Software Defined Networking (SDN) is a communication alternative to increase the scalability and resilience of microgrid hierarchical control. The common architecture has a centralized and monolithic topology, where the controller is highly susceptible to latency problems, resiliency, and scalability issues. This paper proposes a novel and intelligent control network to improve the performance of microgrid communications, solving the typical drawback of monolithic SDN controllers. The SDN controller’s functionalities are segregated into microservices groups and distributed through a bare-metal Kubernetes cluster. Results are presented from PLECS hardware in the loop simulation to validate the seamless transition between standard hierarchical control to the SDN networked microgrid. The microservices significantly impact the performance of the SDN controller, decreasing the latency by 10.76% compared with a monolithic architecture. Furthermore, the proposed approach demonstrates a 42.23% decrease in packet loss versus monolithic topologies and a 53.41% reduction in recovery time during failures. Combining Kubernetes with SDN microservices can eliminate the single point of failure in hierarchical control, improve application recovery time, and enhance containerization benefits, including security and portability. This proposal represents a reference framework for future edge computing and intelligent control approaches in networked microgrids. Microgrid hierarchical control aims to regulate the network frequency and voltage through collaborative work between distributed energy sources. This strategy has changed the impact of distributed generation. However, it has imposed several challenges in power control systems, especially those related to integrating power electronics, telecommunications, fault monitoring, and security issues . The treThe primary level regulates the network’s frequency and voltage, ensuring power-sharing between the distributed generators (DGs) . The moscurrents . At thisThe literature provides evidence that integrates the power system with communications architectures in networked microgrids (NMG). For example, refs. ,6,7,8 prSoftware Defined Networking (SDN) is a modern approach to networking that allows for controlling and managing network resources and traffic flow through software abstractions . SDN proThe main limitation of SDN technology is the use of a centralized control plane and the inconveniences associated with a single point of failure of this critical node. The centralized control plane can potentially lead to network downtime if not properly managed. In ,14,15, tOne promising approach is to distribute the functions of the SDN controller into multiple microservices ,17. The There is a wide variety of SDN controllers developed using different programming languages ,19, amonnetworks . The ONOAn orchestrator that automates network management, load balancing, and new instances provides an intelligent topology that uses microgrid resources efficiently. Combining SDN with Kubernetes provides an intelligent system that analyzes traffic and application requirements in real-time to adjust network configuration and application deployment. Recent literature ,27 suggeReliability : Bare-meComputational cost : Low cosLow latency : MicrogrOptimal resource utilization ,35: MicrScalability : NetworkAccording to literature ,30, the Despite the previous comments and the benefits of Kubernetes, there is no evidence of SDN microservices being used to solve the disadvantages of microgrid hierarchical control. Decoupling the applications from the monolithic controller into a series of sub-functions enables the deployment of a highly flexible SDN architecture. The most critical impact of this research is the ability to coordinate different applications as microservices and provide the guidelines for programming APIs in microgrid hierarchical control.This paper proposes a novel hierarchical control architecture based on microservices to address the limitations of SDN controllers in networked microgrids. Implementing a set of controllers as a distributed system in the Kubernetes bare-metal cluster increases the redundancy and resilience of the communication system. The load is distributed among various devices based on communication and power system restrictions. Rather than using a monolithic controller, the controller functions are divided into a group of microservices. The key contributions of this research are presented as follows.A new architecture, based on microservices, as a solution to the centralized SDN controller problem regarding load balancing, scalability, and low latency. The proposed methods improve the global resilience of the system and allow the integration of SDN controllers as pod services in distributed Kubernetes platforms. The proposed approach allows the deployment of bare-metal Kubernetes cluster parameters and can be applied to multiple configurations of AC/DC microgrids.A new SDN communication architecture has been developed for hardware-in-the-loop platforms connected to Raspberry pi, serving as both a Kubernetes worker and an OpenFlow communication device. Furthermore, this paper analyzes the most significant drawbacks of the SDN control plane in networked microgrids.Provides a proof of concept to apply This implementation can be replicated and modified through our project’s GitHub repository. Furthermore, it designs a monitoring tool integration that allows visualization of logs and measures metrics to carry out a complete analysis of the networked microgrid.The rest of this paper is organized as follows. This section includes the fundamental disadvantages of SDN controllers, comparing monolithic and centralized architectures versus microservices-based architectures. The contrasted elements allow determining the most relevant metrics that mark the performance of the SDN protocol. The scalability of the communications system proposed by SDN integrated with Kubernetes allows the deployment of an intelligent DG architecture at a reduced cost and increases the overall security through SDN controller functions.Although Software Defined Networking has several benefits, it has certain limitations that must be considered. Additionally, the security elements of SDN solutions are still a concern, as the centralized control plane can be a target for cyberattacks. The most significant drawbacks of SDN technology are summarized below.The most widely used architecture for microgrid control uses a centralized SDN controller as an intelligent element within the topology. However, critical aspects such as latency, network convergence (less than 100 ms), reliability  solutions. Some of the most popular SDN controllers  use The close relationship between control applications and the controller type presents a challenge that restricts the ability to reuse applications and module configurations. In several situations, modifying the programming language and readjusting critical plugins becomes necessary due to the interdependence between the modules and the controller’s central component.The principal reason for the lack of reliability and scalability is the high dependency between the SDN controller and the communication events handled by the control plane. Furthermore, a monolithic architecture is complex to scale into a standalone system due to the relationship between the application of the SDN controller and the communication device. Any failure in one component will result in a cascade failure of the entire system.Hierarchical control is a practical approach to managing power sharing in a Microgrid. The primary control level determines the amount of power to be generated by each DG based on factors such as power demand, availability of energy, and system constraints, as Power sharing between DGs is usually carried out by parallel inverters connected to a common AC bus with multiple loads . The proThe control strategy is evaluated according to different events within the microgrid. The droop control is activated during the first second until it reaches the steady state condition. As shown in Research studies have used a hierarchical control approach with an SDN-based communication architecture to enhance overall system intelligence ,37,45. HSDN controllers implement different modules to handle the most relevant aspect of the communication devices. These modules afford key functionalities, such as selecting the best route for message forwarding, monitoring topology changes, and enhancing security ,47, as oPrevious functionalities are the components that support segmentation in microservices.In this proposal, the SDN controller deploys a set of microservices in several Docker containers, as shown in The Kubernetes cluster is deployed in K3s  to obtaiThe northbound interface (NB) allows the interaction between the SDN controller and external applications. On the other hand, the southbound interface (SB) standardizes the operation of the communication protocols, as in the case of OpenFlow . REST APμONOS) is a new version of the SDN controller, developed by the Open Network Foundation , which ion  . The netg to ONF , the onoonos-config, is responsible for linking the module’s functionality to the specific microservices that are executed in a distributed manner.The onos-config, as it manages the configuration of devices through gNMI interfaces and registers all events to send them to the Atomix driver. The Atomix driver implements an API to scale the The essential microservice of undation .onos-config module strives to handle network and device alterations by invoking the NetworkChange and DeviceChange services, respectively. These services keep records of all change logs and pass them to the Atomix drivers via the gRPC interface.The onos-config only supports it through gNMI. Furthermore, the YANG models set the configuration and topology architecture into onos-config service. The deployment of this module requires a Kubernetes cluster capable of running Helmcharts as detailed in its deployment page [onos-config and onos-cli allows the user to define rules or route paths through the gNMI interface. To execute it, access the onos-cli pod and run the plugins from there (you can view the list of plugins by running onos-config get plugins).For connecting devices through the southbound interface, ent page . The intonos-config service are deployed, and six pods of Atomix increase the availability and distribute the services across the nodes. All steps to deploy this proposal are available in the GitHub repository [pository .eth0 is the default ethernet interface of the Raspberry pi 4. It serves as the Linux bridge and is used for configuring Kubernetes clusters, exchanging pods control information, accessing Rancher and the load balancer, and connecting to the Internet gateway. It means that eth0 acts as an overlay interface for external communications. On the other hand, eth1 is used by the OpenFlow protocol to communicate between SDN service pods. Conversely, the eth1 interface, connected via a USB to Ethernet adapter, enables the substitution of the veth interfaces of the pods with kbr-int-ex. Each pod in the cluster will use the kbr interface instead of its veth to avoid routing and forwarding issues.This paper implements two network interfaces for each Raspberry, as shown in Calico CNI (Kubernetes Container Network Interface (CNI)) deploys a Daemonset on each node, ensuring communication between gRPC and the K3s distribution  allows dAnsible automates node creation, storage configuration, network interfaces, services, and deployment processes. This tool allows (in a simple way) the cluster to be deployed through the execution of a series of scripts developed in Ansible. All the manifest and Ansible inventory files are in the shared GitHub repo.Possible communication alternatives between Raspberry and PLECS are SPI, I2C, and CAN protocols. However, the PLECS RT Box only has two SPI communication modules (SPI1 and SPI2), leaving one of our worker nodes unconnected. In , the aveEach Raspberry will serve as an OpenFlow communication device that ensures the exchange of secondary control information. According to the price of this proposal, Different factors, such as hardware resources, load, or communication architecture, limit the number of pods executed on each device. However, with Rancher, these pods can be scaled automatically without compromising the cluster’s overall structure. To configure automatic scaling in Rancher is necessary to select the deployment. From there, the “Scaling” tab specifies the minimum, maximum, and desired number of replicas for the deployment and also sets the scaling policy based on CPU or memory usage. This proposal shows the number of replicas for each service in The solution to monitoring the communication devices’ status and the tools’ interaction is presented in Prometheus sends the information to the local storage to collect operating system metrics. We use the Finally, Grafana allows importing a series of dashboards with information on the DG flows. This tool obtains the knowledge of the packet flows that pass through the USB ethernet adapter to the SDN controller. An essential element to consider when implementing a high-availability Kubernetes cluster on Raspberry is the performance of the computational resources. As the cluster scales, the computational resources become more limited. Increasing the number of pods in Kubernetes can be done to minimize the impact on service performance as follows.Ensure that the nodes in your cluster have enough resources  to support the increased number of pods. The notification system and the alerts configured in Grafana allow the monitoring of resource usage and global capacity.Using horizontal pod autoscaling (HPA) automatically adjusts the number of pods based on resource usage and demand. HPA can be configured based on CPU usage, memory usage, or custom metrics.To prevent resource contention and performance issues, pod anti-affinity rules ensure that pods are not placed on the same node. This method avoids the scheduling of pods on the same node.Optimize pod resource requests and limits to function correctly.Use pod disruption budgets (PDB) to ensure that a minimum number of pods are available during node maintenance or failures. By setting a PDB, you can guarantee that the service is unaffected by removing pods from the cluster.Monitoring the service’s performance following the previous points and adjusting the settings as necessary to optimize resource utilization and performance is crucial.To analyze the results of this proposal, a series of critical elements were tested, which imposed restrictions on the communications and power systems. update1 and update2 in The evaluation tests of this proposal consider the measurement of two types of latency. The first column in first1 and update1, while the connections between DG1 and the SDN controller are represented by first2 and update2. In OSPF, the connection is established between the two nearest DGs. As can be seen, the highest latency is originated when the first flow is sent between two nodes. Power data (frequency and voltage) shared by hierarchical control in PLECS are shipped using the SPI and CAN protocol, and the results are summarized as average round trip time.The second experiment considers the average latency for the rest of the packets using OSPF routing and SDN technology. As shown in However, even though OSPF and SDN with centralized control have slightly higher performance, the need to use a load balancer is evident, especially in the topology with a monolithic SDN controller and multiple DGs. Furthermore, when the traffic increases, its performance starts to degrade. For the OSPF routing strategy, it can be seen that the sending of the first packet of the topology is slightly higher than its competitors. This is mainly due to the neighbor discovery algorithm and the SPF algorithm needing to know the entire topology for proper performance. To avoid a single point of failure, the proposal of this paper incorporates a distributed load balancer, following the recommendation in .The researchers performed three communication tests to evaluate the response of the proposed alternatives as a solution to the hierarchical control problem in electrical microgrids. The findings reveal that monolithic architectures can offer lower latency since all the system components are closely integrated and communicate directly, reducing network communication overhead. However, this close coupling can also limit the system’s horizontal scalability and ability to handle high throughput requirements. On the other hand, microservices architectures can provide higher throughput as the system can be scaled horizontally by adding more instances of individual services as needed. However, the added network communication between services can increase latency and reduce the system’s response time. Typically, the Raspberry Pi 4 (ARM64) can achieve consistent transfer rates of 600–700 Mbps with appropriate network configuration and optimization. Therefore, the choice between monolithic and microservices architectures depends on the system’s requirements. A monolithic architecture may be the better choice if low latency is critical and high throughput requirements are manageable with a tightly-coupled system. A microservices architecture may be more appropriate if high throughput is critical and latency can be tolerated with loosely-coupled services. Our proposal handles the surge in demand by increasing the transmitted packets. In contrast, the monolithic architecture and OSPF demonstrate reduced resilience, scalability, and multiple retransmissions.In this way, it is evident that the three strategies have an acceptable behavior according to Latency: Regarding latency, OSPF is a distributed protocol that relies on exchanging routing information between devices. It’s designed to find the shortest path between two points, which can help to minimize latency. In general, monolithic architectures can offer lower latency since all the system components are closely integrated and communicate directly, reducing network communication overhead. However, this close coupling can also limit the system’s horizontal scalability and ability to handle high throughput requirements. On the other hand, SDN microservices rely on a central controller that manages the network, and the latency can be affected by the communication between the controller and the devices.Throughput: OSPF is a protocol that supports link-state routing and can quickly adapt to network topology changes. As a result, it can provide high throughput in a stable network environment. In contrast, SDN microservices can provide higher throughput as the system can be scaled horizontally by adding more instances of individual services as needed.Recovery time: OSPF is designed to support fast convergence and can quickly recover from a link or device failure. However, the convergence time can depend on the size and complexity of the network. SDN microservices can also provide fast recovery times, but it depends on the specific implementation and configuration.Link failure: OSPF can detect a link failure and reroute traffic along an alternate path, which helps to maintain connectivity. SDN microservices can also detect link failures and potentially provide more granular control over how traffic is rerouted.Device failure: In OSPF, if a device fails, the routing tables are recalculated, and the network can continue to operate. In SDN microservices, the central controller can detect a device failure and reconfigure the network accordingly.Controller failure: In SDN microservices, the central controller is a single point of failure. If the controller fails, the network may not be able to operate correctly. However, many SDN solutions provide redundancy and failover mechanisms to minimize the impact of controller failure.Overall, OSPF and SDN microservices have different strengths and weaknesses, and the choice of which one to use depends on the specific network requirements and goals. All of these values are within the ranges defined by the IEEE 61850 standard  for safeThroughput is generally used to determine how well SDN routers and controllers can handle traffic and how efficient they are at this task. This test measures the number of packets sent per second in the case of OSPF, while SDN measures the number of flows installed on the devices. Equation  presentsiperf3 tool obtains the maximum receiver bandwidth, while a simple ping returns the round-trip time. The Combining Kubernetes with a set of SDN microservices can improve application recovery time by eliminating the single point of failure in hierarchical control. In a traditional network architecture, the control plane and the data plane are tightly coupled, which means that a failure in the control plane can lead to significant disruptions in the network’s operation. This hierarchical control model has a single point of failure, which can be a bottleneck for recovery time.However, with Kubernetes and SDN microservices, the control plane is decoupled from the data plane, and the control functions are distributed across the network. If a failure occurs in one part of the network, the rest can continue normally, and recovery time can be significantly reduced. Moreover, the combination of Kubernetes and SDN microservices offers a significantly automated and customizable network setting that enables quick and flexible network topology adjustments in response to any modifications in the infrastructure or application. This attribute further reduces the network reconfiguration time, hence enhancing the recovery period, which would otherwise require manual intervention. Combining Kubernetes with SDN microservices can improve application recovery time by eliminating the hierarchical control’s single point of failure and providing a highly automated and programmable network environment. This can help ensure that applications and services are always available and performing optimally, even during network failures.A communication system failure (closer to the distributed generation sources) is simulated in this scenario. The objective is to verify which strategy has better performance from the point of view of communications without degrading the power-sharing between the local controllers of the MG.The failure is generated, for instance, containing the SDN monolithic, and they are compared with the losses produced in one of the instances that include the microservices. The orchestrator is expected to be able to instantiate a new subsystem instance without degrading the performance of the MG. Kubernetes has been configured to be scaled automatically according to the research shown in . FurtherOur proposal uses a proactive approach to latency testing and a reactive approach to manage topology changes. The architecture will react immediately if a new distributed generation source is added, allowing proper power sharing, as Monolithic controllers have several drawbacks concerning scalability and reliability. In most cases, these architectures do not meet the requirements of fault tolerance and rapid adaptability, which are imposed by networked microgrids. This proposal’s most significant contribution was the property to dynamically reconfigure control flows based on a microservices architecture and the automatic deployment of microservices instances.Using a bare-metal Kubernetes cluster on a Raspberry pi and deploying distributed microservices allowed us to improve the reality of a distributed energy control system. Microservices testbeds demonstrated the SDN controllers’ rapid deployment, portability, high availability and resiliency to application failures.The Kubernetes orchestrator provided good scalability of the communication system, as well as improved the fault tolerance and replication capacity. This is due to the high fault tolerance, capable of managing and distributing the load between microservices. From a comparative perspective, this proposal significantly improves failure recovery time and resilience concerning communications devices.The API REST microservice topology allowed the splitting of the SDN controller’s core functionalities into small, well-defined functions. In all test case scenarios, reliability showed excellent behavior. Furthermore, the portability of all the nodes in the topology is possible due to the Docker containers. The ability to exchange control information between DGs over an SDN network allows them to regulate the system’s response and reach a steady state more quickly. The results show that to increase the resilience of the network, more sophisticated control strategies and highly available programmable communications networks are required. Finally, the monitoring architecture allows the export of logs in real-time and detects failures through notification software.


The cross-border e-commerce supply chain network (CBESCN) has extensive geographical coverage, trade barriers and complexity of cross-border logistics issues, which makes its construction and development face many challenges. This article focuses on solving the operation optimisation problem of CBESCN under the background of the Internet of Things. A genetic algorithm constructed and solved the resource scheduling model of the supply chain of e-commerce enterprises in international trade. In addition, the mobile edge computing (MEC) optimisation scheme based on partial computation unloading is involved. The initial offload ratio is set and supply chain resources are allocated, then the remaining computing resources are distributed according to the server’s computing power. Finally, the offload is optimised according to the resource allocation. The experimental results show that time delay and cost adjustment strategies can improve the CBE supply chain’s comprehensive ability. The supply chain optimisation scheme proposed in this article can effectively use supply chain resources according to the requirements of computing tasks to reduce the total delay of task execution and the consumption of node computing. Various countries have been impacted by the spread of the COVID-19 epidemic and the measures to prevent and control the outbreak have seriously affected international trade and investment activities, which has broken the regular operation of the existing supply chain and industrial chain. In addition, the sudden change in the global political situation has made the international market turbulent. In this context, China’s complete supply chain presents significant advantages and even plays a vital role in ensuring global supply, among which cross-border e-commerce has made essential contributions . Cross-bWith the continuous development of international trade, the supply chain and inventory management of e-commerce enterprises have become more and more complicated. To improve efficiency and reduce costs, many e-commerce companies are looking for effective solutions . MEC tecThis article discusses the role of MEC optimisation in the supply chain and costs optimisation control of e-commerce enterprises in international trade. The main innovations are:(1) The time scheduling optimisation model of CBESCN with time constraints is established, with the total cost, order completion time and CBE service provider’s satisfaction as the optimisation objectives;(2) Analyse the influence of MEC on the supply chain and inventory management of e-commerce enterprises and how to optimise the node computing efficiency of the supply chain network using MEC.The reasonable arrangement of CBESCN can enhance its reliability. In the node scale design of a supply chain network, In putting forward the optimisation goal, fuzzy optimisation, robust optimisation, topological network theory and system engineering are used to study some optimisation problems of CBESCN. In the existing research on the joint optimisation of resource allocation and computing and unloading, the main consideration is the scenario of complete unloading. There are few types of research on partial unloading and resource joint optimisation; significantly, when the number of users increases, the number of computing increases, and the computing capacity of edge servers is limited. How to optimise the amount of computing data for unloading is the leading research content of this work.Much attention has been paid to improving the overall performance of the MEC system by offloading computation and jointly optimising various resources . Dai, LiThe scenario of complete offloading is mainly considered in the existing research on joint optimisation of resource allocation and computing offloading. In contrast, the research on joint optimisation of partial offloading and resources is less, especially on optimising the offloaded computing data when the number of users increases and the computing capacity of the edge server is limited.Consider a typical CBESCN spanning two different countries or regions, in which the network boundary is the supply chain transportation route, and the nodes are suppliers, warehouses, cross-border checkpoints, manufacturing plants and end customers in the logistics transportation route, as shown in Since the cross-border inspection point is located downstream of CBESCN, the warehouse delivery process should be emphasised. If unique warehouse picking and distribution operations are arranged to adapt to any particular situation, the chance of delay can be significantly reduced. Secondly, at the cross-border inspection point, the delivery of goods requires cross-border inspection procedures, including product inspection and verification of delivery documents. Diversifying the cross-border inspection process will lead to longer and longer transportation time and higher transportation costs. Given this, reducing the barrier effect of the cross-border supply chain that the delivered products meet the inspection is a fundamental rule.This article constructs a resource scheduling model of the supply chain of e-commerce enterprises in international trade.0. In objective function K1, the delay of the previous process due to the enterprise service process leads to the time delay cost of the next process, which is realised in different cross-border enterprises. It can be expressed asThe objective function K1 represents the total cost in CBESCN. It consists of four parts: the total cost of all services in the supply chain, including conventional and other logistics services that are different from other logistics models. The second part is the time delay cost caused by the delay of the previous process due to the enterprise service process. The third part, the last process, is compressed by the enterprise service process, which leads to the time compression cost of the next process. The fourth part is the cost of sorting and packaging in overseas warehouses C0Total cost = Normal service cost + Delayed service cost + Compressing service cost + CThe objective function K2, which consists of three parts, indicates that all logistics service orders in CBESCN should be completed as soon as possible. This article considers minimising the difference between expected and normal service time, extra service time and total time. That is, the expression is:0Time = expected service time - normal service time - extra service time + TThe objective function K3 indicates that the weighted satisfaction of all service provider enterprises can be maximised in the CBESCN. It consists of two parts: the first refers to the ratio of regular service cost to all average total costs generated by all service provider enterprises, representing satisfaction with the price. The other part is satisfied with service time. The second one is related to time, which refers to the ratio of the average operation time of service provider enterprises to the sum of standard time and extra time. Regarding constraints, the m-th service process can sustain the upper limit of time compression. This is a strong constraint because it is necessary to ensure a continuous running time link of the supply chain in the process of providing imported logistics services. The second constraint is that CBE service integrators put forward the completion time requirements for service orders of corresponding service provider enterprises. The third constraint is to ensure the satisfaction of each service provider enterprise, which must be higher than their acceptable lower limit. In terms of time, cross-border e-commerce logistics service integrators tend to follow customised time requirements and set corresponding requirements related to order completion time for service providers. The satisfaction of each service provider will directly determine the quality of the order and the likelihood of completion.This article selects the linear weighting method to solve the CBE time scheduling optimisation model, and the above model is transformed into a single objective programming problem. The linear weighting method can make the interaction of each evaluation index get linear compensation and ensure the fairness of the comprehensive evaluation index. Firstly, the data is imported, then the multiple linear regression is carried out on the data, and the regression is carried out on all variables. The stepwise regression can also be used for factor screening, and the model after the preferred factor can be obtained and the objective function is finally solved.In this article, the cost adjustment factor d is introduced into the model, which represents the relationship of cost increase in this case. d > 1 to express the limit of cost increase. Because I set a new constraint, the original time scheduling optimisation model becomes a goal-planning problem about time and satisfaction. V2 and V3, and make them add up to 1. Objective function K2 And objective function K3 respectively means that the service order is completed on time as much as possible, and the satisfaction of the service provider is maximised. This article needs to standardise them. Therefore, K2 and K3 Divide by the maximum possible value and subtract from the corresponding results. t the comprehensive objective function K can be obtained as follows: The model constructed in this article has three objective functions and four constraints. We combine the specific problems and make a choice analysis, which will help solve the problems and improve efficiency. We introduce etc., to determine the amount of data unloaded by each user and the allocated channels and computing resources, thereby reducing the calculation delay and energy consumption of users.MEC is used to optimise the solution process proposed in ‘Resource scheduling model of CBESCN in international trade’ to improve the efficiency of node calculation. It is assumed that the MEC system knows relevant information such as channel gain, calculated data volume, calculated energy consumption, k contains a computation-intensive task with limited delay to complete, and the maximum delay of the task is Sk. The CPU cycle required to compute each bit on the client side is Ck . When users k When the computing power of cannot meet the requirements of task delay or energy consumption, all or part of the task can be unloaded to the edge server of the base station, and the unloading ratio is λk ∈  . Therefore, the time that the task runs locally is k.Each supply chain node k is The energy consumption per CPU cycle of node The user unloads a part of the task to the edge server, downloads the calculation results from the edge server, and calculates the remaining tasks at the same time. Because the calculation result is very small, the download time of the calculation result is not considered. Task execution time only considers unloading task upload time Multi-user partial unloading with resource allocation under time delay and energy consumption constraints in MEC is considered as an optimisation problem, which is to minimise the total delay of task completion. The goal of problem optimisation is expressed as: The optimisation goal of the system is to minimise the total delay in task completion. As can be seen from Formula σ, that is, a computing resource is allocated to user k, and the computing rate difference before and after the computing resource is allocated is expressed as Firstly, the computing resources are initially allocated according to the following delay constraints: on the one hand, the unloading delay of some data must not exceed the local computing delay, that is, k∗ = argmax(σ).where After completing the initial allocation of resources for each supply chain node, the system determines the available computing resources of the edge server. It updates the user’s unloading ratio so that more computing tasks of mobile users are unloaded to the edge server for execution, and the computing delay is reduced. When the calculation time of the local task and partial unloading calculation time is balanced, the delay reaches the minimum. The user’s updated unloading ratio can be obtained from Because the computing resources are dynamically changing when Take the optimisation of the CBESCN location of a CBE enterprise as an example to analyse. To meet the decentralised needs of consumers and reduce the logistics cost of the whole cross-border supply chain, the optimisation of terminal distribution path selection from network nodes such as overseas warehouses to demanders is also a common decision variable in the location scheme. MEC simulation scenario considers a base station and multiple nodes, and the base station deploys edge servers. The radius of the coverage area of the base station is 500 m, and the supply chain nodes are randomly distributed in this area.Q = 1 and the cost adjustment coefficient is d = 1.15, the calculation result of the objective function K is equal to 0.6612. The time parameters of each service provider in each service process are shown in Assuming that the recombinant inbred lines are 200 and the genetic algebra is 300 when the time adjustment coefficient is From the results of an example, in completing the CBESCN, among the 15 service provider enterprises, six completed time-compressed orders and nine completed time-delayed orders. It shows that when different functional service providers face service orders, CBE service integrators will delay or compress the service time in different service processes, although the compressed time will be more responsive to customer needs.K value. With the cost adjustment coefficient increase, K also increases, which is stable at 0.6710. It means that when the cost adjustment coefficient of CBE service integrators increases, the comprehensive level of CBESCN is also improved.The above analysis and comparison show that the time adjustment coefficient of the CBE service integrator can be divided into two stages. When the time is compressed to the time delay, the comprehensive level of CBESCN increases with the increase of the time adjustment coefficient. However, after reaching a specific value, the comprehensive level of CbesCN will be stable, and the effect will be relatively apparent. Both the time delay strategy and the cost adjustment strategy can somewhat improve the comprehensive capability of CBESCN. However, the former works better.The proposed method is simulated by Python and compared with local computing, complete and binary unloading . Local cThe influence of the number of nodes on the total delay is shown in  Because all tasks of local computing run on user terminals, the total delay increases linearly with the number of users. Complete unloading and unloading all tasks to the server for calculation. The delay of the server is lower when the number of stages is small. The computing resources allocated to each node decrease when the number of nodes increases. The total delay increases faster than when the number of nodes is small, but it is still lower than the local calculation. The adopted method is partial unloading. When the number of nodes is large, the competition for supply chain resources increases and the computing pressure of the server increases. Rational use of server resource allocation to optimise the number of task unloading can maximise the use of server computing resources, thus reducing the time delay of task completion.The influence of server computing power on the average delay of nodes is shown in Because local computing has nothing to do with the server, the average delay remains unchanged. The time delay of the complete uninstall method is only affected by network transmission and server computing power. With the increase in server computing power, the average time delay of users decreases significantly. In binary unloading, with the improvement of server computing power, the average delay of the system shows a slow decline trend. With the increasing capacity of the server, due to the limitation of network resources, the time delay gradually approaches the complete unloading mode. In this method, some tasks are transmitted to the server, and the user terminal and the server execute in parallel. Because the allocation of server computing resources is considered, the average delay of this method is low. When the server’s computing power reaches a certain level, the impact on the average delay of users mainly comes from network transmission.Cross-border e-commerce service integrators should reasonably use time schedules to solve optimisation problems, minimise unnecessary demand for time compression, and prevent a sharp decline in the comprehensive level of the cross-border e-commerce logistics service supply chain. If it is necessary to improve the complete ability of cross-border e-commerce logistics service supply chain, cross-border e-commerce logistics service integrators should give priority to using the delay time strategy to analyse the influential factors of the cross-border supply chain network’s robustness, sources of uncertainty and reliability, to form a more comprehensive and systematic cross-border supply chain network system. This model provides theoretical support for quantitatively evaluating cross-border supply chain networks, node location, network design and other optimisation problems. The model is suitable for determining the separation point of customer orders under the background of mass customisation.Based on the study of CBESCN in many aspects, an optimisation model with CBESCN characteristics in the corresponding mode is constructed. Through the joint allocation of node equipment computing resources, supply chain resources and edge server computing resources, a method of partial computation unloading node computing intensive task to edge server is proposed. When different functional logistics service providers face service orders, enterprises delay or compress the service time in other service processes. This result is reflected in the increase of the cost coefficient; the objective function also increases and finally tends to be stable at 0.6710. In addition, this method transmits some tasks to the server, and the user terminal and the server execute them in parallel. Because the allocation of server computing resources is considered, the average delay of this method is low. Although it is helpful to provide new ideas for the theoretical development of CBESCN and its service supply chain, in this experiment, the information asymmetry brought from the perspective of service providers is not considered in the setting of the scheduling model, and the common GA algorithm is only used to solve the model. Our future research direction is how to use deep learning models further to optimise the operational efficiency of supply chain networks.10.7717/peerj-cs.1407/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj-cs.1407/supp-2Supplemental Information 2Click here for additional data file.


The bond between a steel reinforcement/rod and glulam plays a crucial role in the resistance and deformation capacity of timbers joints. Existing studies provide different bond–slip models for reinforcements and rods with different anchorage lengths, in which the relationship between local bond stress and global bond behaviour cannot not be established. This study presents a unified analytical method for predicting the bond–slip behaviour of ribbed bars and threaded rods along the grain using a local bond–slip model of reinforcement at the elastic and post-yield stages. In the analytical method, equilibrium, compatibility, and constitutive models for reinforcement and rods are considered. The method is verified using test data of rebars and rods with different anchorage lengths. Comparisons between the experimental and calculated results suggest that the analytical method yields reasonably good predictions of the load–slip relationship and failure mode. Furthermore, the embedment lengths required for yield and the ultimate strengths of the reinforcement and rods along the grain are determined by assuming uniform bond stress distributions over the elastic and post-yield steel segment. The average bond stress over the entire anchorage length is calculated and compared with existing equations. Design recommendations for anchorage lengths are proposed for ribbed bars and threaded rods glued in glulam. Glued-in rods have been widely used for column foundations and moment frames in timber structures due to their high resistance and stiffness ,2. In thVarious methods have been proposed to calculate the pull-out resistance of steel rods with different lengths glued in glulam ,4,5. In Steel rods may remain elastic when designed with a practical range of anchorage length as a result of the high yield strength, unless the cross-section of the rods is intentionally reduced by removing the thread . Pull-ouThis study presents a simplified method for evaluating the bond–slip behaviour of reinforcement glued in glulam along the grain. In our method, the relationship between a local bond–slip model of short reinforcement and the global response of long reinforcement is established, and the bond stresses of ribbed bars and threaded rods at the elastic and post-yield stages are considered. The force–slip relationship of the reinforcement is obtained via an analytical study, and the variations in steel strain and bond stress over the length of the reinforcement are also calculated. The analytical results show the profiles of steel strain and bond stress at various load levels, which enable the development of a design equation for quantifying the average bond strength. With the average bond strength, the lengths of glued-in rebars and rods required for the rebars and rods to reach the yield and ultimate strengths are calculated.Pull-out tests can be performed to obtain a bond–slip model of steel glued in glulam. Different loading methods are recommended for pull-out tests , among wThe test results ,9 showedLing et al.  conducteEquation (1) expresses the local bond–slip relationship. Note that the bond stress in the equation acts on the reinforcement, and the slip refers to the total value of deformation of the reinforcement, the glulam, and the adhesive between the reinforcement and glulam. In this study, the peak bond stress for rebars is set to be 9.1 MPa, taken from pull-out tests of short rebars anchored in glulam, and the values of It should be pointed out that the foregoing equation is only valid for reinforcement at the elastic stage. If the anchorage length of the reinforcement is adequately long so that its yield strength can be reached at the loaded end, a different value of bond stress has to be adopted for the yielded steel segment. Previous studies on steel reinforcement embedded in concrete showed that bond stress remained nearly uniform over the yielded steel segment . HoweverEquation (2) shows the expression for the post-yield bond stress. In the equation, By using the abovementioned method, the post-yield bond strength of rebars or rods glued in glulam can be determined as 16-200-2 . Similar16-200-2 , the redWith the local bond–slip relationship, the bond–slip behaviour of long rebars or rods can be analysed by dividing the whole anchorage length into a group of steel segments, as shown in 3 was used in the specimens, and its mechanical properties parallel to the grain can be found in Most test data only provided the load capacity of glued-in rebars or rods under pull-out forces, and a limited number of load–slip curves were included in the literature. Ling et al. ,9 conducIt should be pointed out that only pull-out failure or fracture of the rebars or rods can be considered in the analytical method, and thus, rebars and rods with the two failure modes were selected from the experimental results and used to verify the accuracy of the proposed analytical method. The force–slip relationship of reinforcement glued in the glulam was calculated using the proposed method. Note that during calculation, the deformation of the glulam itself was neglected.Two more pull-out tests conducted by Ling et al.  were useBesides the load–slip curves, the variation in steel strains along the anchorage length of the reinforcement can also be obtained using the analytical model, as shown in In addition to ribbed bars, the bond–slip behaviour of steel rods tested by Ling et al.  can alsoBased on the calculated bond stress distribution along the anchorage length of the rebars or rods, the minimum length required for the reinforcement to develop yield strength can be calculated as follows.For the mechanical and geometric properties of the steel reinforcement, rods, and glulam listed in Nevertheless, it should be pointed out that even if a longer embedment length is provided in the design, steel reinforcement may still be pulled out from the glulam, as shown in As the post-yield bond strength is generally smaller than that at the elastic stage, the embedment length of the reinforcement associated with the ultimate strength is expected to be significantly longer than that corresponding to the yield strength. By using the mechanical and geometric properties in 2 is suggested.1.5.Even though the proposed method can be used to calculate the load resistance and slip of steel rebars and rods glued in glulam, a simplified design equation may be preferred if only the load capacity is of concern. Riberholt  proposedThe design code for timber structures in Germany  incorporSteiger et al.  proposedRossignon and Espion  recommenOn account of the differences in the mechanical properties of rebars and rods, the abovementioned equations may not be suitable for calculating the average bond strength of glued-in rebars. The analytical results show that when the steel reinforcement is at the elastic stage, namely, the anchorage length is less than 10 times the rebar diameter, the average bond stress can be taken as the peak bond stress in Equation (1). Otherwise, both the elastic and post-yield bond stresses have to be considered in calculating the average bond stress.For a given anchorage length greater than 10 times the rebar diameter, Equation (12) can be used to quantify the average bond stress. In the calculation, bond stresses are assumed to be uniform over the elastic and yielded steel segments. Thus, the average bond strength depends on the yield strength and anchorage length of the steel reinforcement. By increasing the anchorage length, the average bond strength can be reduced due to yielding of the rebars near the loaded end and the resulting reduction in bond stress, as suggested by previous researchers.Our analytical study shows that when the load capacity of glued-in rebars is attained, the reduction in average bond stress with increasing anchorage length can mainly be attributed to the yielding of rebars at the loaded end and the ensuing decrease in bond stress over the yielded steel segment. However, with regard to high-strength steel rods, it is not possible to reach yield strength with a practical range of anchorage length, and the nonlinear distribution of bond stress results from the high yield strength. Similar results can be expected if steel rebars with high yield strength of basalt fibre-reinforced polymer  are usedThis paper describes an analytical study on bond–slip behaviour of ribbed bars and threaded rods anchored in glulam along the grain. In the study, the relationship between a local bond–slip model and global bond behaviour is established. Comparisons between experimental and analytical results show that the analytical method can be used to evaluate the bond–slip behaviour of reinforcement with good accuracy. The following conclusions can be drawn from the analytical study. By using the bond–slip curves measured from tests of short rebars or rods, the load capacity, slip, and failure mode of long rebars and rods along the grain of glulam can be predicted using the analytical method with good accuracy. In the calculation, the post-yield bond stress of rebars calculated from test data is around 70% of the peak elastic bond stress.The analytical results show that when the load capacity of the rebars is achieved, the bond stresses can still be assumed to be uniform over the elastic and yielded steel segments, respectively. Equations are developed for calculating the anchorage lengths of rebars associated with the yield and ultimate strengths.For the given material properties in the experimental tests, the lengths for the yield and ultimate strengths of the rebars are determined to be 10 and 18.6 times the rebar diameter, respectively. Nonetheless, the required length for the yield strength of the threaded rods is 22.3 times the rod diameter as a result of its relatively high yield strength compared with the steel re-bars.An equation is also derived for average bond stress over the anchorage length of the long reinforcement, which takes account of the effects of yield strength, post-yield bond stress, and anchorage length. Comparisons with existing equations of average bond strength indicate that the design equations proposed by Riberholt and DIN 1052 underestimate the average bond strength of deformed rebars, whereas Steiger’s equation yields overestimations of the average bond strength.


Diabetic macular edema (DME) is one of the main ocular complications of diabetes mellitus (DM) that can lead to important vision loss in diabetic patients. In clinical practice, there are cases of DME with unsatisfying treatment responses, despite adequate therapeutic management. Diabetic macular ischemia (DMI) is one of the causes suggested to be associated with the persistence of fluid accumulation. Optical coherence tomography angiography (OCTA) is a non-invasive imaging modality, able to give in-depth information about retinal vascularization in a 3-dimensional manner. The OCTA devices currently available can provide various OCTA metrics that quantitatively assess the retinal microvasculature. In this paper, we reviewed the results of multiple studies that investigated the changes in OCTA metrics in the setting of DME and their possible contribution to the diagnosis, therapeutic management, follow-up and prognosis of patients with DME. We analyzed and compared relevant studies that investigated OCTA parameters related to changes in macular perfusion in the setting of DME and we evaluated the correlations between DME and several quantitative parameters, such as vessel density (VD), perfusion density (PD), foveal avascular zone (FAZ)-related parameters, as well as complexity indices of retinal vasculature. The results of our research showed that OCTA metrics, evaluated especially at the level of the deep vascular plexus (DVP), are useful instruments that can contribute to the assessment of patients with DME. Diabetic macular edema (DME) is known to be the main cause of vision loss in the working-age category of diabetic patients . CurrentIn clinical practice, an unsatisfying treatment response was noticed in some cases of patients with DME, suggesting that the association between DME and diabetic macular ischemia (DMI) may decrease the response to the treatment modalities for macular edema, with the persistence of long-standing fluid accumulation .Moreover, one of the most important consequences of DMI, in the presence or absence of other ocular complications of diabetes mellitus, is the decrease in visual acuity which may be progressive and irreversible . When asEven though fluorescein angiography (FA) has been the mainstay in imaging the retinal vasculature, its usage is limited to a two-dimensional visualization of the superficial vascular plexus (SVP) in the retina .Optical coherence tomography angiography (OCTA) is a noninvasive modality of investigating the retinal and choroidal circulation, without the necessity of intravenous dye injection . It can In light of the aspects mentioned above, the assessment of the quantitative microvascular parameters can objectively evaluate the degree of macular ischemia in diabetic patients with DME and may represent a relevant topic regarding the therapeutic decision and the prognostic issues.The aim of this review was to compile the results of various relevant studies that investigated the changes in OCTA metrics in the setting of DME.It is well known that the retinal vascularization is dependent on two vascular sources. The inner two-thirds of the retina is supplied by the central retinal artery, whereas the outer third of the retina is supplied by blood coming from the choroid . There aThe foveal avascular zone (FAZ) is a relatively circular area around the fovea which lacks vascularization, delimited by an annulus of vascular elements coming from the three retinal plexuses . FAZ is Many OCTA devices have specific software incorporated, designed to make quantitative evaluations of the macular perfusion. Generally, after the OCTA image acquisition is performed, the grayscale en face OCTA image undergoes two main processes for the quantitative assessment of vascularization: binarization and skeletonization.Binarization is a process that transforms the original grayscale image into a black-and-white one, based on a threshold value . AlgoritSkeletonization is another process used for OCTA metrics calculation. Skeletonization is based on reducing the caliber of each vessel to a single pixel, thus not taking into account the capillary diameter when doing the analysis . SkeletoVarious quantitative parameters can be measured by means of OCTA. However, at the moment, there is heterogeneity regarding certain aspects such as the nomenclature of the parameters, the methods and algorithms used for their calculation, the units of measurement and the segmentation modalities, being difficult to reach a consensus between the results of different studies .One of the parameters that can objectively be measured by means of OCTA is vessel density (VD). According to some sources, VD is defined as a ratio between the total length of perfused vasculature per unit area in a certain region . HoweverAmong other parameters of interest, in patients with DME, there is also the vessel diameter index (VDI), which is calculated as a ratio of total vessel area on a binarized image to total vessel length on a skeletonized image .2), FAZ perimeter (mm), and FAZ circularity index (CI). The CI reflects how close a certain shape resembles a circle [2) [Furthermore, FAZ-related parameters, which are most investigated related to DR and DME, encompass FAZ area (mma circle  and is cimeter2) . A ratioimeter2) . Among timeter2) .Regarding the OCTA variability of the microvascular metrics between different retinal capillary plexuses in healthy adults, it was reported that the mean VD values were significantly higher in DCP compared to SCP in all age groups . MoreoveThere are various studies in the literature that investigated the modifications in the quantitative OCTA parameters in patients with DME.Vessel density (VD) is a parameter defined by the total length of perfused blood vessels per unit area in the region of measurement ,22. ThisVessel skeletonized density (VSD) reduces the impact of large vessels on measurement and is considered to be more sensitive to retinal microvascular changes ,23.When comparing quantitative parameters between eyes with the same DR severity, in eyes with mild NPDR and DME, there was significantly lower skeleton density (SD) in the superficial retinal layer (SRL) and the deep retinal layer (DRL) compared to those without DME .The measurement of OCTA metrics with a wider field swept-source OCTA device revealed that in mild NPDR associated with DME, there was a decrease in VSD in the DCP on 6 × 6 mm angiograms, whereas on 12 × 12 mm angiograms there was reduced VSD in the SCP and the full-thickness retina . In the Regarding the influence of various treatment modalities on the quantitative parameters assessed by OCTA, in patients with DME treated with intravitreal anti-vascular endothelial growth factor (anti-VEGF), the first-line treatment for DME at the moment, one study concluded that the vessel length density (VLD)—based thresholding was more accurate for quantifying the retinal vascular changes after a single injection . HoweverAnother study found that, at the second month of follow-up after an intravitreal dexamethasone implant (IDI), the vascular density in the perifoveal ring in the SCP on a 6 × 6 mm scan was significantly decreased . FurtherRelated to the correlations between visual acuity and quantitative OCTA microvascular parameters, in DME, it was noticed that low skeleton density in the DCP was correlated with poorer best-corrected visual acuity (BCVA), suggesting that macular ischemia plays an important role in the visual acuity drop associated with DME .Perfusion density, defined as the total area of perfused blood vessels per unit area in the region of measurement, is another metric used to quantitatively assess DME by OCTA. Compared to vessel density as defined above, this parameter takes into consideration both the length and the diameter of the vessel for the analysis, therefore being better in estimating the real vascular density . HoweverIn diabetic chronic cystoid macular edema, compared to non-diabetic subjects, the mean value of this parameter was reduced in both SCP and DCP . HoweverAnother study concluded that the global capillary density index (CDI), an equivalent metric used for quantifying the area occupied by vessels, was lower in patients with DME compared to patients without DME, independent of the capillary plexus affected .In patients with diabetic retinopathy, a lower PD of SCP was associated with an increased risk of DME development, independent of known risk factors . When co1c, mean arterial blood pressure and severity of DR at baseline [DME development was also associated with lower values of this metric in the SCP, independent of established risk factors including age, duration of diabetes, HbAbaseline . Howeverbaseline .The OCTA assessment with a wider field swept-source OCTA device revealed that, on 6 × 6 mm angiograms, in mild NPDR associated with DME, at the DCP level, there was a decrease in the total area of perfused vessels per unit area in the region of measurement . In the Differences were also noted regarding the OCTA quantitative parameters in patients with DME of different grades of severity . It was It was also shown that treatment naïve diabetic eyes with moderate or severe NPDR and DME had significantly lower superficial and deep perfusion values compared to healthy eyes . MoreoveRelated to the influence of various therapeutic approaches on the perfusion density measurements in patients with DME, when comparing responders to anti-VEGF treatment with non-responders, it was noticed that in both groups of patients, there were lower values in the DCP than in the SCP , but pooA study on patients treated with fluocinolone acetonide intravitreal implant showed an increase in the parafoveal and perifoveal SCP perfusion density at the 4-month follow-up . The impRegarding the intravitreal dexamethasone implant (IDI) for the treatment of DME, it has been shown that the SCP density and the DCP density in the foveal and parafoveal area did not modify significantly during the follow-up at 7 days, 30 days, 60 days, 90 days and 120 days after the IDI implantation, despite the significant reduction in the macular thickness . This waAfter subthreshold micropulse yellow laser (SMYL) treatment in patients with previously treatment-naïve DME, no significant differences were found regarding the PD in the SCP, DCP and choriocapillary plexus (CCP) . In anotVessel diameter index (VDI) is defined by the proportion of area occupied by vessels divided by the skeletonized density  and it rWhen studying angiopoietin-like levels in the aqueous humor of patients with DME, it resulted that the levels of ANGPTL4 and ANGPTL6 were significantly higher in patients with DME, and ANGPTL4 correlated positively with the FAZ perimeter .The measurement of the OCTA metrics with a wider field swept-source OCTA device showed that in mild NPDR associated with DME, there was a decrease in FAZ circularity on 6 × 6 mm angiograms . FurtherIt was also concluded that patients with severe DME presented a significant increase in the acircularity index, compared to early and advanced DME .Moreover, the treatment naïve diabetic eyes with moderate or severe NPDR and DME had a significantly larger FAZ area at the level of the SCP than the diabetic eyes without edema and also than healthy subjects . FurtherWhen comparing responders to anti-VEGF treatment with non-responders, it was noticed that the DME eyes had a larger FAZ in the DCP than in the SCP, in both groups of patients . Poor reAfter SMYL laser treatment in patients with previously treatment-naïve DME, it resulted that the FAZ did not change significantly in the SCP, but there was a significant reduction in it in the DCP at 6 months compared to the initial evaluation . In anotThe fractal dimension characterizes the architecture of the vascular network and provides an index of the branching complexity of the capillary network . When coRegarding the correlations between the visual acuity and the quantitative OCTA microvascular parameters, in DME, a low FD in the DCP was correlated with a poorer BCVA, suggesting that macular ischemia plays an important role in the visual acuity drop associated with DME  Table 5Table 5.The OCTA quantitative assessment of patients with diabetes mellitus has been a subject of interest, in the attempt to identify the starting point of the retinal microvascular impairment. Studies have shown that in patients with type 1 diabetes mellitus with no or mild signs of DR, there is reduced parafoveal vessel density in the DCP, compared to non-diabetic subjects  suggestiRegarding diabetic macular edema, most investigations are in agreement with the fact that, even though abnormalities of the superficial vascular plexus (SVP) have been identified, DME is mostly associated with decreased or absent vascular flow in the deep vascular plexus (DVP) as well. Many of the studies included in this review concluded that, at the level of the deep capillary plexus, in patients with DME, there was a significant decrease in the parameters used for the assessment of macular ischemia, such as vessel density, perfusion density, as well as FAZ enlargement. Several theories that explain this association have been proposed. It was stated that under normal circumstances, the fluid is produced at the level of the superficial vascular layer, and is absorbed, with the help of Müller cells, at the deep capillary plexus . MacularOne of the most important errors in the OCTA quantitative analysis is that of segmentation. In cases of retinal edema, there is an increase in the retinal layers’ thickness, and a decrease in the contrast between the retinal layers, therefore the segmentation algorithms that are based on a healthy retina cannot be reliable, generating errors . The imaAnother suggested cause of error in the quantitative OCTA evaluation of DME is the presence of cystoid spaces, that could exert a mechanical effect on the vessels, displacing them and falsely creating the impression of non-perfusion in the areas of the cysts . This idOne more potential source of error regarding the OCTA metrics assessment is the axial length. It was reported that, for healthy eyes with long axial lengths, in order to obtain an accurate quantification of the superficial retinal vessel density and of the foveal avascular zone area, correction formulae should be applied to compensate for the image magnification . MagnifiSignal strength is another essential element that can influence the OCTA measurements, with images with higher signal strength providing better clarity and improved segmentation and leading to increased accuracy of the measurement, whereas lower signal strength could lead to an underestimation of the vascular quantitative parameters .Quantitative optical coherence tomography angiography parameters represent promising instruments that can aid in the diagnosis, therapeutic decisions, follow-up and anatomic and functional prognostic in patients with diabetic macular edema. The standardization of nomenclature and the development of new strategies that can offer the possibility of data comparison between different devices represent some of the further directions that need to be addressed for a better understanding of the utility of OCTA metrics in clinical practice.


This paper proposes an end-to-end neural network model that fully utilizes the characteristic of uneven fog distribution to estimate visibility in fog images. Firstly, we transform the original single labels into discrete label distributions and introduce discrete label distribution learning on top of the existing classification networks to learn the difference in visibility information among different regions of an image. Then, we employ the bilinear attention pooling module to find the farthest visible region of fog in the image, which is incorporated into an attention-based branch. Finally, we conduct a cascaded fusion of the features extracted from the attention-based branch and the base branch. Extensive experimental results on a real highway dataset and a publicly available synthetic road dataset confirm the effectiveness of the proposed method, which has low annotation requirements, good robustness, and broad application space. Visibility refers to the maximum distance at which a target object can be seen and recognized against the sky background by a person with normal vision under current weather conditions . That isFog is a very common weather phenomenon, consisting of water vapor condensates composed of small droplets or ice crystals suspended in the atmosphere near the Earth’s surface. Haze, on the other hand, is a turbid phenomenon formed by the suspension of a large amount of smoke, dust and other particles, the causes of which are still unknown. In fog and haze, the human visual system is severely disturbed, visibility is reduced, and perception of distance becomes unreliable ,4. For eExisting visibility measurement methods include the use of transmission and scattering visibility meters, but these devices are expensive and difficult to deploy on a large scale. With the widespread application of deep learning, obtaining visibility values directly from a single image acquired by a camera has become a reality. Image information obtained by cameras widely deployed on highways or other roads can be used to obtain visibility values.In recent years, some researchers have applied deep learning to visibility estimation . ConvoluIn foggy images, the distribution of fog is non-uniform, with more texture features present in the foreground of the image, while the distant regions mostly contain fog-related information, lacking actual scene texture features. To address the problem of visibility estimation more effectively, Wai Lun Lo et al. ,16 and JVisibility levels are classified based on the actual distance range of visibility, and visibility features tend to be more similar within neighboring visibility classes, which poses challenges for feature learning. The labels corresponding to visibility images also have similar ambiguities to those in the age estimation  task. ThConsidering the characteristics of foggy images, non-uniformity, and fuzziness, this paper proposes a visibility estimation network based on weakly supervised attention learning and label distribution learning. Firstly, we rely on weakly supervised attention learning to extract ROI and utilize two serial branches for further feature extraction. Secondly, label distribution learning is employed to capture the fuzziness between adjacent labels of visibility features. Finally, the predictions from both branches are fused to obtain the final visibility estimation result. This approach fully leverages the non-uniform characteristics of foggy images and effectively improves the prediction accuracy.However, deep learning requires a large amount of information from image data, and collecting these images as training data is time-consuming and labor-intensive. Currently available public datasets for visibility estimation are all synthetic datasets . Collect(1)We propose a weakly supervised localization module to find the farthest visible area in a single image without the need for additional manpower, which is served as auxiliary information to help the network learn to capture fog features.(2)We propose a discrete label distribution learning module. The fog in foggy images is usually unevenly distributed. By using Gaussian sampling to transform the original fixed classification labels into Gaussian distribution labels, the network can learn this uneven distribution, thus better adapting to the distribution of visibility levels in the image and achieving better results.Compared to existing methods, our main contributions are as follows:ResNet, proposed by Kaiming He et al., enables the construction of deeper networks and faster training by introducing residual connections, and has shown excellent performance in image classification tasks. ResNet comes in various versions based on the number of convolutional layers, with ResNet18 being the one with the fewest convolutional layers, the lowest number of parameters, and the shortest training time.The structure of ResNet18 is shown in Inspired by bilinear pooling , bilineaAs shown in As shown in Subsequently, global average pooling is employed to further transform The image features are ultimately represented as a feature vector During the process of BAP, the attention maps Then, by utilizing the attention normalization map Furthermore, the mask For the task of visibility estimation, images captured by cameras often encompass a wide range. Due to the non-uniformity of fog distribution, different sub-regions of the same image may correspond to different visibility values. The original single label fails to effectively represent the visibility features of the image. Due to the inherent ambiguity, we introduced discrete label distribution learning, which converts the traditional single label into a set of label vectors that describe the visibility distribution of the entire image.In deep learning classification methods, usually a label corresponds to an image sample, and for a dataset To generate label distribution According to Equation (7), a label The label distribution Dividing each component by the Euclidean norm gives the final labelling distribution The proposed method is a visibility classification model that integrates weakly supervised localization. The attention mechanism is employed to generate the farthest visible region in the original fog image, where the red box in The method proposed in this paper consists of two branches, namely the base branch (BB) and the attention-based branch (AB), as shown in As shown in As shown in As previously mentioned, our method comprises two branches, the base branch and the attention-based branch, which generate two logits under the supervision of the original label and the label distribution, respectively. Regarding the two different outputs, two distinct loss functions are utilized.Since the output of the neural network might be less than zero, this may result in an issue when calculating the KL divergence loss and cross-entropy loss in the next step. To solve this problem, we adopted the SoftMax function to transform the original output to a probability distribution with a range of .In the base branch, as the label In the attention-based branch, we utilize the cross-entropy loss function.Based on the distinct loss functions in the two branches, the overall loss function of this method is defined byIn order to validate the effectiveness of the method, we conducted extensive experiments on two completely different datasets. These datasets were the synthetic foggy road image database (FRIDA) ,39,40 anThis dataset was constructed with the assistance of the Anhui Meteorological Bureau and consists of real fog images captured by 84 surveillance cameras distributed on highways in Anhui Province, with a resolution of FRIDA is a synthetic fog image dataset consisting of 84 different road scenes and 4 different fog conditions. All images in this dataset were generated through the same algorithm, which combines different road scenes, fog conditions, and visibility levels. The dataset is divided into nine visibility levels, with level 9 having the lowest visibility and level 1 having the highest visibility. The entire dataset contains 3024 images with a resolution of In order to compare with other excellent methods, this paper uses classification accuracy (ACC), root mean square error (RMSE), and F1-score as evaluation metrics.ACC represents the percentage of correctly classified visibility level samples in the total number of samples and is defined byThe RMSE represents the magnitude of the error between the predicted values and the ground truth. It is defined byThe F1-score is a harmonic mean of precision and recall, which measures the overall level of a model’s classification. In binary classification, it is defined byIn multi-class classification, this paper uses macro-F1 to calculate the F1-score, which refers to the average of F1-scores for each class and is defined byBoth the method in this paper and the comparison methods are implemented using Pytorch. The batch size is 48 and the learning rate is 0.001 decaying by 0.9 times every 5 rounds. All models are trained using the Adam optimizer for 100 epochs. The remaining details are shown in The method proposed in this paper includes 4 hyper-parameters: the number of attention maps channels Firstly, this paper used a model without a discrete label distribution learning module to study the impact of the number of attention feature map channels on overall model performance. As shown in Secondly, this paper added a discrete label distribution learning module to the above experiments, aiming to investigate the impact of varying standard deviations Thirdly, this paper introduced an attention-based branch to enhance the original model’s extraction of visibility features, exploring the impact of the two branches on overall model performance by adjusting the weight Subsequently, the following experiment continued to study the impact of the mask Finally, the best combinations were selected based on the hyperparameter experiments, with In order to demonstrate the effectiveness of our proposed method, we compared it with other classic classification methods and some improved methods based on visibility classification, as shown in The innovations of our proposed method mainly include two aspects: the introduction of dual-branch weakly supervised localization based on bilinear attention pooling and discrete label distribution learning. To verify their effectiveness, we conducted ablation experiments on the combination of these two modules, and the experimental results are shown in First, we investigated the impact on the method of introducing the dual-branch weakly supervised localization based on bilinear attention pooling. Specifically, we considered three scenarios: ResNet18, ResNet18 combined with the base branch, and ResNet18 combined with both the base and attention-based branch. The experimental results show that after adding the BAP, the model can utilize the attention mechanism to focus on local features in the image. After adding the attention-based branch, the image from the weakly supervised localization module can enhance the feature region information that is strengthened by attention in the base branch, thereby improving the accuracy of the model.Furthermore, we further investigated the impact of incorporating the discrete label distribution learning module into both the base branch and the attention-based branch. The results show that adding the discrete label distribution only to the base branch has a positive impact on the network, while adding it to the attention-based branch has a negative impact on the model. This suggests that the visibility feature distribution in the farthest fog-visible region generated in the base branch is more concentrated, and the global scattered distribution of visibility features no longer needs to be described by a discrete label distribution. Therefore, incorporating only the discrete label distribution into the base branch is more advantageous for the visibility estimation task in our proposed method.The predicted results for different visibility levels on the RFID and FRIDA datasets are shown in Compared with other methods, the method proposed in this paper has significantly improved accuracy in the intermediate visibility levels. As shown in We also studied the computational resource consumption of several deep learning methods. This paper proposes a novel end-to-end deep learning method for visibility estimation of foggy images. Due to the non-uniform distribution of fog concentration in foggy images, it is difficult for a single category label corresponding to a single image to be advantageous for network learning. Therefore, it is essential to fully exploit the useful information in non-uniform foggy images. This method employs the method of discrete label distribution to optimize the extraction of non-uniform fog concentration information in foggy images, along with the bilinear attention pooling method in weakly supervised localization to extract the farthest visible fog regions in images that favor visibility information extraction, enabling the network to fully exploit the local features in the image. In real weather conditions, images with low visibility are rare. In order to balance the data volume of different categories in the dataset, the overall size of the dataset can only be maintained at a low level. However, data-driven deep learning models require a large amount of image data. Therefore, this paper spent a lot of time building a dataset containing 5149 real images. To evaluate the performance of this method, we conducted experiments on two datasets, the RFID and FRIDA, and compared our method with other state-of-the-art deep learning-based methods. The results of extensive experiments indicate that the method proposed in this paper is more effective and needs less annotated information in the training set compared to other methods. In addition, by using an efficient ResNet18 as the backbone and weight sharing, the overall network’s performance requirements were maintained at a low level. The weakly supervised localization module based on BAP and the DLDLM has a small number of additional parameters, making it better able to meet real-time requirements in road visibility warning and traffic control.