are usually combinations of the original ones. Examples of feature extraction techniques include linear discriminant analysis (LDA), principal component analysis (PCA), and canonical correlation analysis (CCA). On the other hand, the feature selection approach uses the original dataset to select an optimal subset of informative features by eliminating the redundant and irrelevant features . GeneralForward Feature Elimination. It is an iterative approach; in the beginning, there is a null model, and then, the model is fitted with each individual feature one at a time; accordingly, the feature with the highest classification accuracy is determined. Thereafter, a model is fitted with two features by trying combinations of the earlier selected feature with all other remaining features, and then, the combination of features that achieves the maximum classification accuracy is determined. This process is repeated until a subset of features outperforms all other determined subsets in terms of classification accuracy .Backward Feature Elimination. In this approach, all features are initially added to the model, and in each iteration, the least significant feature is removed based on some evaluation criteria. This process continues until no progress is detected by eliminating the features .Recursive Feature Elimination. It is an optimization algorithm and aims to find the finest feature subset. Unlike previous approaches, this approach continually produces a new model .In filter methods, the most relevant features are selected through the data itself; i.e., the features are evaluated according to the intrinsic and statistical properties of the data, without using any machine learning (ML) algorithm to guide the search of relevant features . Hence, In embedded methods, ML models are used with their own built-in feature selection methods . ExampleK nearest neighbors (KNN), SVM, and NB for the prediction of cancer among other diseases. They report that KNN model outperforms the other two models. In :X) and max (X) are the minimum and maximum values of the feature column X.Each feature value F-statistic, and MI , then the 8 will be considered an outlier, since 8 > 6. Thus, the row will be modified to .In the RT, the outliers (extreme) of the rank values are detected as follows:(4)  The next three columns are filled with the rank values of the 3 filters after moderation.  For each feature, the overall rank (OR) value is deduced by summing the three rank values of the feature's row to be a single value in the fifth column.An overall rank table (ORT) with 5 columns is constructed, and the first column is filled with feature names. Next, the following procedures are performed:(5)Ascendingly, the ORT is sorted using the OR values of the fifth column as a key. The features will be ordered from the most important, at the top, to the least important at the bottom.In this section, the two processes of feature selection and classification are explained.Feature selection is a very crucial step because the inclusion of inconsequential and redundant features negatively affects the model performance significantly. By selecting relevant features from the raw dataset, the learning model is improved in many ways: (i) avoiding learning from noise and overﬁtting, (ii) improving accuracy, and (iii) reducing training time. In addition, working with more informative features contributes to early diagnosis. As mentioned in In this article, a modified wrapper-based sequential forward selection technique is presented. In this model, the selection technique starts by adding the highest overall rank feature to an empty subset and then it measures the model's performance. Next, a set of successive iterations are performed. In each iteration, only one feature is added to the subset and performance is measured. If the newly added feature improves the performance of the model, it will remain within the subset. Otherwise, the added feature will be removed. Likewise, the remaining features are added and evaluated one by one to the features kept in the subset. In the last iteration, the features that are kept in the subset are the features that optimize the classification accuracy.KNN.The classification technique is applied to categorize data into a set of classes using supervised ML techniques. There are a variety of classification techniques for classifying microarray datasets. Based on the recent literature on cancer prediction  is the number of cases belonging to the class and correctly labeled as such, FP  is the number of cases belonging to the class but incorrectly labeled as not, TN (true negative) is the number of cases not belonging to the class and correctly labeled as such, and FN  is the number of cases belonging to the class but incorrectly labeled as not.In addition, the accuracy is used as a vital metric for evaluating the performance of ML models. The accuracy is deduced as follows:(i) Feature Selection and Classification Algorithm. After ordering the features from the most significant to the least based on OR values in the ORT, the feature selection procedure is performed. The complete feature selection and classification process are shown in (1)The most important feature that is in the first row of the ORT to an empty feature subset is added.(2)10-fold cross-validation is used for the feature subset and tune hyperparameters using the grid search technique.(3)An ML model is built using this subset of features.(4)The accuracy of the ML model is calculated, and it is called as the previous accuracy.(5)The next feature that is in the next row of the ORT to the feature subset is appended.(6)10-fold cross-validation is used for the feature subset and tune hyperparameters using the grid search technique.(7)An ML model is built using this subset of features.(8)The accuracy of the ML model is calculated, and it is called as the current accuracy.(9)  If the current accuracy is less than or equal to the previous accuracy, then the last added feature is excluded from the feature subset.  Otherwise, if the current accuracy is greater than the previous accuracy, then the previous accuracy is made equal to the current accuracy.The current accuracy is compared with the previous accuracy as follows:(10)The steps starting from step 5 are repeated until reaching the end of the ORT.(11)The optimum feature subset and its accuracy (the previous accuracy) are returned.The proposed system was tested by performing extensive experiments on four publicly available microarray datasets  shown inIt should be noted that Spark provides an interface for programming entire clusters with implicit data parallelism and fault tolerance. It can work with structured data such as CSV files and unstructured data such as JSON files . Spark pThe methods outlined in F-statistic, and MI, applying equations , an, anF-staquations , respectFor the feature ranking process, after creating a feature score table (FST) for each dataset, a rank table (RT) is created for each of them as shown in Tables KNN. These models in particular are chosen based on reviewing the recent research on cancer prediction as summarized in Four ML models were explored for cancer prediction, namely, SVM, DT, RF, and In this experiment, for each dataset, the performance of the four ML models when trained and tested on all features was measured.As can be seen in In this experiment, for each dataset, the performance for the four ML models was measured when they were trained and tested on subsets of features that were selected according to the proposed wrapper method.For each dataset, the best subset of features that achieves the best accuracy is shown in KNN models register the best average accuracy at 100% using only 5 features. For the ovarian cancer dataset, the SVM model outperforms the other models by achieving the best average accuracy at 100% using only 6 features. For the SRBCT dataset, the SVM model also outperforms the other models by achieving the best average accuracy at 100% using only 8 features. While for the lung cancer dataset, the SVM model achieves the highest average accuracy at 99.57% using 19 features.As can be seen in This article presents a robust machine learning (ML)-based algorithm to diagnose different cancer diseases using microarray datasets. The algorithm can effectively eliminate irrelevant and redundant genes. The output of the algorithm has high stability and classification accuracy. When the results of the algorithm are compared with those of similar algorithms, the proposed algorithm showed clear superiority. In particular, it selected a smaller number of genes and yielded a higher level of accuracy. Furthermore, the time and storage cost of the algorithm are very appealing, making it optimal for big data.An interesting future extension would be to adapt and verify the proposed algorithm on more realistic and benchmark microarray datasets of bigger sizes. Also, implementation using Hadoop/MapReduce platforms could be explored. In particular, to make the algorithm faster and more efficient when dealing with high-dimensional data, we intend to develop a parallel version to be run on cluster/cloud computing facilities.


This systematic review aims to investigate the possibilities of ultrasound imaging in the field of periodontal tissues exploration to visualize periodontal anatomical structures and to assess reliability in clinical evaluation using the PRISMA guidelines. An electronic search through the MEDLINE database was realized to identify studies that have explored ultrasonography in the field of periodontal imaging published from 2000 to March 2022. The search resulted in 245 records; after exclusions, a total of 15 papers were included in the present review. Various publications have shown the possibility of using intraoral ultrasound for a precise exploration of intraoral tissues and to perform measurements of periodontal structures. Studies argue that ultrasounds open the prospect of a complete paradigm shift on the diagnosis and follow-up of periodontal disease. However, there is currently no clinical device dedicated to periodontal ultrasound. This field is still under-studied, and studies are needed to explore the large field of applications from periodontal assessment to treatment reassessment, including surgery. Researchers should focus their efforts to develop special intraoral ultrasound device and explore the possibilities of clinical periodontal applications. Periodontitis is an inflammatory disease of the periodontium (tooth supporting tissues) of bacterial origin. It can be treated and controlled successfully, to avoid the progressive destruction of the tissues  . A patieRadiographic evaluation is an essential element of periodontal diagnosis. A radiograph of periodontal health includes a normal lamina dura, presence of bone in furcation areas, and 2 mm distance from the most coronal portion of the alveolar bone crest to the cementoenamel junction of the tooth . AlveolaIn view of these limitations, it is important to consider a new type of exploration with less time-consuming and easier to use in clinical practice. Since the middle of 1980s, several publications have presented ultrasound imaging applied to the exploration of the oral cavity in animals ) OR (“cementoenamel junction” [Mesh]) OR  OR  OR  OR  OR (“periodontitis” [Mesh]) OR (“gingivitis” [Mesh]) OR (“periodontium” [Mesh]) AND (“sonography” [Mesh]) OR (“diagnostic ultrasound” [Mesh]) OR (“ultrasonography” [Mesh]).References of the eligible studies on the topic were manually checked, and two independent operators (F.D. and M.R.) screened the studies according to the inclusion/exclusion criteria. In case of disagreement, a 3rd reviewer (R.M.) was asked.We included experimental or clinical studies , in healthy patients or patients with periodontitis, that explored the link between ultrasound imaging and periodontology or oral tissues or explored an association between ultrasonography and histological or histometric characterization of periodontal tissues. According to the type of ultrasound imaging, we included only studies that presented a mode B ultrasound device. We excluded conferences, abstracts, reviews and editorials. Publications concerning the detection of carious lesions and publications relating the utilization of ultrasound to increase the healing and osseointegration potential of dental implants were not included, and we excluded publications related to other medical disciplines.Each study that met the inclusion criteria was analyzed from several aspects such as authors, date of publication, study design, ultrasound device description, image classification, results, limitations and discussion.The list of titles and abstracts to identify the potentially relevant papers based on the inclusion criteria previously announced were independently screened by two reviewers (F.D. and R.M.). If the abstracts were identified as non-relevant, the full studies were reviewed to decide if they should be included or not according to the inclusion criteria. A scan of the references of the previously selected articles completed the selection to improve the systematic review. When a discrepancy in the selection decision appeared, the two reviewers engaged in discussion until a consensus was found. If needed, a third reviewer (M.R.) resolved the possible conflicts concerning eligibility.The initial studies retrieved from the databases were first selected, and studies that met the eligibility criteria were reviewed and analyzed. After 220 reading abstracts and 7 full articles, only 15 articles were selected from the 245 studies. The percentage of agreement between the reviewers was 100%. The complementary detection did not result in the selection of new publication for analysis. Finally, a total of 15 articles were included in the analysis .Among the 15 studies included in the analysis , we wereUsing ultrasonography for the visualization of the structures of the oral cavity was not an actual possibility, and publications existed for many years already. According to the periods of publications used in this review, we have noticed that there is a renewed interest in ultrasound technologies for periodontal exploration from the 2010s . There wAccording to our analysis, researchers have set up feasibility trials ,33 for iMost of the studies were in vivo studies. In vitro studies used pig jawbones while ex vivo studies were performed on cadavers. The literature presents a set of ultrasound probes used for the majority with an intraoral approach. The probe is in contact directly with intra oral tissue for image production providing a sagittal slice. In two publications ,33, we hIn the study by Salmon et al.,  the probRegarding the acoustic parameters of the probes, it should be remembered that periodontal imaging aims to image structures close to the probe head. The depth of exploration is less than 10 mm, and the structures to be explored are sub-millimetric in size. In this specific case, emission of frequencies needs to be between 15 MHz  up to 40Within the periodontal tissue, bone structures are more echogenic because they reflect more ultrasound waves. Impedance rupture between hard and soft tissues allows them to be clearly distinguished. Therefore, hard tissues appeared whiter than soft tissues on the gray scale. First images need to be processed by computer. The authors added different colors according to the tissues in order to allow a good tissue differentiation. Periodontal tissues images from more recent publications, such as that of Tattan et al.  show betDetection and classification of periodontal disease is based on measurements of periodontal tissue. The studies almost systematically present a comparison between the ultrasound measurements of the periodontal tissue and the measurements obtained by procedures used in clinical routine , qualified as the gold standard. Publications show measurements of the sulcular depth , the thiStudies on porcine jaws show direct transgingival measurements using an endodontic file ,34,36, dp < 0.05) compared to the ultrasound measurement. The greatest measurement variation between the two means of measurement did not exceed 0.5 mm. Tsiolis et al. [p < 0.001 for the measurement of the distance between the cemento-enamel junction and the alveolar ridge. After publications analysis, ultrasonography demonstrates reproducibility and precision. Ultrasonography appeared reliable in comparison with to other means of measurement  in periodontal tissue application.Several authors have used statistical tools to establish the correlation between ultrasound measurements and other means of measurement ,32,36,37s et al.  have cals et al.  highlighUltrasound for periodontology has benefited from renewed interest since the 2010s. However, there are only few teams working on this topic. The teams that presented several publications were made up of researchers from different research centers with different levels of expertise. The team of Chan et al. ,33 was mUltrasound imagery produces artifacts that are unique such as the “drop shadow”. This is due to the fact that a structure always appears less echogenic (blacker) than it really is when it is preceded (on the path of the ultrasound) by a hyperechoic structure. The study by Salmon et al.  reportedThe patients recruited for the studies were mostly healthy patients. Only Chifor et al.  enrolledThis work should not give rise to hasty conclusions due to the low number of publications and the intrinsic limits of the studies. Indeed, the use of only one electronic database is a particular limitation of this study. On the other hand, there are many biases in these studies and those related to the operators’ manipulations. In addition, many of the studies presented are animal studies that do not fully correspond to clinical conditions. These are feasibility studies and pilot tests with a medium level of proof (grade B). In addition, the heterogeneity of frequencies and acquisition protocols used in the current literature may hinder direct comparison between studies and necessitate more studies with homogeneous ultrasound measurements. All of the studies presented here do not allow to draw conclusions on the routine clinical use of ultrasounds in periodontology and require the setting up of randomized clinical studies.To improve our analysis of the literature, certain sources of complementary information from other fields of science are necessary. For example, there are specific databases for biotechnology engineers and acousticians. We can find technical information that would consolidate the state of the art. The articles exclusively dedicated to implantology also present US technologies allowing indirect exploration of periodontal tissues.High-resolution images have an equal or greater degree of precision than conventional imagery. It is a non-ionizing imaging that overcomes the discomfort of periodontal probing for diagnosis. Ultrasound pocket depth measurements appear to be as reliable and reproducible as those obtained by manual probing, even with an electronic probe.The ultrasound system combined with an artificial intelligence (AI) data processing system opens the way to new perspectives regarding the distinction of the sulcular space and the measurement between the cemento-enamel junction and the sulcus. On this type of standardized measurements, the process could be automatized, and the data integrated into periodontal charting. We would then have a reliable, less time-consuming device involved in patient follow-up. The AI will allow a better handling of the device.The use of ultrasound can be beneficial at all times of periodontal surgery. The ultrasonography can be allowed to see the quality of the graft directly before surgery. They would allow the incision path to be refined to avoid vasculo-nervous structures. Postoperatively, the healing or not of the graft could be monitored by inspecting the interactions with the recipient bed. Finally, inter-site contamination that may be caused by manual probing could be avoided.Interest in intraoral ultrasound technologies has grown over the past decade. The various publications highlighted a reliable means of imaging allowing a precise exploration of the periodontal tissues offering the possibility of carrying out measurements of the periodontal structures themselves or between them. However, there is currently no clinical device dedicated to periodontal ultrasound. For the moment, the use of ultrasound in periodontology remains confined to the field of research. Ultrasound opens the prospect of a complete paradigm shift on the diagnosis and follow-up of periodontal disease, by reducing the examination time of periodontal pockets, being more reproducible and more efficient. In addition, the implementation of software including an artificial intelligence system allowing the direct measurement of the periodontal pocket and the early detection of the inflammation of the deep periodontium could permit easy diagnosis and early treatment of periodontal disease. Moreover, this new approach could allow an evaluation of the initial treatment and permit more reliable periodontal maintenance. In addition, the direct measurement of periodontal pockets without ionizing radiation is a major advance on the complementary examination allowing to reduce the number of periapical X-rays. Periodontal ultrasound is not intended to replace the conventional means of evaluation of periodontal tissues. However, the associated opportunities are immense with a lot of applications from periodontal assessment to treatment reassessment, including surgery.


The above results show that we have proposed a yield estimation method to provide accurate yield estimations by combining data assimilation and machine learning. This study provided deep insights into understanding the variations in FVC and revealed the spatially explicit yield prediction ability from the time series land surface parameters, which has significant potential for optimizing water and soil resource management.Accurate yield estimation at the regional scale has always been a persistent challenge in the agricultural sector. With the vigorous emergence of remote sensing land surface observations in recent decades, data assimilation methodology has become an effective means to promote the accuracy and efficiency of yield estimation by integrating regional data and point-scale crop models. This paper focuses on the black soil area of Northeast China, a national strategic grain production base, applying the AquaCrop crop growth model to simulate the fractional vegetation cover (FVC) and maize yield from 2000 to 2020 and then forming a reliable FVC optimization dataset based on an ensemble Kalman filter (EnKF) assimilation algorithm with remote sensing products. Using the random forest model, the regression relationship between FVC and yield was established from the long-term time series data, which is crucial to achieve better yield estimation through the optimized FVC. The major findings include the following: (1) The R Agricultural production is the foundation of human survival. Accurate prediction of crop yield enables farmers to estimate profits and adjust crop-planting patterns. Governments also benefit from yield prediction information, which helps to promote the development and reform of food security, sustainable utilization of water and soil resources, agricultural trade and many other aspects .The northeastern Chinese black soil area is a major black soil zone of the world and a strategic guarantee base for national food security by producing crops such as maize and soybean . The speCrop growth models are an important tool to quantitatively describe the growth and yield formation process of specific crops under specific environments based on point scales , and it Simulation and observation are two basic strategies of geoscience research . Since aData assimilation (DA) is an important integrating methodology that automatically adjusts the process model forward direction continuously by relying on observations and then generates the minimum-deviation state variable set with spatiotemporal consistency, which is usually used for modeling and dynamic prediction of complex systems . With thLooking at the relevant studies integrating crop model and remote sensing data in recent years , the mos2 and root-mean-square error (RMSE) between the predicted yield and the measured yield were 0.81 and 0.54 t/ha and 0.61 and 0.86 t/ha, respectively, before and after combining RF. Although many studies have indicated the effectiveness of using crop models and remote sensing data assimilation for yield mapping, the expansion accuracy from the field to regional scale still lacks exploration . SilvestThis study completed the calibration and validation of the AquaCrop model in Northeast China via field test data and applied 21 years of regional-scale simulations from 2000 to 2020. Then we selected FVC for AquaCrop model assimilation not only because it is one of the outputs of AquaCrop but also because it considers the important role it plays in surface process simulation. Due to the accumulation of sufficient assimilated FVC data and crop yield data, which reflect various environmental conditions, the relationship between yield and environmental factors was established through the machine learning method of random forest. Relying on the FVC assimilation curve, a high-precision estimation of crop yield can be obtained. This study aims to establish an assimilation system to better monitor FVC growth and provide better maize yield estimation, which is significant for local agricultural management.2 and a large part of it is dominated by rain-fed agriculture. It has a temperate continental monsoon climate, the average annual temperature is approximately 0.4°C, the average annual precipitation is approximately 534 mm, and the altitude is approximately 250∼450 m. In 2021 The Songnen Plain  is located in the middle of the Songliao black soil basin in Northeast China, with a total area of approximately 206404.3 km–2 day–1), as input to the AquaCrop meteorological module , minimum and maximum temperature (°C) and solar radiation  products from 2000 to 2020 were collected for regional data assimilation. Multisource high-resolution optical remote sensing images in 2018 and 2020 were collected for relative accuracy verification of the GLASS FVC product and assimilation tests.2. The inversion algorithm is based on multisource remote sensing data and measured site data  can be retrieved according to the pixel dichotomy:s is the NDVI of the pure soil pixel, and Vv is the NDVI of the pure vegetation pixel.where VI is the NDVI of the pixel, VThe remote sensing FVC curves obtained from different sensors and inversion methods are roughly the same, reflecting the reliability of the GLASS FVC product in Northeast China. National statistical yearbooks are formed by governments’ sampling surveys and have acknowledged the authenticity. This study collected province yearbooks from 2000 to 2020 for Jilin, Heilongjiang, Liaoning and Inner Mongolia, which are under the coverage of the Songnen Plain. The established yield dataset of Northeast China included 3666 statistical maize yields per unit area of 258 districts and counties, which was used to establish the regression relationship between FVC and yield based on spatial location. The linear fitting results of yearly yield are shown in The methodology adopted in this study mainly involved three parts: regional application of the AquaCrop model, FVC data assimilation by model outputs and remote sensing products, and yield estimation relying on the RF regression model .The AquaCrop model simulates the transpiration process of crops by inputting climate, crop, soil, and field management data and finally outputs the daily prediction results of CC, rooting depth, biomass and yield . A signiTr is the crop transpiration coefficient. ET0 is the relative evapotranspiration without stress. CC* is the adjusted canopy cover. KcTr,x is the coefficient for maximum crop transpiration, which represents an integration of the effects of the characteristics that distinguish the crop with a complete canopy from reference grass.where Tr is the leaf transpiration. Kc0 is the initial canopy coverage (%), generally taking the average seedling coverage at 90% emergence. CCx is the maximum value of canopy coverage (%). CGC is the canopy coverage growth rate, which indicates the increase in canopy coverage per unit growth degree day (% GDD–1). CDC is the canopy coverage decrease rate, which represents the reduction in daily canopy coverage per unit growth degree day (% GDD–1).CC is canopy coverage (%). t is the time accumulated from emergence. CCi), daily atmospheric evapotranspiration demand  and normalized water productivity (WP*), and crop yield is calculated by the biomass and harvest index, as shown in Equations 6-7.The accumulated biomass is calculated by daily transpiration  is a typical classifier that uses multiple decision trees to train and predict from input samples. It determines the category of test samples by voting and then takes the average output of each decision tree as the final result.Referring to the Scikit-learn python machine learning library, this study uses the daily FVC value to estimate yield optimally through the RF model. In order to compare the impact on yield estimation accuracy before and after FVC assimilation, three random forest models were established to describe the regression relationship between the FVC curve and yield. The difference is in the input FVC, including the FVC simulated by AquaCrop, the FVC provided by the GLASS remote sensing product and the FVC obtained by data assimilation. Finally, the model with the highest accuracy is selected for maize yield prediction, so as to achieve the research goal of optimal yield estimation.2, using Equations 11-12.The total dataset of RF1-3 is composed of 21 growing seasons from 2000 to 2020, three types of FVC data of 155 simulation units and the corresponding statistical yield data. Each RF model should have 3255 records, each record have a set of FVC and a statistical yield. The actual number of records is finally determined by the amount of data with well assimilation effect. The scale of statistical yearbook data is suitable, which is of 258 districts and counties can be matched with the three series of FVC data on 155 simulation units. Another consideration of choosing statistical yield instead of AquaCrop simulated yield is to avoid the accuracy interference caused by the same model output as FVC_AC, and more objectively reflect the real harvest. The samples were randomly divided into two parts with a ratio of 8:2 the large part used for training and the other part used for accuracy evaluation . The accRunning the AquaCrop model of multithread scheduling for the 155 soil representative cells in Songnen black soil region from 2000 to 2020, we explored the spatial pattern of predicted yield by mapping the results after two empirical Bayesian Kriging interpolation to In general, the spatial distribution and the temporal differences of predicted yield are reasonable reproduced, which is consistent with that of statistical yield shown in . Among tIn terms of time series, the inter-annual differences were mainly caused by the differences of hydrothermal conditions in each growing season, especially the water factor. The output showed a stable trend, with 2000, 2001, 2004, 2007, 2010, 2017 being the good harvest years for the entire region, while other years clearly make out the spatial difference. Abnormal precipitation events during crop growth period, especially in the process of yield formation after flowering, are easy to cause low crop yields. Mild and continuous natural precipitation provides optimal water conditions for crop growth and development. The neglected soil erosion and the administration policies also affect the estimation accuracy.This study implements a multithreaded univariate EnKF assimilation algorithm based on MATLAB language, which can realize the optimal estimation combining the daily FVC simulated by the AquaCrop model and the multitemporal remote sensing FVC in the corresponding growing season. The results show that EnKF assimilation can indeed integrate remote sensing data into simulation results, achieve higher spatiotemporal resolution and provide FVC estimation with good accuracy. All the assimilation results are defined into 4 types . IncludiThe unsatisfactory assimilation results were probably caused by mixed-pixel RS inversion, spatial mismatch and inaccurate phenological parameters that led to discrepancies between the simulation and reality. It should be noted that remote sensing data can reflect real surface information only when the spatial resolution is sufficiently high. The accuracy of the method will be dramatically promoted when the resolution of remote sensing input data is improved.At the end of the growth period, FVC observed by remote sensing is not of maize crops, but background interference such as surface weeds, it will have no impact on yield simulation by removing the last 10 days of data before adding to the RF model.Based on the FVC array and yield data in the last 20 years, this study established three RF models to describe the regression relationship between the three FVCs and the yield of the statistical yearbook. RF1 used the FVC simulated by the AquaCrop model, RF2 used the remote sensing GLASS FVC product, and RF3 used the optimal FVC assimilated by the two. Considering that the unsatisfactory assimilation results reflected the unreliability of FVC_AC or FVC_RS, the three random forest models only used the data corresponding to well-assimilated fraction of FVC in 2 increases from 0.555 to 0.557, and MAE decreases from 1.004 ton/ha to 0.888 ton/ha. RF2, the yield estimation model based on remote sensing values alone has the lowest accuracy, probably because the amount of data input is far less than that of the other two models, and the quality of the data is greatly influenced by the scale effect. RF3 proved the feasibility of estimating yield with optimal FVC curve.Based on the optimal FVC curve, RF3 showed the best performance on maize yield prediction in the black soil area of Northeast China. RF3 is slightly better than RF1, which proves that the addition of remote sensing observation data still has a gain on the yield simulation model, RFrom the results, the addition of assimilation only nets a slight improvement to the yield estimation accuracy, which may lead to doubts about the method effectiveness. Therefore, we establish the following assumptions to explain the benefit of the assimilation algorithm on yield estimation accuracy:o and simulation errors s:First, assume that Fs(t) is the FVC simulated by the AquaCrop model at time t, Fo(t) is the FVC observed by remote sensing at time t, and Ft(t) is the real FVC, which is unknown. Then, there are two errors, observation error Furthermore, assuming that the error of observation value and the simulation value are unbiased and have no correlation:a(t) that is closer to Ft(t). The reciprocal of variance is defined as the data precision.At this time, by calculating the variance of the observation error Assuming that the estimated value is unbiased:a(t):Then, minimize the variance Obviously, the variance of the estimated value is always less than the observation error variance and simulation error variance. The coupling of observation and model simulation information is confirmed to obtain a better state estimation value.However, no data source can guarantee the unbiased of its error nature. In terms of remote sensing data, if the observations are collectively higher than the true values, the addition of observed values during assimilation will lead the simulation process to a higher direction but make the estimation results more distorted. Therefore, it is necessary to control and reduce the reliability of each input data of the assimilation algorithm to ensure the final prediction effect. This requires the continued development of remote sensing technology and traditional mechanism models.This paper mainly has uncertainty and limitations in the following two aspects: data assimilation by remote sensing and machine learning. In the ideal case, the AquaCrop model assimilation system coupled with multitemporal remote sensing products integrates the advantages of the two. On the one hand, the addition of a mechanism model makes up for the lack of biophysical significance of the system. On the other hand, the addition of remote sensing observations improves the reliability of the system and expands the application scope. But in fact, the analog of state variables in the crop model is not detailed enough, and many variation characteristics of FVC observed by remote sensing are not reflected in the simulation results. It should also focus on developing regional crop models to allow the input and output of surface parameters to better integrate and utilize regional products and serve regional research. In regional studies, remote sensing data are generally expected to be used due to their large scale and ready availability. However, the unverifiable authenticity of remote sensing data caused by mixed pixels must not be overlooked, and the final error may be three times the input LAI error . Althoug2 of random forest reached 0.557, demonstrating that the construction logic of the system is tenable. It revealed that crop yield is not only reflected by FVC, which may account for 55.7% of the representation. The maize yield estimation accuracy was limited by the correlation between FVC and maize yield itself, which can hardly be surpassed by technology. For regional yield estimation, this is still a rare attempt to provide a relatively accurate yield forecast based only on time series FVC data.Introducing the data-driven method, this study established the regression relationship between time series FVC and yield based on the machine learning method of random forest. According to the crop yield predicted by the assimilated FVC and the statistical yield, the R2 was 0.93 and the RMSE was 1.15 ton/ha. 2, while our study using 500 m resolution product so as to achieved 20 km2 of yield estimation. 2 of the estimated yield was 0.33, and the root mean square error (RMSE) was 0.371 ton/ha. Their study has only been verified in 8 research points for 5 years, while our study verified on 155 points for 21 years.Several previous studies have also found the significant association between surface state variables and crop yield, and all committed to estimating yield through these variables. Present yield estimation accuracy of 0.888 ton/ha through FVC assimilation has an advantage over previous assimilation studies. The results of this paper also show that there are many potential development space for the method of yield estimation based on the assimilation of surface state variable and machine learning. This finding is similar to those reported by This study proposed a yield prediction method based on a crop model and remote sensing data assimilation for maize in the black soil region of Northeast China. The calibrated AquaCrop model already has a good simulation effect at the point scale, which confirms the availability of the AquaCrop model in this area. Profit from the physiological response of crops to environmental and management conditions is intuitively reflected by the AquaCrop model. We applied the model to simulate the growth of maize crops in the Songnen black soil area from 2000 to 2020 and accumulated a large database. After confirming the accuracy of the remote sensing surface parameter products, synchronous time series observations are added to the AquaCrop simulation results of 21 years through the EnKF filtering assimilation algorithm, and an optimal FVC dataset is established. Using the optimal FVC and the regression relationship between FVC and statistical yield trained by random forest, a yield estimation method is formed. Data assimilation combines the two geodetic research methodologies of simulation and observation, while this study proposed that the method further integrates the idea of a mechanism model and machine learning and provides a feasible idea for crop yield estimation. Overall, the main contribution of current study is offering new insights and perspectives for the following two issues: one is how to integrate satellite remote sensing data into the crop model at the regional scale; the second is how to obtain more useful yield information from the available surface parameter data.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.YC: conceptualization, methodology, software, formal analysis, investigation, and writing—review and editing. SL: conceptualization, writing—review and editing, supervision, and project administration. XL and HG: visualization. YX: data curation, conceptualization, and supervision. YH: data curation. All authors have read and agreed to the published version of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


HERAS is a tool developed in Matlab for the analysis of reflector antennas using physical optics (PO) theory. Its graphical user interface (GUI) and source code are freely available for educational and research purposes. It has the necessity of being a flexible tool to provide adaptability to system engineering requirements and can also be of interest to antenna engineers working on the design of reflector antennas. Due to the increasing demand of broadband services, satellite communications systems are becoming highly complex in order to meet connectivity requirements. To fully exploit the benefits of these systems, multidimensional optimisations are crucial, which call for an efficient estimation of the coverage characteristics. Reflector-based solutions are one of the preferred architectures for very high-throughput satellite (VHTS) systems. A detailed description of HERAS is presented in this paper which has been validated with available commercial software packages. In addition, some examples are described in which the tool has been used for the efficient estimation of VHTS systems performance. Satcom systems are increasingly moving from broadcast to broadband services, adapting to fast evolving consumer needs for high-throughput connectivity . This marks the shift from broad-shaped beams providing regional or continental coverage to multiple spot-beam antenna architectures enabling spectrum reuse with a cellular-like coverage ,2,3,4,5.As we move towards the next generation of very high-throughput satellite (VHTS) systems, which target total throughput in the order of 1 Tbps, the number of beams is likely to grow from hundreds to thousands in order to achieve significantly larger spectrum reuse factors compared to existing HTS systems. This requires a careful design of the antenna system to provide a high carrier-to-interferer ratio  allocation policies and interference mitigation techniques  . ConsequWhen it comes to the antenna development, unlike heritage broadcast missions where shaped antennas could be designed against effective isotropic radiated power (EIRP) and gain-to-noise-temperature (G/T) contours, MBRAs for multi-beam and VHTS missions should thus be considered in the context of end-to-end system performance . The co-Traditional methods for the analysis of reflector antennas usually rely on numerical integrations, which are the main contributor to the total computation time. Physical optics (PO) is the preferred technique to predict the scattered field of electrically large structures such as reflector antennas, radar cross section of targets, etc. . GRASP fIn this paper, we present HERAS (Heriot-Watt reflector antenna solver), a tool for educational and research purposes that comes from the need for a flexible tool for the computation of far-field characteristics of a reflector antenna. HERAS was designed and developed to provide adaptability to system engineering requirements. HERAS is also of interest to antenna engineers working on the design of reflector antenna systems and was, in fact, originally developed to enable the analysis of antenna systems using reflecting polarisers ,23,24,25As discussed previously, there are several options commercially available for the analysis of reflector antennas that employ different numerical methods. Finite integration technique (FIT), finite element method (FEM), and method of moments (MoM) are widely used by antenna engineers to solve electromagnetic problems for electrically small structures ,27,28. Tk is the wave number, r is the radial component, S onto the focal plane, i.e. the plane orthogonal to The aperture distribution method obtains the radiated far-field of the reflector antenna from an aperture field distribution derived from ray tracing ,30:(1)E→nal cost . In addinal cost .S, and S. These parameters are depicted in The current distribution method is well-established as the preferred approach to model the radiation characteristics from reflector antennas . SimilarOther techniques to improve the accuracy of the results and the computational costs can be found in the literature ,34,35. DThe tool described in this paper uses PO for the analysis of reflector antennas’ radiation characteristics. This technique is generally well adapted to evaluate the performance of electrically large reflectors as generally used in communication satellites. Numerical techniques for the analysis of feeds and their illumination properties in addition to the use of coordinate system transformations are used in the tool and further detailed in .HERAS is a tool developed in Matlab  employinHERAS is a simplified version of this internal tool which focuses on reflector antennas with PEC surfaces. While these systems could be analysed using existing commercial software, an open-source code provides more flexibility in adapting the tool to specific needs and in particular system-level MBD analyses, where accuracy may be traded-off with computational efficiency. This proved particularly useful for the analysis of VHTS reflector antenna systems, as mentioned in the introduction. A graphical user interface (GUI) is available which allows us to define a specific reflector configuration and to obtain the performance in the main far-field cuts, as shown in A folder can be found which contains all OOP classes that can be used in the software. These include classes for objects such as reflector architectures, feeds, etc. This folder can be added to the MATLAB path in order to create individual instances of objects and use them in a specific project. As an example, the flowchart of the steps to create a single MATLAB script to compute the far-field of a reflector antenna configuration using the tool is shown in POobject and POoperation. The first one is used to define the different objects which compose the reflector antenna architecture such as the feeds and the reflector. The second class is used for the operations related with PO theory and the output of the results. The subclasses POreflector and Feed inherit from POobject  to define its geometry, which is used for the PO integral. Every object of the system has its own local coordinate system which is defined with the CSLocal class. Once the antenna system is defined with the appropriate objects, PO instructions can be executed, with the use of the POOperation subclasses (see POSurfaceCurrents and POSurfaceCurrentsSub are used for the illumination of the reflector(s) object(s) from the feed(s). The PO integral is computed through the Currents2Farfield object, which also stores the results in the format given by FarfieldSphericalGrid or FarfieldSphericalCut. Each class can perform different operations, which are implemented in the specific class methods. These can include coordinate system conversion, feed illumination, PO integral, plot to figure, etc. The specific operation of each class is detailed in the code.The basic building blocks of the tool are the classes ject see , which dsses see . POSurfaAs an example of the performance of the tool, a comparison of the results given by the tool and those obtained with GRASP student version using PO are provided in FFFeed classes in HERAS can include a spherical wave expansion (SWE) module to import real feeds. As an example, this allows the inclusion of simulated feed far-fields from a full-wave simulation software as well as measured far-field patterns to be used as feeds  antenna architectures. The degrees of freedom in the design of these systems, such as the definition of the optics and the feed array characteristics, call for multidisciplinary optimisations in which the antenna parameters need to be modified multiple times to meet mission requirements. In reflector-based configurations, this is translated to thousands of time-consuming numerical integrations. This is often the bottleneck in the system optimisation time. In this case, computational time is a primary driver provided the coverage metrics are evaluated with an acceptable level of accuracy. Some acceleration techniques applied to the tool described in this paper were presented in  in the cthreshold method) which can be implemented directly in HERAS. Instead of computing the far-field pattern for every beam at every coverage point, the computation starts at the estimated centre of the beam and continues with surrounding coverage points until the ratio of the computed field to the peak directivity is below a given threshold. This threshold enables the user to find a suitable compromise between computation time and accuracy. In order to avoid stopping at a null of the far-field pattern, a number of surrounding points are checked in every iteration.While the beams typically have high directivity in the main lobe, the gain envelope decreases rapidly at the side lobes. Consequently, only a limited area around the main beam is relevant for interpolation between beams across the coverage as means to reducing the number of beams numerically evaluated using PO. In particular, this technique exploits the fact that, with the exception of a shift in the pointing direction along the angular domain, neighbouring feeds otherwise produce very similar radiation patterns. The interpolation process is thus performed using two or more surrounding beams to estimate the far-field pattern of a given unevaluated beam. Using the corresponding local coordinates of each beam allows to account for the shift in the angular domain observed between successive beams. The estimated centre point of the beam is therefore computed as the average of the far-field strength obtained in the centre point of the surrounding beams, and the process is repeated for every point, considering the relative distance from the beam centre. This can be performed with one command by virtually aligning the centre of the beams and obtaining the average of their far-fields’ strength. An interpolation path specifies which beams in the coverage are computed with PO and which are interpolated. Since the computational time associated with taking a weighted average to interpolate a beam is negligible compared to the time required to perform the PO integral, the acceleration obtained with this method is directly related to the percentage of beams that are interpolated.Another acceleration method exploits parfor has been used [Further computational savings can be achieved by adjusting the number of points defining the reflector mesh grid. This grid defines the discrete set of points along which the surface currents on the reflector, een used . This alA schematic representation of the general working operation of the tool embedding HERAS for the evaluation of reflector antenna systems is shown in A combination of all these techniques demonstrated a total acceleration factor of 80 in the scenario proposed in , which cented in  are reporibed in .Taking advantage of the flexibility provided by this approach, a system study may start with a broader parametric evaluation tolerating a slightly higher error, and gradually increase the accuracy as the antenna geometry becomes consolidated. A more refined analysis and fine-tuning of the design may then be conducted at a sub-system level using dedicated tools, such as GRASP, to further improve the performance using a more realistic feed model or introducing reflector surface shaping, for example. It is also noted that the aforementioned acceleration techniques may be implemented using commercial software packages. This is the case for the beam interpolation, for example, which can be directly applied using commercial solvers; the threshold technique is more readily implemented directly in the code and thus benefits from the access to the source code.The fixed coverage characteristics of passive SFPB/MFPB antenna architectures do not allow a favourable match of the satellite capacity to evolving traffic demands. With the technology developments in solid-state power amplification (SSPA) and digital payloads, phased-array active antenna solutions emerge as an attractive candidate to deliver the desired flexibility. Despite the favourable characteristics, the deployment of DRAs at an aperture size suitable to meet stringent link budget requirements for broadband geostationary satellite missions will remain challenging for the foreseeable future. In particular, the limited digital processing capacity of existing and near-future payloads suggests a requirement for extensive implementation of analogue beam-forming networks, which combined with the thermo-mechanical demands associated with distributed SSPA increases the complexity and costs of DRA-based payloads.AFRs in imaging configuration where the feed array assembly is collectively used to generate each beam are gaining attention for future VHTS systems due to their flexibility ,57,58. IThe analysis method for AFR systems entails multiple steps. These include the calculation of the beam-forming coefficients, which defines the weighted contribution of each feed in the formation of each beam; power normalisation, which ensures that each feed-radiated power is within the capability available at the corresponding amplifier; and PO computation, which transforms the reflector illumination to the associated far-field characteristics.threshold and interpolation) can be directly applied. It is noted that in this case, the beam-forming matrix should be defined in advance of the coverage computation. In particular, Equation  but also on the phase. This requirement, in turn, brings challenges associated to interpolating phase wrapped far-field characteristics. Consequently, exploiting interpolation becomes more challenging.Therefore, a new acceleration method has been studied which, rather than interpolating the far-field characteristics across different beams, exploits interpolation to reduce the number of far-field points that are computed within a given beam. Assuming that the amplitude and phase of the radiation at a subset of far-field points is known, the remaining points are estimated using interpolation performed in both the amplitude and phase domains. An example is illustrated in W was presented in [This solution was introduced in  and provented in . The stuented in , and zerented in .CFM and ZF methods can only be evaluated directly if the far-field of each feed is first computed, i.e., when beam-forming at a secondary level is applied in the calculation. These methods produce better system performance in terms of The HERAS software for the analysis of reflector antennas using physical optics has been presented. This tool, with source code in MATLAB, is available freely for educational and research purposes and may be of interest to antenna engineers for parametric studies and custom reflector antenna system design. HERAS may also be of interest to satellite communicationspayload and system engineers due to its adaptability and applicability in end-to-end performance investigations. Some projects where the tool has been of contribution related to VHTS systems have been presented, showing the potential of the tool for the design, analysis, and optimisation of such systems, which employ thousands of beams to achieve higher capacities. Specifically, this tool has been used for the efficient estimation of SFPB antenna systems, where several acceleration techniques were introduced in order to reduce the computational cost of the calculation of thousands of beams. In addition, the tool has also demonstrated its potential for the analysis of AFR configurations in combination with several signal processing techniques such as beam-forming and precoding for the analysis of these systems in terms of the final system performance.