The middleware framework for IoT collaboration services should provide efficient solutions to context awareness and uncertainty issues among multiple collaboration domains. However, existing middleware frameworks are mostly limited to a single system, and developing self-adaptive IoT collaboration services using existing frameworks requires developers to take considerable time and effort. Furthermore, the developed IoT collaboration services are often dependent on a particular domain, which cannot easily be referenced in other domains. This paper proposes a cloud-based middleware framework that provides a set of cloud services for self-adaptive IoT collaboration services. The proposed middleware framework is generic in the sense that it clearly separates domain-dependent components from the layers that leverage existing middleware frameworks. In addition, the proposed framework allows developers to upload domain-dependent components onto the cloud, search for registered components, and launch Virtual Machine (VM) running a new MAPE cycle via a convenient web-based interface. The feasibility of the proposed framework has been shown with a simulation of an IoT collaboration service that traces a criminal suspect. The performance evaluation shows that the proposed middleware framework runs with an overhead of only 6% compared to pure Java-based middleware and is scalable as the number of VMs increases up to 16. In line with rapid development of the Internet of Things (IoT) technologies, many intelligent IoT services for various domains, such as Intelligent Traffic System (ITS) , smart hAs more complex software systems and diverse devices are involved, developing IoT collaboration services requires more time and effort to handle device-specific or domain-specific components, and self-adaptive features such as context awareness and uncertainty. For example, multiple intelligent systems should detect situational context changes from the unintentional behaviors of users and provide appropriate services with no separate explicit operation, which allows us to achieve more by doing less . BesidesOver the past decades, various studies including MAPE-K cycle ,12,13,14This paper proposes an easy-to-use, cloud-based middleware framework that can be used as a reference framework for self-adaptive IoT collaboration services. This framework clearly separates the MAPE components implementing domain-dependent adaptation logic from the skeleton components for driving the MAPE cycle to support dynamic collaboration reconfiguration. As a result, developers can take advantage of the self-adaptation related capabilities provided by the middleware framework, just by invoking the Application Programming Interfaces (APIs) corresponding to the connector between the general framework and domain-dependent components. Moreover, by creating and managing a dynamically bound Virtual Machine (VM) of the MAPE cycle skeleton and domain-dependent MAPE components on the cloud, it is possible to provide IoT collaboration services anytime and anywhere. In summary, this paper makes the following contributions.Cloudizaion of MAPE cycle for IoT collaboration service: The proposed middleware is one of the first attempts to cloudize the MAPE cycle for self-adaptive IoT collaboration services. The domain-specific and device-specific components are separated from the implementation as much as possible and the interfaces are provided as cloud service APIs to support the easy development of high-performance self-adaptive IoT collaboration services over the clouds.Development of a convenient web-based interface: The proposed middleware also provides a convenient web-based interface that allows developers to easily upload their own implemented components, search existing components, register participant systems/devices and launch a VM for starting each IoT collaboration service. These capabilities can reduce the burden of developers and make them focus on enhancing the quality of a particular IoT service component.Implementation and evaluation on a real testbed: The feasibility of the proposed framework has been demonstrated by simulating an example IoT collaboration service that tracks a criminal suspect. A part of this use case is also prototyped using unmanned patrol cars and CCTVs. It is worthy to note that the proposed framework is not only a conceptual framework but also a workable framework. The benchmarking results show that the proposed cloud-based middleware runs with little overhead of only 6% compared to pure Java-based middleware and is scalable up to 16 VMs compared to standalone applications.The composition of the paper is as follows. Over the past few decades, many self-adaptive middleware frameworks have been introduced. Among them, the most prominent frameworks are TOGAF , RainbowTOGAF  is a proEach of the above self-adaptive middleware frameworks has characteristic contributions, but there is a common limit called solution designed to aim the target of self-adaptation with a single system. Therefore, additional extension work on the adaptation framework by developers is required to support collaboration among multiple systems based on IoT using such frameworks. To solve this problem, recently proposed several studies ,12,13,14The frameworks ,18,29,30Genericity: a generic framework (Generic)/ a specific framework for a target domain (Specific)Abstraction level: just a conceptual architecture framework / an executable architecture framework for a tangible use case of an IoT collaboration service (Concrete)/ both of Conceptual and ConcreteProvided as cloud services: The proposed middleware framework is provided as a cloud service (Yes) or not (No)Service development in a device-independent environment (Yes) or device-dependent environment (No)Among the commented previous studies above, we select ones that suggested an architecture containing specific components for IoT services and compare it according to several distinct characteristics in As is shown in Publish-Subscribe Communication Layer. As is named, this layer provides a high-performance scalable communication among a large number of IoT devices based on the publish-subscribe communication model. This layer delivers newly published data to consumers who subscribe from multiple but different subsets of sensing data simultaneously. MAPE Core Bundle Layer, which implements the connectors between the four MAAPE components, the Publish-Subscribe Communication Layer, and the ParticipantRegistry. The other layer is the IoT Service Bundle Layer, which consists of concrete MAPE components required to control a specific IoT collaboration service. The former layer is provided equally to developers, literally, as a middleware framework, and the latter layer includes the components developed by IoT service developers according to the domain requirements. The components belonging to both layers are in the form of OSGi bundles. Each MAPE cycle for controlling the collaboration of multiple systems and devices is created into one VM in the cloud area. To construct a generic conceptual architecture, we have designed to separate IoT service domain-dependent components from the core MAPE loop components, which are domain-independent parts. Each VM is divided into two layers. One is the IoT Service Launcher by itself works as one of the VMs created in the cloud area like other VMs for implementing IoT collaboration services. To help developers easily manage the IoT Service Bundles, we provide each operation of the IoT Service Launcher in the form of a cloud service. The developers can easily perform a series of tasks until the actual IoT service is launched, including the creation/deletion/start/stop of each IoT collaboration service VM. The addition/removal of a specific service bundle can be done by using the cloud service provided by the IoT Service Launcher as well. The IoT Service Participant Manager provides an auto-registration mechanism of participant systems or devices collaborating in IoT collaboration. Whenever the devices or systems which can participate in an IoT collaboration are power-on, information of the participant is automatically registered to the Participant Registry. The address of the IoT Service Participant Manager should be saved in the devices and systems before. The Adaptation Executor can look up a specific object among the registered systems and devices in the Participant Registry as needed.The The developer accesses the web page provided by the proposed framework and searches required MAPE bundle components to comprise a designed IoT collaboration service.Service Bundle Manager, and the Service Bundle Manager searches the information of bundles stored in the IoT Service Bundle Registry and lists them up on the web page.The search request is delivered to the Bundle Registry, the developer can implement the required bundle component and register it on the web page →pub→pub according to the pub-sub messaging pattern. The purpose of wrapping these repeated messaging sequence with an operation is to reduce the development load of the developer by hiding the information which could be patterned.The specified communication is like the following: a MAPE cycle is activated by an environmental change detected by a particular participant (P1). As a result of analyzing the detected change, a new reconfiguration plan is executed, which instructs a participant system(P2) to perform a specific operation (// 8. Do something) and makes a new system(P3) participate in the collaboration. Among the objects at the top of the sequence diagram, shaded objects indicate the bundle components that are included in the VM and operate in the cloud, whereas the non-shaded objects indicate the participant systems or devices in collaboration through the Registration and search of MAPE bundle using a convenient web interface are supported.Minimize the development efforts by separating concerns from the implementation: explicit design of layers for the domain-independent parts and device-independent parts in the architecture makes developers focus on creating only a specific IoT collaboration specific components.Auto-registration of candidate systems and devices is also supported.The proposed middleware framework is a generic framework which can be adopted by any kinds of IoT collaboration domain and it has the following three unique features: The IoT-related solutions introduced through literature until now belong to the public service domain related to personal safety such as smart city, smart transportation, and smart healthcare. In this vein, the present study also selected the smart public security service as the target domain of the proposed middleware framework as well. Among the smart public security service cases, we design a criminal suspect arrest use case by a collaboration of multiple unmanned patrol cars and CCTVs. The collaboration designed in the use case is an IoT-based self-adaptive service, in that the scope of systems and devices to participate in the criminal suspect arrest is variable depending on the severity of the crime and the escape route of the criminal suspect cannot be predicted beforehand.A theft case was registered in the police agency system, and according to the reporter, the theft suspect is not riding a car.The police agency system registers the theft case report point as the initial location of the theft suspect in global knowledge and creates a collaboration (VM) for tracking the theft suspect. A log for theft suspect tracking collaboration of a similar case in the global knowledge is searched and registered in the global knowledge of the newly created collaboration.The current location tracking radius of the theft suspect is calculated based on the difference between the theft case occurrence time and report time. Then the impression and tracking radius of the theft suspect is sent to the ITS (Intelligent Transportation System). All the images of CCTVs in the tracking radius are analyzed and the transmission of photographs of people who match the impression of the theft suspect is requested.The police agency system notifies the place of theft case occurrence to unmanned patrol cars within +10 km of tracking radius and the locations of traceable cars are identified.Participant Listener to update the current location of the theft suspect. Whenever the Participant Listener detects update, the tracking route is reset by the shortest distance between the escape route of the theft suspect and the current location of oneself through analysis of similar tracking log data in global knowledge.The unmanned patrol cars participating in the tracking activate The ITS receives real-time images from CCTVs within the tracking radius, compares them with the impression of the theft suspect, and identifies the current location of the theft suspect. If it is determined that the theft suspect has been captured by a CCTV, the current location of the theft suspect is updated.Participant Listener for the update of the current location of the theft suspect. If the current location of the theft suspect is updated, the CCTV determines whether the current location of the theft suspect is within the visible range of itself. If it is, the camera direction is adjusted toward the current location of the theft suspect and sends the images of the suspect to the ITS until the suspect movers out of its visible range.The CCTV activates the Steps 4 to 7 are repeated.If the theft suspect is besieged by unmanned patrol cars, or if an official of the police agency decides to close this case because further tracking is no longer meaningful, the use case is terminated.The following is a scenario specification example for the criminal suspect arrest use case depicted in For the selected scenario to be carried out successfully, not only the QoS  issue of the middleware framework proposed in this paper but also the functionality of the MAPE component itself that directly affects goal achievement through actual collaboration must be satisfied. However, it is difficult to test the goal achievement of the scenario by activating multiple unmanned patrol cars and CCTVs in the streets. Therefore, to verify the reliability for the achievement of the collaboration goal of the MAPE component itself, we have constructed a simulation environment of criminal suspect arrest in Java, and the GUI screen for the simulated environment is shown in To verify within which degree of reliability the collaboration goal of criminal suspect arrest can be achieved by the collaboration model between unmanned patrol cars and CCTVs included in the simulation, the behavior logic included in the simulation model implemented in Java was expressed as a model in the form of timed automata using UPPAAL  as shownTo verify the degree of achievement of the IoT collaboration goal for criminal suspect arrest, simulations of the designed model were performed 1000 times while increasing the number of unmanned patrol cars on a 15 × 15 sized map from 1 to 10. Space and cost constraints are too high to prove the feasibility of the proposed middleware framework through the demonstration of IoT service among real unmanned patrol cars, police agency systems, and CCTVs controlled by the ITS. Therefore, we evaluated the functionality of the MAPE components implementing the IoT collaboration service through the construction of a simulated application and a timed automata model considering various environmental variables. The results in Furthermore, we performed prototyping of limited scope to verify the effectiveness of the supportability of the middleware framework for actual communication between devices. We constructed a testbed for the IoT based collaboration by developing prototypes of the unmanned patrol car and the CCTV, which are specified in the arrest of a criminal suspect scenario. We developed 2 unmanned patrol cars with a smartphone and an Arduino smart car. We also made 6 CCTVs with WebCams, Arduinos and Rasberry PIs. IoT Service Launcher is implemented as the form of a cloud service based on PHP [IoT Service Bundle Registry, and then, the bundles are bounded to the MAPE core bundles, which will compose a new VM to control the collaboration. IoT Service Bundle Registry and Participant Registry were constructed in MySQL 8.0 server. We implemented the Publish-Subscribe Communication Layer in the reference architecture using the Mosquitto MQTT (Message Queuing Telemetry Transport) Broker [As is depicted in d on PHP  and Apacd on PHP . The upl) Broker , which i) Broker .Among the various potential situations in the simulated application introduced in In the previous section, we have already shown a tangible scenario for the arrest of a criminal suspect can accomplish the goal by using a simulated application and a probability model checking environment. And, to prove the feasibility of the proposed middleware framework, we have also shown a demonstration of IoT collaboration among multiple participating systems which are supported by the implemented middleware framework.In this section, we discuss the quantitative QoS  evaluation results. We set the two QoS factors to measure the quality of the proposed middleware framework: overhead and scalability derived from the cloudization of the middleware services. In the scenario discussed in Pure Java application: Implementation as a pure Java application in each CCTV controller OSGi bundles in a local system: Implementation as an OSGi-based bundle in each CCTV controllerOSGi bundles in OpenStack: Implementation of a VM corresponding to each CCTV controller in OpenStack. Each MAPE component is an OSGi-based bundle.One feature of the middleware framework proposed in this study is that the bundles for performing MAPE cycles to control IoT collaboration are provided as VMs in a cloud. This feature provides the advantage that IoT collaboration services can be activated anytime, anywhere, but it can cause additional communication overhead through the middleware. To analyze those middleware overheads from cloudization of the IoT collaboration control, we implemented the middleware for supporting the collaboration of CCTVs to track a car in the following three different versions.The graph in The number of participating systems or devices in open IoT collaboration cannot be restricted in advance. For this reason, scalability is a key QoS that must be satisfied by the middleware framework that supports open IoT collaboration. To estimate the increasing trend of overhead that may occur when multiple domains are performed in a cloud, we measured communication overhead between VMs and CCTVs through the middleware while increasing the number of VMs corresponding to CCTV controllers from 1 to 16 in a collaboration scenario among CCTVs. The average values of the measured communication overhead are shown on the graph in The proposed middleware framework support auto-registration of each device, which is a candidate for a participant of an IoT collaboration service. As the number of devices increased, we verified how much averaged time it would take for the middleware framework to automatically register each device at the moment the device is powered on. As in the previous experiment, we added 16 CCTV devices incrementally and measured the average time for registering each device. The result is depicted in Our experiments on the scalability of the proposed middleware framework were limited within 16 CCTVs as there are spatial and budgetary limitations in the construction of a testbed. However, as we found, the result of the two experiments can show that the proposed middleware framework does not have, at least, a serious issue in terms of scalability.In many cases, IoT collaboration services between various systems and devices are continuously provided even when we do not feel them in our daily lives. As a result, the support of middleware framework is essential to detect environmental changes and to re-configure IoT collaboration services as a response to the detected environmental changes at runtime. Although various frameworks supporting self-adaptation have been introduced, it is difficult for experienced developers to easily apply most of the previously introduced frameworks to IoT-based collaborative services because of the issues such as the scope of self-adaptation, generality of applicable domains, and the level of abstraction of the framework itself.To solve this problem, this paper proposed a middleware framework as cloud services, which make developers easily utilize the MAPE cycle in any device, at any time, even though they are not familiar with the mechanism for running the MAPE cycle. It was possible due to the separation of domain-independent mechanisms from other implementation of the IoT collaboration services in the proposed framework. Furthermore, the auto-registration provided by the proposed framework allows developers to focus on implementing IoT collaboration services that are developed without caring about the type of participating devices. The feasibility of the proposed cloud-based middleware framework was demonstrated both by the simulation and by prototyping of a case of a collaboration service among unmanned patrol cars and CCTVs to arrest a criminal suspect. Through this feasibility test, we have shown that the proposed media frameworks can be easily instantiated as frameworks for developing IoT collocation services while being useful as a reference architecture framework. The key quality attributes in an open IoT environment such as scalability and communication overhead were evaluated by using a simple case of the collaboration between CCTVs for tracking a moving car. The amount of overhead incurred by cloudization of the middleware framework was not so severe considering the convenience of services provided by the proposed framework. As future work, we are planning to upgrade the QoS of middleware frameworks by applying the middleware framework proposed in this paper to various IoT collaboration service domains. It is expected that it will be able to contribute to reducing developers’ development burden when constructing a new IoT collaboration service by identifying and reflecting the domain-specific collaboration pattern in the framework itself.


A computationally efficient method is described for simulating the dynamics of the left ventricle (LV) in three dimensions. LV motion is represented as a combination of a limited number of deformation modes, chosen to represent observed cardiac motions while conserving volume in the LV wall. The contribution of each mode to wall motion is determined by a corresponding time-dependent deformation variable. The principle of virtual work is applied to these deformation variables, yielding a system of ordinary differential equations for LV dynamics, including effects of muscle fiber orientations, active and passive stresses, and surface tractions. Passive stress is governed by a transversely isotropic elastic model. Active stress acts in the fiber direction and incorporates length–tension and force–velocity properties of cardiac muscle. Preload and afterload are represented by lumped vascular models. The variational equations and their numerical solutions are verified by comparison to analytic solutions of the strong form equations. Deformation modes are constructed using Fourier series with an arbitrary number of terms. Greater numbers of deformation modes increase deformable model resolution but at increased computational cost. Simulations of normal LV motion throughout the cardiac cycle are presented using models with 8, 23, or 46 deformation modes. Aggregate quantities that describe LV function vary little as the number of deformation modes is increased. Spatial distributions of stress and strain change as more deformation modes are included, but overall patterns are conserved. This approach yields three-dimensional simulations of the cardiac cycle on a clinically relevant time-scale.The online version of this article (10.1007/s10237-019-01168-8) contains supplementary material, which is available to authorized users. The mechanical pumping performance of the left ventricle (LV) depends in a complex way on the ventricular geometry, the passive mechanical properties of the myocardium, the arrangement of cardiac muscle fibers, and the fibers’ contractile force generation. Quantitative understanding of the effects of these characteristics on ventricular function requires the use of theoretical models to simulate the dynamics of the LV. Such models typically employ a continuum mechanics approach in which the active and passive components of stress at each point in the myocardium are expressed as time-dependent functions of local myocardial strain. The equations of equilibrium of mechanical stresses are then solved using approximate methods, subject to boundary conditions that include the external forces acting on the tissue.Three-dimensional models of the LV are typically developed through the application of the finite element method (FEM)  througha defines the focal length of the ellipse. These coordinates are illustrated in Fig. Prolate spheroidal coordinates mentclass2pt{minimWe define the myocardial domain in the reference configuration in terms of its endocardial, epicardial, and basal boundaries. The endocardial and epicardial surfaces are given by f in prolate spheroidal coordinates is described in the supplementary material Section S2. We also define a function The formulation of the bicubic spline functions The myocardium may be deformed by an arbitrary displacement from reference coordinates In this section, we show how three-dimensional volume preserving deformations of the LV wall can be derived, given specified displacements of the endocardial surface. It is emphasized that this analysis is independent of the choice of functions used to describe the shape and deformation. The constraint of incompressibility is directly imposed on the deformation modes. While this assumption is not strictly true  determine the number of basis functions in the Fourier series, and therefore the overall deformable freedom for the coordinate under consideration  is introduced with base vectors in the fiber direction The helical arrangement of cardiac muscle fibers is defined according to observations  representation isMyocardial elasticity is represented using a transversely isotropic material law, referred to as the “Guccione law,” , a length–tension relationship The active contractile force of the cardiac muscle is assumed to act only in the fiber direction Nash :31\docum Sollins . We use ted from .The traction at the endocardial surface generated by LV chamber pressure isFor the system to conserve energy, the LV chamber must be closed to define the cavity volume and work done by motion at the base must be incorporated into the virtual work equations. An appropriate closing surface is difficult to define in prolate spheroidal coordinates, and so the surface entclass1pt{minimat. The total PK2 stress can be expressed asUnder the above assumptions, the virtual work equations  may be wWith these definitions, the virtual work system  yields41Under equilibrium conditions, the time derivatives vanish and the pressure E system  to a nonm. The reference myocardial domain The system ,42 is anficients . The volTo validate the proposed approach, we describe two sets of simulations. In the first, we validate the model by comparison to analytic equilibrium solutions to the strong form equations Malvern :44\documWe verify the variational method solutions using two types of analytic solutions. In the supplementary material Section S12, we evaluate the ability of the model to solve for the deformation of an infinitely extended hollow cylinder. Here, we test the ability of the variational method described in Sect. k system  includinTo illustrate the degree of kinematic freedom that is required for describing cardiac dynamics, we simulate the cardiac cycle in two cases. First, we simulate the full cardiac cycle. Second, we examine the fiber stretch and stress distributions under end-systolic and end-diastolic equilibrium conditions. In both sets of simulations, we compare models that use the Fourier-series deformation modes  with 8, We use simplified lumped-parameter models Below is the link to the electronic supplementary material.


There is scarce literature describing treatment of volar dislocation of the distal radio-ulnar joint (DRUJ). Irreducible dislocation is usually treated surgically. We present the case of a 37-year-old male with acute right wrist pain and loss of pronation. A diagnosis of volar DRUJ dislocation was made. Reduction using conventional technique was unsuccessful. A second attempt was successful by applying pressure over the interosseous membrane of the forearm and manipulating the ulnar head. At three weeks, the patient had minimal pain, a stable DRUJ, and near complete range of motion. This modified technique for reduction of a locked anterior DRUJ dislocation can be used to avoid an unnecessary surgical intervention. Volar dislocation of the distal radio-ulnar joint (DRUJ) is a rare occurrence in the literature, with only 35 cases reported in the literature. Multiple methods of reduction and fixation have been described, ranging from closed reduction to open reduction and internal fixation with suture anchors , 2. TherA 37-year-old right-handed male presented to the emergency department with right wrist pain and decreased range of motion of the forearm following a friendly grappling match. On history, he was mildly intoxicated by alcohol at the time of the injury. His friend had performed an arm-bar holding the patient's right arm between his legs while pulling on the forearm with his hands. The patient tried to escape the maneuver by forcefully pulling and pronating his forearm. He immediately felt pain in his right forearm and was unable to use it afterwards. His past medical history was significant for alcohol, tobacco, and cocaine use. He was not known to be suffering any other medical conditions and had never suffered any injury to his right wrist or forearm in the past. On physical examination, the forearm was locked in supination, with no passive or active pronation elicited. There was loss of the dorsal ulnar prominence, and a palpable and tender solid mass was felt on the volar aspect of the wrist, which was presumed to be a volarly dislocated ulnar head . The skiAfter obtaining informed consent, closed reduction was planned under procedural sedation. The reduction was first attempted by pronating the forearm while applying a posteriorly directed force to the ulnar head. After an unsuccessful first attempt, a second attempt was performed with an assistant applying pressure on the interosseous membrane (IOM) of the forearm using the palm of both of his hands, in an effort to free the impacted ulnar head from the distal radius . With thAt the three-week clinical follow-up, the splint was removed and physical examination was repeated. The patient showed full range of motion of the wrist and elbow in flexion and extension. Compared to the contralateral forearm, there was a 10° lack of pronation and 25° lack of supination. Pain and tenderness were minimal, and no instability could be elicited. Diagnostic imaging confirmed that the reduction was maintained. The patient was discharged from the clinic with instructions for range of motion exercises and avoidance of loading activities for an additional three weeks. No additional follow-up visits were planned.Volar dislocation of the DRUJ is infrequently encountered in practice, with approximately 35 cases reported. Thus, the diagnosis can be initially missed in the emergency department, leading to chronic disability . The priThe usual causal mechanisms of a volar DRUJ dislocation include a fall on an outstretched hand , 13–15, Applying pressure over the IOM in an effort to distract the impacted ulna from the radius proved successful in reducing this rare case of anterior DRUJ dislocation. This modification of the standard reduction technique has, to our knowledge, not been described in the literature to date. The technique can be easily applied with the help of an assistant and avoids the risks associated with open reduction.


In the underlay cognitive radio networks, the main challenge in detecting the idle radio resources is to estimate the power spectrum maps (PSMs), where the radio propagation characteristics are hard to obtain. For this reason, we propose a novel PSMs estimation algorithm based on the generative adversarial networks (GANs). First, we constructed the PSMs estimation model as a regression model in deep learning. Then, we converted the estimation task into an image reconstruction task by image color mapping. We fulfilled the above task by designing an image generator and an image discriminator in the proposed maps’ estimation GANs (MEGANs). The generator is trained to extract the radio propagation characteristics and generate the PSMs images. However, the discriminator is trained to identify the generated images and help to improve the generator’s performance. With the training process of MEGANs, the abilities of the generator and the discriminator are enhanced continually until reaching a balance, which means a high-accuracy PSMs estimation is achieved. The proposed MEGANs algorithm learns and utilizes accurate radio propagation features from the training process rather than making direct imprecise or biased propagation assumptions as in the traditional methods. Simulation results demonstrate that the MEGANs algorithm provides a more accurate estimation performance than the conventional methods. As wireless communication technologies continue to grow, radio resources are facing huge demands. Cognitive radio (CR) technology is an important technology in wireless communications. To achieve better exploitation of the radio resources, the CR transceivers intelligently change their transmitting parameters based on detecting and utilizing the radio “white holes” ,2. The tThe cognitive radio networks (CRNs) play a fundamental role in the applications of the CR technology. There are two main components in the cognitive radio networks: the primary users (PUs) and the secondary users (SUs) . The PUsCRNs typically work on two main modes: the overlay mode and the underlay mode, as shown in Regarding the underlay CR networks, which are also known as the spatial reuse CRNs, CR transmissions are permitted on the condition that the interference from SUs is under certain limits and does not degrade the quality of service (QoS) of PUs due to the attenuation in the propagation paths . This apTo achieve the spatial reuse of the radio resources, SUs have to sense the spectrum and exploit the spatial “white holes” in the CRNs’ region. Herein, the power spectrum maps (PSMs) can be used as a powerful tool to determine the PUs’ signals across a finite geographical area. Based on the estimation result of the power spectrum maps, we can obtain the distribution of the signal strength and estimate the spectrum utilization in a particular region. The power spectrum map can be seen as a visible cartography of the power spectrum. In addition, it is a developing technology that visually overlays power spectrum information on a map, enabling rapid frequency deconfliction and maximizing the utilization of the available spectrum. Many schemes are focused on the applications of the power spectrum maps. For example, in , the autAs for the underlay CRNs, the PSMs portray the primary users’ power distribution in frequency and space ,12. KnowAs shown in The above task is actually undetermined. In fact, there is an infinite number of PSMs functions which can satisfy the known parameters; i.e., there are numerous solutions for the above task. To reduce the solution space of the estimation task, initial efforts have been made for the PSMs estimation by utilizing the prior information or assumptions of the radio environment of the target region. Traditional methods for the estimation task include spatial interpolation algorithms and the basis expansion (BP) algorithm.The conventional spatial interpolation algorithms include the Kriging interpolation ,15 and tThe IDW interpolation algorithm assumes that the power spectrum only depends on the distance Regarding the basis expansion algorithm ,20, the All the algorithms mentioned above are effective in a particular environment. However, the actual radio environment is often complex. Inappropriate or biased assumptions may lead to inaccurate PSMs estimation.G) and the discriminator (D). The strategy of GANs is defining a game between the generator and the discriminator [Deep learning, as the core technology of the artificial intelligence (AI), has unique advantages in power spectrum map estimation. By learning and adjusting the deep neural network’s parameters, the deep learning methods can achieve infinite approximations of any complicated functions. Through extracting the essential characteristics of the radio environment, we can collect all kinds of states and prior information for CRNs by the deep neural network, which makes the PSMs’ estimation more precise and intelligent. Estimating PSMs from secondary users’ PS measurements is actually a regression task. Generative adversarial networks (GANs) are recently introduced as a powerful framework to handle regression problems in deep learning . There aiminator . The genIn this paper, we propose a novel GANs-based power spectrum maps estimation algorithm named maps estimation GANs (MEGANs) for underlay CR networks. First, we analyze and construct the PSMs model of the target region as a regression model in deep learning. Once the power spectrum maps matrices have been normalized and transformed by color mapping, the colored PSMs images are constructed. Through the color mapping process, we convert the PSMs estimation task into an image reconstruction task. We fulfill the above task through constructing an image generator and an image discriminator in the proposed MEGANs. We design the generator based on the analogy of auto-encoders, which is used to exploit the training data set and learn abstract radio propagation features of the target region. Regarding the discriminator, we utilize a deep convolutional structure to identify the generated PSMs images and help the generator to improve the PSMs estimation performance. Finally, as verified by simulations, the proposed MEGANs algorithm provides a more accurate PSMs estimation performance than the conventional methods.Through the process of color mapping, we converted the PSMs estimation task into an image reconstruction task and accomplished it by generative adversarial networks. Utilizing GANs for the PSMs estimation task has not been reported until now.With the analogy of auto-encoders and the deep convolutional structure, we designed the generator and the discriminator of the proposed MEGANs to estimate the PSMs and enhance the estimation accuracy.We extracted and utilized the radio environment features of the target region from the training process by the proposed MEGANs algorithm rather than the traditional methods, which make direct biased or imprecise assumptions about the spatial propagation characteristics. The MEGANs algorithm provides a more accurate estimation performance than the traditional methods, as verified by simulations.The original contributions of our work are as follows:The rest of the paper is organized as follows. In S. The receiving SUs are willing to cooperate in estimating power spectrum maps of the target region under an additive white Gaussian noise with a known variance. Let We suppose that there are Let S.As shown in Equation (3), our task is the following: using the above-known power spectrum relations (Equation (1)) and parameters to estimate the power spectrum maps model (Equation (2)); i.e., the power spectrum maps of region The above task is actually undetermined. In fact, there is an infinite number of PSMs functions which can satisfy Equation . To reduS into S into S according to the power values at different frequencies; i.e., map the power components of different frequencies to different colors uniformly, as shown in Divide the target region The colors of the grids indicate the power value of each location in power spectrum maps. The brighter the color, the bigger the power value is. White squares represent the grids where there are no receiving SUs. The power components in these white squares are exactly our targets that need to be estimated.Through the process of color mapping, we convert the power spectrum maps estimation task into an image reconstruction task in deep learning. Thus, we can use the powerful regression framework—generative adversarial networks, to handle the PSMs estimation task; i.e., we train the GANs to regress for the missing pixels of the incomplete power spectrum maps images.To circumvent the estimation errors from the inaccurate direct assumptions about the prior radio environment information in the conventional methods , we propose a novel GANs algorithm named maps estimation GANs to estimate the power spectrum maps without any direct spatial characteristic assumptions, as shown in r” to denote the real or true power spectrum distribution of the target region, superscript “g” for the generated or reconstructed power spectrum distribution from the generator, “X” for complete power spectrum maps images and “Y” for incomplete power spectrum maps images. Thus, we define the real complete PSMs images as Throughout, we use superscript “Random-block-patches (RBPa): We set pixels inside of Random-block-pixels (RBPx): We independently set each pixel of the input PSMs image to zero with probability Random-block-patches-pixels (RBPax): This measurement function is the superposition of the RBPa and the RBPx.We use S; we choose the RBPax measurement function if there are buildings and streets in the region S. The receiving SUs are uniformly distributed in the streets. The color pixels stand for receiving SUs and the patches stand for buildings where there are no receiving SUs. In fact, we can change and design the measurement functions according to the actual environment and the distribution of the receiving SUs in the target region.The principle that we use in the selection of the measurement functions G denote the generator. We suppose D denote the discriminator. It measures the gap between the real complete PSMs and the reconstructed PSMs from the generator. With the training process of the MEGANs model, the abilities of the generator and the discriminator are enhanced continually until achieving a balance, which means the discriminator cannot tell the reconstructed PSMs images from the real PSMs images; i.e., Let The generative adversarial networks are powerful frameworks to handle the regression problems in deep learning. The two main components of the proposed GANs are the generator and the discriminator.As for the generator, we designed its structure on the analogy of auto-encoders  Figure , which wRegarding the discriminator, we utilize a deep convolutional neural network (CNN) to identify the PSMs images generated and help the generator to improve the PSMs estimation performance, as shown in Input layer: As for the generator, we set the incomplete power spectrum maps images X represents the feature matrix and l represents the index of the convolutional layer. We use W to denote the weights of the convolution kernel and b to denote the convolution offset.Convolutional layer (CONV layer): The CONV layer is composed of multiple filters, which are used to implement convolution operations. Every convolution kernel can be regarded as a feature recognizer. The feature map contains the “features” extracted by each filter from the original images. We set several convolutional layers to extract more abstract and deeper features progressively. For example, front convolutional layers can extract low-level features; middle convolutional layers can extract middle-level features; rear convolutional layers can extract high-level features. We extract and compress the features continuously to obtain higher-level features. In short, the original features are condensed step by step and the final features are more reliable. After processing by the activation function Equation .(4)Xl=fActivation function: The main effect of the activation function is to provide the nonlinear ability of the network. The neural network can only express linear relationships without the activation function, which makes the whole deep neural network equivalent to the single-layer neural network. Therefore, the deep neural network gets the nonlinear mapping ability only when we use the activation function.x represents the feature vector and T denotes the matrix transposition.Fully connected layer (FC layer): The FC layer plays the role of classification and feature combination in the discriminator network. Unlike the CONV layer, which maps the original image data to the local hidden feature space, the FC layer can classify and combine the local features to the globe feature space. After processed by activation functions, the FC layers result in the new feature map, as shown in Equation .(5)xl=fOutput layer: We set the reconstructed complete power spectrum maps images The MEGANs model is an incomplete connected neural network, which consists of the input layer, convolutional layer, activation function, fully connected layer and the output layer. The explanations of the above modules are as follows.The MEGANs algorithm includes two processes: the training process and the testing process.In the training process, the real, complete power spectrum maps images During the training process, the generator is trained to generate a high-accuracy estimation of the PSMs and fool the discriminator; i.e., the generator tries to increase the identification scores of The most commonly used training method of the deep neural network is the back-propagation algorithm . We can As mentioned above, the objective function is the key function for the back-propagation algorithm in the training process. To speed up the MEGANs’ training process and enhance the PSMs estimation performance, we consider the white squares in each incomplete PSM’s image as the image noise or redundant information. We use the image denoising regularization  norm ) as a peThe third term in Equation  is the gM is defined as follows.M and ith row and jth column of the image.The fourth term in Equation  is the tThe TV regularization, also known as the total variation denoising, is a process mostly used in digital image processing. It is based on the fact that images with excessive and possibly false details have a high TV norm. Based on the above principle, reducing the TV norm of the images removes unwanted details and preserves important details, such as edges. Therefore, we add the TV regularization to the loss function for searching for a close match to the original PSM images.S in advance. For example, as discussed in In the supervised deep learning method, we use the known paired data in the training set  to train the deep neural network for the classification or the regression task. The proposed MEGANs algorithm is a supervised deep learning method. Estimating PSMs from secondary users’ PS measurements is actually a regression task. The incomplete PSMs’ images and their corresponding, complete PSM images are the known paired data in the training set. In our MEGANs training process, we regard the complete PSM images as the labels in the supervised deep learning. As for the PSM images in the training set, they should be independent and identically distributed as the images in the testing set. Therefore, we should collect the training complete PSMs’ images from the same or similar radio propagation environment as the PSM images in the testing region S. For example, if the testing region S is the urban area with the quasi smooth terrain, we can use the Okumura–Hata model and/or other similar radio propagation models to generate the training data. In order to help the MEGANs to learn the real underlying radio propagation characteristics and improve the generalization performance, we should use multiple sets of different parameters in the radio propagation models to generate the training data. Furthermore, if we have already collected a small number of real power spectrum maps, adding the generated data into the collected data set to extend our training set is also a good choice.In fact, collecting the training PSMs images or collecting enough PSMs images from the same or similar radio environment is not always an easy task. We should acknowledge that the goal of estimating the high-accuracy power spectrum maps is admittedly very ambitious. However, the PSMs estimation results do not need to be super accurate, but precise enough to identify the spatial “white holes” and the unused bands. This relaxed objective motivated us to choose one or more suitable radio propagation models  to generate the training data according to the radio environment in the testing region The direct visual observation of the PSM images’ reconstruction performance.The power spectrum estimation performance for PUs.The average image reconstruction errors (AIREs) over different numbers of receiving SUs.To examine the effectiveness of the MEGANs-based algorithm, it is necessary to test the performance of the proposed method through some testing indicators. We chose three indicators to test the proposed algorithm:The testing process for the direct visual observation of the reconstruction performance was relatively easy. We input the testing incomplete PSM images into the trained generator and then observed the reconstruction performance. It was an intuitive and qualitative testing method.As for the power spectrum estimation performance, we compared the MEGANs-based estimated power spectrum with the real power spectrum of PUs. The testing result demonstrated the estimation performance for the unused bands based on the proposed algorithm.q frequency points within the transmitting bands of PUs and defined the average image reconstruction errors as shown in Equation AerrIn this section, we describe the test of the estimation performance of the proposed algorithm on the above three indicators in In the practical radio environment, the signal is attenuated in a random fashion. The attenuation is mainly caused by the radio propagation loss, the shadow fading, the multi-path effects, etc. We usually construct the radio propagation loss as the deterministic model, e.g., the Okumura-Hata model, the inverse polynomial law model, etc. In addition, the shadow fading and the multi-path effects are estimated by random models, i.e., the log-normal distribution for the shadow fading and the Rayleigh distribution for the multi-path effects, etc. In our simulations, we use the same deterministic radio propagation model as used in  rather tThe core purpose of the simulations was to test whether the proposed MEGANs algorithm could learn the accurate radio propagation features from the training process rather than making direct imprecise or biased propagation assumptions, as in the traditional methods. In order to exclude the influence of stochastic factors and intuitively show the propagation features learned from MEGANs, we used the deterministic radio propagation model for the propagation features, which can be easily expressed by a formula. Furthermore, the deterministic propagation model was employed for ease of the comparison experiments with the traditional methods. As for the random attenuation models, the MEGANs can also achieve good estimation performance if the training set and the testing set share the same random distribution of the radio propagation features.S into S in the simulations [d denotes the distance between the transmitter and the receiver. Divide region ulations . γtr denS. Suppose there are two active transmitting PUs located at grids  and  in the presence of an additive white Gaussian noise with known variance S, accounting for about 15 percent of all grids. Suppose the primary users transmit random signals. We can estimate their corresponding power spectra based on the periodogram method after sampling the PUs’ signals. In our simulation, we directly set the power spectra of PU1 and PU2, as shown in As for the testing set, we supposed S and use the random-block-pixels measurement model with As for the training set, we emploedy the same radio propagation model but different preselected constants from the testing set. We generated 30,000 training samples from three sets of environmental propagation parameters: For the training process, we summarize the learning parameters as follows: the adaptive moment estimation (Adam) algorithm was used for the MEGANs training; the learning rates of the generator and the discriminator were 0.0001; the total variation coefficient was 0.005; the gradient penalty coefficient was 10 ; the batThe maximum training epoch in our simulations was set to 600, and it produced sufficient convergence on the training data set. The convergence curves of the generator and the discriminator in the training process are shown in jth real complete PSM and the jth generated complete PSM in every training batch. b stands for the batch size. The convergence curve of We define the Euclid distance Equation .(9)dEucAs shown in The convergence curve of the Euclid distance also proves the above convergence analysis about the training process of MEGANs. As shown in To verify the estimation performance of the proposed algorithm, we compared the MEGANs algorithm with the conventional Kriging interpolation algorithm and the IDW interpolation algorithm on the testing set. As for the simulation of the Kriging algorithm, we denote the Kriging with the linear variogram as L-Krig and the Kriging with the exponential variogram as E-Krig. Additionally, we set the power value nd space .We tested the estimation performance of the proposed MEGANs algorithm in three aspects: (1) the direct visual observation of the reconstruction performance; (2) the power spectrum estimation performance for PUs; (3) the average image reconstruction errors over different numbers of receiving SUs.(1)The direct visual observation of the PSMs images reconstruction performance.After 600 training epochs, we input incomplete PSMs images of the testing data set into the trained generator. The PSMs estimation results for PU1 at 25 MHz and PU2 at 75 MHz are shown in Compared with the real, complete PSMs images, the MEGANs algorithm outperforms the Kriging algorithm and the IDW algorithm from the direct visual observation in the estimation results of PU1 and PU2, especially in the area near the PUs. Furthermore, the exponential Kriging algorithm performs poorly for PU1 at 25 MHz because the variogram assumption is of significant deviation from the real data distribution. Furthermore, the reconstructed PSMs images from the proposed MEGANs algorithm are smoother because of the total variation penalty term that we added into the training objective function in Equation .(2)The power spectrum estimation performance for PUs.The power spectra transmitted by PU1 and PU2 are centered at 25 and 75 MHz. They are depicted by the black solid line in The IDW interpolation algorithm assumes that the power spectrum only depends on the distance As for the above two Kriging algorithms in S from the training data set. It should be noted that the training set does not contain the testing set images, as mentioned in The proposed MEGANs algorithm has a better estimation performance because we do not directly assume the prior information of the radio environment but train a generator network to learn the power distribution characteristics in region (3)The average image reconstruction errors (AIREs) over different numbers of receiving SUs.As defined in As shown in As for the Regarding the (a) The measurements data contains little information for the Kriging method in the beginning. The AIREs of the curves decrease from 10% to 20% of the SUs’ grids because of the increase of the measurements data from SUs.(b) The real distribution of the power spectrum measurements shows a relatively big difference from the imprecise variogram assumptions with the increase of the measurements data from 20% to 90% of the SUs’ grids. The AIREs of the curves rise because the more measurement data from SUs, the larger the deviation between the features of real complex radio environment and the Kriging variogram assumptions.In this paper, we proposed a novel power spectrum maps estimation method named maps estimation GANs algorithm for underlay CR networks based on deep learning. On the analogy of auto-encoders and the deep convolutional structure, we designed the generator and the discriminator of the proposed MEGANs to estimate the PSMs and enhance the estimation accuracy. The MEGANs algorithm learns and utilizes accurate radio environment features from the training process, rather than making direct imprecise or biased radio propagation assumptions, as the traditional methods do. Simulation results demonstrate that the MEGANs algorithm provides a more accurate estimation performance than the conventional methods. In our future research, we will focus on the extension of the MEGANs-based power spectrum maps estimation to more practical radio environments; e.g., the shadowing and small-scale fading environment.


The authors describe the case of a patient treated with several cycles of chemotherapy due to an advanced stage non-Hodgkin lymphoma. One daafter the last cycle, he was admitted to our Intensive Care Unit with a septic shock-like clinical picture which didn't respond to the aggressive treatment and the patient died a few hours later. The autoptical findings cast some doubts on the diagnosis, and demonstrated the presence of other factors imitating its symptoms. In this article, the mimickers of septic shock are reviewed and discussed, as some of them require an aggressive immunosuppression instead of the recommended treatment for septic shock. In the last few years, the outcome of patients with hematologic tumors has improved following the introduction of new agents directed against specific receptors exposed on the surface of the neoplastic cells or able to boost the immune capabilities against them, such as the Chimeric Antigen Receptor Modified T-cell (CAR-T) , 2; consThe classical symptoms of SS include fever or hypothermia, tachycardia, arterial hypotension, and other signs related to the MODS making the diagnosis relatively straightforward. Nevertheless, in patients with hematologic cancers causes other that SS can account for this clinical phenotype, including a life-threatening hyper-inflammation associated either to the underlying disease and/or to its treatment. The recognition and treatment of these conditions appear particularly challenging for the intensivist since (a) they are relatively uncommon; (b) they can occur in the very same circumstances of SS and the related symptoms could overlap; (c) the time course can be so fast that the clinical presentation could be represented by an overt MODS just from the onset; and, perhaps most important, (d) the mainstay of the treatment is based on an aggressive immunosuppression, which is contraindicated in SS.Hereby we describe and review a case of a patient treated for a hematologic cancer in whom the admission in ICU with the diagnosis of SS appear to have been too simplistic, because other noninfectious factors may have contributed to the MODS and to the outcome.3 failed to correct the metabolic acidosis. Despite this extremely aggressive approach, the clinical conditions further deteriorated, and the patient died six hours after the ICU admission.A 53-year-old man was admitted to the Emergency Department due to 6-hour-lasting acute abdominal pain; the first CT scan demonstrated an edematous pancreatitis and a small amount of ascites; a second CT confirmed the results at 6 h from the first one. A couple of hours after hospitalization, he was transferred to our Intensive Care Unit (ICU) because he became confused, hypotensive, and anuric. The history revealed an advanced stage non-Hodgkin lymphoma  discovered two months before the current admission and treated with 5 cycles of Rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone (R-CHOP), the last completed the day before the admission in ICU. On a scheduled outpatient visit occurred two weeks before this hospitalization, the patient was prescribed a 10-day course of oral valganciclovir due a reactivation of CMV, but it was suspended after 7 days due to a rise of hepatic liver enzymes and the disappearance of the viral DNA. In the ICU, the patient was intubated and mechanically ventilated; lab investigations demonstrated a deep metabolic acidosis, hyperlactatemia in association with severe leukopenia, and reduced platelet count; these abnormalities worsened in the following hours . With thAt the autopsy, the liver and the spleen were enlarged and a massive purulent peritonitis was present in the absence of visceral perforations despite a severe mucosal ischemia that involved the enteric tract completely in the absence of mesenteric vascular obstructions; the pancreatic head was mildly edematous; the adrenal glands appeared hemorrhagic ; the heaE. coli strain sensible to the administered antibiotics was isolated from the blood culture.Microscopically, the bone marrow presented an extensive hemophagocytic lymphohistiocytosis (HLH) in the absence of residual traces of the NHL ; an E. cThe current Surviving Sepsis Campaign (SSC) guidelines for the treatment of SS recommend the prompt administration of wide-spectrum antibiotics possibly associated with antiviral and antifungal agents in selected cases . HoweverIn our patient, the fulminant course of MODS could have been determined by different factors acting alone or in combination.E. coli in the bloodstream and the severe peritonitis in the absence of perforation supports this hypothesis, even if we could not perform an echocardiography due to the fulminating course of the MODS. The cause of the reduction of the CO is hard to identify, but it could be assumed that it was due to the anti-NHL treatment: actually, doxorubicin and the otheranthracyclines can cause a dose–dependent cardiotoxicity eventually leading to a progressive irreversible heart failure,although cases of sudden-onset cardiogenic shock have also been described [2corresponding to an odd ratio of cardiotoxicity <7% [First, a low cardiac output (CO) could have initially occurred, determining the widespread necrosis of the enteric mucosal and the subsequent escape of bacteria and their derivates from the gut lumen, leading both the activation of septic mediators and the peritonitis. The isolation of escribed –14. In ocity <7% . The difSecond, although an infective trigger for the MODS is highly plausible, the further rapid deterioration of the clinical conditions despite the administration of an appropriate antibiotic treatment makes the presence of other concomitant conditions likely: actually, Vincent et al. demonstrated that in SS patients the death is associated more with a lack of improvement than with an unrelenting worsening of the clinical conditions . Conversde novo hematologic tumors. Considering the interval from the last administration of rituximab, we guess that the profound and unresponsive hemodynamic collapse observed in our patient could be related more to the decrease of immune capabilities determined by the repeated cycles of R-CHOP than to a rituximab-induced anaphylactic reaction.Third, the patient underwent several cycles of a regimen that included Rituximab, a monoclonal anti-CD20 antibody largely used in the treatment of hematologic cancers and other disorders caused by chronic inflammatory conditions and an ever-increasing list of immunologic disorders . The admγ, TNF, lL-6, IL-10 etc., [Fourth, the clinical picture could be ascribed to a hemophagocytic lymphohistiocytosis (HLH). This disturbance of the immune function exists in a familiar and in an acquired form and it is characterized by the massive production and release of inflammatory mediators caused by the dysregulated activation of T-lymphocytes, natural killer (NK)-cells, and macrophages. The familiar form is caused by the mutation of specific genes regulating the cytotoxic granule pathway leading to the impairment of the cytotoxic activity of NK cells and cytotoxic T-lymphocytes while leaving intact the production of inflammatory cytokines, whereas in the latter the underlying mechanism is less understood and has been associated with a number of factors, including rheumatologic and autoimmune disorders, viral infections, and tumors ; altoget10 etc., –21. The 10 etc., , 21. As 10 etc., . In pati10 etc., . The dia10 etc., . To over10 etc.,   antibodies [Fifth, a similar stormy clinical course is described in patients with a catastrophic antiphospholipid syndrome (CAPS), which is determined by the widespread occlusion of the microvascular network by microthrombi triggered by the Lupus anticoagulant (LAC) and the anti-cardiolipin (aCL) and anti-tibodies . Althougtibodies .The diagLastly, it is difficult to establish a cause-effect relationship between the adrenal hemorrhage (AH) and the MODS. Its occurrence is uncommon and is facilitated by physiological and anatomical factors including the elevated adrenal blood flow passing directly from the arteriolar network into the capillary plexus . As a reIn conclusion, it is difficult if not impossible to individuate a single shooting gun responsible for the rapidly fatal MODS observed in our patient almost each potential diagnosis has its own pro- and against- factors  as well β2GBPI when the hemodynamic conditions fail to respond to a sepsis-oriented treatment in order to restrict the immunosuppressive treatment to patients with a defined diagnosis.In patients with hematologic tumors, different factors can determine a MOF, including SS and/or other conditions associated either to the underlying disease and/or to its treatment; actually, it is hypothesizable that the prevalence of these latter will increase with a more widespread use of agents influencing the immune system such as of CAR-T. In our patient, the fulminant course can be likely ascribed to the purulent peritonitis likely determined by the massive bacterial translocation from the ischemic intestinal mucosa, although also other concomitant causes such as HLH could have triggered a massive release of inflammatory mediators. It could be advisable to measure the blood values of some related markers such as ferritin, LAC, aCL, and a


Dewetting is the hydrodynamic process where a uniform layer of liquid destabilizes and decays into distinct patterns of stationary droplets by virtue of interfacial and intermolecular energies. These patterns can now be predicted theoretically, and their evolution can be followed numerically in striking similarity to experimental results. The droplet arrays observed during the quasistatic evolution are generated by two distinct types of instabilities: droplet shedding of moving liquid rims and satellite droplet pinch-off during the decay of stationary ridges. The mechanism causing the emergence of different droplet patterns is the dissipation at the liquid–solid interface modeled by an effective Navier slip. Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns. The no-slip condition is widely accepted as an appropriate boundary condition for flows of Newtonian liquids sheared along a solid surface. A notable exception arises in the presence of a moving contact line between a viscous liquid and a rigid solid substrate, where the use of the no-slip condition leads to a nonintegrable singularity in the stress field , 2. In t3For retracting rims as they emerge after a hole or trench has opened, the magnitude of slip has a direct impact on the dewetting dynamics. When the slip length is very small or zero, the retraction rate is independent of the size of the growing rim and hence, approximately constant, except for logarithmic corrections . For sling) rate , which hng) rate –15. In bng) rate –18, but ng) rate . As a cong) rate . EventuaThe evolution of the polymer melts during these dewetting regimes from early stages after hole formation to the late stages of rupture of the ridges, where the hole boundaries meet, is most appropriately modeled by thin-film models. A systematic asymptotic derivation from full Navier–Stokes equations , 23 explWhile thin-film models have been shown to be of great advantage for the analysis of free boundary problems, predicting the evolution over long time and large spatial scales deep into the nonlinear regimes is still a major computational challenge. The primary problem is to resolve the length scales associated with nanoscopic residual layers that remain after the film has dewetted, typically about In this article, we present a numerical algorithm that is able to answer this need featuring a strategy for local adaptivity and an optimized treatment of the intermolecular potential. We will show that the difference in slip lengths indeed leads to the instability patterns seen in experiments. Our numerical solutions also confirm the Rayleigh–Plateau-type instability of the residual ridges during the late phases of the dewetting for both cases, the no-slip and the intermediate-slip cases, with similar wavelengths at the onset, which had been predicted previously based on a linear stability analysis , 20. SimOur numerical method allows us to follow the evolution until rupture and predicts significant morphological differences. In particular, it reveals that, for the no-slip case, the breakup is accompanied by the formation of a cascade of satellite droplets that has never been studied before in this context. Moreover, for the intermediate-slip regime, no satellite droplets appear. Interestingly, a closer look at experimental results confirms these predictions. In other contexts, such as liquid jets or fluid filaments, formation of satellite droplets during rupture is well known, and their destabilization was observed to have a rich structure of intermediate asymptotic regimes  was prepared (ii) the cleaned Si wafer was dipped into a solution of a fluoropolymer layer .Hydrophobic Si wafers were achieved by two different preparation methods: Dewetting is initiated by heating the glassy polymer film above its glass transition temperature. The dewetting of the retracting straight fronts was monitored in situ by optical microscopy on a heating plate (Linkam) or by atomic force microscopy .The dewetted distance was typically obtained from optical micrographs. In AFM experiments, the dewetted distance can also be calculated from 3D scans of the rim on the basis of volume preservation. The values resulting from both approaches were checked for consistency.Slip lengths have been calculated using the rim profile analysis method , 54; strIn For the remaining part of the paper, we will only consider experiments that can be captured with a no-slip (AF1600 coating) or intermediate-slip (DTS coating) regime with PS(13.7k) or PS(10.3k) and use corresponding theoretical models with cubic We now explain the intricacies of numerically resolving the multiple length scales of the problem. We focus on the two cases of no slip and intermediate slip, as most of the experimental results regarding the various instabilities fall into either of these two regimes.Our solution of the thin-film model in equation 5 is multmulation 10a. EvalThe FEM constitutes a method for the construction of a finite-dimensional subspace The precursor thickness ϕ″ > 0 for To allow the control of the minimum and the derivatives of rs h⋆,ε⋆ , in part studies , 57 thatWe still need to specify the initial data To study the systematic effect of the slip boundary condition on dewetting patterns, we study the contact line instability of moving rims and stationary ridges for the mobility functions Toward the final stages of dewetting process, for long times and domain size far beyond terature , 24, 26.SI Appendix , SI Text and Figs. S1–S3, we present the details of the linear stability analysis and show that solutions of the nonlinear problem follow the predicted exponential amplification while the linear regime is valid. Furthermore, we checked that the alternative choice of potential To study the instability of a capillary ridge, we first compute a 1D stationary solution se state , 51. We However, we are interested in using the numerical simulation as a tool to observe features in the nonlinear regime that are distinctive features of the mobility law. Therefore, to resolve finer features of the ridge shape , the general form of the intermolecular potential is the same, but we use a smaller We now consider nonlinear simulations using the stationary ridge with very small monochromatic perturbations as initial data. Specifically, we consider an unstable perturbation with As long as the perturbations are small enough, the evolution of the corrugations in the nonlinear model closely follows the predictions from the linear stability analysis. After the perturbations become comparable with the size of the rim, nonlinear terms become relevant, and the growth rate changes.Regarding the morphological evolution of the ridges for the no-slip and intermediate-slip cases, our numerical simulations show qualitatively and quantitatively very similar behavior during the linear regime. However, deep into the nonlinear regime, the breakup into droplets follows different scenarios. In the no-slip case, a cascade of satellite droplets emerges, while for the intermediate-slip case, they disappear. Starting with the same initial condition, the evolution for both cases is shown in We have introduced a highly adaptive finite element-based numerical approach that correctly captures the complex dewetting process described by a class of thin-film models with degenerate mobilities. We showed that, for the no-slip condition, the droplet pinch-off is absent during the retraction of the rim, while for the intermediate-slip case, self-repeating droplet pinch-off occurs in excellent agreement with experimental observations. The ability to resolve the different length scales for long timescales also enables the prediction of phenomena, such as the formation of satellite droplets, as a function of the mobility. The emergence of satellite droplets is well known during the break up of liquid jets and the related problem of liquid filaments. For the latter problem, destabilization is due to the difference in the axial contribution to the capillary pressure between thicker and thinner parts. In this system, the pressure is higher in the thinner parts and squeezes the liquid into the bulges, thus increasing the perturbation until the filament breaks up. Apart from the huge literature on experimental studies, the problem has sparked numerous numerical and analytical investigations , 60, 61.For the situation of a ridge that destabilizes on a solid substrate, the additional influence of the substrate enters the linear stability analysis, in particular through the contact angle dynamics. It will be interesting to investigate analytically the rupture behavior for this problem to help understand the influence of the boundary condition at the substrate. Similarly, it remains an interesting open question how the dissipation due to a dynamic contact angle would affect the whole pattern formation process. Such a study would certainly require even more sophisticated finite element techniques , 64.The decision about the pathway leading to specific droplet patterns is then often decided by the specific influence that the dissipation has on flow instabilities. In this study, these instabilities are the shedding of droplets from moving rims and the symmetry of the Rayleigh–Plateau instability leading to satellite droplets, and they are influenced by the magnitude of the interface dissipation encoded in the Navier slip condition.We conclude that, by controlling dissipative effects in this dewetting films system, we can steer pattern formation without changing the driving forces.Supplementary FileSupplementary File


Lack of fusion can often occur during ultra-thin sheets edge welding process, severely destroying joint quality and leading to seal failure. This paper presents a vision-based weld pool monitoring method for detecting a lack of fusion during micro plasma arc welding (MPAW) of ultra-thin sheets edge welds. A passive micro-vision sensor is developed to acquire clear images of the mesoscale weld pool under MPAW conditions, continuously and stably. Then, an image processing algorithm has been proposed to extract the characteristics of weld pool geometry from the acquired images in real time. The relations between the presence of a lack of fusion in edge weld and dynamic changes in weld pool characteristic parameters are investigated. The experimental results indicate that the abrupt changes of extracted weld pool centroid position along the weld length are highly correlated with the occurrences of lack of fusion. By using such weld pool characteristic information, the lack of fusion in MPAW of ultra-thin sheets edge welds can be detected in real time. The proposed in-process monitoring method makes the early warning possible. It also can provide feedback for real-time control and can serve as a basis for intelligent defect identification. Edge joint weld is a type of welding joint that is commonly used in ultra-thin-walled (thickness ≤ 0.15 mm) precision metal parts and components in industries of aircraft, aerospace, nuclear power, petrochemical, metallurgy, etc., such as the bellows-type accumulator in launch vehicle ,3. TheseThe edge welding of ultra-thin sheets is very sensitive to the changes in both heat input and heat sink. Lack of fusion, as a one of the most serious defects in edge weld, can often occur during the welding process ,7, and sAt present, the defect detection for ultra-thin sheets edge welds in industry mainly rely on post-process non-destructive inspection. There is an urgent need to improve the detection efficiency and reduce the labor intensity. Taking the bellows components in aerospace accumulators as an example, the edge welds of the component are tiny and numerous, and have strict demands on weld quality and sealing property. A series of expensive, time-consuming, and labor-intensive weld inspection are carried out for the edge welds, including appearance inspection, dimension measurement, mechanical property test, hydraulic seal test, and air-tight test ,8,9.In-process defect monitoring/detection can indicate the presence and location of potential defects for guiding post-process inspection, and significantly improve the detection efficiency ,11,12,13During processes of arc welding and laser welding, various types of sources can provide online information relevant to the weld quality, such as arc voltage , weldingSo far, the researches on weld pool visual sensing for in-process process monitoring and defect detection are mainly focused on the visualization of weld pool in a macro scale and targeted at LBW, GTAW, K-PAW, and GMAW. Few of their methods are available for the observation or monitoring of a dynamic meso-scale weld pool in strong arc lights condition. To our knowledge, far too little exploration and systematic investigation have been reported in literature on the in-process defects monitoring or detection in MPAW of ultra-thin sheets edge welds.The primary objective of this study is to investigate the feasibility of achieving in-process monitoring of lack of fusion in MPAW of ultra-thin sheets edge welds by using machine vision approach. We focus on the following aspects:• Micro-vision sensing of dynamic meso-scale weld pool in condition of strong arc lightsUnlike the welding process of other types of weld, an edge welding of foil-thickness metal sheets using MPAW has high intensity arc lights radiation and a very small weld pool with a diameter generally less than 0.3 mm. A fundamental and key issue to achieve effective visual sensing and reliable defect detection during MPAW of ultra-thin sheets edge weld is to build clear imaging conditions for the dynamic weld pool at the meso scale. To sense such weld pool using the vision methods requires a high magnification optical detecting technique with proper optical filtering approaches. In addition, the plasma arc length is normally kept between 0.5 and 2 mm to obtain consistent weld quality, the weld pool can only be observed at a quite small angle to weld surface due to the block and limitation by the plasma welding torch nozzle. As a result, to ensure that the entire weld pool can be imaged clearly at the meso scale, a vision system that has an enough deep depth of field (DOF) is also necessary. However, it is a complicated and difficult task to balance the conflicting demands of the weld pool visualization for high optical magnification and deep DOF of vision sensor.• Real-time image processing and features extraction of pulsed current MPAW weld poolThe reliability and the real-time performance of defects detection heavily rely on image processing and understanding techniques. However, image quality can be easily degraded by the complex and time-varying disturbance that is introduced by the pulsed arc lights and specular reflection of weldment surface during pulsed current MPAW process. This will directly affect the accuracy, reliability, and algorithm speed of the features extraction. How to reduce these interferences and achieve characteristics extraction with an acceptable efficiency are the critical issues that need to be addressed. • Relation between weld pool behaviour and lack of fusion in MPAW of ultra-thin sheets edge weldThe physical processes of both arc welding and laser welding have already indicated that there is a certain correlation between optical features and geometrical feature. It is expected to predict welding quality, and especially some weld defects by establishing the mapping relation model. For the MPAW process of edge welds, the understanding of weld pool surface tension, fluid flow inside the weld pool and the mechanism causing lack of fusion are still very limited. To achieve in-process detection of lack of fusion and to provide a basis for a better knowledge of the weld pool thermo-physical behavior in the edge welding, it is essential to establish the relations between the changes in weld pool characteristics and the presence of a lack of fusion.In this study, a passive micro-vision sensor based on object-side telecentric optical design was first developed to acquire highly magnified and enough clear images of the dynamic mesoscale molten pool during MPAW of ultra-thin sheets edge welds. Then, an image processing algorithm based on symmetric nearest neighbor filter (SNNF) and Otsu’s method was proposed to extract geometrical characteristics of molten pool from the acquired images in real time. Finally, welding experiments were carried out with 304 stainless steel diaphragms of 120 μm thick to provoke the generation of lack of fusion defects by different perturbation factors. By using the proposed visual monitoring approach and the scanning electron microscopic (SEM) analysis technique, the relations between the weld pool characteristics parameters and the lack of fusion in edge welds were investigated and a promising indicator of the lack of fusion was found. The lack of fusion in MPAW of ultra-thin sheets edge welds can be detected in real time by using such weld pool characteristic information. The proposed in-process monitoring method makes the early warning possible. It also can provide feedback for real-time control and can serve as a basis for intelligent defect identification.As shown in L denotes the magnification lens, and D stands for diameter of the entrance pupil. Object point B1 and B2 are in the two sides of object plane N separately, and the image point B1’ and B2’ are also in the two sides of image plane N’. Object distance and image distance are, respectively, p and −p. The projection of B1 on N’ is circle of confusion Z1’, and the projection of B2 on N’ is circle of confusion Z2’. The Z1 and Z2 are conjugate sections of the Z1’ and Z2’, respectively. Unlike the commonly used pinhole model in machine vision, a small aperture stop is placed at the image-side focal point of the magnification lens f0, thus only the light rays parallel to the optical axis from the object side are allowed to pass through the aperture stop and form the image on N’. Ignoring the distortion, this imaging model can be expressed byWX, WY, WZ]T is the coordinate of the object point P in the world coordinate system {W}. T is the coordinate of P’s image point in pixel coordinate system {P}. ε is the effective magnification of the lens. Δu and Δv are the unit metric lengths of a pixel in the u and v directions, respectively. θ is the skew angle of the imaging sensor pixel array. Denote CRW and CtW as the rotation matrix and the translation vector of the transformation from the world coordinate system {W} to the camera coordinate system {C}, respectively, the  and  are the first two rows of the rotation matrix CRW, and xt and yt are the first two elements of CtW.In our micro-vision sensor, a design that is based on object-side telecentric optical model  is used.1 + Δ2) introduced by high optical magnification lens can be improved somewhat. The entrance pupil is located at infinity on the object side, and an orthographic projection of objects in the world space is produced. This solves the problem of image magnification variation with object distance, which cannot be ignored in the precision detection of micro objects. The band-pass optical filter is used to reduce the interference from the strong arc light during the MPAW process, for obtaining images of weld pool region with enough signal-to-noise ratio.In this model, the aperture stop setting allows for a smaller aperture angle of light rays to emerge from the object side and a smaller circle of confusion to be formed on image plane. Therefore, the shallow DOF  are defined as the characteristic parameters of weld pool. Particularly, parameter mW and Parameter mL represents the maximum width and length of the weld pool, respectively. Parameter C represents the centroid coordinates of the weld pool in the pixel coordinate system {P}. As shown is I1. The steps of the algorithm are as follows:I1 are calculated. The window that has the maximum sum is selected as the ROI, so that it can include the entire weld pool region. The ROI can help to exclude part of arc and spatter as well as reduce the computational effort. Denote the ROI as R1.Selection of the region of interest (ROI). The sums of intensity values in sliding windows within the image Contrast stretching. The operation saturates the bottom 1% and the top 1% of all pixel values, and it maps other pixel values linearly.N1. Noise reduction with the SNNF. The SNNF  is a twoImage segmentation with Otsu’s method. Otsu’s method  calculatS. As a result, the weld pool can be identified. Search of the maximum connected domain, namely Extraction of the weld pool contour and features. A feature extraction algorithm for images that are captured by the above sensing method was proposed to detect the edges and geometrical characteristic parameters of weld pools. The feature extraction algorithm was written in C++ and OpenCV library. Denote the captured original image as mW can be calculated by:u and v denote horizontal coordinate and vertical coordinate in pixel coordinate system, respectively.The parameter mL can be calculated by: The parameter cu and cv, namely centroid coordinates, can be figured out by: A is the number of pixels in region S, which represents the area of weld pool.The parameter The schematic diagram of micro plasma arc welding experimental system is shown in mW, m,L and uc show their obvious sensitivity to the presence of this defect respectively. Particularly, the curve of uc showed a significant change during the same period of time, rising sharply to reach a peak value, and then return back to the value close to normal gradually. There are no conspicuous variations but smooth fluctuations in the curve of vc. The curves of mW and mL present similar trends of fluctuation where the defect occurred, which decline rapidly first and then return gradually. It is also observed that the curve of characteristic parameter mL fluctuates more severely than other parameter curves during the whole welding process, which can probably ascribed to the fact that its feature extraction is disturbed by the time-varying arc light reflected by solidified weld metal at the rear of molten pool.During practical ultra-thin sheets edge welding, impurities or oxides existing on the pool surface can cause unstable arc and significantly affect the surface tension of melted joint edges, and as a result give rise to the lack of fusion. Careful cleaning procedures to remove surface contamination on workpiece before welding is necessary to decrease the occurrence of such impurities and oxides. In the first experiment, the workpiece was not cleaned before welding in order to obtain a surface-contaminated edge weld. cu and vc are highly sensitive to the occurrence of these defects of lack of infusion. The curve of uc presents obvious fluctuations that rise firstly and then fall during the formation of each defect. It is noteworthy that a similar trend of variation, with smaller peak value, was also observed in the curve of vc. This result may be related to the perturbation on the plasma arc caused by the changing weld joint gap due to the excessive fit-up tolerance. The monitoring results indicate that the curves of mW and mL present some abnormal and irregular variations during the whole welding process, respectively, but the significant abrupt changes or singularities in both feature curves do not necessarily correspond in time domain with the presence of these defects.In the edge welding of a 0.12 mm thick aerospace accumulator bellow, a maximum allowable joint gap width is 0.024 mm to ensure that both joint edges are in good contact and that both edges melt simultaneously and fuse together into a smooth fusion weld. In addition, a fit-up tolerance of 20% the sheet thickness is also required in order to prevent warping of the joint. Even so, variations in joint gap width may happen for some unexpected disturbances and lead to lack of fusion in succession, which need to be detected in early time. In the second experiment, a decreased fit-up accuracy was used to cause joint gap variations. uc demonstrates the best performance in indicating the presence of lack of fusion. The curve of vc also presents a strong relationship with these defects, though a few of its peaks are relatively small. This phenomenon indicates that a fluctuation of the weld pool position in the direction vertical to weld seam has taken place in the generation of each defect, which can be attributed to the arc instability caused by weld misalignment. Especially, there are only few correspondences between the significant changes in the curve of mW or mL and the occurrence of these defects. The reason for this is not clear, but it may have something to do with the instability of molten pool intensified by the asymmetry thermal distribution on the workpieces or the process disturbance from molten metal flow around the neighbouring defect.High positional accuracy is needed in MPAW of ultra-thin sheets edge weld, but in the continuous industrial manufacturing process it is quite difficult to position the workpieces with sufficient accuracy for every weld. A small offset can result in lack of fusion because the edge welding has a low tolerance to the asymmetry of thermal distribution in the workpieces. In the third experiment, the lateral offset between the torch axis and the weld seam center are set to 0.3 mm before welding by adjusting the rotary table position. The Steenbeck’s minimum principle (SMP) is widely used in the study of arc discharge plasmas, and it can be broadly understood as follows: The arc discharge steadily with a column radius that the axial electric field in the arc attains the minimum value under the given current and boundary conditions. It means that any change in the radius resulting from external interference will leads to a unstable arc, and the unstable arc will vary in a way that the axial electric field in the arc attains a minimum value. This principle has been proved by numerous practices and extensively invoked in investigations on many gas discharge phenomena, in particular, cylindrical arcs.uc has exhibited obvious coincidence with the presence of lack of infusion. It indicates that the lack of fusion caused by these different physical origins is all related to the fluctuations in weld pool position, which result from the deflection of plasma arc during the welding processes. A possible explanation for this complex physical process is that the surface contamination, variation in the joint gap width, and weld misalignment can all lead to a disturbed plasma arc. Due to the arc discharge mechanism based on SMP, the disturbed plasma arc is deflected along the welding direction from its normal path and gives rise to the great fluctuation in weld pool position. The edge weld located underneath the plasma torch cannot be uniformly heated so that the weld fails to correctly melt and solidify. As a result, the lack of fusion is formed. A typical example of the dynamic change of weld pool during the formation of lack of fusion can be intuitively and clearly seen from the As can be seen from the above results, the fluctuation in characteristic parameter cu. The reference signals have been previously monitored and recorded during the welding processes with sound welds, respectively. Both the monitoring signals and the reference signals were filtered by using the simple moving average method to reduce noise. The corresponding thresholds are given by:M smoothed reference signal samples, respectively, which are calculated by:m = 1, 2, …, M is sampling number and m-th sampling values.It can be observed that all of the defects formed in these welding processes were detected based on STDM, as the monitoring signal exceeded the established threshold value where each defect presence was verified. uc. The lower the k of K consecutive sample points are out of tolerance. Thus, in practical applications, the sensitivity of our monitoring system to defects detection can be modified by operating three parameters: k, K, and By adjusting the value of mW, mL, uc, and cv have different degrees of sensitivity to lack of fusion. The great fluctuation in u-coordinate of weld pool centroid (cu), which stands for an abrupt change of weld pool centroid position along weld length, was considered to be the most favourable indication for the presence of lack of fusion. The proposed in-process monitoring method using machine vision provides a powerful means of detecting lack of fusion in ultra-thin sheets edge welds during the MPAW process, which makes the early warning possible, and it can provide feedback for real-time control and serve as a basis for intelligent defect identification. Further research should be undertaken to the further development of the micro-vision system and its applications in detecting other weld defects and imperfections occurred in ultra-thin sheets edge welding, like humping weld or uneven weld bead. Also, more systematic process monitoring approaches need to be investigated by means of combining machine vision with other sensing techniques, like arc sensing and multi-spectral sensing, which would be helpful in defects identification and better understanding of defect formation mechanisms.In summary, the results of this study indicate that the characteristic parameters (1)The developed micro-vision sensing system can overcome the strong arc disturbance and the trade-off between optical magnification and depth of field. Thus, the morphology of mesoscale weld pool and its tiny dynamic variations can be successfully observed and stably monitored in MPAW of ultra-thin sheets edge welds, which are crucial for reliable process monitoring and defects detection. The resolution of the images is 6 μm/pixel by camera calibration. (2)The proposed image processing algorithm based on SNNF and Otsu’s method is applicable to effectively extract geometrical features from the acquired weld pool images, e.g., maximum width, maximum length, and centroid position of weld pool, which have close relationship with the weld bead formation and defects. The processing time is less than 10 ms per frame, which is enough to satisfy the demands for monitoring and detection in real time.(3)u-coordinate of weld pool centroid (cu) shows obvious coincidence with the occurrence of the defects caused by various factors.The variations in extracted characteristic parameters during MPAW process show various degrees of sensitivity to the weld defect of lack of fusion. Particularly, the change in weld pool centroid position along weld length is found to be a promising indicator of the lack of fusion, as the fluctuation in (4)cu, the presences of lack of fusion defects in MPAW of ultra-thin sheets edge welds can be detected in real time. The proposed in-process monitoring method makes the early warning possible. It also can provide feedback for real-time control and can serve as a basis for the intelligent defect identification. It is expected to be applied in edge welding of precision metal parts and components in the industry of aircraft, aerospace, nuclear power, petrochemical, etc., and it is especially suitable for the welded bellows and micro pipelines.By using the characteristic parameters This paper proposed an effective vision-based weld pool monitoring method for detecting lack of fusion during MPAW of ultra-thin sheets edge welds. The main conclusions are summarized, as follows: