Capability-based planning as an approach to defense planning is an almost infinitely complex engineered system with countless nodes and layers of interdependency, influenced by state and non-state diplomatic activities, information, military and economic actions creating secondary and third order effects. The main output of capability-based planning is the set of capability requirements needed to achieve the expected end-state. One revitalized qualitative technique that allows us to gain insights into unstructured and fuzzy problems in the military is wargaming—in its simplest form this involves manual wargaming. At the same time, there has been a push to bring computer assistance to such wargaming, especially to support umpire adjudication and move more generally towards full automation of human elements in wargames. However, computer assistance in wargaming should not be pushed, regardless of cost, towards quantitative techniques. The objective complexity of a problem often does not allow us to replicate the operational environment with the required fidelity to get credible experimental results. This paper discusses a discovery experiment aiming to verify the concept of applying a qualitative expert system within computer assisted wargaming for developing capability requirements in order to reduce umpire bias and risk associated with their decisions. The innovation here lies in applying system dynamics modelling and simulation paradigms when designing the theoretical model of capability development, which forms the core of the expert system. This new approach enables qualitative comparisons between different sets of proposed capability requirements. Moreover, the expert system allows us to reveal the effects of budget cuts on proposed capability requirement solutions, which the umpire was previously unable to articulate when comparing individual solutions by relying solely on his own knowledge. Players in the wargame validated the proposed concept and suggested how the study might be developed going forward: namely, by enabling users to define their own capabilities and not being limited by a predefined set of capabilities. Information gathering through data processing and its transformation into knowledge is a critical aspect in decision-making ,2. The cQualitative and quantitative methods to study the problem form two basic families of approaches that can benefit from each other . WhetherThe next part describes firstly the status quo of military defense planning as the main subject of the study, and secondly elaborates on wargaming as the primary applied qualitative method of the study. This is followed by a review of the literature on quantitative methods applied in defense planning or related domains, demonstrating its current limitations. In their general experience of war, nations have learned that it is resource- and time-effective to prepare themselves in advance to protect their national interests. Defense planning is one way of doing this. In the early 1960s this area of planning was discussed at the US DoD when facing the challenge of finding a military forces structure to satisfy US political guidance . The samLeaving the Cold War era behind, NATO decided to engage more in crisis response operations and to rebuild their defense capabilities to fulfil the corresponding spectrum of military as well as non-military tasks. The practical result of this shift, embodied in the NATO Defense Planning Process (NDPP), is that output of this process is a set of capability requirements instead of list of required forces . This apEven though NATO nations as well as their partners have been encouraged to synchronize their processes with NDPP, i.e., to orient towards capability planning instead force planning, there are still states whose defense planning remains primarily fixated on force planning . The CBPNATO defines military capability as the ability to create an effect by employing an integrated set of aspects, categorized as doctrine, organization, training, materiel, leadership development, personnel, facilities, and interoperability . Hinge dNational political guidance, in parallel with strategic analysis that predicts the political and military climate at a 20-year horizon, starts the CPB process and forms scenarios at the strategic level describing the future operational environment. Selected scenarios create stimuli for a wargame that generates capability requirements covering all potential threats and national political ambitions. A comparison is drawn between current forces and required capability, producing capability gaps. A capability development plan contains milestones for each capability development, driving all mid- and long-term military investment. Capability development assessment creates feedback to the CBP through updated political guidance reflecting the necessary changes in capability development .Spiegeleire specifies the trends in capability-based planning, clearly articulating the need to have more insight on the defense planning process in the complex operational environment of the future .Qualitative approaches for investigation involve open-ended questions and personal definitions or interpretations in order to describe or understand an event . In the Historically, wargames are a military staple. In the 5th century B.C., Sun Tzu introduced Wei Hai (encirclement) as a fundamental tool for understanding concepts in the Art of War. The most serious advance in wargaming occurred, however, thanks to the efforts of George Heinrich Rudolph Johann von Reisswitz, who pioneered realism in his kriegsspiel .The following definitions of a wargame enable us to formulate its fundamental elements and helps us understand the study methodology.Perla defines a wargame as: “A warfare model or simulation, using rules, data, and procedures, not involving actual military forces, and in which the flow of events is affected by, and in turn affects, decisions made during the course of those events by players representing the opposing sides .”NATO (2015) defines a wargame as: “A simulation of a military operation, by whatever means, using specific rules, data, methods and procedures .”Red Teaming Guide (2013) defines a wargame as: “A scenario-based warfare model in which the outcomes and the sequence of events affect, and are affected by, the decisions made by the players .”Even if these definitions emphasize different elements of wargames, together they form the fundamental elements of a military wargame. The wargame (WG) scenario is the scene opener for the players. It is an exhaustive description of the scene and it contains geopolitical information about the area of operation, describing political, military, economic, social, information, and infrastructure (PMESII) factors. A WG order of battle (ORBAT) contains the capability of your own forces and its characteristics. WG maps and charts create the interface between the scenario and the players. It is an extra add-on to the scenario, immersing players into the operational environment. The WG clock is the driver of the flow of the game. It should reflect needs of the objectives and the players. The WG rules and data create boundaries for the players’ moves and the decision-making process and are enforced by the umpire during the game. WG players give the wargame its dynamic quality. They manage the planning and decision-making process. Typically, there are two teams of players—blue and red. WG analysts study the results of the wargame’s execution, develop arguments to support the umpire in his decision and imposed analytical questions. The WG umpire rules over the executed plans of the players. The umpire is the main enabler of the successful cognitive sub-phase of the wargame. He is in charge of formulating the achievements, setbacks and limitations that follow from the execution of a single wargaming cycle. For further reading on wargame elements and the wargame life cycle in the military domain, refer to the Wargaming Handbook . For theThe aforementioned definitions of WGs have a single commonality—the use of modelling and simulation (M&S). Every WG requires the replication of the operational environment in a manner corresponding to the maximum approximation of reality. Modelling processes create model of an operational environment and the model’s behavior is scrutinized in the simulation by the execution of the model in time. Simulation stimulates the players: the wargaming environment first forces them to employ their creativity in the wargame planning phase, and second it forces them to learn in the game’s cognitive phase.There is no single WG classification accepted by the WG community. The Guide for Understanding and Implementing Defense Experimentation classifies WGs based on the form of the simulation type . The RedA manual WG (MWG) does not have any computer means involved in executing the WG. Human-in-the-loop simulation represents the manual WG, where the operational environment, courses of action, and effects are all fully controlled by humans. A MWG analyses an unstructured problem representing a complex system with a high level of fidelity to human behavior because it does not replace any WG human element. The fully automated WG (FAWG) has all WG human roles, like umpire, player and analyst fully automated. The closed-loop simulation with an automated analyst represents FAWGs. There is no human intervention in FAWGs, and to the authors’ best knowledge there is no such solution available. If a FAWG was implemented using state-of-the-art artificial intelligence technology, it would have low fidelity to human behavior. Computer-assisted WG (CAWG) automates specific WG human behavioral elements. As more human behavior elements are automated in CAWGs, fidelity to human behavior decreases.Therefore, a MWG tends to be the more qualitative technique to discover information employing high levels of creativity; conversely, a FAWG represents a quantitative way to analyze a problem by a hypothesis testing. By decreasing levels of complexity, we are able to use more quantitative approaches to study a problem and vice versa.The following examples depict the status quo when it comes to qualitative and quantitative techniques related to defense planning or related military problems.Some examples of quantitative approaches are aimed at allocating resources to different weapons in order to effectively eliminate threat from hostile countries by optimizing single objective functions, such as effectiveness or profit. Gu at al. implemented a planning model for an armed forces structure by maximizing expected effectiveness . HåkenstZhuang at al. recognize that the complexities of the wargame structure make any analytically derived solution impossible . In theiHernandez at al. used a combination of the previous effort  to automNajgebauer at al. proposed quantitative methods designed for evaluating required capabilities, assessing existing ones, and identifying capability gaps as a reflection of scenarios identified for a country. The main limitation of the study is the verification part and the extent of plausible military operations. The discrete simulation tool used for verification is only able to verify capabilities like firing, maneuver and movement. Although such methods are therefore well implemented in current military simulations at the operational level, the rest of the effects—especially profiling at the strategic level—are not elaborated and cannot be verified. Moreover, the proposed solution is based on a closed-loop simulation, and therefore it falls into the family of CAWGs with automated players and umpire. The human element involved in finding capability requirements is missing .The Joint Defense Planning Analysis and Requirements Tool Set (JDARTS) supports the NATO defense planning process. It comprises interconnected applications that drive defense planners through NATO defense planning. Two fundamental applications, the Defense Planning Mission Study Tool (D-MIST) and the Defense Planning Capability Assignment Logic Calculator (D-CALC), form the philosophical approach to NATO defense planning. D-MIST develops and stores mission types that then compose operational scenarios. The lowest level of mission decomposition is task oriented and all together they create the stimuli for D-CALC. D-CALC develops and runs scripts generating capability requirements. These scripts can take any inputs replicating implemented NATO doctrine . This soNorway, as explained in , has alrOther national efforts involve launching programs of defense planning with a defined architecture for capability-based planning, supported by various decision support tools like knowledge management, capability engineering support, concept development and experimentation, and simulation . This stBychenkov at al. proposes implementing a quantitative expert system while breaking capabilities into functional groups . The stuFrom this review, we conclude that: (1) quantitative techniques, despite their applicability, bring a high level of simplification to the operational environment; (2) MWGs should be supported by their elements automation to reach analytical rigor; (3) current CAWGs employing quantitative techniques are not able to deal with the high level of objective complexity in solving a problem without loss of credibility.The main contribution of this paper is its verification of the concept for using a qualitative expert system to support adjudication in CAWGs for CBP as a selected approach to defense planning. The innovation here lies in applying system dynamics modelling and simulation paradigms when designing the theoretical model of capability development, which forms the core of the expert system. The system dynamics methodology facilitates the policy determination process in management of complex system behaviours over time . This neThis paper is organized as follows: We have conducted a review of the literature on military defense planning, WGs and the quantitative methods applied in defense planning while defining the problem. We understand military defense planning as a complex system with a high level of subjective complexity. The main rationale is that CBP is an almost infinitely complex engineered system with countless nodes and layers of interdependency, dynamic and emergent behaviours, with the different types of information flow and causality in general stochastic processes, inferences and coupling structures and parameters of system dynamics . It is iHowever, the main drawback in MWGs stems from their form of adjudication, which is mostly free. In such cases the umpire makes his decision based on his best knowledge and “gut feeling” and this creates a risk to the credibility of the WG results. It contrasts to rigid adjudication where, in fact, the umpire can be automated. From our review of quantitative techniques applied in the defense domain, we conclude that they are not applicable for defense planning. Therefore, overall, we define a problem as:“Revealing the applicability and limitations of the qualitative approach applied in the form of a qualitative expert system supporting umpire adjudication in CAWGs for CBP, especially for its role in defining capability requirements.”We have limited our study to the moment when capability requirements are being developed based on a scenario reflecting political guidance and strategic analysis, as described in NATO has approved and implemented an approach to experimentation that recognizes three types of experiment . The “diFollowing this experimentation terminology, we have designed a discovery experiment whose objective is to verify the concept of applying a qualitative expert system in CAWGs for developing capability requirements to reduce umpire bias and risk associated with their decisions.The methodology section contains two parts: the first describes the experiment design involving a general description of the WG design concept instantiated in The experiment design has five main phases. It starts with the WG preparation phase; the scenario scripting following the main conclusions drawn from the strategic analysis of the future operational environment. It follows the principle and structure of specific military scenario design  with theOur case therefore involves a CAWG in the second round of the WG, where computer assistance is represented by the qualitative expert system. This design of the discovery experiment and the wargaming design concept allows us to verify the proposed concept of using a qualitative expert system to support adjudication in CAWGs for CBP.The expert system creating the core of the study and the means of supporting the CAWG adjudication is composed of two main parts. The first is the internal data structure of the expert system, and the second is the system dynamics capability development model.The expert system is founded at the strategic level; it therefore demonstrates the effects of selected and developed capabilities on the operational environment through external factors. These external factors formulate a common understanding and reflect the strengths and weaknesses of the capabilities through PEMSII lenses. Ten external factors have been identified: Dependence on Foreign Military Capability, Dependence on Foreign Civilian Capability, Dependence on National Civilian Capability, Dependence on National Governmental Capability, Deterrence, Limitation , Detection, Interoperability, Adaptability, and Escalation Character. The internal data structure of the expert system is formed as a two-dimensional array, where each capability FOC Cost, the required building time Time to Build FOC and the required maintenance cost Maintenance Cost.Another part of the expert system internal data structure is the capability catalogue structured in the main capability categories, namely Prepare, Command and Control, Inform, Engage, Protect, Project and Sustain. The catalogue contains a limited set of capability cards, describing the attributes of these capabilities. Each capability is characterized by a capability statement explaining the capability’s effects, the resources required to build the capability The second part of the expert system is the capability development model based on a system dynamics paradigm that forms the gaming mechanics based on internal economy . The purMaintenance PCT:Cap.The ratio The system dynamics approach is based on two basic building blocks—stock and flows. Stocks represent accumulation in the system, e.g., money on an account, while flows are variables which cause stock changes, e.g., incoming payments (inflow) or outgoing payments (outflow). Changes of a stock value is allowed only by inflows or outflows. The theoretical single capability model is represented by the scheme in the Cap stock which represents an individual capability. The constants FOC Cost, Maintenance Cost and Time to build FOC determine required resources and time to build and maintain the capability. The Cap in inflow is money consisting of investment to build the capability B resource spent and money to maintain the level of capability already built M resource spent. If maintenance is lower than required, the capability exponentially degrades; this is represented by the Decay outflow. The Bresource required and M resource required variables are the required building and maintenance resources respectively. Bresource required depends on the capability Start Time, which is compared to the system variable Model Time, and on the auxiliary variable B rate used to determine requirement for resources per month. The Bresource required variable is 0 if Model Time < Start Time or B Cap deficient = 0 which means that the capability building process has not been started yet or have been finished (required building resources have been spent). The stock B Resource spent total with its inflow Cap B in accumulates building resources and it is used by the B Cap deficit variable to determine whether FOC has been achieved. The Cap norm variable express ratio Cap/FOC and Model Time is a system variable. Meaning of the M Resource Coefficient and B Resource Coefficient variables is explained below.The central variable is the A capability instance is a capability card used in a solution presented by players with a specific Start Time. The value is given according to (Cap norm(t) = 1, and a capability decay started from the 29th month due to a lack of maintenance resources.Time to Build FOC parameter for each capability instance in their solution.The same capability card can be used multiple times, with the same or different start times and times to build FOC; thus, all instances of Universum B Resource Coefficient and Universum M Resource Coefficient, ensuring that available resources cannot be exceeded. If resources given to players are the same or lower, there is no conflict and these coefficients are equal to 1.If the overall resource requirement exceeds available resources, the actual resources allocated to a single capability are proportionally reduced by the coefficients External variables characterize the impact of a capability on external factors. The Universum is the space where the impacts of the capability set on external variables are calculated.N is the number of different capability cards used in the evaluated solution.For each capability set For example, the impact on Deterrence caused by the capabilities of three instances of mechanized brigade (MB) and two instances of an intelligence cell (IC) is calculated as:Start Time and Time to Build FOC values. The other external factors are expressed the same way.Each instance of capability can have different According to the scenario played, the importance of specific factors can be highlighted by the assigned weights This section contains a use case of the WG preparation and execution and conclusion from the use of the qualitative expert system to support the CAWG adjudication for CBP. It describes in details who played the WG, how it was played and the way the qualitative expert system supported the second round of the WG.General Staff course members took the role of players in the two-day discovery experiment. They are senior officers with a solid background in defense and operational planning. They were divided into three teams; each team had eight members and was supported by a facilitator who ensured that players followed the rules of the WG and were given the same level of advice. They were not inform about the main objective of the discovery experiment, i.e., to prove the concept and the existence of the qualitative expert system was not disclosed. These highly motivated teams played the WG as a part of their collective training. There was a single umpire, the former head of the Czech General Staff Defense Planning Branch, and an analytical team was composed of five retired senior officers familiar with implementation details of the qualitative expert system.Global Impact(t). These were set by the analytical team before the WG execution.The qualitative expert system was set up before the WG; namely, a weight for each of the ten external factors  was set as a constant value independent of any scenario for each capability from the capability catalogue. The only scenario-dependent internal data structure consisted of weights of external factors in respect of achieving the required end-state in the scenario, expressed in the time function The umpire and their analytical team introduced the scenario to all teams together before the execution of the first round of the WG, played in the form of a MWG. The scenario was drafted as a hypothetical one, situated in 2035 in a fictitious situation after the gradual collapse of a military alliance and an economic union of countries existing on the continent. The scenario was developed to be exploited with small sized country “A” as the central player in new geo-political conditions. New geo-political conditions materialized in a regional power on the continent, with growing capabilities (military and non-military), looking to increase its influence over the continent with the ultimate goal of regional dominance. Then the umpire introduced the WG’s objective for the first day—to develop the capability requirements needed for country “A” to reach the end-state articulated in scenario, i.e., country “A” ensures its sovereignty.Three teams developed their solution for capability requirements from the capability catalogue, which contained descriptions of ninety NATO/national existing capabilities, although their costs were concealed. This meant they planned their capability requirements without financial restrictions and produced the list of needed capabilities to reach the end-state The analytical team and umpire did not use the qualitative expert system during the first round of the WG, and they didn’t introduced any conclusion that day.The CAWG was played on the second day of the experiment. As the second round of the WG, it started with the umpire stating his conclusion from the first round of the WG, solely constructed by his and the analytical team knowledge, that only Team1 achieved the required end-state and explaining the vital capabilities needed to reach the end-state. In parallel, the analytical team demonstrated the total cost of all proposed solutions from the first round of the WG, as described in Start Time while controlling the Financial Limit. Teams were therefore forced to design their solution within the Financial Limit.Then the umpire introduced the WG objective for the second day—to develop the capability requirements needed for country “A” to reach the same end-state as in the first round. However, this time a yearly financial limit was imposed on capability development and maintenance, set in the ratio of 0.5  corresponding to each team solution from the second round of the WG. Team1 and Team3 created significantly better solutions than Team2, as demonstrated by the value of the Global Impact at time = 120 months. This corresponds to the fact that these teams were able to spend almost completely the given Financial Limit. Team1 created a slightly better solution than Team3, not only because of the higher value of Global Impact at time = 120 months, but mainly because they were able to increase the global impact more quickly at the beginning of planning cycle; at time = 20 months, Team1 had already generated significantly greater effects with their solution than Team3.All teams were able to compose their capabilities to reach the end-state written in the scenario. Financial Limit: in time = 60 months they reduced maintenance resources to the same value of 20 billion of cost units for all Teams. This reflects a very common situation in all MoDs, i.e., budget cuts introduced during the long-term planning cycle. The effects of that financial cut on the second round of the WG solutions expressed as the Global Impact(t) is described in Figure 8. The Team1 solution occupied a superior position over the others until time = 160 months. From that moment on, the Team3 solution generated slightly better effects than Team1′s.The most important moment—clearly demonstrating the value of our approach—happened during the conclusion session of the second round of the WG, when the analytical team made changes in the qualitative expert system to the Detection (t) corresponding to each team solution from the second round of the WG. This importing finding, confirming the superiority of the Team1 solution, is reaching the maximum level of Detection even before the end of planning cycle. It corresponds to the situation in which all Detection-related capabilities are already in the FOC.The qualitative expert system expresses the functions of ten external factors; as an example, However, the finding described in In its essence, every MWG is biased because of the human decisions reflected in the WG dynamics. Nonetheless, players’ bias is desirable: it enables the involvement of an individual’s creativity in the proposed solutions. On the other hand, umpire bias increases the risk of the WG results becoming less credible, especially when they are used for experimentation purposes and not for training or education. Concurrently, there is a constant drive within the wargaming domain to automate the human elements of WGs by quantitative approaches, thereby bringing the analytical rigor that customers need. However, the defense planning process, in our case represented by developing capability requirements, is a complex system and does not allow a move towards FAWGs, i.e., achieving full automation and validation of players and umpire. We have therefore designed a qualitative expert system as a part of CAWGs, not replicating the umpire per se, but reducing his bias and the risk associated with his decisions.The innovative advance of this proposal lies in applying system dynamics modelling and simulation paradigm when designing a theoretical model of capability development. It allows us to reveal the effects of budget cuts, which the umpire was previously unable to articulate when comparing individual solutions for capability requirements, as described in Global impact (t), and the values of external factors, e.g., Detection (t), are also expressed in quantum, the expert system remains essentially qualitative, because its very core—weighting the effects of a capability on each external factor—has been created in qualitative way by the panel of experts’ technique. CAWGs should not be driven, regardless of cost, towards quantitative techniques. The objective complexity of a problem does not allow the operational environment to be replicated with the required fidelity to gain credible experimental results.Even though the internal data structure is working with the quantitative values and outputs of the model like the Participants in the discovery experiment and the WG players validated the concept of supporting comparisons between capability requirement solutions using a qualitative expert system, and also appreciated the educative dimension of the concept, which was a secondary effect of the study. Players proposed possible ways in which the study might be developed in future: namely, by extending the concept to the whole capability-based planning process and enabling users to define their own capabilities and not being limited by the current capability catalogue.


In response to the SARS-CoV-2 pandemic, unprecedented travel restrictions and stay-at-home orders were enacted around the world. Ultimately, the public’s response to announcements of lockdowns—defined as restrictions on both local movement or long distance travel—will determine how effective these kinds of interventions are. Here, we evaluate the effects of lockdowns on human mobility and simulate how these changes may affect epidemic spread by analyzing aggregated mobility data from mobile phones. We show that in 2020 following lockdown announcements but prior to their implementation, both local and long distance movement increased in multiple locations, and urban-to-rural migration was observed around the world. To examine how these behavioral responses to lockdown policies may contribute to epidemic spread, we developed a simple agent-based spatial model. Our model shows that this increased movement has the potential to increase seeding of the epidemic in less urban areas, which could undermine the goal of the lockdown in preventing disease spread. Lockdowns play a key role in reducing contacts and controlling outbreaks, but appropriate messaging surrounding their announcement and careful evaluation of changes in mobility are needed to mitigate the possible unintended consequences. In response to the SARS-CoV-2 pandemic, unprecedented travel restrictions and stay-at-home orders were enacted around the world almost simultaneously. These ranged from restrictions on human movement on a local scale to travel restrictions on regional and international scales. These policies were designed to reduce the spread of the SARS-CoV-2 virus by restricting the contact between infectious and susceptible individuals and to slow the spread of the virus out of epidemic hotspots.In general, the public’s response to announcements of lockdown policies—defined here as restrictions on local movement or long distance travel—will determine how effective these kinds of interventions are. Governments must give some warning to the public about upcoming travel restrictions to allow for necessary preparations, but a surge of travel prior to the lockdown being put in place risks the opposite of the desired effect, sending potentially infectious individuals out into previously unaffected regions around the country or internationally. In order to design effective policies in response to resurgence of SARS-CoV-2 or indeed in the context of future pandemics, understanding the human response to interventions is critical.3, including this pandemic5. Studies have shown that mobility patterns on local scales correlated with transmission within the city of Wuhan, for example7, and recent analyses have found associations between mobility and SARS-CoV-2 transmission in the United States8. Seasonal travel related to holidays, which creates a surge of travel out of cities, for example, can also have an important impact on the spread of infection9. Indeed, travel related to the Lunar New Year may well have spread SARS-CoV-2 across China as the epidemic started to emerge in Wuhan10. Since infected individuals are often infectious prior to symptoms, and many may have no symptoms at all, the possibility of infected travelers unwittingly spreading the virus during large travel movements is significant.Analyses of aggregated data from mobile phones have been used to monitor movement patterns in the context of outbreaksHere, we evaluate the effect of lockdown related travel behavior on epidemic spread by analyzing aggregated mobility data from mobile phones from multiple countries including India, France, Spain, Bangladesh, and the USA, on local and national spatial scales. We show that in numerous urban centers in the U.S. and around the world, there was a surge in travel out of cities immediately preceding lockdowns, likely in anticipation of restrictions. Importantly, this surge is not observed in surrounding areas. We observed urban-to-rural migration in each country analyzed. Drawing on this empirical evidence of the behavioral response to lockdowns, we use a simple agent-based spatial model to examine how different behavioral responses to lockdown policies could impact the spread of epidemics. We find that travel surges following announcements of lockdowns have the potential to increase movement of people to less urban areas. This movement can accelerate seeding of the epidemic in these areas compared to situations in which lockdowns do not increase travel to these regions. This change in the rate of disease exportation may therefore undermine the goal of preventing disease spread. Without detailed genetic analyses and in the absence of reliable epidemiological data in many cases, it is challenging to confirm from case data how much the changes in movement observed in the mobility data impacted the course of epidemics. However, through simulations, we show the potential for changes in behavior due to lockdown announcements to contribute to epidemic spread. This work highlights the importance of messaging and close evaluation of changes in local travel networks in the implementation of outbreak related travel restrictions.To understand the impact of lockdown announcements, which are generally made a few days before the lockdown goes into effect, we analyzed the percent change in weekday Facebook population across various urban centers in the United States, during three segments of the day: Morning, Evening, and Night. We compared these population data to a baseline of the previous 90 days conditioning on the day of the week and time of day. Daily population data, split into these three temporal bins, capture the number of people who spend the majority of that time bin in a location. Changes in population data compared to an appropriate baseline therefore capture both long-term changes in residency and short-term changes in movement into or out of that location.We find that city centers around the US showed a spike in day-time mobility prior to March 16, 2020 , suggestive of mobility related to preparations for these restrictions Fig. . In geneThe data suggest that the decrease in daytime population in Manhattan was not only driven by fewer workers coming into the city during the day, but also an exodus of residents out of the city overall, characterized by a decrease in nighttime population. Note that this is unlikely to represent changes in a nighttime worker population, because we see no increases in overall nighttime population in surrounding regions S1. In Fig. 11, which correspond to population density and reflect the urban-to-rural gradient. In each country, to varying degrees, there was a consistent decrease in population in areas with the highest nightlight intensity (urban centers) and a reciprocal increase in population in less electrified regions .We further evaluated changes in urban versus rural populations on a national scale in France, Spain, India, and Bangladesh; four countries for which Facebook data pipelines were available to cover the timing of lockdowns. In Fig. 14. Figure In Bangladesh, we find a substantial decline in population in areas with the highest nightlight intensity—primarily in the capital, Dhaka, and areas with a high concentration of garment factories. The announcement of the lockdown in early March, and the closing of the garments industry, was followed by large movements of people from these densely populated urban areas to more rural areasTo examine the potential epidemiological implications of these behavioral responses to lockdowns, we implemented a metapopulation model reflecting the general behaviors we measured in the Facebook data. As shown in Figure We evaluated the probability of travel . The post-lockdown mobility network, on the other hand, simulates the spread of the epidemic regionally, but still allows for identification of potentially high risk regions not identified in a simple gravity model.The choice of timing between lockdown announcement and implementation must balance the increased risk of exportation from longer delays with the need to provide enough warning for people to adequately prepare for the lockdown. Our model shows that decreasing the time between announcement and lockdown implementation reduces the number of exported cases. As shown in Figure The COVID-19 pandemic led to an unprecedented and nearly simultaneous set of lockdown policies that were implemented globally. The extent to which they were effective in containing the spread of SARS-CoV-2 remains unclear, but the impact of physical distancing policies on human mobility is measurable at scale for the first time due to the widespread availability of data from mobile phones. Here we have shown that characteristic travel behaviors were repeated across different cities and countries around the world in response to lockdowns, with pre-lockdown surges in local activity and rapid urban-to-rural migration characterizing the human response to the policies. Our results suggest that these social responses are predictable and generalizable to some extent, and must be taken into account when planning the implementation of future lockdown policies, particularly with respect to messaging and surveillance.The mobility data analyzed here highlight that even with lockdown orders, barring draconian policies, populations do not stop moving completely, but rather change their mobility patterns Figure . Our sim15, and an analysis of SARS-CoV-2 viral genomies in Bangladesh found movement was a key driver of disease spread16. Case data from Spain17 also show increases in cases across a wide range of locations following the lockdown implementation. While many factors likely contributed to the similarities in the epidemic curves across locations, the increase in travel in the mobility data suggests seeding from urban areas may have played a role. Given the limitations of of epidemiological case data, more detailed genomics analyses and reconstruction of transmission networks are necessary to disentangle the contributions of these many factors.There is some evidence that the long-distance seeding of SARS-CoV-2 cases due to travel behavior may have occurred. For example, an analysis of the genetic relatedness of viral genomes found that many outbreaks across the United States were seeded by travelers from New York CityMany simplifying assumptions were made in the simulation model for clarity, including homogeneous mixing within locations on the lattice, a gravity model for connectivity, and the inclusion of a single urban center. Additionally, we assumed transmission dynamics were the same between symptomatic and asymptomatic individuals, and that symptomatic individuals stopped traveling immediately. We further assumed that increases in movement observed in the data following lockdown announcements were a reasonable proxy for increased contact rates, particularly in light of the anecdotal evidence of “panic buying” However, in future outbreaks, interventions such as masks and social distancing, which were not consistently implemented in many places when lockdowns were first initiated, may reduce the meaning of this proxy. Finally, the mobility analyses absorb the limitations of the Facebook data, which are limited to Facebook users with location services enabled. These users are just a subset of the population, and may represent a biased sample. However, the consistency of the patterns across countries suggests that the data are indeed capturing a real phenomenon. Despite these limitations, our results highlight the need for careful implementation of lockdowns to mitigate their potential unintended consequences.12 will require different interventions and messaging than people choosing to leave crowded cities for more remote second homes18. For example, depending on the setting, lockdown announcements could include messaging on how to safely prepare and expectations of the local supply chain to decrease instances of panic buying and hoarding, thereby decreasing the spike in local travel immediately preceding a lockdown19, and governments could consider providing resources needed for people to stay. Decreasing the window of time between announcement and implementation of lockdown policies could also reduce both the local contact rate and the probability of out migration while balancing the needs of the population. While the exact policy implications will be context specific, our results suggest that lockdown announcements should be accompanied by additional messaging and resources to minimize potential unintended consequences. In particular, there are longstanding, global disparities in access to healthcare between urban and rural areas21, which have been further exacerbated by the SARS-CoV-2 pandemic22. Travel surges of the kind we observed here thus necessitate increased coordination, surveillance, testing, and treatment in rural areas that historically are understaffed and under resourced23.Strategies for mitigating travel surges will greatly depend on the reasons behind people’s movement. Movement of people to rural homes from urban centers due to sudden lack of work from the pandemic24. This interface allows researchers and response workers to request aggregated and anonymized datasets generated by an open cohort of individuals who are: (1) Facebook users; (2) have a smartphone, and; (3) are providing information through the Facebook app by having location services enabled. Data are requested for a geospatial region and defined by a spatial bounding box. For this analysis we used the movement and population datasets.Facebook’s Data for Good team developed and provides access to the Geoinsights portal to provide movement and population level data in response to crisesWhen the data aggregation pipeline is initiated, all individuals who are in the cohort described above and inside the bounding box contribute information to the datasets. For each user, location information is collected, and user location is categorized to Bing Tiles. The resolution of the Bing Tiles used varies by type of dataset with population data being offered at a higher resolution than movement data due to computational restrictions. Data are then aggregated into 8-h bins. Population is determined by the modal location for each individual during this 8-h bin. Movement for a given 8-h bin is defined as a vector of transition with the destination being the modal location in the current 8-h bin and the origin being the modal local for the preceding 8-h bin. For each population tile and movement vector, Facebook provides a baseline which is calculated as the average number of users who were categorized as being in a given location (population) or who had made a given directional transition (movement) during the baseline period, conditional on day of week and time of day. The baseline period is defined as the 45-day period preceding the initiation of the pipeline for movement data and the 90-day period preceding the initiation of the pipeline for the population data.On February 27th, Facebook’s Data for Good team initiated the data collection pipeline for major cities in the United States of America. In the following weeks bounding boxes, and subsequent pipelines, were generated for regions as requested, including internationally. Our analyses are constrained to the locations with available data for the relevant time periods, and we use a combination of Facebook mobility data and nightlight data in different areas, as described below.We analyzed the percent change in weekday Facebook population during various segments of the day compared to a baseline of the previous 90 days, conditioning on the day of the week and time of day in various urban centers in the United States. We use this measure of percent change as it allows for us to standardize population change against an expectation and therefore account for within-region fluctuations in weekly and daily population. Large deviations from baseline (or a percent change close to 0%) are not expected in the short term without some exogenous event.We performed sub-city level analyses for several U.S. cities for which we had contemporaneous Facebook mobility data. We restricted our regional sub-city analysis to New York City (S1) as (1) there are clear geographic borders (boroughs) with heterogeneity in the demographics of the population and land use in each region, (2) there were a large number of users included in the Facebook data set for each region, and; (3) the boroughs are of a large enough spatial scale to allow Facebook to capture highly granular movement and population data. City level analyses were restricted to the United States as Facebook initiated a city specific data collection pipeline for select cities on February 27th, well before the implementation of lockdown measures. Country level analyses were restricted to Spain, India, and France as all three countries quickly implemented strict lockdown measures, and Facebook initiated data collection pipelines for the whole country before these measures were put into place.25.To assess the potential impact of different lockdown implementations and travel restrictions, we developed a simple metapopulation model, consisting of 100 communities, evenly spaced on a ten-by-ten lattice. One community in the center represents an “urban” area with a higher population size and population density than the other 99 “non-urban” locations. We make the simplifying assumption that all non-urban locations are homogeneous in terms of size and density and only differ in their distance from the urban. We seed an epidemic in the urban center with five initial cases. Within each community, the epidemic follows a density-dependent stochastic Susceptible-Exposed-Infectious(Asymptomatic)-Infectious(Symptomatic)-Recovered natural history. At each time step, all susceptible individuals have a chance of infection from the infectious individuals in their community, based on the parameter beta . Asymptomatic and symptomatic cases are assumed to have the same beta, meaning the only difference between them in the model is whether or not they show symptoms. Detailed parameters of the outbreak are listed in Table Following the time step specific movement through the disease generation process individuals in each community are given a chance to travel. This travel is driven by three factors: 1) the probability that an individual travels out of a given community, entclass1pt{minima∣α0 and;  the dise the probi to location j, standardized for all travel out of location i for that day. This resulted in a value bounded between 0 and 1 describing the probability of travel to location j from location i given that an individual traveled out of location i on that given day. In the Facebook mobility data from Spain, we had 5 days of pre-lockdown data. For our simulation model we generated three time-varying mobility matrices: (1) the first which followed the true change in mobility network; (2) the second which randomly sampled from the mobility network of the pre-lockdown days through the entire period of the simulation, and; (3) the first which simulated a simple distance based gravity model with no input from the mobility data. We also expanded the initial pre-lockdown period to 14 days to allow for an initiated epidemic to propagate in our simulation by randomly sampling from the pre-lockdown mobility matrices.Using the movement between tiles data from Facebook, we calculated the time-varying number of transitions between all provinces of Spain. We then constructed a mobility matrix for transitions from location We designed our model to describe three distinct periods of time: (1) n Figure . As descWe simulated the stochastic epidemic 100 times. In each of the 100 communities, we calculated the proportion of simulations in which that community had at least one case by day 30. We also calculated the average time to first infection across simulations in each community. We compared these two metrics across variations of the six parameters described above. For our primary analysis we held Supplementary Information.


With a purely optical modulation of fluorescent behaviors, stimulated emission depletion (STED) microscopy allows for far-field imaging with a diffraction-unlimited resolution in theory. The performance of STED microscopy is affected by many factors, of which aberrations induced by the optical system and biological samples can distort the wave front of the depletion beam at the focal plane to greatly deteriorate the spatial resolution and the image contrast. Therefore, aberration correction is imperative for STED imaging, especially for imaging thick specimens. Here, we present a wave front compensation approach based on the genetic algorithm (GA) to restore the distorted laser wave front for improving the quality of STED images. After performing aberration correction on two types of zebrafish samples, the signal intensity and the imaging resolution of STED images were both improved, where the thicknesses were 24 μm and 100 μm in the zebrafish retina sample and the zebrafish embryo sample, respectively. The results showed that the GA-based wave front compensation approach has the capability of correction for both system-induced and sample-induced aberrations. The elimination of aberrations can prompt STED imaging in deep tissues; therefore, STED microscopy can be expected to play an increasingly important role in super-resolution imaging related to the scientific research in biological fields. FortIdeally, the center intensity of the donut-shaped depletion beam should be 0. In this case, the effective PSF is reduced infinitely with the increase in depletion intensity. However, the performance of STED microscopy critically depends on the quality of the depletion beam, especially the intensity distribution symmetry and the contrast between the central minimum intensity and the surrounding illumination. As a result, the actual resolution in STED microscopy is very susceptible to aberrations brought by the optical system and biological samples, which distorts the wave front of the depletion beam in the focal plane. The system-induced aberration is basically fixed in a certain optical system, but the sample-induced aberration is complicated and unpredictable because of the surface roughness and the inhomogeneity of the refractive index , 17. UnfThe purpose of aberration correction is to restore the original laser wave front after propagating a certain distance. An important method for aberration correction is adaptive optics (AO), which was first applied to compensate for the distorted wave front induced by atmosphere turbulence , 23. In In this work, we present a wave front compensation approach based on the genetic algorithm (GA) to find the corrected phase. In the experiments, the modulation of the wave front phase and the conversion of the depletion beam from Gaussian to donut-shaped were controlled by only one SLM, which allowed for aberration correction without any modification to the original STED system. By using the back-scattering signal of gold nanoparticles as feedbacks in the GA optimization, the distorted wave front of the depletion beam can be rapidly restored. Previous studies on wave front shaping have shown that the GA is an efficient and robust method that can optimize many phase segments in parallel and maintain a high stability in the noisy environment . We have2In a STED microscope, a donut-shaped depletion beam is delivered to a home-built confocal laser scanning microscopy system to quench the fluorescence from the peripheral area of the emission spot through stimulated emission. As shown in The excitation beam with the wavelength of 635 nm was provided by a picosecond diode laser head , and a widely tunable, mode-locked Ti:sapphire laser  with a temporal width of 140 fs was tuned to 760 nm as the depletion beam at a pulse repetition rate of 80 MHz. In the excitation path, the repetition rate and laser intensity of the excitation beam were modulated by a laser drive , which was externally triggered by the depletion laser source. In order to maintain linear polarization and adjust the laser intensity in both excitation and depletion paths, a half wave plate  and a glan-laser polarizer  were used as a combination. Then, a delay line controlled by a retro reflector  in the excitation path adjusted the interval of the two series pulses for a better performance of STED imaging. In the depletion path, the wavelength of the depletion beam modulated by Ti:sapphire laser can be tuned from 680 nm to 1080 nm. A glass rod  and a 100 m single-mode polarization maintaining fiber  temporally stretched depletion pulses to approximately 200 ps. A SLM  as an important adaptive element was introduced for the generation of donut-shaped depletion beam and aberration correction. In order to eliminate the influence of stray light, a blazed grating phase was always loaded on the SLM to form a series of diffraction spots. A pinhole was placed in the focus of the lens (L4) to select the first-order diffraction spot. The excitation beam and the depletion beam encountered and overlapped at the dichroic mirror DM1. After a pair of galvanometer scanning mirrors , a quarter wave plate ; converted the depletion beam to right-hand circular polarization for better imaging resolution. Afterwards, the sample was fixed in a 3D stage  with full travel of 25 mm and a minimal step size of 62.5 nm in each axis. An oil-immersion objective  focused two laser beams on the sample and collected the fluorescence signal. The detection path allowed the transmission of fluorescence signal to a photomultiplier tube . A preamplifier was placed before the computer to amplify the signal, and the output signal was transmitted to two data acquisition devices  for imaging and aberration correction, respectively. An open-source program, Scan-Image  developed in MATLAB , was used to control the scanning mirrors and acquire images.Inspired by the natural species evolution, GA is a stochastic, parallel method to search the optimal solution globally. As an efficient evolutionary algorithm, it can simulate the behaviors of biological populations  , 31. By To assess the correction effect and find the optimal corrected phase, the voltage value converted from the back-scattering signal of a gold nanoparticle was treated as the criterion for the image quality metric. An SLM mounted in the depletion path serves three different purposes: first, it loads a blazed grating phase to eliminate the influence of stray light on the image quality; second, it loads a spiral phase to generate a donut-shaped depletion beam; and last, it changes the phase level to compensate for the wave front distortion. The SLM was controlled by MATLAB software .As shown in 2×9 segments (n is a positive integer). Each segment has the same number of pixels with the same phase level  and fluorescent microspheres  to a coverslip and mounting the coverslip to a microscope slide with a mounting medium .The correction of more complicated aberrations can better verify the capability of the GA . Therefore, the gold nanoparticle was imaged at ±0.5 μm and ±1.0 μm away from the focal plane . The absIn the experiments above, the control region on the SLM was divided into 81 segments (9×9 segments) to improve the calculation speed and the convergence performance of the GA procedure, of which each segment has the same phase level. A larger segment number should certainly provide a more accurate correction of the wave front distortion; however, it will take more iterations to find the optimal solution because of the slow convergence rate. More experiments were performed for different segment numbers, which is shown in After correcting the system-induced aberration, we can observe the improvement of image quality by comparing the STED images of the fluorescent microspheres before and after the aberration correction. As shown in 3.2To further prove the capability of GA in simultaneously correcting system-induced and sample-induced aberrations, i.e. full aberration correction, two types of zebrafish samples were firstly prepared, including zebrafish retina and zebrafish embryo sections. As shown in When the laser beam passed through the retina sample, the intensity of the laser focus gradually decreased with the depth because of light scattering and absorption. The situation is worse for the depletion beam than for the excitation beam because of the donut-shaped wave front. Since the sample-induced aberration is more complicated and unpredictable, the control region on the SLM was modeled in a mixed mode of the segment mode and the Zernike polynomial mode. After performing the full aberration correction on the depletion beam in the zebrafish retina sample, the scattering intensity of the bottom gold nanoparticle illuminated by the Gaussian depletion beam at the wavelength of 760 nm was increased (the mean intensity of the scattering image increased from 9.003 to 10.341 for the Gaussian beam and from 6.939 to 7.520 for the donut-shaped beam). Importantly, the distorted donut-shaped wave front recovered the uniform intensity distribution after combining the corrected phase see .A better image quality can also be achieved in zebrafish embryo samples after performing the full aberration correction. As shown in Finally, tubulin structures in HeLa cells labeled with ATTO647N were used to demonstrate the capability of GA in full aberration correction of biological structures. In the preparation of the HeLa cell sample, the detection of Anti-α tubulin  was performed using secondary antibodies labeled with ATTO647N . The detailed steps can be found in the literature . The sig4In this paper, a wave front compensation approach based on the GA has been proposed. A SLM mounted in the depletion path was controlled by the GA procedure to change the phase level, so that the distorted wave front of the depletion beam can be accurately recovered at the focal plane. By comparing the quality of the STED images before and after the aberration correction in different samples, the approach has been proven to have the capability of correcting the system-induced aberration and the sample-induced aberration. As a result, both the imaging resolution and the signal intensity were improved in STED images, and the imaging depth reached 24 μm and 100 μm in the samples of zebrafish retina and zebrafish embryo sections, respectively. In this work, aberration correction was focused on the depletion beam to improve the quality of the STED super-resolution images. However, the aberrations could also defocus and diffuse the focusing spot of the excitation beam, resulting in the attenuation of the signal intensity. Dividing the liquid crystal display of the SLM into two parts can be a solution. It can not only simultaneously compensate for the distorted wave front of both laser beams but also reduce the expenditure of the experiment system. In conclusion, super-resolution images with an excellent quality will certainly give an impetus to the application of STED microscopy in the future.Suppl 1


Cyber-physical systems (CPSs) have sophisticated control mechanisms that help achieve optimal system operations and services. These mechanisms, imply considering multiple signal inputs in parallel, to timely respond to varying working conditions. Despite the advantages that control mechanisms convey, they bring new challenges in terms of failure prevention. The compensatory action the control exerts cause a fault masking effect, hampering fault diagnosis. Likewise, the multiple information inputs CPSs have to process can affect the timely system response to faults. This article proposes a failure prognosis method, which combines time series-based forecasting methods with statistically based classification techniques in order to investigate system degradation and failure forming on system levels. This method utilizes a new approach based on the concept of the system operation mode (SOM) that offers a novel perspective for health management that allows monitoring the system behavior, through the frequency and duration of SOMs. Validation of this method was conducted by systematically injecting faults in a cyber-physical greenhouse testbed. The obtained results demonstrate that the degradation and fault forming process can be monitored by analyzing the changes of the frequency and duration of SOMs. These indicators made possible to estimate the time to failure caused by various failures in the conducted experiments. The cyber-physical system (CPS) concept, describes a family of systems that tightly connect the physical world with the information (cyber) world and obtain control information directly from real life processes, very often in run time and in real time . These tCurrently available CPSs are equipped with self-tuning capabilities that provide sophisticated control mechanisms that help to achieve stable, and optimal system operation. It enables the system to modify its own set points by changing the operational intensity of the actuators, as well as their activation and deactivation times, in order to respond to external disturbances. A typical example is a cyber-physical greenhouse, aiming to keep the best environmental conditions for the crops. If there are changes on the surrounding environment , the CPS will modify its settings, by increasing the intensity of the heater (or by extending the time it last on), and closing the windows, in order to keep the desired temperature. These new settings determine a system operation mode.Autonomous and optimum control of complex infrastructures ,Monitoring of complex physical processes,Provisioning of critical services in geographically distributed environments.The adaptation capability that CPSs present, facilitates the provisioning of a range of new services including:Due to the criticality of the provisioned services, CPSs should assure a continuous and reliable operation, protecting human life, the surrounding environment and the involved economical assets. This situation strengthens the need of preventing failures, and conducting a suitable fault management whenever it is needed.Current systems are equipped with online measurement tools that support decision making and adjust system operation in real time . These tHealth management and failure prognosis has emerged as an opportunity for assuring the reliable operation of CPSs. These methods enable the real-time measuring of system variables in order to determine the extent of deviation from the normal operative conditions . It alloExisting health management and failure prognosis methods do not manage to cope with the intensive interaction between CPSs and their surrounding environment. They often present some of the following limitations: (i) they implement important simplifications in order to model the behavior of systems and their aging processes, (ii) the adaptation mechanisms of CPSs lead to disturbances in system signals that can be misinterpreted as faults, (iii) some of the existing methods make assumptions about the deterioration process of systems, which do not apply in dynamic and changing systems such as CPSs, and/or v) they are underpinned on empirical or experts knowledge, that cannot be easily updated and is limited to situations previously experienced.Besides of the already mentioned limitations, the changing operative conditions of CPSs constitute the main challenge for the existing failure prognosis and health management methods. Self-regulation capabilities enable CPSs to compensate early-phase fault effects, assuring the desired system performance. However, they also mask fault symptoms hindering fault detection and diagnosis . This afThis article, proposes a novel health management and failure prognosis method that aims to overcome the aforementioned limitations. Unlike traditional approaches that are mostly focused on studying system signals, the proposed method studies frequency and duration changes of system operation modes to predict remaining useful life of small-scale, self-tuning CPSs. The proposed method presents an important advantage over the existing approaches. It is a non-dedicated fault and system degradation indicator that can be used in any kind of small scale CPS. The proposed method combines time-series based analysis, and linear discriminant analysis. Time-series based analysis was utilized for forecasting the future values of system operation mode frequency and duration. It was also used as input for the failure prognosis model. Linear discriminant analysis was used to determine the failure mode causing the degradation process.This article is organized as follows: Despite failure prognosis in CPSs is not widely covered in the literature, there are multiple approaches available for complex systems. When analyzing literature, it can be observed that these approaches can be split into those, which are focused on determining the expected life of systems based on static models, and those that estimate system reliability indicators in run-time (failure prognosis in running-time).The implementation of static-models for failure prognosis are mainly based on statistical analyses that aim to evaluate the accumulated failure rate of a sample of components, in order to determine their average useful life. These methods are developed based on the assumption that the obtained time to failure records fit a particular statistical distribution , which cOne of the most commonly used types of statistical distribution is Weibull. Weibull distribution allows representing the “decreasing, constant and increasing part of the bathtub curve”  that desAlthough statistics based models are easy to interpret, not all systems present the same tub curve . These mTime-series-based analysis can overcome the limitations of the statistical-based analysis. In these methods, changes of the failure indicator variable are explained based on past observations . Unlike Although the time-series-based methods are suitable for failure prognosis, the self-tuning capabilities of CPSs represent a challenge for their implementation. The system operation mode (SOM) transitions triggered by self-tuning control mechanism of the system may influence the trends of signals that are associated to deterioration. Likewise, they also hamper the occurrence of seasonal and sequential patterns that are necessary information sources of failure prognosis. The lack of proper failure indicators in self tuning systems is a driver for exploring failure descriptors that characterize the deterioration pattern caused by progressive failures and enable time-series-based failure prognosis.Data-driven methods can also be used for failure prognosis in run-time. It makes them suitable for conducting health management. Some of the most common methods reported in literature are the Wiener process, Gamma process and Markovian models.Wiener process is a data-driven method that can represent non-monotonic degradation processes , in order to estimate the remaining useful life (RUL) of systems and their time life . This meUnlike the Wiener process, the Gamma process is used for modeling monotonic degradation processes where deterioration takes place gradually . As for Markovian models are, by far, one of the most popular methods for failure prognosis in run-time and health management. This method estimates the forthcoming system degradation based on the current degradation state, ignoring the past observations. One of its main characteristics is that Markovian models evaluate the transition probability among states in order to determine the future state of the system . For insLimitations of Markovian models include the memoryless assumption that may cause neglecting relevant information for estimating the future system state, or for diagnosing the forming failure mode. Likewise, transition probabilities are set based on empirical knowledge or through an important number of samples that are difficult to obtain . This laThe applicability of existing methods has several prerequisites for failure indicators  and/or prior knowledge of the impact of failure on system behavior. These prerequisites are not applicable for CPSs, as these systems present dynamic behavior and operate in environments subjected to high levels of uncertainty.The non-predictable degradation presented by CPSs make the application of predefined statistical distribution patterns unreliable for capturing the process.The varying working conditions that characterize CPSs demand application of failure prognosis models that can be updated in run-time.There is lack of failure prognosis methods that do not rely on prior knowledge regarding failure manifestations, failure probability, and preventive means.There are not “universal” indicators that can be used for forecasting multiple failure modes.Methods used for prognosis in other disciplines should also be studied in order to find new ways to study the failure forming process in CPSs.The above-presented literature review cast light on some important research challenges concerning the development of failure prognosis methods for CPSs:In conclusion, any failure prognosis method addressed to CPSs should be executed in run-time (based on sensed system performance); it should not be based on assumptions concerning the degradation process, or to rely on a predefined degradation path; and it should overcome the masking effect caused by fault tolerance.CPSs should adapt themselves to changing operating conditions in order to assure optimal performance. For this purpose, CPSs adapt their operational behavior by autonomously changing their system settings in response to sensed disturbances. This self-tuning mechanism is typically operationalized by modifying the working parameters of system actuators, which in conjunction determine the system’s operation mode (SOM).SOMs can be considered as a subset of the state concept, as they describe the situation of the system at a particular time t . A systeFor the sake of a formal treatment, SOM has been defined as a singular combination of operation modes (COM) of all components of the system in a particular time t. COMs are regarded as the component state at a time t. The actuators can obviously be in multiple various states during their operation. As the most basic ones, in our study we considered the active and inactive states. For instance, the states of an outflow valve in charge of irrigation in a greenhouse can be symbolically represented as This SOM concept aims to capture the dynamic and adaptive system behavior in failure analytics, as it allows representing system behavior based on the joint effect of the actuators’ states on system performance. It relies on analyzing changes of component operation modes, which normally leads to the new SOMs that enables failure prognosis regardless of changes in system configuration. This article will focus CPSs built from components with discrete two-state (binary) COMs, i.e., active and inactive states, as a first approach for exploring the applicability of SOMs in failure prognosis.CPSs change their system operation modes in order to assure optimal system performance for every working condition. This adaptation process can be described by the following sequence of steps: (i) system sensor perceive changes on the surrounding environment or system performance, (ii) the control system evaluates these changes and activate specific COMs to respond to the new working condition and (iii) the new combination of COMs leads to a new SOM.SOM changes occur every time there are variations on the working conditions. Under regular system operation, all systems tend to activate certain SOMs more frequently than others. These SOMs are usually activated with a similar frequency, in akin time windows. Likewise, SOMs are prone to present a similar duration time, every time they are activated. Based on this line of reasoning, it can be argued that system faults, or the occurrence of abnormal events affects the frequency of occurrence and duration time of SOMs, making possible their use as fault indicators. This phenomenon has already been reported in , where tFq) will refer to the number of times a SOM is activated during a time period, while the term SOM’s duration (D) is the average time while a SOM is active.In order to provide a formal definition, in this article, the term SOM’s frequency  data segmentation, (ii) extraction of the frequency and duration of SOMs, (iii) processing the measured data, (iv) forecasting the future values of the frequency and duration of SOMs and (v) failure diagnosis based on measured or forecasted data . These sThe frequency and duration of SOMs was estimated in fixed time-windows, in order to determine the regular number of occurrences of every SOM and their regular duration time in a standardized time length (L). This time length (L) should be set, according to: (i) main system tasks (processes), (ii) time required for tasks accomplishments and (iii) task sequences. A scheme that graphically represents system tasks versus their occurrence time is shown in The time length (L) was determined through an iterative process in which the size of L was systematically changed. In every iteration, multiple time-windows with the same L were sequentially arranged, in order to analyze if the key tasks present a similar number of occurrences. This iterative process was stopped whenever a convergence in the size of the different windows was achieved. It allowed for assigning a fix value to L for providing means to make comparisons between the number of occurrences and duration time of every SOM, from different data samples.Once the standardized time length L has been set, the frequency and duration of every SOM in L should be estimated. This stage aims to get historical data of In this article, the “fault progress step” would be denoted as t .The second matrix is a The detailed procedure is described in b = 1, …, c, where c is the total number of transitions observed); In algorithm (i), w.This step aims to eliminate the variations that may occur in the proposed .Ord = 3), which denotes the polynomial order applied by the Savitzky–Golay filter, and Frame_length, which denotes the number of equally spaced data-points to be obtained after the application of the filter. Vectors corresponding to frequency are temporally put together in a The algorithm (ii) related to this step see  uses FreFq and D. These matrices contain the frequency and duration data of all observed SOMs from different and consecutive fault progress steps. This step returns Fq and D.b denotes the forecasting horizon. This process can be described as:This step  shown in the Fq and D matrices obtained in step iii were used as input for the forecasting algorithm, as well as the forecasting horizon b. The extrapolated data of frequency and duration of SOMs were stored in b elements.In this step, the This step can be conducted, either to diagnose actual failures or to analyze forming faults. Failure diagnosis is performed once a fault has reached its critical threshold by using measured data of All the F, which denotes the occurring failure mode or fault-free  of classification is shown in Once the results from the failure diagnosis and failure prognosis processes are obtained, they should be delivered to the system operators, who shall take decisions about the most suitable actions to be performed.(1)(2)To validate our hypothesis  we conducted an experiment on a small-scale cyber-physical greenhouse testbed. Two aspects were evaluated:The above-mentioned hypothesis, as well as the proposed prognosis method were evaluated through an experimental approach that aims to provide real-life conditions for analyzing fault manifestations. For this purpose, a testbed of a small-scale cyber-physical greenhouse was designed and built. The testbed enables to systematically induce and reproduce system failures for experimental purposes. A description of the setup of the testbed and the conducted experiments is presented below.The instrumented small-scale cyber-physical testbed is a scaled prototype that emulates real conditions of a fully operational greenhouse system. Greenhouse operation requires controlling several interrelated variables , which are sensitive to environmental changes. Together with a set of tasks to be accomplished by the system , these environmental changes require self-tuning capabilities, which are supposed to provide an optimal environment for plant growth, despite varying climate conditions.Controlled core area (CCA).Extended field of application (EFA).Cross domain networking (CDN).Based on , the ins2 control). The EFA coordinates the embedded systems and takes high-level decisions . Then, CDN enables the interaction with external systems.These three layers describe a hierarchical system  of different failure modes (or fault types) into the testbed was implemented. The three main failure modes experimentally induced, were:In the case of (1)The consistency of trends (of (2)The discriminant power for distinguishing different ‘Failure modes’ (Our hypothesis on the proposed failure prognosis method is that frequency and duration of SOMs can enable to reliably monitor the fault forming process (or degradation process), as well as determining the occurring failure mode. In this evaluation process, we analyzed:It can be argued that, if observed trends from different datasets but the same ‘Failure mode’, Statistical tests were implemented for evaluating the degree of similarity between the trends presented by the frequency and duration of SOMs as an effect of failures. In order to carry out this analysis, the trends of In both equations, The observed The observed Due to the fact that trends are better characterized by non-parametric distribution, Kruskal–Wallis   gathered during the fault-free Twenty data samples corresponding to SOM frequency Twenty data samples corresponding to ‘Irrigation pipe blocked’  for each class, so that, none of the failure modes would present a low classification accuracy. Samples used for the analysis presented in w steps. The first 20 fault progression steps correspond to fault-free (Once the model was available (delivered and tested) ases see . Unlike ases see  where thThe analysis conducted aimed to determine to what extent the observed SOMs’ frequency The results of the investigation are graphically presented in a bar-plot in  the low number of data samples corresponding to 2 concentration levels in the greenhouse. However, there are no further control actions that involve the components affected by the failure mode . Two sets of curves could be identified in the TTF plot at The graph depicted in d 15 see . AlthougBased on the presented results, it can be observed that the predicted TTF was shorter than the actual TTF. The failure prognosis analysis delivered an average In all analyzed cases, the observed trends of the SOMs’ frequency The analysis conducted aimed to evaluate the hypotheses that underpin the proposed health management and failure prognosis method. The obtained results demonstrated that degradation and fault evolution was manifested through variations of the frequency and duration of SOMs, which were influenced by the effect of the compensatory actions, carried out by self-tuning systems. SOM frequency and duration allows monitoring fault progress based on data derived from control signals. This last characteristic is relevant, as it enables considering variations of system behavior and environmental factors that can affect the lifetime of the system.Frequency and duration of SOMs can be considered fault indicators. They allow studying the system degradation process. In the conducted experiments, trends of SOM frequency and duration showed strong similarity for different events corresponding to the same failure mode. They also showed significant differences between trends from different failure modes. A combined analysis of the trends of SOM frequency and duration showed that they had high discriminant power enabling failure diagnosis.The discriminant power of The availability of a generic indicator for failure analysis represents a step forward towards the advent of further generations of CPSs. The reason is, the adaptable and evolvable behavior these types of systems will present strengthens the need of having indicators that work properly despite changes on system configuration, and system topology.The evaluation of the implementation of Results concerning the discriminant power of the indicators, as well as their potentials for prognosis, were positive. They suggest that SOM frequency and duration are suitable predictors for diagnosing progressive faults. Nevertheless, it can prevent the detection of failures that are manifested through transient faults. Transient faults manifest intermittently, i.e., they are not manifested through long-term trends and therefore they can be mistaken as noise effect. This particular aspect requires further study as the analysis here presented is based on the historic manifestations of failures.Finally, the proposed method is addressed to small-scale CPSs. Their application in large-scale CPSs may present problems, due to large number of possible COM combinations that a CPS composed by many components have. Further studies should be conducted in order to determine the maximum CPS size in which this method is still valid.In this article, a failure diagnosis and prognosis method for small-scale, self-tuning cyber-physical systems was proposed. Self-tuning cyber-physical systems are characterized by their capability of modifying their system settings autonomously with regards to adapting themselves to the varying working and environmental conditions. This characteristic is desirable, as it provides these types of systems with fault tolerance capabilities and it fosters a more efficient system operation. Nevertheless, it can also mask fault symptoms hampering a timely fault detection and diagnosis.The proposed method is underpinned on the varying frequency The assumptions underpinning the method, as well as its capability for failure prognosis were tested through an experimental approach where a small-scale, self-tuning cyber-physical greenhouse was instrumented in order to systematically inject different failure modes. It was found that, changes in the frequency and duration of system operation modes caused by a self-tuning system have a discriminative power in terms of failure classification, enabling failure diagnosis. Likewise, these changes show a strong correlation with the trends of system degradation, making it possible the monitoring of the fault progress with regards to failure prognosis. One of the main advantages of this method is that (1)Firstly, a proper validation of the frequency and duration of SOMs for failure diagnosis and prognosis should be performed. In the present work, only a case study based on an instrumented testbed was conducted. However, a representative set of several and heterogeneous types of self-tuning CPSs should be considered with the aim to test the limitations of the proposed concept.(2)Secondly, the analysis of variations of actuators intensity is also required. So far, variations on frequency and duration of SOMs as means of self-tuning have been analyzed. However, variations on actuators’ operation intensity can also provide relevant information about the fault forming process.(3)Thirdly, more fault forming patterns should be evaluated to determine their effect over the frequency and duration of SOMs. Due to their heterogeneous nature, faults can present multiple variations on their associated degradation process that can affect the analyzed long-term trends. For instance, faults with non-linear progression trends may influence the changes of frequency and duration of SOMs. It is argued that they cause sudden upward or downward trends that could affect the estimations of TTF, as well as the prediction of the forming failure mode.Results obtained demonstrated that the proposed method manage to discriminate and to predict the forming failure mode. Nevertheless, some aspects still require further study:The above-mentioned factors can be addressed in further investigations. Nevertheless, the present work is a step towards the understanding the potential of the proposed failure diagnosis and prognosis concept.


The performance of marker-based, six degrees of freedom (6DOF) pose measuring systems is investigated. For instruments in this class, the pose is derived from locations of a few three-dimensional (3D) points. For such configurations to be used, the rigid-body condition—which requires that the distance between any two points must be fixed, regardless of orientation and position of the configuration—must be satisfied. This report introduces metrics that gauge the deviation from the rigid-body condition. The use of these metrics is demonstrated on the problem of reducing robot localization error in assembly applications. Experiments with two different systems used to reduce the localization error of the same industrial robot yielded two conflicting outcomes. The data acquired with one system led to substantial reduction in both position and orientation error of the robot, while the data acquired with a second system led to comparable reduction in the position error only. The difference is attributed to differences between metrics used to characterize the two systems. The pose of a rigid object is defined by its location and orientation in three-dimensional 3D) space. A location is determined by a lgorithm . An apprD space. lgorithm . In imaglgorithm .In practical applications, it is important to know the accuracy and repeatability of the robot’s pose. Many measurement systems can rapidly acquire repeated measurements, filter out noise, and return mean values of individual 3D points. These preprocessing steps substantially reduce the uncertainty of the derived pose. However, a reliable estimate of the systematic pose error is a more difficult task. It requires comparisons of 6DOF poses as measured by an instrument under test (IUT) to ground truth (GT) measurements. Since the GT sensor and the IUT acquire data in two different coordinate frames, a transformation between both frames must be calculated. Thus, the error defined as the difference between the IUT and the GT pose includes a registration error. To minimize the registration error, the relative pose in the GT frame is compared to a corresponding relative pose in the IUT frame. This may be achieved by means of the ASTM E2919-13 standard for evaluating the performance of static 6DOF pose measuring systems [Since the 6DOF pose is derived from processing multiple 3D points, it is important to understand how noise and bias in the points propagate to the derived pose. For many pose measuring systems, no explicit formula is available. However, for a class of systems that derive pose by measuring several markers, extensive research has yielded analytical formulas that link the uncertainty and bias in the marker measurements with the uncertainty and error of the derived 6DOF pose. Such marker-based systems estimate pose by performing point-based, rigid-body registrations between two sets of corresponding points. Closed-form equations for propagating the uncertainty of the measured markers to the pose were derived in ,8 while In this paper, new metrics gauging the performance of marker-based, pose measuring systems are proposed that do not require a GT measurement system. The metrics gauge how well the rigid-body assumption  is preserved, with the premise being that, if the rigid-body condition is better preserved, the system will yield a better pose measurement. The value of these metrics is demonstrated on the problem of reducing robot localization error using an external pose measuring system. The Restoration of Rigid Body Condition (RRBC) procedure  was usedThe paper is organized as follows: A short review of methods to reduce robot localization error is provided in Most robotic tasks in manufacturing require precise manipulation and placement of an end-of-arm tooling. For example, automated drilling in the aerospace applications must satisfy a position error of the drill bit less than 0.25 mm . Errors To further reduce any residual errors remaining after calibration—as well as other, non-kinematic errors—different compensation techniques have been developed. Many of these techniques require dynamic tracking of the robot’s movement by external, vision-based systems, as in video servoing ,23 or diEven after remastering, a robot may still exhibit significant pose error as a result of non-kinematic causes. As such, another approach to recalibration generates static, pose-correction maps to correct for kinematic errors without having to measure DH parameter offsets. Corrections to the robot’s pose are calculated in predetermined locations from data acquired before regular robot operations begin. These corrections are then interpolated to get the correction for an arbitrary robot pose during regular operations. Different interpolation procedures have been used. For example, trilinear, cubic, and fuzzy interpolation were tested in computer simulations . The kriAnother method that does not require dynamic tracking, and that can reduce both position and orientation error, was introduced in . The ResIn this paper, the RRBC method was used in another experiment using the same robot arm as in , but a dIn the RRBC method, small corrections to the commanded robot poses (target poses) are linearly interpolated from previously determined corrections calculated from fiducial poses measured by a pose measuring system and derived from the robot kinematic model. Fiducial poses are measured in both robot and sensor frames while the target poses are usually only measured in the sensor frame but need to be accessed in the robot frame. To calculate the corrections, a rigid body transformation from the sensor frame to the tool center point (TCP) frame is needed.Generally, when there is a constant offset transformation, loped in . The oriribed in . After tloped in , and , and The weights, Two metrics are defined in this paper to gauge how well the rigid-body condition is preserved by marker-based pose measuring systems. Additionally, a third metric is defined which can be used to compare any two corresponding 6DOF datasets acquired in two different coordinate systems . In the context of reducing errors using the RRBC, we associate the first frame, j-th pose of the rigidly-mounted markers. At least three markers must be used to uniquely define a 6DOF pose. To identify each marker given an arbitrary marker configuration, the layout of the markers should be such that the distances between the centroid of all markers and each individual marker are distinct, and can be easily sorted from the longest to the shortest  was a fThe robot was commanded to ribed in . For thej-th pose, the AIK module was used to calculate all j-th pose A different set of Histograms of the distances Histograms of the angles Histograms of angles The histogram of the numbers The histogram of standard deviations The performance of the RRBC procedure was gauged by uncorrected and corrected orientation errors, The position errors obtained from the data acquired with the laser tracker in Experiment 1 are shown in A summary of the results of the RRBC procedure applied to data acquired in Experiment 1 is provided in As seen from The two systems belong to two different classes of instruments, which may be appropriate for different types of applications. The laser tracker yields measurements with lower uncertainty and higher accuracy than the motion capture system. Both systems derived 6DOF pose from the measurements of three 3D points. This approach requires that the configuration of the three points behaves as a rigid-body, which means that the distances between any two measured 3D points are fixed. While none of the systems used in the experiment fully complied with this requirement, the laser tracker provided data that better satisfied the rigid-body condition than the motion tracking system, as the plots in The metrics provide useful inputs when selecting a pose measuring system for robotic applications. To simultaneously reduce both position and orientation errors, the biases in the data acquired with the pose measuring system should be sufficiently small. The data shown in A comparison of the angles While the laser tracker may provide more accurate measurements of 3D points than the camera-based motion capture system, it is not obvious that the more accurate positional measurements will always yield more accurate orientation data as characterized by smaller The two metrics  and (7). Consequently, large outliers are seen in the corrected position error, As mentioned earlier, most of the fiducial poses surrounding each In summary, the metrics proposed in this paper helped to explain the conflicting outcomes of the reduction of robot localization error. Two of these metrics are convenient as they gauge the performance of marker-based systems by evaluating a deviation from the rigid-body condition. Thus, they do not require ground truth sensors. It remains an open question as to how to develop similar metrics for other, markerless pose measuring systems.