Edge computing exhibits the advantages of real-time operation, low latency, and low network cost. It has become a key technology for realizing smart Internet of Things applications. Microservices are being used by an increasing number of edge computing networks because of their sufficiently small code, reduced program complexity, and flexible deployment. However, edge computing has more limited resources than cloud computing, and thus edge computing networks have higher requirements for the overall resource scheduling of running microservices. Accordingly, the resource management of microservice applications in edge computing networks is a crucial issue. In this study, we developed and implemented a microservice resource management platform for edge computing networks. We designed a fuzzy-based microservice computing resource scaling (FMCRS) algorithm that can dynamically control the resource expansion scale of microservices. We proposed and implemented two microservice resource expansion methods based on the resource usage of edge network computing nodes. We conducted the experimental analysis in six scenarios and the experimental results proved that the designed microservice resource management platform can reduce the response time for microservice resource adjustments and dynamically expand microservices horizontally and vertically. Compared with other state-of-the-art microservice resource management methods, FMCRS can reduce sudden surges in overall network resource allocation, and thus, it is more suitable for the edge computing microservice management environment. With the recent development of emerging technologies, the information industry is vigorously developing the integration of edge computing and cloud computing and the introduction of edge computing into the vertical field. The rapid development of the Internet of Things (IoT) has promoted the development of various flexible and decentralized computing architectures in the industry. In the edge–cloud computing architecture, edge computing plays a role in the local learning and filtering of data transmitted by a terminal device, while simultaneously sharing the computing and storage tasks of the cloud ,2,3. FroEdge computing is a distributed network infrastructure that allows data to be preprocessed and analyzed closer to their source. Edge computing can be used in various applications, such as IoT, artificial intelligence, and big data. The microservice architecture involves the development of applications as a collection of small services, wherein each service can implement business functions, run its process, and communicate through HyperText Transfer Protocol (HTTP) application programming interfaces (APIs). Each microservice can be deployed, upgraded, expanded, and restarted independently of other services in the application . TherefoMicroservices are functionally meaningful applications that are sufficiently small to focus on a specific business function or requirement ,9. MicroEdge computing microservice resource management is currently facing two major challenges ,19: (1) In traditional network service resource management methods, researchers usually design various computing resource management algorithms or mechanisms to manage the computing resources of the program. These management algorithms and mechanisms evaluate the resource expansion requirements of applications or microservices based on metrics such as the resources usage amount of the programs. Accordingly, the algorithms calculate that more or less computing resources are to be allocated to applications and microservices.However, the amount of computing resources used or required is usually based on a vague vocabulary. In particular, the network topology of the edge computing network changes rapidly, and the operating status of the computing nodes and running microservices in the edge computing network also changes frequently. These factors have caused many ambiguities and uncertainties in microservice resource management requirements . If thesFuzzy theory models the process of human subjective thinking or judgment. Designing fuzzy logic systems based on fuzzy theory does not require an accurate mathematical model of the controlled object. Instead, fuzzy sets are used for quantitative processing. Fuzzy theory has been widely used in various products that combine computers and human subjectivity . Fuzzy tCompared with traditional algorithmic systems, fuzzy logic systems are simple in design and easy to apply. The fuzzy logic system can simplify the complexity of system design and is especially suitable for non-linear, time-varying application systems. However, the fuzzy-based resource management method still has some shortcomings . For insIn this study, we use the advantages and characteristics of fuzzy theory to improve the resource management methods for edge computing network microservices. We focus on designing and implementing a prototype of an edge computing microservice resource management platform, which includes a fuzzy-based microservice computing resource scaling (FMCRS) algorithm. FMCRS represents the state of computing resources of microservices running on edge computing nodes in the form of fuzzy sets and evaluates the scaled extent of computing resources of microservices based on 27 fuzzy rules. The major contributions of this work are summarized as follows.(1)In this study, we design and implement a prototype of an edge computing network microservice resource management platform. This platform can provide a solution to cloud computing service providers and edge computing system users for realizing the effective resource management of each microservice in an edge computing network. The system prototype designed in this work provides users of edge computing networks with a new option to meet the increasingly complex network application requirements.(2)We design a fuzzy-based microservice computing resource scaling (FMCRS) algorithm that can dynamically control the resource expansion scale of microservices to meet their resource consumption requirements in a timely manner. FMCRS can ensure the lowest availability of various microservices.(3)We apply the particle swarm optimization (PSO) algorithm to optimize the proposed fuzzy inference system for microservice resource management to achieve the best resource expansion strategy for various microservices in an edge computing network.(4)To verify the effectiveness and performance of the proposed platform and algorithm, we perform extensive experiments in six scenarios of the Internet of Vehicles edge computing network. The experimental results show that the proposed approach improves microservice resource management efficiency in terms of reaction time and reduces surge burdens.The remainder of this paper is organized as follows. In this section, we first introduce the research background for the issues to be addressed in this paper. Subsequently, we review and discuss two major approaches in the related literature, namely, system architecture/framework and management mechanism/algorithm.The resource management of microservices has always been an important research topic in academia and industries ,28,29,30Designing new network architectures and system frameworks to improve edge computing microservice resource management efficiency is an important research approach. Gand et al.  proposedYan et al.  presenteSome researchers have attempted to design various novel mechanisms and policies to tackle the issues related to managing microservice computing resources in edge computing. Cicconetti et al.  designedThe deployment of containerized microservices in edge computing has become increasingly important in recent years. Most current studies have focused on designing new system architectures or new microservice deployment methods. To date, however, discussions on providing efficient solutions to the service resource management of microservices in edge computing remain minimal. The current work presents an innovative prototype of an edge computing network microservice resource management platform. In contrast with the aforementioned studies, we designed and implemented a microservice resource management fuzzy inference system based on fuzzy theory and PSO.This section consists of two parts: the description of the model and the content of the FMCRS algorithm. First, we define the membership functions and calculation methods of the fuzzy management system for edge computing microservice resource management. Then, we separately describe the four core components of FMCRS, including the generation of fuzzy sets and rules, the optimization of fuzzy system membership functions, horizontal scaling, and vertical scaling mechanisms.n pairs of data. Each pair of data includes a z-dimensional input and a k-dimensional output. If the number of rules of the resource fuzzy inference system of a microservice is m, then a certain rule l in the fuzzy inference system can be expressed as Equation (1) [lth fuzzy set We assume that the resource status data of microservices running on an edge computing network are tion (1) :(1)If x1tion (2) :(2)μMJl generating fuzzy sets and rules, (2) optimizing the fuzzy membership function, (3) horizontal scaling, and (4) vertical scaling.Through some open-source tools, network users can easily detect and collect the computing resource usage data of each microservice running on an edge network’s computing nodes. We use CPU and memory usages as the input of fuzzy sets. The use of CPU and memory by microservices is divided into three levels: high, medium, and low. The scaling extent of the computing resources of microservices is the output of the fuzzy inference system. We define the scaling extent as the amount of computing resource capacity that needs to be properly expanded when the computing resources of a certain microservice are insufficient in the edge computing network environment. The scaling extent is a percentile measurement. In the fuzzy inference system, the scaling extent is converted into a format that conforms to the definition of the fuzzy rules, and it is converted into three levels—high, medium, and low—according to its percentage value. The scaling extent is calculated using the FMCRS algorithm designed in this article. Therefore, the designed fuzzy sets include two input parameters, one output parameter, and seven fuzzy rules. lth fuzzy set, respectively. Membership values are computed for each input value in x. The subgraph in the upper part of ith particle at time t+1, and ith particle at time t. ith particle has ever traveled. g is the best position that all the particles have ever traveled. i at time t+1 is provided in Equation (6). The PSO algorithm uses a fitness function to determine where the particles should go, i.e., the best position, being the position with the most food sources for birds.PSO is an algorithm developed by Kennedy and Eberhart  to obserThe membership function of the fuzzy inference system considerably influences the performance of the system; thus, selecting the best membership function, including the shape of the function, the number of fuzzy rules, and the parameters of the function, affects the accuracy of the fuzzy inference system. Accordingly, the current study uses the PSO algorithm to solve the problem of optimizing the designed fuzzy inference system of microservice resource management. Let The horizontal scaling mechanism of the FMCRS algorithm can create new microservices on the same edge computing node without having to migrate microservices that requiring resource expansion to new edge computing nodes. When a microservice on an edge computing node needs to expand computing resources, the FMCRS will first check whether the amount of computing resources required by the microservice is lower than the computing resources available on the edge computing node where the microservice is located. If it is lower than the computing resources available to the computing node, the FMCRS will start the horizontal scaling mechanism, and directly allocate the required computing resources to the microservice from the computing node where the microservice is currently located. This mechanism ensures that the microservice application can continue to execute, and avoids the short interruption caused by the microservice being migrated to other nodes.Compared with those of cloud computing networks, the computing resources of edge computing networks are limited, and an increase in hardware computing resources is inelastic. Differently from the horizontal scaling mechanism, vertical scaling will migrate microservices that require the expansion of computing resources to new edge computing nodes. When a microservice on an edge computing node needs to expand the computing resources, if FMCSR estimates that the required expansion resources are greater than the remaining available computing resources on the edge computing node where the microservice is located, the microservice uses the vertical scaling method to perform the resource expansion. Vertical scaling can reasonably distribute the load of each edge computing node.An application composed of microservices has different priorities at each edge computing node. Thus, when many microservices are required to be migrated to other edge computing nodes, FMCRS must still determine which microservice should be moved to the node with a lower resource load based on the priority of each microservice. Equation (8) is used to define the priority of the adjustment resources of each microservice. Algorithm 1 Algorithm for fuzzy-based microservice computing resource scaling (FMCRS)Initialization:Gaussian membership function of fuzzy interference system with standard deviation σ and mean value μ;1:ForDo2:ForDo3:  Calculate Gaussian membership values according to (2) and (3), respectively;4:  Optimize Gaussian membership function according to (5), (6), and (7), respectively;5:  6:  ifthen7:    Run horizontal scaling;8:  else9:    Calculate the priority of microservice according to (8);10:    Run vertical scaling;11:  end if12: end for13:end forOutput: Microservices with the scaled computing resources.FMCRS is summarized in Algorithm 1. First, we initialize the fuzzy sets and parameters of the microservice resource computing fuzzy management inference system. When an iteration occurs, the algorithm calculates the fuzzy membership functions of all the fuzzy sets for each microservice on all the edge network’s computing nodes (Steps 1 to 3). Then, FMCRS optimizes the fuzzy membership functions using the PSO algorithm (Step 4). All the fuzzy rules are integrated and defuzzified to calculate the estimated required scaling computing resources: This section presents the system architecture design and implementation in detail. We describe the conceptual model and representation of the system with various diagrams. We also show how our proposed platform is physically built and operated.We designed and implemented the edge computing microservice management platform prototype from the perspective of the network operator. The platform can provide network service operators with multiple microservice resource management mechanisms to achieve the scalability of computing resources. The platform includes a microservice computing resource fuzzy off-loading system. This system can implement functions, such as resource monitoring and deployment management, under different microservice resource usage conditions. The platform architecture is illustrated in Our platform refers to the architectures proposed in the MEC architectural documents ,44,45 puIn the designed platform system architecture, the orchestrator is responsible for the centralized resource management of the entire edge computing network environment. It provides the most basic centralized operations for each microservice, including resource allocation, service deployment, and microservice status adjustment. The resource monitor module contains a variety of microservice operating status detection programs to collect the operating statuses of microservices, including connection, network delay, and computing resource occupancy statuses. When the cloud computing network deploys microservices to the edge computing nodes in accordance with the client’s requirements, the resource monitor on the platform monitors the status of each edge computing node in real-time.The FMCRS offload system module is responsible for the allocation and management of the computing resources of each microservice. The designed algorithm is implemented in this module. This algorithm adjusts the edge network on the basis of the collected data and triggers the execution control module to issue resource adjustment rules and operating instructions to each edge computing node. The lower layer in the platform architecture diagram shows the collection of all the edge network’s computing nodes. Each edge computing node runs the microservices required by the cloud computing network. Here, each microservice has an “agent” responsible for monitoring and receiving data, and then the aggregator deployed on each edge computing node periodically collects the status of each microservice and sends it back to the upper data collector. Microservices use a RESTful API  to commuTo verify the effectiveness of our proposed microservice resource management platform prototype for edge computing, the designed management platform was implemented on Xen servers. We implemented two resource management mechanisms in the designed edge computing microservice resource management platform prototype. The purpose was to realize the resource utilization of microservices and reduce resource consumption. For example, the resource detection and scaling mechanisms in the platform aim to detect the load situation of the computing resources of microservices in time and realize the automatic expansion function of computing resources. The purpose of the resource adjustment mechanism is to reduce the consumption of microservice computing resources and improve the rate of obtaining microservice resources. The aforementioned multiple mechanisms, combined with the FMCRS algorithm, achieve a high degree of autonomy in system and microservice management. The implementation methods of each system module and management mechanism are described in detail in the succeeding sections.The control module in the resource controller component implements common management functions for microservices, including deployment, scaling, deletion, and configuration. The control module deploys a microservice with specifications, including whether the type of microservice is single or expandable. The deployment specifications also include basic initialization setting instructions and microservice external network communication ports. Moreover, this module is responsible for providing configuration files that should be downloaded and executed when a microservice is started. All the configuration files are stored in the form of YAML scripts. A microservice downloads and executes these configuration files for normal operation.The status-collecting module is responsible for collecting and storing data related to microservices. After the resource controller deploys a microservice, this controller transmits the status data of the microservice to the status-collecting module through an agent. cAdvisor can be used as the collection agent for the microservice status data. It accesses container-based microservices and resources on each node, including CPU usage and memory usage. In the designed status-collecting module, Prometheus is used to access each cAdvisor actively. We implemented the designed FMCRS algorithm in the FMCRS fuzzy offload system and requested the resource controller to adjust the corresponding resources of the computing nodes in the edge computing network. The FMCRS algorithm has four important computing mechanisms: a fuzzy inference system, optimization of the fuzzy system, horizontal scaling, and vertical scaling. These four computing mechanisms are implemented in the service detecting and scaling modules. These modules periodically read the status-collecting module data to obtain the latest status of microservices running on each edge computing node. Then, the FMCRS algorithm is automatically executed in accordance with the status of the microservices to adjust the resource usage requirements of the microservices and achieve the efficient use of resources.The status-collecting module receives the service functions and status data of each microservice every second and then sends these status data to the service-detecting module. The latter analyzes the CPU and memory usages of microservices to calculate the probability of expanding their computing resources. The calculation method for the CPU and memory usages of the microservice is provided in Equation (9), where The service scaling module dynamically adjusts the number of microservices based on user needs and the calculation results of the service detection module to maintain the quality of service of the computing system and reduce the deployment cost of network service providers. This module calculates the number of additional microservices that are required to be deployed on the basis of the resource usage of microservices in real-time and then sends the results to the deployment module in the resource controller component to filter new edge computing nodes for the corresponding microservice deployment. When the external cloud network accesses the computing nodes in the edge network, the load balancer delivers the computing services to the corresponding microservices.To verify that the platform we designed can be effectively applied in the edge computing environment of the Internet of Things, we examined the use case of Internet of Vehicles (IoV) cloud computing, with edge computing as the experimental performance analysis environment. The experimental system architecture diagram is shown in The collected data volume is extremely large since the OBD connectors collect vehicle condition data and driving behavior data per second. To reduce the amount of data sent to the cloud platform, reduce the cost of cloud computing, and reduce the delays in application services, we performed edge computing on the Raspberry Pi mini-computer installed on the motorcycle. We deployed some application microservices of the cloud computing platform on the raspberry pi mini-computer of the motorcycle. These microservices can perform filtering, cleaning, and preprocessing of big data, and then send the preprocessed results to the IoV cloud computing platform. Six experiments were conducted on the basis of the implemented microservice resource management platform in such an IoV cloud/edge computing network, and the performance of FMCRS was compared with a state-of-the-art microservice scaling management method.We conducted a series of experiments in six scenarios to examine the performance of our proposed microservice resource management method from three aspects. Experiments 1 to 3 aimed to verify that some necessary microservice computing resource management functionalities were able to be realized on the platform we designed. Experiments 4 and 5 were designed to test the performance of the proposed horizontal and vertical scaling mechanism. Experiment 6 compared the performance of the FMCRS mechanism and the Kubernetes auto-scaling mechanism in the stress test.This experiment was used to test the time required to deploy different types of microservices on the designed platform. We divided the necessary services of IoV applications into various types of microservices and then deployed them on each computing node in the edge computing network to test the deployment time of these microservices. The microservices have 11 types, i.e., three types of database microservices and eight types of website core function microservices. These microservices are as follows: carts, carts-db, catalogue, front-end, pay, rabbit, queue, order-db, order, user-db, and the user.The deployment of all the microservices consists of three steps: scheduling, pulling, and establishment. In the scheduling phase, the microservices are allocated to the corresponding computing nodes of the edge network in accordance with the deployment algorithm. The pulling phase pulls down the Docker images of various microservices from the Docker repository to each computing node. During the establishment phase, some basic functions and configurations are configured to the microservices. The first two of the three stages take a longer time because the microservice deployment algorithm in the scheduling phase analyzes the resource requirements of each microservice and the available resources of each computing node to determine the deployment location of a microservice. In the pulling phase, the size of the Docker image of a microservice affects the download time. The larger the Docker image of a microservice, the longer the pulling time. Compared with the first two stages, the establishment time of microservices is relatively stable because only the basic parameters of the microservice startup should be initialized, and thus, the establishment time of each microservice does not differ considerably. As shown in This experiment was used to test the time it takes to scale up and down different numbers of microservice computing resources on the designed platform. We tested the time required to scale up and down one to 20 microservices. As shown in When microservices require the scaling down of resources, the time required to reduce a microservice resource is not equal to the time required to expand a microservice. Moreover, it may even be four to five times the time required to scale up resources. Simultaneously scaling down the resources of 20 microservices takes more than 1 min because our system management platform does not forcefully delete microservices directly. Instead, the system adopts a sophisticated microservice termination process. In this process, microservices can be terminated and restarted at any time in a decentralized computing environment. When ending and restarting, however, microservices on edge computing nodes must first refuse to accept the service requirements of new users, and then microservices are terminated after the previously processed computing requirements are executed. Therefore, when microservices perform resource scaling down on our platform, they experience an exit time of a preset termination period.The results of the experiment also proved that the time it took one microservice to scale up computing resources was 2.7 s on our platform. The time it took to scale up resources for 20 microservices simultaneously was 12.6 s. The scaling-down time of resources for one microservice was 18.1 s, and that for 20 microservices simultaneously was 62.3 s. The designed microservice resource management platform system displays the capability to process the scaling up and down of microservice computing resources rapidly in an IoV edge computing network environment with relatively insufficient computing resources.This experiment aimed to verify that the designed platform can monitor the computing performance status of each computing node in an edge computing network and each microservice running on that node in real time. In this experiment, we used the open-source project Prometheus and deployed microservices on each edge computing node. We preinstalled an export program on each computing node, as shown in This experiment was a continuation of the previous experiment to verify that the designed platform can quickly expand new microservices horizontally when it detects that microservices require resource expansion. The designed platform has a microservice detection mechanism. Thus, when it detects that the computing resource load of a certain microservice is too high and will trigger a resource expansion, the designed FMCRS algorithm can calculate the extent of resources that need to be expanded and starts a new microservice during the time when microservices off-load the computation of microservices that were originally overloaded.As shown in This experiment verified that the designed FMCRS algorithm can vertically expand the computing resources of microservices. When the load of a computing node in an edge computing network is excessively high, the designed platform detects the abnormal state of the computing node’s resource usage in time and compares the priority of the computing node with the computing logic in our algorithm. Low microservices are removed from the computing node and migrated to other edge computing nodes with a lower load.This experiment compared the efficiency of the designed FMCRS microservice resource management method with that of another cloud microservice resource management method, namely, Kubernetes auto-scaling. In this experiment, we applied JMeter which is an open-source software designed used to design load test functional behavior and measure performance to simulate a large number of edge node users accessing the cloud computing platform simultaneously. We used JMeter’s stepping thread group mode to send HTTP requests to the IoV application server. JMeter provides the interface of the dashboard to allow users to view the analysis results, such as network traffic. We implemented two resource management algorithms, namely, the designed FMCRS scaling and Kubernetes auto-scaling, on the microservice resource management platform and compared their performance. The parameters of the experimental environment are provided in We observed that the FMCRS scaling algorithm and the Kubernetes auto-scaling algorithm were able to reflect the demands for the expansion and reduction of microservice resources on the platform promptly. When the computing load of a microservice CPU or memory exceeded a high critical value, both algorithms were able to quickly expand microservice computing resources to achieve the load distribution. However, the resource expansion response of the Kubernetes auto-scaling algorithm changed drastically. The Kubernetes auto-scaling algorithm suddenly increased the number of scaled microservices and suddenly shrunk microservices. Kubernetes auto-scaling exhibited drastic changes in its scaling strategy. In an edge network with limited resources, such changes consume additional computing resources and affect the stability of the overall computing network. Compared with Kubernetes auto-scaling, the designed FMCRS scaling method was able to immediately meet the needs of microservice resource expansion and reduction, and thus, no drastic change occurred in the microservice resource management strategy. Therefore, FMCRS scaling is more suitable for the microservice resource management environment in edge computing networks.In this study, we designed and implemented a prototype of a microservice resource management platform for edge computing networks. The core of the platform includes a fuzzy-based microservice computing resource scaling (FMCRS) management algorithm for microservice resource expansion based on fuzzy theory. This study also introduces the PSO algorithm for optimizing the fuzzy membership function of the proposed fuzzy microservice resource management algorithm. In addition, we designed and implemented two methods for horizontal scaling and vertical scaling in accordance with the available resources of edge computing network nodes. In this study, we conducted extensive experiments to verify the effectiveness of the proposed platform and the performance of the FMCRS algorithm. The results of the experiment proved that the proposed microservice resource management platform was able to reduce the response time of microservice resource adjustments and dynamically scale microservices horizontally and vertically. Moreover, the performance of the proposed FMCRS was similar to that of a currently widely used cloud computing microservice resource management mechanism, namely, Kubernetes auto-scaling. However, no dramatic change in the microservice resource management strategy occurred in FMCRS. FMCRS was able to avoid the sudden surge in overall network resource allocation, and thus, it is more suitable for the edge computing microservice management environment. Therefore, the system prototype designed in this study will provide users of edge computing networks with a new option for meeting the increasingly complex network application requirements.In a future study, the proposed microservice resource management platform will be implemented as a service/software as a service (SaaS) on the various public cloud service platforms, such as AWS, GCP, and Azure. More IoT edge computing application use cases, such as smart farming and smart factory, will also be tested on our platform to see what needs to be improved. We will also study how to combine machine learning and deep learning models in our FMCRS algorithm to improve the efficiency of microservice resource management, such as reducing latency and improving the service quality.


Cloud computing is an important milestone in the development of distributed computing as a commercial implementation, and it has good prospects. Infrastructure as a service (IaaS) is an important service mode in cloud computing. It combines massive resources scattered in different spaces into a unified resource pool by means of virtualization technology, facilitating the unified management and use of resources. In IaaS mode, all resources are provided in the form of virtual machines (VM). To achieve efficient resource utilization, reduce users' costs, and save users' computing time, VM allocation must be optimized. This paper proposes a new multiobjective optimization method of dynamic resource allocation for multivirtual machine distribution stability. Combining the current state and future predicted data of each application load, the cost of virtual machine relocation and the stability of new virtual machine placement state are considered comprehensively. A multiobjective optimization genetic algorithm (MOGANS) was designed to solve the problem. The simulation results show that compared with the genetic algorithm (GA-NN) for energy saving and multivirtual machine redistribution overhead, the virtual machine distribution method obtained by MOGANS has a longer stability time. Aiming at this shortage, this paper proposes a multiobjective optimization dynamic resource allocation method (MOGA-C) based on MOEA/D for virtual machine distribution. It is illustrated by experimental simulation that moGA-D can converge faster and obtain similar multiobjective optimization results at the same calculation scale. Cloud computing is an emerging technology in the field of computers. Although it has been applied, its development is not perfect. Many technical standards have not yet formed, and are still in the period of growth. As long as we grasp the rare opportunity, we can occupy a place in the future cloud computing field –3. In thIn cloud computing applications, Infrastructure as a Service (IaaS) is an important service model, through which cloud providers can provide massive computing resources to cloud users through the Internet. In addition, the price fluctuation and the uncertainty of demand and other factors make this problem more complicated. Therefore, in order to meet the resource usage requirements and minimize user expenses, the VM allocation scheme must be optimized. This problem is called VM allocation optimization shown as  8, 9]., 9.8, 9]The emergence of cloud computing platform virtualization technology brings new opportunities to realize energy saving in the cloud computing environment. The use of virtualization technology enables multiple users to share the computing resources pool according to the actual demand. The emergence of this technology has greatly improved the resources utilization. With the emergence of a shared resource pool, the number of servers in the cloud environment has reduced, thereby increasing the income of the cloud service provider , 10, 11.At present, many energy-saving resource scheduling methods of cloud platform focus on how to reduce the number of active servers to achieve energy saving and green computing. However, the above resource scheduling schemes often ignore the dynamic change of application load caused by the change of user demand in the cloud environment, and they also fail to consider the stability of application load distribution on each physical node. Although the distribution of application VMS among physical nodes in the current state makes fewer physical nodes active, the change of user requirements will lead to changes in the load of each application; in this case, the dynamic change of the required load will lead to resource hot spots on these physical nodes in the future with the change of the application load. The status of these physical nodes may reappear in the near future, which will directly trigger a new round of dynamic resource configuration requirements . To solvWith the development of cloud computing, people find that although cloud computing brings convenience, its energy consumption is also huge compared with the traditional service mode. Now, some suppliers in order to meet user requirements, which can respond to dynamic changes in user needs. However, in the actual environment, this will cause a great waste of resources and increase unnecessary energy consumption. With the change of user demand, the application load request resources will change accordingly. Therefore, how to reduce energy consumption while ensuring service quality is a problem to be solved. In a cloud computing environment, the optimal VM resource distribution scheme can effectively save energy by properly deploying VM resources on physical nodes , 16. VirAt present, the research of cloud computing is still in the initial stage. In terms of the development direction of the future mainstream cloud computing industry, there are also two different camps among the big companies that master the core technology of cloud computing. Emerging companies represented by Google and Amazon are pushing the Internet cloud first, while traditional IT enterprises represented by IBM and Microsoft are pushing the IT cloud. In addition, due to commercial interests, many high-end cloud computing technologies are not disclosed as business secrets of enterprises . Google As mentioned above, the widespread interest in cloud computing stems from its successful commercial application, so the earliest cloud computing research institutes are mainly concentrated in several major Western IT technology companies. However, with the gradual increase of the influence of cloud computing, its many excellent characteristics make people see its application in other fields such as military scientific research. Cloud computing technology began to receive attention from various countries and has become an important aspect for countries to compete for the commanding heights of future science and technology . In ChinResource management and allocation is a key problem in cloud computing. In the IaaS mode, resource allocation is a virtual machine allocation problem. Virtual machine allocation, like other cloud computing technologies, is in a state of constant discovery. Literature  proposedFrom the above analysis, we know that the above methods have studied virtual machine resource allocation optimization in cloud computing to some extent, but some problem still exists. On the other hand, no scholar has applied multiobjective genetic algorithm to this field till now, so the research here still draws a blank, which has great theoretical research and practical application value.The proposed evolutionary algorithm provides a new solution idea for solving NP problems, and the emergence of multiobjective optimization algorithm brings a new solution idea for complex multiobjective optimization practical problems.Because of its good development prospects, the multiobjective optimization problem has become a research hotspot in the academic world. In this paper, MOGANS- and MOEA/D-based multiobjective optimization scheduling schemes are proposed according to the solution idea of multiobjective optimization.The contributions of this paper are as follows:This paper consists of five parts. The first and second parts give the research status and background. The third part is the MOEA/D-based virtual machine resource allocation in cloud computing. The fourth part shows the experimental results and analysis. The experimental results of this paper are introduced, compared, and analyzed with relevant comparison algorithms followed. Finally, the fifth part summarizes the full paper.χ is the convergence factor of particle swarm. For the particle in each iteration, the particle changes its velocity and position according to the following formula:d=i=1,2,…, m, k is the number of iterations, and c1, c2 are decay acceleration factors.Conventional particle swarm optimization (PSO) is an intelligent bionic method, which was jointly proposed by social psychologists Kennedy and Dr. Eberhart in 1995. It has become the mainstream intelligent optimization processing method at present and has been comprehensively applied in the academic and industrial circles. Its optimization performance is mainly reflected in convergence , 28.(1)χThe (PSO) method here is determined by cloud user U and cloud VM, that is, the utility function of cloud user U is used to obtain the optimal position of particle search, and VM is used to obtain the optimal position of overall particle swarm search, that is, one particle represents one cloud user, The whole particle represents the virtual machine resources in the cloud computing environment of the whole field, which corresponds to the particle swarm optimization method. In this way, not only can each cloud user get the maximum benefit but also can make the whole cloud computing environment VM get global optimization.At present, many scholars have put forward many excellent algorithms for solving multiobjective problems, among which the representative ones are NSGA-II, PSO, etc. However, these algorithms do not adopt decomposition thought in solving the MOP problem. These algorithms mainly deal with the MOP problem through some algorithms, and finally integrate the MOP into a whole. Then, it is solved by single objective optimization problem. But the downside of this is that it becomes very difficult to allocate fitness. However, many of the target values are independent, so there are many different cases of how to judge the superiority of a solution, and there are many other cases of the relationship between the solutions besides being dominant. Therefore, it is difficult to specify suitable fitness for these solutions to compare the advantages and disadvantages of these solutions in order to perform selection operations. In view of this problem, the decomposition idea is put forward, and the decomposition strategy idea is to transform multiple objectives into solving the problem of each single objective, mainly by solving the problem with multiple objectives. It is decomposed into a single solution optimization problem. By optimizing the solution of each sub-objective space, the solution of the whole solution set can be optimized to achieve the purpose of multiobjective optimization, and finally the global optimization solution based on Pareto is obtained. Therefore, MOEA/D comes into being.N subspace through decomposition of the solution space. Among them, the solution in the subspace transforms a multiobjective problem into a single-objective problem by means of aggregation method, and the common aggregation methods include Chebyshev method, weighted sum method, and so on. In this paper, the aggregation function is implemented by Chebyshev:The decomposition idea of MOEA/D is that, unlike other multiobjective optimization algorithms, the multiobjective problem is not processed as a whole through integration. Instead, it transforms the multiobjective solution into solving the single-objective optimization problem in i=1mλi=1, z∗=T are the reference points. And, z∗ is the optimal value of each target value in all solutions.And ∑MOEA/D algorithm does not transform the multitarget values into a single-target progressive solution through the traditional method but decomposes the multitarget space, thus transforming the multitarget solution problem into the optimization problem of solving the sub-target space solution, and the sub-target space solution can be transformed into a single-target solution problem according to the vector of the solution space.An excellent core idea of MOEA/D is to update the new solution by exchanging information of neighborhood solutions. This strategy greatly speeds up the search of understanding space, and has lower time and space complexity compared with some other multiobjective optimization solutionsThe main characteristics of MOEA/D algorithm are as follows:Because the resource scheduling problem in cloud computing environment can finally be transformed into solving a multiobjective optimization problem through evolutionary algorithm, the resource scheduling scheme based on MOEA/D algorithm is proved by experiments to reduce the time complexity of the algorithm compared with MOGANS, so as to solve the shortage of MOGANS in computing performance.N sub-target space, where OMEGA represents the target space, so omega can be decomposed into a sub-target space composed of . Individuals in the population can be mapped into different subspaces according to the generated sub-target space, so as to achieve the classification of the population. The vector composed of each target value of individuals in the initial population is mapped into N sub-target space to ensure that each sub-target space has a solution. The division of target space and population classification can be realized by the following formula:Z is a reference point and Δ(F(x), λi) is the optimal solution of each target vector. It is also the cosine of the angle. In this way, POP population is divided into N classes. So there is a solution in every subspace and you have a variety of systems that help maintain the solution. Then, the multiobjective solving problem can be transformed into a single-objective optimization problem by the following aggregation function, which is in the form of the following:The algorithm mainly consists of four parts: target space decomposition, population classification, crossover, and mutation. The core of the multiobjective optimization problem is to decompose the solution space into And the letters in formula  are the In the optimization process, two schemes are proposed for users to choose. One is the scheme without considering the time factor, which only optimizes the cost and minimizes it while ignoring the time factor. It is suitable for users who do not care about time. Another kind is considering two factors of cost and time; the scheme firstly sets up a relatively small default time threshold. If the user has higher requirements, processing time can be dedicated to provide users with a time threshold that can be set up, after the cost optimization. The linear programming method is adopted, with the minimum cost as the optimization objective, and the processing time of resource price, virtual machine quantity, and supplier's supply capacity as the optimization conditions.Formula  represenIt includes a control node and four computing nodes  but due The main reason is that the algorithm makes a reasonable planning of resources in the virtual machine configuration stage in this chapter, so as to maximize the revenue of cloud services and optimize resource allocation. However, the utility optimization algorithm based on cooperative game cannot guarantee the optimal game. With the increase of time cycle, both the algorithm in this article and the game-based utility optimization algorithm maintain good returns under the effect of utility function optimization, while the resource reservation allocation algorithm starts to allocate on-demand resources with higher prices.Through the simulation experiment, the algorithm in this article is compared with the noncooperative game-based utility optimization algorithm, resource reservation algorithm, and user utility on the unit revenue of cloud data center. 0.4 is selected as the interval, and the statistical utility value is between , 5. The The experimental results show that with the increase of user utility, unit income also increases gradually, but the increasing trend gradually becomes slow, indicating that the utility function has a certain promoting effect on the increase of unit income, but this promoting effect will begin to fail after reaching a certain peak. At the stage of stimulative effect, the increase of yield per unit area is manifested. After reaching the peak, the stimulative failure is mainly related to the resource itself. Therefore, resources will not increase the unit infinite revenue of the non-cooperative game optimization algorithm with the increase of the utility function, the profit per unit increases steadily at first and then falls sharply, indicating that on-demand resources play a decisive role in the allocation process.In addition, the user utility difference between the algorithm in this article and the virtual machine instance based on noncooperative game utility optimization algorithm and resource reservation algorithm of the same user request is also compared as shown in The experiment compares the performance of OpenStack random scheduling algorithm and the algorithm in this article in computing resource CPU utilization, as shown in The experimental results of memory resource utilization performance of OpenStack random scheduling algorithm and the algorithm in this article are compared as shown in Under the same initial conditions , the four algorithms are run to obtain the new distribution states of each VM, respectively. The number of migration times in the stable time and the number of idle physical nodes of these new distribution states are shown in Tables As can be seen in Tables In order to compare the computational overhead between MOGANS algorithm and MOGAD algorithm, the experimental data tested in this section are basically the same as the parameters as the former experiment, including two variables: population size and population total algebra. The values of population size and population total algebra are constantly changed to measure the running time of the algorithm, respectively. The experimental results are shown in It can be seen from Aiming at the deficiency of some current resource scheduling schemes of energy-saving resource scheduling in the current cloud computing environment, this paper proposes a multiobjective optimization scheme MOGANS based on NSGA-II multiobjective optimization.However, MOGANS has insufficient computing performance, especially when the amount of data to be calculated increases, the performance of MOGANS is not satisfactory. After the test of the same amount of computation, the energy-saving resource scheduling scheme of the new opportunistic MOEA/D algorithm, MOGA-D, performs well. Compared with MOGANS, the computational performance is significantly improved with the same calculation scale. The similar multiobjective optimization results can also be obtained.


With the development of more/all electric aircraft, replacement of the traditional hydraulic servo actuator (HSA) with an electromechanical actuator (EMA) is becoming increasingly attractive in the aerospace field. This paper takes an EMA for a trimmable horizontal stabilizer as an example and focuses on how to establish a system model with an appropriate level of complexity to support the model-based system engineering (MBSE) approach. To distinguish the nonlinear effects that dominate the required system performance, an incremental approach is proposed to progressively introduce individual nonlinear effects into models with different complexity levels. Considering the special design and working principle of the mechanical power transmission function for this actuator, the nonlinear dynamics, including friction and backlash from the no-back mechanism, and the nonlinear compliance effect from the mechanical load path are mainly taken into consideration. The modelling principles for each effect are addressed in detail and the parameter identification method is utilized to model these nonlinear effects realistically. Finally, the responses from each model and experimental results are compared to analyze and verify how each individual nonlinearity affects the system’s performance. With the development of partly/fully electric aircraft, the application of power-by-wire (PBW) actuations has received significant interest ,2. The PThe introduction of electrical actuation for flight control raises new challenges, including power sizing, back-drivability, load rejecting, cushioning and damping, response to failures, and heat rejections . In suchHowever, to execute this process, there still remain two major challenges. The first one refers to the issue of realistically modelling different categories of nonlinear effects, such as backlash, preload, and friction. A recommended method is to attempt to combine the knowledge models (from scientific points) and representation models . The next challenge mainly concerns how to individually evaluate physical effects. With regard to an electromechanical system with only linear or simple nonlinear effects, the known methods, such as system principle analysis or automatic control theory, are sufficient to solve this problem with higher efficiency and lower cost. However, when the physical effects are mixed and complex, the traditional approaches are no longer the superior option. A practical approach is to adopt an incremental methodology during the model development process. The model complexity can be progressively increased based on whether each nonlinear effect is considered. This incremental methodology can ensure standard interfaces and replaceability in multi-level modelling. Additionally, when the multi-domain effects are concerned, the bond graph can be introduced as the modelling language . The rest of this article is organized as follows: This research deals with a trimmable horizontal stabilizer actuator (THSA) for aircraft, which mainly functions for auxiliary pitch control ,15. As sElectrical motor control unit (EMCU): Based on the motor speed feedback and trim speed command from the flight control computer (FCC), velocity loop regulation and current command generation for power drive electronics (PDE) are executed in the EMCU. Meanwhile, according to signals sampled from sensors, such as the linear variable differential transducer (LVDT), rotary variable differential transducer (RVDT), etc., the EMCU is in charge of fault diagnosis with specific strategies . The diaPDE: The power flow between the electrical supply and the motor, as well as the current loop regulation, is conducted. Motor and brake assembly (MBA): THSA involves a primary MBA and a backup MBA, which are configured in torque summing mode. In principle, the backup MBA operating in passive mode functionally offers no resistance to the primary MBA.Gearbox: In addition to the fundamental velocity reduction function, a torque limiter is internally integrated inside, which is responsible for motor protection under overload situations. Dual RVDTs, installed in the gearbox and backing up each other, feedback the current THS surface position to the EMCU and FCC for monitoring and fault processing.Screw-nut mechanism: The rotary motion is translated into linear motion via a ball screw–nut mechanism. The secondary nut works as a backup and remains unloaded in normal mode.Mechanical load path: The mechanical load path enables the transmission of an external axial load to the airframe. In addition, dual mechanical load paths, the respective components of which are illustrated and distinguished with different colors in No-back device: The fundamental function of a no-back mechanism is to mechanically lock the surface position . The detUsually, the basic model for a component can be easily determined from its function and property. However, in order to successfully establish complex models, further modelling principle analysis is inevitable, which can locate where the nonlinear effect functions and conduct accurate mathematical description. Based on actual needs, knowledge models or representation models  can be used to evaluate the nonlinear effects.The modelling procedure requires prior planning in order to follow the incremental methodology. As depicted in From the above system description of THSA, compared to a conventional EMA , the majIn order to propose more suitable models for friction and compliance effects with backlash or preload, the following hypotheses are considered:Hypothesis 1.The primary source of no-back friction torque results from the inserted friction disks.Hypothesis 2.The variable stiffness phenomenon is neglected when two components gradually eliminate the backlash and achieve entire contact deflection, i.e., the stiffness nonlinearity is evaluated by the sign function.Hypothesis 3.For the no-back mechanism, the backlash phenomenon depends on the direction of rotation of the screw and the position of each tooth of the ratchet wheel determines which one will eventually mesh with the pawl. For simplification, the contact stiffness is considered constant, as the number of tooth and the direction vary during the meshing .The basic function of the ball screw–nut mechanism is to translate rotary motion into linear motion. Its internal compliance effect is merged into a mechanical load path; for this reason, only the friction effect is taken into consideration here.Basic modelp and efficiency coefficient η, respectively. The output force and linear speed can be defined as:Translation from rotational into linear motion occurs at the screw–nut coupling and the sliding/rolling frictions arising at the contact between the threads are characterized by a screw pitch 2.Advanced modelFor simplification, the friction effect will be characterized consistently with the basic model for two reasons. Firstly, the friction inside the screw–nut mechanism is the result of the combination of operating quadrant (aiding or opposing load), normal force and relative nut–screw velocity, which is difficult to evaluate without sufficient experimental data . SecondlThe mechanical load path enables the transmission of an external axial load to the airframe. Obtaining its realistic servoelastic behavior is particularly necessary, because the compliance effect may significantly impact the dynamic performance and the service life of the actuator. Overall analysisThe respective components of dual load paths are illustrated in Tg and screw velocity ωs from the gearbox, whereas the power output is the trimming speed of the surface and drive force to balance the aerodynamic force FL. Torque input Tg can be decomposed into several components: inertia torque loss Js, friction torque loss Tb from the no-back mechanism, and screw driving torque Ts. A working principle diagram of the mechanical load path components is provided in The transformation of rotary motion to translation motion is accomplished via the ball screw–nut mechanism. The control surface load is transmitted via the screw–nut mechanism and exerts an axial load to the screw. This axial load eventually is supported by the screw housing and rear attachment components.2.Basic modelIn addition, the compliance effect existing in joints between the surface and actuator, as well as attachments between the screw housing/body and airframe, is considered ideal, i.e., no backlash or preload deflection. Consequently, the drive force and speed of the surface can be derived as:3.Advanced modelThe components of the screw housing and rear attachment are illustrated in Based on the above geometry investigation of the no-back mechanism components in x0 with positive or negative signs, respectively. For a no-back mechanism with bilateral backlash bpb and preload -bds, the total transmitted force from screw to airframe is:xst is the additional linear displacement caused by the compliance effect of the load path between the screw housing and rear attachment components and the airframe; kp,l, kp,u and kds are the equivalent no-back stiffness and stiffness of the preload disk spring; dp is the contact damper rating; Fb,l and Fb,u are, respectively, the transmitted force by the lower and upper no-back mechanism. With the addressed modelling hypothesis, the constant parameters kp,l and kp,u are denoted as equivalent no-back stiffness for contact, whereas the stiffness is imposed to none for free play.For convenience, the backlash or preload effect can be defined by a proposed single parameter Considering the compliance effect of the load path, the surface speed is modified as:kp,l, kp,u, kds and backlash parameter bpb must be identified by utilizing the widely used particle swarm optimization (PSO) algorithm. The load force Fst and surface displacement xst, which are accessible from the force sensor and linear displacement sensor installed on the nut, are the data input for this identification model from Equation (3). Each particle represents a different set of parameters  and the minimum identification error for load force Fst is regarded as the optimization objective. These particles are conceptual entities that travel through the multidimensional search space. At any particular time, each particle has a position and a velocity. The position vector of a particle represents a trial solution to the search problem. This search process will continue until the global best solution is acquired [The stiffness parameters acquired . The steacquired .The identification results and the comparison between measured force and identified force versus displacement are, respectively, plotted in Attributed to the no-back mechanism, the surface position can be mechanically locked and the power transmission chain is forced to be irreversible, which mainly rely on two pawl and ratchet wheel assemblies, as well as the friction disks inserted between its components, as in Overall Analysis of Modelling Principleωs = 0), and a compressive load (positive sign) Fst is transferred to the screw when a load of the same direction is exerted on the nut. Moreover, two virtual force sensors are inserted to acquire the real-time impact forces Fb,u and Fb,l of the bidirectional no-back assembly components:-Tfr,l is developed from the lower brake mechanism in either direction, which is because the minor impact force Fb,l remains between its components;the upper brake mechanism is axially tightly engaged and essentially no friction torque -the upper ratchet wheel is blocked by its pawl to avoid the screw revolving due to the axial force exerted by the load on the nut;-TL generated on the screw by the external load is balanced by the stick friction torque Tfr,u produced by the upper friction disks.the load torque To realize the bidirectional irreversibility function, the no-back pawls block the rotation of their respective ratchet wheels relative to the actuator body, each operating for a different rotation direction, as is shown in ωs. Therefore, the movement has the same direction as the force exerted by the load on the actuator: the load aids this. The actuator must develop a driving torque Ts on the screw in order to override the breakaway friction torque Tfr,u produced from the upper friction disk. Functionally, essentially no friction torque is developed from lower brake mechanism, since the lower ratchet wheel is permitted to be freewheeling in the opposite direction. For one and the same direction of load force, if the actuator is active, it must move the nut upward, corresponding to a negative sign of screw velocity ωs (the load is opposing), the ratchet wheels for the lower brake mechanism and upper brake mechanism are blocked and permitted to be freewheeling, respectively, which implies that operation states for both ratchet wheels are inversed. Consequently, the friction torque Tfr,l generated from the lower friction disk is overridden, whereas essentially no friction torque Tfr,u is developed from the upper brake mechanism. The amplitude of Tfr,l is finite since the impact force Fb,l is limited within the spring preload and grows smaller with the increase in compressive load. On the contrary, if the actuator must move the nut downward, corresponding to a positive sign of 2.Basic modelTb generated from the no-back mechanism as a coulomb torque, which is the combination of the upper no-back mechanism Tfr,u and lower no-back mechanism Tfr,l. To guarantee the no-back function of THSA, the amplitude of this coulomb torque is imposed to:The basic model is to introduce the friction torque 3.Advanced model(1) Realistic frictionμs and μc are the stick and coulomb friction coefficient, respectively; ωst is the stribeck reference velocity; F is the normal impact force; fs is the viscous friction coefficient.Friction loss is a very complex phenomenon that is highly dependent on velocity, external load, and temperature . The sugIt is emphasized that this proposed model includes the impact force transmitted from the external load, this significant effect being generally ignored in the modelling of mechanical transmission devices. Based on the modelling approach in Equation (6), the friction modelling can be accomplished with the following parameter identification process. As discussed above, the friction torque that requires identification is generated from the friction disk. A dedicated test rig is designed for this purpose . This te(2) Backlash effectAs addressed above, each ratchet wheel exists in two operation states, i.e., freewheeling and blocked. When the screw velocity changes to the opposite direction, the state of each ratchet wheel inverses functionally. However, as shown in The model matrixes in To demonstrate how different nonlinear dynamics affect system performance, the critical components in the proposed THSA model should be packed separately to modify its complexity levels incrementally. These levels must include the same ports to ensure that they are independent and replaceable. Since the nonlinear effects that we focus on are friction and backlash in the no-back mechanism and the compliance effect in the mechanical load path, four models with progressively complex levels, which are part of the alternatives of the model matrix in As shown in To analyze how nonlinear dynamics, including friction parameters and compliance parameters, affect system performance, it is necessary to compare the system performance differences between the simulation and experimental results, when each individual nonlinear dynamic is progressively introduced. In addition, model levels should be flexible to match various purposes. The impact on system performance of no-back friction parameters is established by comparing the speed and current response of models with different level (b), (c) and experimental results. The effect of rotary backlash parameters on system performance is evaluated by comparing the speed response of different level models (b), (c) and the experimental results. For these purposes, a speed command with four periods and a positive ramp aerodynamic compressive force  at time 1 s is first introduced. The bipolar trapezoidal trim speed commands with an amplitude 15 mm/s and acceleration 30 mm/s^2 are, respectively, applied at time 1 s and time 6 s. Moreover, the actuator is disabled during the rest periods, i.e., no active torque output for the motors. Based on the friction analysis in The effect of rotary backlash on system performance is established by comparing the speed responses of different level models  and experimental results, and the working principle analysis of the no-back mechanism in For further investigation, the speed command signal and aerodynamic force input are redefined as in 2 is applied at time 1 s. Simultaneously, a triangular signal with an amplitude of 29 kN and period of 15 s is taken as the aerodynamic force input  and the experimental results. For this purpose, a negative trapezoidal trim speed command with an amplitude of 15 mm/s and acceleration of 30 mm/sce input a.The clearance variations in the mechanical load path versus the external load for model (d) are depicted in This paper takes THSA as an example and focuses on utilizing an incremental approach to progressively introduce individual nonlinear effects into models of different complexity levels. By combining the modelling principles analysis and parameter identification methods, the representative model is used to model the nonlinear effects realistically. Finally, the responses from each model and the experimental results are compared to analyze and verify how nonlinearities affect system performance, with the aim of establishing an approximate complexity model to support the MBSE process.According to the response comparisons between models of different levels and the experimental results, both the nonlinear compliance effect and friction show significant impacts on system performance. When trimming under aiding load conditions, the significant increase in no-back friction generated from the friction disk leads to approximately three-times larger current demands and a speed perturbation (around 0.1 s) at the activation stage. Before the surface position is mechanically locked by blocking the respective ratchet wheel with corresponding pawls, the no-back rotary backlash must be eliminated first, which causes the screw to be back-driven by the aerodynamic load. Moreover, the maximum back-driven speed can approximately reach 40 percent of the command speed amplitude.When the aerodynamic force amplitude is not large enough to eliminate the initial clearance of the mechanical load path, the structural stiffness is mainly dependent on the preload disk spring, which causes the oscillation of surface speed and an overshoot with around 30 percent of the command signal. Additionally, the clearances from the upper and lower no-back mechanism are unilateral and symmetrical; for this reason, they show opposite variation trends under the same load direction.


Recent progress in printable electronics has enabled the fabrication of printed strain sensors for diverse applications. These include the monitoring of civil infrastructure, the gradual aging of which raises concerns about its effective maintenance and safety. Therefore, there is a need for automated sensing systems that provide information on the performance and behavior of engineering structures that are subjected to dynamic and static loads. The application of printed strain sensors in structural health monitoring is of growing interest owing to its large-area and cost-effective fabrication process. Previous studies have proven the suitability of printable strain sensors for dynamic strain measurements on bridges; however, the analysis of the long-term stability of printed sensors during static strain measurements is still lacking. Thus, this study aims to assess the long-term stability of printed strain sensor arrays and their suitability for the static strain analysis of large civil structures. The developed sensors and a dedicated wireless data acquisition system were deployed inside a gravity dam, which was selected as the field test environment. This test environment was chosen owing to the relatively stable temperature inside the dam and the very slow static strain changes associated with periodic water level changes. The results exhibited an average signal drift of 20  The development of sensing systems for the diagnosis and health assessment of civil engineering structures is essential to ensure the safety of bridges, tunnels, buildings, pipelines, and dams. Such diagnosis and health assessment processes that utilize automated sensing systems that comprise networked sensors, data acquisition devices (DAQ), and diagnostic algorithms are usually described as structural health monitoring (SHM). More specifically, SHM refers to the process of implementing a damage detection strategy and systems to identify structural damage in analyzed engineering structures ,2. It inDiverse sensing systems have been developed to monitor civil infrastructure. Such systems are typically based on the use of optical fibers ,5,6, aco sensors ,16 and s sensors ,18,19.Another group of sensors that is worth considering consists of printed strain sensors. Their principle of operation is similar to that of commercially available strain gauges. When a sensor is subjected to mechanical deformation, the electrical resistance of the material used to fabricate the sensor changes as a function of the applied strain. However, the primary difference compared with standard strain gauges is the fabrication process. Recent progress in additive manufacturing, which is widely used for flexible printed electronics , enablesAlthough there are several published reports on printed strain sensors for SHM, there is still a lack of experimental data recorded under practical conditions. However, such data are necessary to assess the long-term durability and performance of printed strain sensors for applications in real-life scenarios of SHM in various engineering structures. We addressed this gap in our previous studies by deploying printed strain sensors on highway bridges and analyzing their performance. In the first field test, an array of 16 printed strain sensors was bonded to a bridge structure to assess its long-term durability . At thatPrevious studies have demonstrated the good performance of printed strain sensors. Nonetheless, the analysis primarily focused on the dynamic response of the printed sensors to traffic on highway bridges. However, within the framework of SHM, static strain measurements are equally important as dynamic strain analysis, especially when the sensors are intended for the analysis of large engineering structures other than bridges. Thus, in this study, printed strain sensor arrays and a wireless data acquisition system were deployed inside a gravity dam. The dam was chosen for the field test owing to the relatively stable temperature inside the dam and the very slow static strain changes associated with periodic water level changes in the dam. Thus, the long-term drift of sensors could be analyzed without the influence of sudden environmental fluctuations, and the sensors were subjected to very slow, gradual static strain changes. A specially prepared network of wireless signal repeaters was used for remote measurements, and they were automatically controlled from outside the dam. An assessment of the long-term stability of printed sensors and their suitability for practical implementation in static strain analysis was conducted for a period of four months.The construction of the sensor array used in this study was similar to that used in our previous study, which focused on a dynamic strain analysis conducted on a highway bridge . HoweverTwenty-five strain sensors were screen-printed on the back of a polyethylene naphthalate (PEN) sheet with a double-sided copper wiring system a. The Cusitivity . The extsitivity ,34,35. Tsitivity ,32. In csitivity . During In addition to the 25 printed strain sensors in the array, an integrated temperature chip  was installed on top of the copper laminate. The temperature sensor provided a local temperature analysis, which was recorded with the strain measurements. The output signals from all sensors were connected to the DAQ via flexible flat cables and connectors .Prior to the deployment of the sensing system inside the dam, the printed strain sensors were analyzed with a laboratory test to assess their strain sensitivity and the linearity of the output signal. To calculate the strain sensitivity, a printed strain sensor array was installed on a metal plate with three conventional sensors , which were used to obtain a reference strain measurement. The printed sensors were attached to the top of the plate, and the three conventional strain sensors were attached to the bottom at locations that corresponded to the positions of three printed sensors selected from the array. The plate was made of steel, and it had a length, width, and thickness of 70 cm, 12 cm, and 2 mm, respectively. One side of the plate was bolted to a stable support, and the other was connected to a hook that was bonded to a tensile test machine . During the analysis, the plate with the attached sensors was subjected to bending deformation. Both types of sensors were subjected to equal strains during bending: positive on the top (printed sensors) and negative on the bottom . The output signals from both types of sensors (voltage) were simultaneously recorded and analyzed using a specially prepared computer program . Based on the recorded data, the relative change in resistance . The operation of the transmitters was controlled by specially designed computer software  that provided an interface with a wireless receiver, which was capable of sending commands to and receiving data from the transmitters connected to the sensors. To provide remote control of the entire sensing system, the computer was connected to a portable long-term evolution router. Therefore, the system could be controlled from any location that had access to the Internet. In this study, the sensors were installed inside a gravity dam, which is a large concrete engineering structure. Thus, the challenging part of this project was remote communication between the transmitters installed inside the dam and the receiver installed outside in a storage building located near the dam c. To enaThe developed data acquisition system enabled a sampling rate of up to 20 Hz. However, in this study, the static strain analysis was of particular interest. Thus, the sampling rate was set to 1 Hz, and the duration of each measurement was set to 10 s. After each measurement, the average of 10 measurement points was calculated, and measurements were repeated every one hour. The transmitters and signal repeaters had an integrated power management module through which their operation could be put into sleep mode. This was done to reduce the power consumption, especially that of the signal repeater installed outside, which used a battery as a power source. Sleep mode was automatically activated after each measurement.The sensor array with the connected wireless transmitter was attached to the concrete wall of the gallery using an epoxy-based adhesive sheet a. The deThe analysis of the results showed that all 25 sensors exhibited relatively low drift, even after four months of measurement. However, it can be observed that some of the sensors were more stable than others. For example, in row 7, for sensor 18, the calculated change in the average strain over four months was only −1.9 However, the comparison of sensors in row 1 demonstrates a very uniform output signal; the measured values are almost superposed. The change in the calculated average strain for row 1 is 2.5 per day) . In thisIn the previous experiment, which was recorded on the undamaged surface, the change in the average strain that was calculated from all 25 sensors was 20 r months . This shr months a. The exThe comparative analysis of the data recorded by the sensor array clearly exhibited the impact of the crack on the measured strain values b. The seAmong the analyzed sensors, those in row 5  were exposed to the greatest strains. The results demonstrate that the developed sensing system is fully capable of damage detection. Based on the long-term static strain analysis, cracks were accurately detected and localized. However, it was observed that the strain magnitude between the sensors in row 5 was different. Such differences in strain sensing may occur depending on the orientation of the installed sensors with respect to the crack direction. Strain sensors generally have one sensing direction along which they exhibit maximum sensitivity. In addition, strain sensors are typically calibrated when the entire sensor structure is subjected to uniaxial deformation. However, in the case of a crack, only a small fraction of the sensor covering a crack is exposed to large strains. Thus, sensor measurements depend on the crack orientation with respect to the direction of the sensors in the array and on the extent to which the sensing area of a sensor covers the crack. Therefore, obtaining reliable field measurements for the actual value of a crack opening remains challenging. However, an assessment of whether (and when) a crack opens or closes is possible, as shown in In the recorded data, as shown in As expected, the highest strain change (−196 This study evaluated printed strain sensors based on long-term static strain measurements conducted inside a gravity dam. The analysis assessed the long-term stability of printed sensors and their suitability for practical implementation in static strain analysis within the framework of SHM.The recorded data exhibited an average signal drift of 20 Overall, the printed sensors exhibited good strain sensitivity and relatively low signal drift. The results show that printed sensors incorporated into automated DAQ can be used as complementary sensing systems to those already existing within the framework of SHM.