David Antonio

Gómez Jáuregui

Nadine Couture
email: n.couture@estia.fr

Tacsel: Shape-Changing Tactile Screen applied for Eyes-Free Interaction in Cockpit

Keywords: Tangibility, eyes-free touch interaction, shape-changing, cockpit control, complex system

: The Tacsel concept providing shape-changing tactile screen. First image: a touch screen displaying a tree. Second image: a group of Tacsels emerging from each apple of the tree to provide eyes-free touch interaction. Third image: user interacting with one Tacsel. Fourth image: apple falling from the tree as a result from the touch interaction, the Tacsel disappears providing an eyes-free interaction as a robust feedback.

INTRODUCTION

Touch screens have become ubiquitous in the last years. By and large, we are witnessing a paradigm shift where typical physical controls are being replaced by touch enabled surfaces on numerous devices of common use. These technologies enable the user to interact directly with what is showed on a screen by touching it through simple or multitouch gestures. They have been adapted to different electronic devices due to their natural and direct interaction, comfortability, flexibility, low cost, etc. We find touch screens in a daily basis in cash machines and ticket-selling points at streets, in mobile phones, or in-home appliances such as washing machines or microwaves, to cite some. However, touch screens are not well suited to eyes-free interaction and cannot be used in dynamic environments subjected to vibrations and acceleration [START_REF] Vinot | Could tangibility improve the safety of touch-based Interaction?[END_REF]. In addition, touch interaction provides poor sensory feedback and they cannot be applied to some activities involving simultaneous tasks since these technologies require complete visual attention and stable manipulation especially within complex systems. Indeed, the design of interactions within a complex system is challenging. A complex system involves many components which may interact with each other. It is common to say that a system is complex when Human is in the loop, otherwise, as much as sophisticated the system is, we can qualify it of "merely complicated ». The system we are studying is therefore of great interest in the context of a complex system. As said in [START_REF] Boy | Unifying Human Centered Design and Systems Engineering for Human Systems Integration[END_REF], human system integration within complex systems requires more flexibility and new approaches including creativity as an integral part and where the functions of people and technology are appropriately allocated. For example, in a cockpit context a touch screen is difficult to manipulate in flight when severe turbulence occurs [START_REF] Vinot | Could tangibility improve the safety of touch-based Interaction?[END_REF], in addition pilots require to manipulate several tasks in critical situations in which the visual attention time is very limited. Another example of complex system is in the case of driving task, where we observe a poor use of physical space related skill [START_REF] Hornecker | Getting a Grip on Tangible Interaction: A Framework on Physical Space and Social Interaction[END_REF]. Using touch screen, the driver visual attention can be drawn away from the road and towards the screen easily. In recent years, advancements in robotics have brought the development of touch screen devices for use in medical surgery [START_REF] Mbabazi | Applications of tactile sensors and displays in robotically-assisted minimally invasive surgery[END_REF]. However, the requirement of visual attention can make the medical surgery task very complicated [START_REF] Mbabazi | Applications of tactile sensors and displays in robotically-assisted minimally invasive surgery[END_REF]. Finally, touch screen technologies are also difficult to be operated for the visually impaired. It is necessary to let these people know where they need to touch. A key point, therefore, is to provide eyes-free interaction in system. Despite numerous advantages supported by touch screen technology, a full touch screen system is not optimal and hence a process of tangibilisation must be undertaken. In this article we introduce and explore the feasibility of introducing adaptable, shape-changing technologies in touch screen devices in the coming years. With this purpose, we have adopted a metaphor. In the same way "pixel" stands for the smallest element of a picture (picture element, for short pi(ct)el = pixel), we propose similarly "Tacsel", the smallest tangible element of a tactile device (tactile screen element, for short tac + s + el = Tacsel) that allows for a shapechanging tactile device, that means tangible touch screen. In our proposed approach, multiple Tacsels will be integrated into touch screens and will emerge according to the use context. In this way deformable and adaptable properties will provide eyes-free interaction to tactile devices. Several functionalities are envisaged such as providing relief to tactile surfaces, pressing a tactile button without looking at it, improve perception in tactile alarms, transform a tactile surface into a joystick, combining several buttons into a larger button that can be manipulated on the sides, etc.

The article is organized as follows: we begin by revisiting the related work. Then, the implementation of a prototype of the Tacsel concept is described. After, the potential of the proposed prototype is validated within a complex system (a cockpit). We explore and validate the possibilities of our proposal by describing three interaction scenarios and conducting a workshop involving different cockpit tasks. Finally, we draw several conclusions and point out future trends.

RELATED WORK

Several authors have proposed touch screen technologies with shape-changing and flexible properties. These technologies could be used to provide eyes-free interaction in complex tasks. Robinson et al. [START_REF] Robinson | Emergeables: Deformable displays for continuous eyes-free mobile interaction[END_REF], showed that deformable displays, called emergeables, have a strong potential for on-demand, eyes-free control of continuous parameters. They showed the value and benefits of tangible controls -which "morph" out of a flat screenin terms of accuracy, visual attention and user preference. Based on the previous work, Rosso et al. [START_REF] Rosso | Simulating an extendable tangible slider for eyes-free one-handed interaction on mobile devices[END_REF] proposed an extendable tangible slider to provide eyes-free and one-handed interaction on mobile devices. The tangible slider's knob extends to maintain the thumb's movement within its comfortable area. Pauchet et al. [START_REF] Pauchet | GazeForm: Dynamic Gazeadaptive Touch Surface for Eyes-free Interaction in Airliner Cockpits[END_REF] introduce GazeForm, an adaptive touch interface with shape-changing capacity that offers an eyes-free interaction according to gaze direction. When the user's eyes are focused on interaction, the surface is flat and the system acts as a touch screen. When eyes are directed towards another area, a salient tangible control emerges from the surface. The proposed interface was implemented in a cockpit context where simple pilot tasks were simulated in an experimental study. An input technology that can be merged with a screen is FlexSense [START_REF] Rendl | FlexSense: a transparent self-sensing deformable surface[END_REF], a thin-film, self-sensing deformable surface that, based on printed piezoelectric sensors, can reconstruct complex deformations in a computer. However, there is major limitation due to its bulkiness. PAPILLON [START_REF] Brockmeyer | PAPILLON: designing curved display surfaces with printed optics[END_REF] is a technology for designing curved interfaces that can both display information and sense two dimensions of human touch. Some of the constraints of this technology is that images are in grayscale with low resolution. Rudeck et al. [START_REF] Rudeck | Rockpaper-fibers: bringing physical affordance to mobile touch devices[END_REF] proposed rock-paper-fibers which is a device functionally equivalent to a touchpad. However, each sensor element is composed of an optical fiber. By using a bundle of fibers, a user can reshape and deform it to enable different applications.

Deformable User Interfaces (DUIs) is a promising domain proposing new tangible and organic interaction metaphors and techniques. Researchers at the Nokia Research Center have developed a prototype of a mobile phone with bendable display and deformable back cover [START_REF] Teemu | What is a device bend gesture really good for?[END_REF]. Yao et al. [START_REF] Yao | PneUI: pneumatically actuated soft composite materials for shape changing interfaces[END_REF] proposed PneUI, which is a pneumatic system made by soft composite material that integrates both sensing and actuation mechanisms. Close to pneumatic systems are the hydraulic systems [START_REF] Watanabe | Artificial tactile feeling displayed by large displacement MEMS actuator arrays[END_REF] since liquids are incompressible, the pressure and force obtained are quite high. Drawbacks on these systems are similar to those from pneumatic systems regarding uniform liquid distribution and fault tolerance. Dielectric-based devices are another type of systems with a good response time that can create Braille pins and vibratory devices. An interesting system is Teslatouch, by Bau et al. [START_REF] Bau | TeslaTouch: Electrovibration for Touch Surfaces[END_REF]. They developed a technology that, based on the electro vibration principle, provides tactile feedback in touch screens. However, its size is too large and the modulated electrostatic field, 10 kvolt, is quite strong for a comfortable use. DeFORM [START_REF] Follmer | DeForm: an interactive malleable surface for capturing 2.5 D arbitrary objects, tools and touch[END_REF] is a digital tangible interface that allows users to imprint 2.5D shapes from physical objects into their digital models by deforming a malleable gel input device.. Since it can recognize physical shape as well as pressure depth, authors advocate their use as a means to provide tangible controls. LineFORM [START_REF] Nakagaki | LineFORM: Actuated Curve Interfaces for Display, Interaction, and Constraint[END_REF] is a shape-changing interface to explore new possibilities for display, interaction and body constraint. This actuated curve interface is able to convey information and provide dynamic affordances according to its current shape. Leithinger et al. created inFORM [START_REF] Follmer | inFORM: dynamic physical affordances and constraints through shape and object actuation[END_REF], a shape display implemented as a surface with multiple actuators (pins) and sensors. The surface is able to render different shapes and provide dynamic feedback when the user touches it, such as vibration or elasticity. This provides great versatility, allowing for the creation of dynamic UIs such as handles, buttons, slides, etc., which react to touch or deformation. It has been used as well to provide physical telepresence by creating shapes that respond to a remote human controller. An evolution of the inFORM display was the TRANSFORM project [START_REF] Ishii | TRANSFORM: Embodiment of "Radical Atoms" at Milano Design Week[END_REF]. This project challenged the conventional notion of static furniture design by providing three inform displays that could reshape a surface on demand.

Despite numerous touch screen technologies allowing shape-changing and deformable properties, most of these existing technologies have several limitations (bulkiness, complex materials, not enough flexibility, etc.) to be used in different contexts involving complex tasks. Inspiring by the state of the art and especially by inFORM our objective has been therefore to create a system small and lightweight, that could be adopted in different contexts.

DESIGN AND IMPLEMENTATION OF TACSEL

Based on this deep study of related work, we imagine a matrix of Tacsels as a flexible and shape-changing tactile screen. The biggest challenge of the high-resolution prototype is to design the technical functionalities, including shape-changing interfaces, combining actuators and sensors in a small form factor. Concerning the specification of the Tacsel, it should travel at a vertical distance large enough to be noticeable by the user, define to be 6cm. The Tacsel also be stable in a medium position, despite a pressure made by a user. It should also move at variable speed to demonstrate different scenarios, which is chosen to be between 1mm/s and 5mm/s. A prototype with one Tacsel has been designed in order to demonstrate the concept, its technical feasibility, its operationality and to test its potential. The vertical movement of the object is made with a micro gear-motor coupled with a threaded rod. A nut is incorporated inside the Tacsel which allows to move the object vertically when the motor shaft is rotating. The Tacsel is a parallelepiped rectangle (Figure 2(a)), integrated in a box of 16 cm high designed to incorporate 4 objects. This box has been designed in 2 parts: the upper part (Figure 2(b)), which covers the motors and guides the moving Tacsel; and the lower part (Figure 2(c)), hosting the motors and electronic devices. All these objects have been designed with the Onshape CAD tool and built with a 3D printer. A picture of the built prototype is shown in Figure 3.

In order to interact with the Tacsel, two sensors have been incorporated to the prototype. The first one is a position sensor, made with a linear potentiometer slider, measuring the exact position of the movable object. The second one is a motor current sensor, which allows to measure the electric consumption of the motor, thus to know if a pressure is made to the movable object. An electronic board has been designed to control the motors, collect information (thanks to the sensors), and communicate with other devices of the cockpit. The microprocessor used is an Arduino Micro.

SOFTWARE ARCHITECTURE FOR CONTEXT AWARE INTERACTIVITY

We are interested in providing a more advanced, richer and eyes-free interaction to the user through context-based dynamic adaptation of tangible controls. In the proposed interaction, the touch screen management system must be able to emerge the necessary tangible controls according to the context of use and the respective situation. Tangible controls can be emerged from two situations: when the user performs a hand gesture event (e.g. open palm) on the touch screen; when the touch screen management system requires a specific intervention from the user. In both situations, the tangible element will provide the necessary tangible controls to the user when needed. Hand gesture events can be detected accurately by embedding to the touch screen small gesture recognition devices such as Leap Motion Controllers. These hand gesture events can then be sent to a particular tangible control designated by the context. Figure 4 presents the software architecture diagram of the proposed interaction. As shown in this diagram, a server module continuously receives the events generated by the touch screen management system and the hand gesture detection module. The server then emerges a tangible control, a Tacsel, that corresponds to the event received and the current context.

APPLICATION FOR AERONAUTICS

Future dematerialization of aircraft panels will allow us to foresee a more interactive, full-tactile cockpit in the dawn of 2035. The trend is towards the replacement of instrument panels by touch screens that combine both the input and output role [START_REF] Angel | The aircraft of the future: towards the tangible cockpit[END_REF][START_REF] Vinot | Could tangibility improve the safety of touch-based Interaction?[END_REF]. However, touch-based interaction requires high demands on the visual attention in several cockpit tasks [START_REF] Voelker | Knobology Revisited: A Comparison of User Performance between Tangible and Virtual Rotary Knobs[END_REF]. Tangible interaction technologies could improve the safety needed by cockpit tasks allowing eyesfree interaction and adaptability to dynamic flat cockpit environments [START_REF] Vinot | Could tangibility improve the safety of touch-based Interaction?[END_REF]. The potential of tangible interactions embodied in flat cockpits have been explorer recently by [START_REF] Pauchet | GazeForm: Dynamic Gazeadaptive Touch Surface for Eyes-free Interaction in Airliner Cockpits[END_REF]. These authors also address the importance of multimodal interaction to support the significant level of multitasking involved in pilot activities. Letondal et al. [START_REF] Letondal | Exploring the Physical Design Space for Situation Awareness and Performance in the Interactive Cockpit[END_REF] explored how advanced interaction techniques (tangible, haptic, organic, etc.) could better support pilot flying and navigation activity. In 2016, Vinot et al. [START_REF] Vinot | Could tangibility improve the safety of touch-based Interaction?[END_REF], studied how tangibility improves the safety of touch-based Interaction in the context of pilot system interfaces. They identified a set of design principles for touch based and tangible embodied interaction in the cockpit. A point of convergence of the previous work with Lorenzo and Couture [START_REF] Angel | The aircraft of the future: towards the tangible cockpit[END_REF], both in 2016. They both acknowledge the existence of similar cognitive requirements in current cockpits (performance in a degraded context, situation awareness, etc.). However, Lorenzo and Couture work's [START_REF] Mackay | Video prototyping: A technique for developing hypermedia systems[END_REF] starting point is the actual existence of a tactile cockpit and how to deal with the potential problems that might prevent its adoption. They proposed a set of 6 properties, from a usability point of view, that should be found in a tangible cockpit: free-form, interactive, morphable, reconfigurable, context-aware and eyes-free. Thereby, they envision a cockpit that, based on both existing and novel technologies, can convey information to the pilots by modifying their shape according to the context. Our proposition of Tacsel responds to all of the properties they defined. The aeronautical industry is not oblivious to this tendency, and so avionics manufacturers have been experimenting with prototypes of touch screen-based cockpits. Two main foreseeable benefits arise from the adoption of these tactile technologies. Firstly, manufacturers are addressing pilots that are still 5-year-old children. This means that they will grow up accustomed to the use of touch screens and many other types of tactile devices, and hence this type of interaction will be intuitive and efficient for them. Secondly, the multi-purpose nature and flexibility of a full software-based system will reduce both capital and operational expenditures, allowing for shorter development and-and-testing periods of newer cockpit generations. Of course, an interactive cockpit based on a continuous tactile surface presents several potential usability problems that must be addressed. Examples are the need for a good visual perception of the on-screen objects, a proper response to fine-motor skills, or hand comfort and palm detection on the touch screen [START_REF] Pauchet | GazeForm: Dynamic Gazeadaptive Touch Surface for Eyes-free Interaction in Airliner Cockpits[END_REF]. There also exist important issues regarding the situational awareness and performance under degraded conditions that are caused by instability in a plane such as turbulences. These drawbacks have limited the adoption of tactile surfaces in the cockpit and, hence, have led to an understandable resistance from the aircrew to remove critical controls from their physical form. However, studies, in cockpits, indicate a clear performance advantage of touch systems accompanied by less workload when compared to, for example, trackball interaction [START_REF] Eichinger | Between laboratory and simulator: a cognitive approach to evaluating cockpit interfaces by manipulating informatory context[END_REF]. So, while it is accepted that some issues exist, the idea of a tactile cockpit is to be kept at the expense of addressing their limitations. This is the reason why newer ways of interaction must be envisioned, and the idea of mixing the digital and the physical world leads us to the concept of a "tangible cockpit" with shape changing and flexible elements. Looking at the current evolution of the cockpit in the last sixty years, we observe how manufacturers have gravitated towards grouping the maximum number of related functions into a common display, as well as increased the number of functions and information available to pilots. To go further it is now important to design a cockpit where the pilot will be provided with an environment in which she does not have to distract her visual attention (i.e. looking at her hands) while she is performing any manual action. In this context, the cockpit must convey accurate learning and representation of information, perhaps not necessarily the same way as a visual display does but provided through physical contact.

User interaction scenarios

We have implemented three different interaction scenarios to demonstrate the potential of the proposed context-based interaction. Each scenario describes a different context or situation showing the eyes-free interaction provided by the emergeable tangible cockpit controls. For this demonstration, we have integrated in a simulated cockpit the Tacsel prototype described previously and a Leap motion controller. For each scenario, we have added to the Tacsel a different interaction device that will be emerged depending on the context of use. Each scenario is described in the following subsections:

First scenario: tactile display (applied to flight instruments) Consider the scenario in which a pilot must read carefully the airspeed variation values showed in a screen during extreme turbulence conditions. While focused on the screen, the pilot must be able to maneuver correctly the aircraft speed in order to prevent the aircraft from being damaged. At the timing when the airspeed variation value changes abruptly, the pilot performs immediately a hand gesture in front of the cockpit (figure 6). Then, a Tacsel containing a small tactile display (smartwatch attached for testing) emerges from the cockpit directly to the position where the hand of the pilot is located (figure 6a). Using the context information (flight context), the Tacsel propose a tactile interface that allows reducing the aircraft speed. The pilot then touches the small tactile device to reduce the aircraft speed and preventing a possible damage in the aircraft (figure 6b). Finally, the Tacsel returns to its original position inside the cockpit.

Second scenario: joystick interaction (applied to navigation instruments)

In this scenario, the pilot is guiding the aircraft toward a landing field. In this task, the pilot must use a yoke to control the plane's attitude. In order to ensure a successful landing, the pilot has limited time to adjust the airframe parameters using a specific joystick. While focused on the guiding, the pilot approaches his hand to any part of the cockpit (figure 7a). Then, using the context information (navigation), a Tacsel containing the specific joystick emerges near the location of the pilot's hand (figure 7b). The pilot then manipulates the joystick to adjust the airframe parameters. Finally, the joystick returns to its original position inside the cockpit.

Third scenario: battery contact activation (applied to systems management)

In this scenario, the pilot is focusing all his attention in landing the aircraft. At the same time, he must perform four necessary tasks to shut down correctly the engine system (figure 8). At the moment when each task must be performed, a Tacsel containing a switch button emerges from the cockpit near the pilot is located (figure 8a). The pilot then notices the Tacsel and proceeds to press the switch button that activates the specific task (figure 8b). Finally, the Tacsel containing the switch button returns to its original position inside the cockpit. Figure 8: System management context. The system knows that the pilot must activate the battery contact.Therefore, a Tacsel containing a switch button (highlighted with a red circle) emerges near the pilot (a). The pilot notice the Tacsel and immediately press the switch button (b).

VALIDATION OF THE CONCEPT

In order to validate the potential of the Tacsel concept, and of its technology within a cockpit, we conducted a workshop. The aim of the workshop was to verify if the concept is, indeed, a good candidate for the design of a shape changing and flexible cockpit, or, in other words, if the Tacsel is able to inspire new metaphors of interaction for cockpit's usages.

Procedure

We invited 18 participants (4F, 12M, age around 23 years old), to take part in 2 half-day sessions. All of them were knowledgeable about aeronautics and human-computer interaction in cockpits. Two of them are pilots. In order to stimulate idea generations, we used the method of creating video-prototypes. The video-prototypes were introduced by Mackay [START_REF] Mackay | Video prototyping: A technique for developing hypermedia systems[END_REF] to illustrate by video how users will interact with a new system. The goal is to refine a single system concept, making design choices that highlight and explore a particular design path. The technique appears similar to video-brainstorming. Both involve small design groups who work together to create and interact with rapid prototypes in front of a video camera. Both result in video illustrations that render abstract ideas concrete and help team members communicate with each other. Both use paper and pencil prototypes or cardboard mockups to simulate the technology. The critical difference is that videobrainstorming expands the design space, by creating a number of unconnected collections of individual ideas, whereas video-prototyping contracts the design space, by showing how a specific collection of design choices work together in a single design proposal.

During the workshop, the video-prototypes was built upon a number of design resources created in two earlier design exercises (also included in the workshop process): brainstorming at first and then cyber physical system design. Therefore, the workshop took place in 3 stages.

Results

Stage 1: 64 concepts generated

After the brainstorming, 37 concepts in first group and 27 in the second group, 64 in all, were generated and written on paper board. All of them illustrate a usage in a cockpit of the interactive Tacsels.

Stage 2: 3 Concept-Designs (CD) generated

During the cyber physical (or mecatronic) design session, 3 concepts (among the 64) were explored by 3 groups of 6.

[CD1] Fly-Pilot is both an actuator and an instrument that indicate the attitude of the plane for the control. It is designed using Tacsels, with those characteristics: 6 cm. of amplitude maximum, speed of movement (vertical): 2cm/s, rounded Tacsels (without edges). The system consisting of 5x8 pimples, which are organized in a rounded shape (like the top of a mouse to correspond to the hand, Figure 10). The system must bear a force exerted by the hand posed without pressing. The system embeds pressure sensors to know when user pushes on the Tacsels in order to modify the position of the plane and position sensors to visualize and give the information in real time). [CD2] breakdown of the artificial horizon is for the pilot to obtain quickly and easily an alert in case of road converging with a relief, according to its route and its position. This system is tangible, this means that it will be able to interact physically with the pilot. In the case of a collision route, the Tacsel associated with the ground will rise to signify the alert. The pilot will then be able to press this Tacsel and receive the information on the obstacle on a related screen. Mechanical technical considerations: given an anticipation of 5 mm between the display and the actual terrain, it is not necessary to have a quick lifting movement of the Tacsels in case of alert. Thus, we consider a movement of an amplitude of 5 cm in 10 s, 5mm/s i.e. 5 revolutions/s with a screw thread of 1mm. A power sensor will allow to perceive the push on the Tacsel that have triggered the alert. The information relating to the obstacle will then be displayed on a screen. [CD3] Tangible Interactive Radar is to indicate to the pilot the location of other aircraft within a radius of 80 kilometers. The pilot's plane is at the center of the radar and is marked with a blue color. The other planes are red or green if communication between the two devices is established. To establish a communication with a device visible on the radar, it is enough for the pilot to touch the top of the representation. The radar shows the altitude of the other planes relative to the ground and proportionally to that of the radar of the aircraft. The maximum height is 15cm (representing 10 kilometers in reality) A refresh of the positions is carried out all in real time. Technical considerations: the radar has a diameter of 20 cm. and a maximum height of 15 cm. Touch surfaces (tactile sensors or pressure sensors) are present on the top of the Tacsels allowing the selection of aircraft for communication. Inside the Tacsels there are two leds (one red for the position of the other devices and one green to know with which one communicates). The maximum lifting speed of the Tacsels is 1 cm/s.

Stage 3: 2 video-prototypes generated

Then, in two groups of 9, participants constructed low fidelity prototypes and then used them to realize the two video-prototypes. They begin with a title card that includes the name of the system, the date and the list of each team's name. Their use narrator voices to explain, at first, and after, to play the situations as it happens in cockpit. Team members can play with low fidelity special effects. For example, record a user pressing a button; change round sticker from red to green (Figure 11c). The two simulations are very convincing. First one was called [VP1] F-PICO (1'27"), it goes further in order to simulate the first concept above (Fly-Pilot). Second was called [VP2] CHECKLIST (1'32"), it simulates the checklist before take-off (Figure 11).

The results of the workshop, their number and their richness, show that interactive Tacsels have a real potential in terms of use in cockpit.

DISCUSSION AND CONCLUSION

We proposed a concept of system, called Tacsel, that provides eyes-free interaction with touch screens. To the best of our knowledge, this is the first concept that combine tactile screen and tangible interfaces for eyes-free interaction by shape-changing of the display. Since no fully general theory of complex systems has emerged, we must design complex systems in domain-specific contexts. This is what we have done this study within the aeronautical domain.

We tackle the problem by considering the main task to be capturing, rather than reducing the complexity of the interaction system following the advice "do not substituting complexity with simplicity" of D. Norman [START_REF] Norman | Living with complexity[END_REF]. We started this paper by justifying the need for a tangibilisation of the touch screens due to the adoption of tactile technologies for different tasks. Then, we review existing technologies that could provide shape changing and eyes-free interaction to tactile technologies. We propose a hardware design in small form factor that proof the technical feasibility of deformable display. We implemented the functional prototype in interaction with gestures of the hand (connect with a leapmotion). Two different interactions are proposed using this prototype: 1) tangible controls can be emerged with hand gestures (open palm) or context-aware. 2) user can interact directly with a Tacsel by touch or joystick manipulation. According to Rasmussen et al. [START_REF] Kirkegård Rasmussen | Balancing User and System Control in Shape-Changing Interfaces: a Designerly Exploration[END_REF], the level of control offered to the user over a shape changing interface can be performed in four different types: 1) directly controlled by the user's explicit interactions; 2) negotiated with the user; 3) indirectly controlled by the users actions; 4) fully controlled by the system. In our prototype the first and the fourth type of interaction is proposed by implementing three interaction scenarios in a cockpit manipulation context. The proposed interactions allow three different types of feedback behavior: 1) if the Tacsel emerges, the Tacsel tells the user to perform an action by touching it. 2) if the action was validated, then the Tacsel disappears and the user knows that the action was correctly done without necessity to look at it. 3) if the action was not validated the Tacsel remains and the user knows that there was a problem with the action by looking the behavior of the Tacsel. These interactions allow to develop adaptive and responsive tactile interfaces.

We also conducted studies that show the generative power of this concept and the adhesion of future designers. These studies proved the potential of a Tacsel based system for shape changing cockpit and validate the generative power of Tacsel in term of usage.

Our system could be improved by using the direction of the gaze. For example, if the user is looking at the touch screen then the touch screen would remain flat, otherwise shapechanging deformation would be created on the touch screen, this has been explored for aeronautics in [START_REF] Pauchet | GazeForm: Dynamic Gazeadaptive Touch Surface for Eyes-free Interaction in Airliner Cockpits[END_REF]. In addition, if the surfaces on the 4 sides of the Tacsel become tactile then new way of interactions would be possible. For example, a Tacsel would behave as a kind of miniature Cubtile [START_REF] De La Rivière | CubTile: a multi-touch cubic interface[END_REF], an interaction device allowing the manipulation of 3D models.

Another key element to consider in the Tacsel is the shape transition. In this case, the shape changing properties of the tangible interface during the actuation could be studied according to the context of usage. For instance, the speed of actuation was studied by [START_REF] Daniel | CairnFORM: a Shape-Changing Ring Chart Notifying Renewable Energy Availability in Peripheral Locations[END_REF]. We plan, specifically, to study the changing phase. Is an instant transition better than a gradual transition? Our next step is to multiply the Tacsels in a Tacsel matrix system and then to focus on experimentation of the Tacsel system embedded in a cockpit simulator such as ODICIS [START_REF]ODICIS Web Site[END_REF] for several scenarios. Finally, we can inspire from new technologies to evolve the Tacsel toward a more flexible tangible element. This would allow to adapt the Tacsel more easily to different tasks such as driving and medical surgery.

Figue 2 :

 2 Figue 2: The design of the Tacsel system

Figure 4 :

 4 Figure 4: Software architecture diagram.

Figure 6 :

 6 Figure 6: Flight context scenario. A Tacsel containing a tactile display (highlighted with a red circle) emerges when the pilot performs a hand gesture (a). The pilot uses the tactile device (b).

Figure 7 :

 7 Figure 7: Navigation context scenario. A Tacsel containing a joystick control (highlighted with a red circle in image b) emerges near the pilot's hand (b). The pilot then manipulates the joystick (c).

Figure 10 :

 10 Figure 10: Video-prototype F-PICO. First image: beginning. Second image: using by moving hand with Synthetic Vision System (SVS) feedback. Third image: real SVS.

Figure 11 :

 11 Figure 11: Video-prototype CHECKLIST: (a) beginning with all buttons on red and the first button of the checklist emerges, (b) the checklist takes place some buttons turn to green, (c) change sticker from red to green.

ACKNOWLEDGMENTS

This work has been conducted over several years, we take advantage of this space to thank the people who contributed for its realization and improvement. First, we thank Sylvain Hourlier from Thales Avionics for identifying, in 2015, the research problem "Interaction with tactile surfaces in a degraded context". We thank also Jean-Luc Vinot for the discussion regarding the cockpit evolution. Special thanks to Juan Angel Lorenzo del Castillo for his collaboration regarding the related work and Sylvain Baudoin for building the first prototype. We thank Catherine Letondal for animating the creativity session (video prototyping) and the engineering students from ESTIA for their participation. Special thanks to the reviewers of the first version of this article submitted in December 2016 to IEEE Pervasive Computing Magazine's special issue on Physical Computing: Flexible and Shape-Changing Interfaces, guess editor Céline Coutrix, for their useful feedback that helped to improve this article to be accepted in this edition of HSI. Finally, special thanks to Irvin Dongo for his contribution in the design of the teaser image.


Seyed Javad
email: seyedjavad.padam@yahoo.com

Padam Bahram Nooshad
email: bahramnoshad@yahoo.com

Designing A Protective Relay for Differential Protection of Power Transformers Using Clarks Transform and S Transform

Keywords: Protective Relay, Differential Protection, Power Transformer, Clarks Transform, S Transform

Given that power transformers are one of the most important components of each network, their protection is an important part that the power transformer errors must be accurately identified and distinguished from each other. Therefore, identification and differentiation of transient phenomena of power transformers, including internal and external errors and magnetic inrush current are essential. In this research, Clarke transform and S transform were used to distinguish between these phenomena that the proposed algorithm is very suitable in terms of three characteristics of accuracy, speed and computational cost. Initially, the simulation of internal, external errors and magnetic inrush current of the transformer was performed for different transformer scenarios. For this purpose, 1060 signal tests were performed under different conditions. Subsequently, the signals of differential current obtained by Clarke transformation and S transformation were analyzed and appropriate criteria were extracted for detecting the current of internal errors from external errors and inrush current. The simulated internal and external errors include three-phase, three-phase to ground, two-phase, two-phase to ground and phase to ground error. Simulations were performed using PSCAD software and implementation of the proposed algorithm in MATLAB environment. The results of this study prevent the unwanted performance of differential protection to prevent undesirable electrifying. It is clear that the description of transient phenomena is the first step towards improving new ideas and criteria for protection with the greater reliability of power transformer which can be controlled better such unusual conditions that are currently used in equipment and relay.

Introduction

Transient phenomena of power transformers include internal errors, external errors, and inrush current. Internal errors of the transformer are related to one of the components of power transformer that the most important of these errors are three-phase, three-phase to ground, two-phase, two-phase to ground and phase to ground. External transformer errors are not related to the power transformer and depend on the network and load. Of external errors can be referred to overloaded, short circuit, overvoltage. The magnetic inrush current also occurs due to the nonlinearity of the transformer core at the moment of the transformer energization. The plan of differential protection for the transformer is a general and comprehensive plan that detects the error current and operates. The primary protective relay is sensitive to any type of unbalance in current transformers or saturation of current transformer, and in some cases the heavy unbalance of the loads connected to the power transformer, and therefore causes the mal-operation of relay. Currently, intelligent algorithms are used to improve the reliability of relay. In this type of relay, there is also mal-operation due to the inrush current.

In the standard relays, internal errors are distinguished from the magnetic inrush current with the help of the second order harmonic. One of the most important features of the high-speed differential relay is during transient phenomena that harmonic differential relays do not have a high velocity. The description of transient phenomena of transformer is the first step towards improving the new ideas and criteria for protection with a greater reliability of the power transformer, which can control better such unusual conditions that are already used in equipment and relay and prevents the unwanted operation of differential protection.

The most important factors that can lead to unwanted performance of the differential protection of power transformer include the ratio of current and power transformers conversion, group vector and transformer connections, inrush current, overflow and the effect of the transformer pulse shift mechanism. Various studies have been done on differential protection of power transformers based on various algorithms. Javad Feyz et al. [START_REF] Faiz | A novel wavelet based algorithm for discrimination of internal faults from magnetizing inrush currents in power transformers[END_REF], based on the wavelet transform have proposed an algorithm that decides to separate the internal error from inrush currents by considering different current behaviors under error conditions and inrush current. Jing Ma et al. [START_REF] Ma | Identifying transformer inrush current based on normalized grille curve[END_REF] have used a normalized window curve to distinguish between inrush current conditions and internal error in two time and frequency domains. The normalized window curve is useful for transient signals and extracts its features by quantitative calculation. Ali Hooshyar et al. [START_REF] Hooshyar | A new algorithm to identify magnetizing inrush conditions based on instantaneous frequency of differential power signal[END_REF] have used average differential power to detect the saturation conditions from the waveform characteristics of signal.

Therefore, this algorithm is independent of the parameters of transformer and its power consumption. That's why the accuracy and speed of this method is high in compare with state and parameter estimation algorithms such as Kalman Filtering [START_REF] Behvandi | A New computation reduction based nonlinear Kalman filter[END_REF], [START_REF] Behvandi | Design, fabrication and 3-DOF control of legless capsule robot[END_REF].

Majid Sanaye Pasand et al [START_REF] Sanaye-Pasand | An adaptive decision logic to enhance distance protection of transmission lines[END_REF] in order to improve the performance of distance relay of transmission lines provide an adaptive logic. The adaptive logic stated in this reference can be used to distinguish between internal errors from external errors and the magnetic inrush current in power transformer. Y.V.V.S. Murty et al. [START_REF] Murty | A Kalman filterbased digital percentage differential ad ground fault relay fora 3 phase power transformer[END_REF] have proposed the design and implementation of time domain of Kalman filter based on the digital percentage protection and ground error for the transformer. Ernesto Vázquez et al. [START_REF] Vázquez | Transformer Differential Protection Using Principal Component Analysis[END_REF] have proposed a protective algorithm based on detecting differential current pattern. This algorithm uses the main component analysis to eliminate waste information and improve the secret pattern in the differential current to distinguish internal errors from inrush current and over-stimulation. Z.

Lu et al. [START_REF] Lu | A morphological scheme for inrush identification in transformers protection[END_REF] have presented a cognitive pattern for detecting the inrush current of the transformer. The proposed plan separates and analyzes the signal based on the analysis of cognitive-mathematical operators in several levels.

Since differential current signals are unstable, it is required a powerful tool for signal analysis. Transform S is a powerful tool for frequency analysis -time series signals. S.R. Samantaray et al. [START_REF] Samantaray | Power transformer protection using S transform with complex window and pattern recognition approach[END_REF] use the S transform to distinguish between inrush currents and internal error. The elements of this matrix are mixed numbers, which determine the amplitude and phase of different frequencies of transient current at any time, so that complete information about the waveform will be obtained.

Sy-Ruen Huang et al. [START_REF] Sy-Ruen | Distinguishing Internal Winding Faults From Inrush Current in Power Transformers Using Jiles-Atherton Model Parameters Based on Correlation Coefficient[END_REF] have used a method using parameters of Jiles-Atherton model for detecting small error current from coil short circuit error in the magnetic inrush current of power transformer. Saeed Jazebi et al. [START_REF] Jazebi | A novel application of wavelet based SVM to transient phenomena identification of power transformers[END_REF] have proposed a differential protection method that combines support vector machine (SVM) and wavelet transform theories. There are two common transient states, i.e. transient inrush current and internal error.

In this research, the purpose of designing a protective relay for the differential protection of power transformer is by using Clarke transform and S transform. Identification of inrush currents and internal and external errors of power transformers is one of the main concerns of electrical engineers. In this research, inrush currents and external errors are identified and distinguish from internal errors. This research is an applied research, which ultimately an intelligent relay is designed and can make the proposed relay. Also, this relay is used in all industries such as electricity, petrochemicals, gas oil and so on. At the present time, harmonic differential relay is used which has very high computing load and low response speed that are not suitable for relay. The innovation aspect of this research is that the Clarke transform and S transform, which are very powerful tools for identifying power transformer errors, are used.

Proposed algorithm of differential protection of power transformer based on Clarks transform and S transform

In this study, Clarke transform and S transform are used. S transform provides enough information to analyze and combine the original signal with a relatively small computational time, and its implementation is very simple in practice. To differentiate between transient phenomena in power transformers from energy, the coefficients of standard deviation of coefficients in a half-cycle time window, which is transient, are used as a feature for categorization. In terms of three characteristics of accuracy, speed, and computational cost, the proposed algorithm based on Clarke transform and S transform is very suitable and can easily implement the above algorithm in practice.

Therefore, in this study, Clarke transform and S transform are used to distinguish between transient phenomena in power transformers. S transform is a very powerful method that connects the distance between the discrete wavelet transform and Fourier transform, and provides very high precision. S transform has a higher characteristic than the discrete wavelet transform and provides Fourier transform. In this algorithm, the length of moving semicircular window is considered, and the sampling frequency is 10 kHz. Due to the use of a moving window in the analysis, transient state information is maintained.

The time window length is obtained as a compromise between the accuracy and the response time after the initial examinations. Differential protection should distinguish internal errors from external errors and inrush current, and only has function in the condition of internal errors. In this algorithm, the differential current of phases first, is obtained from the differential secondary current of transformers of primary and secondary of power transformers and then the following steps are performed to distinguish the transient phenomena:

1. In this algorithm, the activation current is calculated first. In the differential protection, the activation current is defined as equation (1) [START_REF] Oliveira | Application of Discrete Wavelet Transform for Differential Protection of Power Transformers[END_REF] 2 . .

2 2 int s p po Set i i k ir k I    (1)
In this equation, I set point is the activation current, k is the percentage differential, ir is the inhibitory current and i2p and i2s are the secondary currents of current transformers in the primary and secondary power transformer. In this section, the size of I set point is considered 0.25 prionite according to references [START_REF] Xiang-Ning | The Ultra-Saturation Phenomenon of Loaded Transformer Energization and Its Impacts on Differential Protection[END_REF] and [START_REF] Vázquez | Transformer Differential Protection Using Principal Component Analysis[END_REF] [0.25]. If the three-phase differential current is smaller than activation current, the normal state and otherwise, other transient phenomena may have occurred.

2. If one of the three-phase differential currents is greater than or equal to the activation current may be occurred one of the transient phenomena, including the magnetism inrush current, internal errors, and external errors in the power transformer. In this algorithm, for the purpose of differentiation between transient phenomena, first, by the help of Clarke transform of ground tide currents, air tide one, and air tide two are calculated using equation (2) [START_REF] Hanli | IEEE, Studies on the Unusual Maloperation of Transformer Differential Protection During the Nonlinear Load Switch-In[END_REF][START_REF] Eissa | A Novel Digital Directional Transformer Protection Technique Based on Wavelet Packet[END_REF]. 1. Under normal conditions and stable performance, changes in the values of detailed coefficients are very small. If sudden change in the detailed coefficients is observed over time, the system may be under error conditions, and energy indices and standard deviation of coefficients are very suitable criteria for distinguishing between internal errors, external errors, and magnetic inrush current and normal state.

                                                
2. In this study, the sampling frequency is 10 kHz. Given that the length of the moving window is considered semicircle, so there are 100 samples per window.

3-In the proposed algorithm, the coefficient of detail is used. Therefore, the computational load of relay decreases sharply, which is one of the important advantages of this relay. Then, by transforming S, the energy of coefficients of ground tide currents (I0) is obtained in various experiments and in various transitional phenomena.

The energy of a discrete signal x (n) is obtained by the following formula [START_REF] Asrami | A novel intelligent protection system for power transformers considering possible electrical faults, inrush current, CT saturation and over-excitation[END_REF][START_REF] Medeiros | Power Transformer Differential Protection Using the Boundary Discrete Wavelet Transform[END_REF]:

     n n x Energy ] [ 2 (3)
After sampling the differential current in different states, the internal and external errors and the magnetic inrush current of the wavelet transform are applied to these signals, that the equation ( 4) is represented by a matrix:

      1 3 3 1     X ED X i i D (4)
In this equation, [X] 3x1 is input signal that can be a differential current in different transient phenomena of power transformers. [ED] ix3 is the energy calculation operator of wavelet transform coefficients up to level i. The energy is the sum of the square wavelet coefficients.

For example, EDij is the i-th energy from the j-th phase. [X-D] ix1 is the sum of the energy of the three-phase wavelet coefficients at the j level that the above equation is displayed for the current signal to three levels is as equation ( 5) [17 and 18]: If the energy of coefficients is not within the minimum and maximum range of equation ( 6), the magnetic inrush current may be occurred. Otherwise, there may be occurred three-phase internal errors, three-phase error to ground, phase error to ground, phase-to-phase error, and phase-to-phase error to ground or three-phase external errors, three-phase error to ground, phase-to-phase error, phase-to-phase error to ground, and external error of phase to ground.

                               c
In the next step, to distinguish between internal errors and external errors, the following vector is defined.

2 2 I D D  (7)
In this equation, 2 2 I D is the vector of coefficients of air tide two (I2). In this stage, the standard deviation of the vector D is calculated in experiments and in different phenomena.

The standard deviation of a discrete signal x (n) is obtained by the following equations [START_REF] Asrami | A novel intelligent protection system for power transformers considering possible electrical faults, inrush current, CT saturation and over-excitation[END_REF][START_REF] Medeiros | Power Transformer Differential Protection Using the Boundary Discrete Wavelet Transform[END_REF]:

    n i i n x x 1 2 ) (  (8)
In these equations, i x

x n and , respectively are coefficients, mean of coefficients, number of coefficients, and standard deviations.

As already mentioned, at this stage, the standard deviation of vector D is calculated in experiments and in different phenomena. If the standard deviation of the vector D associated with internal errors according to ( 9) is considered as threshold, external errors are also distinguished from internal errors. Simulation results

1-Simulation of external and internal errors

To simulate external and internal errors, the power grid is considered in Fig. 1. External and internal errors are occurred in the outside and inside of the protection zone of differential relay in the load side. Types of external and internal errors simulated are three-phase error, three-phase error to ground, phase to ground error, phase-to-phase error, and phase-to-phase to ground error, which is obtained by considering the effect of transformers of primary and secondary current of differential current. In Figure 2 The length of the time series is 101 points As it is shown in Figures 3 and4, the error is occurred in 0.2 seconds in all three phases which is seen in the form of waves. On the other hand, due to the fact that the errors are external, the range of differential currents is low. In addition to the three-phase differential current, the three-phase frequency rage is shown in terms of frequency which the output of S transforms during the window information period which is semi-cycle. Given that the error is occurred in three phases, the frequency range of each three phase is very large. In Fig. 5 and Fig. 6, the differential currents and frequency range resulting from the output of S transform related to two -phase and two-phase to ground external error is shown. The error in phase A and B is occurred in 0.2 seconds, which is seen in the form of waves. The range of currents in phase A and B is much larger than the phase C, it is due to the fact that there is no error in phase C. In addition to the three-phase differential current, the three-phase frequency range is shown in terms of frequency, which output of S transform during the window information period, which is semi-cycle.

Given that error is occurred in phase A and B, the frequency range in phase A and B is very large. In Fig. 7, the differential currents and frequency range resulting from the output of S transform related to phase-to-ground external error are shown. In the time of occurring phase-to-ground external error, the range of differential current of relay is very low and is not very effective. Also, as it is seen, the frequency range is very low during the time of information window, which is semi-cycle.

The differential currents and the frequency range resulting from the output of S transform due to internal errors in various modes are shown in Fig. 8 to Fig. 12. In the internal errors simulated, the error is occurred in 0.2 seconds. As it is shown in Figs. 8 and9, the error is occurred in each three phases in 0.2 seconds, which is seen in the form of waves. On the other hand, given the internal errors, the range of the differential current is very large compared with external errors. In addition to the threephase differential current, the three-phase frequency range is shown in terms of frequency that the output of S transform is during the information window period that is semi-cycle.

Given that the error is occurred in three phases, the frequency range of each three phase is very large. In Fig. 10 and Fig. 11, the differential currents and frequency range resulting from the output of S transform are shown related the two-phase internal error and two-phase to ground. Error in phase A and B occurred in 0.2 seconds, which is seen in the form of waves. The range of current in phase A and B is much larger than the phase C that it is due to the fact that there is no error in phase C. In addition to the three-phase differential current, the three-phase frequency range is shown in terms of frequency which output of S transform during the window information period which is semi-cycle. Given that the error occurred in phase A and B, the frequency ranges in phase A and B is very large. In Fig. 12, the differential currents and frequency range resulting from the output of S transform related to phase-to-ground internal error are shown. Given the phase-to-ground internal error, the range of differential current is very high in phase A and is low in phases B and C. Also, as it is seen, the frequency ranges during the time of information window, which is semi-cycle, is very high in phase A, but in phase B and C it is very low due to the lack of error.

SIMULATION OF THE MAGNETIC INRUSH CURRENT

For simulation of the magnetic inrush current, Fig. 1 In Fig. 14 and Fig. 15, the differential currents and the frequency range resulting from the output of S transform related to inrush currents due to the change in conduction angle and change in residual flux variation are shown. Given that in the secondary magnetic inrush current, the connect transformer is open, so that the primary current of power transformer reaches to the differential relay be considering effect of current transformer in the primary side which differential current range and frequency range resulting from the output of S transform is relatively large.

Differentiation between internal and external errors and magnetic inrush current using Clarke transform and S transform

The minimum and maximum energy of coefficients in the first level in ground tide are presented in Table 1. According to Table 1, if the minimum and maximum energy of ground tide coefficients are related to internal errors as thresholds, the phenomenon of inrush current is not placed in the range between minimum and maximum and this phenomenon is separated from internal errors.

To distinguish between internal errors and external errors, first, according to equation ( 7), the vector D is calculated and then the standard deviation of vector D is obtained in different experiments. The minimum and maximum standard deviations related to internal errors are considered as thresholds.

In Table 1, the minimum and maximum standard deviation of D vector is also presented in internal errors and external errors. According to Table 1, if the minimum and maximum vector D related to internal errors is placed as thresholds, the external errors are not placed in the range between the minimum and the maximum and are distinguished from internal errors.

According to Table 1, the minimum and maximum energy of ground tide coefficients related to internal errors are 0.32693 and 2.676427, respectively that according to the table, the energy of ground tide coefficients related to the magnetic inrush current is not placed in the above range. Therefore, this phenomenon is distinguished from internal errors.

The minimum and maximum standard deviation of vector D in the first level related to internal errors according to Table 1 is 10,9025 and 120,70,921. Based on the results, the minimum and maximum standard deviation of the D vector in the first level related to threephase external errors, three-phase to ground, two-phase, two phase to ground and phase to ground are not placed in the above range. Therefore, these phenomena are also distinguished from internal errors. Therefore, using the proposed algorithm with defined criteria, internal errors can be distinguished from external errors and the magnetic inrush current and prevent the unwanted performance of differential protection. Differential protection of the standard power transformer is based on the second-order harmonic to avoid malfunctioning of the differential protection of transformer against inrush currents and external errors. In the algorithm, the second-harmonic component of the differential currents component was used in which the differential current signal was processed by the Fourier transform function in order to be identified second harmonic components and, consequently, the relationship between the second harmonic component and the main component to be used as a criterion for detecting error from inrush current and external errors in differential relay. Given that in standard differential protection, the Fourier transform algorithm is used, so the speed of response of differential protection is low, and intelligent algorithms should be used. Differential protection is a limited protection that response speed is very important in it. At the time of internal errors, differential protection should be reacted immediately. So the trip time is very important. In the standard relays, the Fourier transform algorithm is used that response speed of this algorithm is not high. Therefore, new algorithms for differential transformer protection are needed.

In this study, Clarke transform and S transform were used as a powerful tool for distinguishing between transient phenomena in differential protection of power transformer. In the proposed algorithm, various types of external errors, internal errors, and magnetic inrush current were simulated and a suitable criterion for distinguishing between these phenomena was presented. In the proposed algorithm, by the help of Clarke transform of ground tide current, air tide 1, and air tide 2 were obtained. Then, using S transform, the energy of the ground tide coefficients and the standard deviation of air tide 2 coefficients were calculated and internal errors were distinguished from the magnetic inrush current and external errors.

The following suggestions are presented based on the findings:

1. One of the other transient phenomena that may occur in power transformer is the ultra-saturation phenomenon that should be considered in the differential protection of the power transformer and distinguished from internal errors. The ultra-saturation phenomenon causes unwanted performance of differential protection and is a very dangerous threat to the power transformer.

2. Some power transformers in power networks have non-linear loads, such as induction arc furnaces and .... In this type of power transformers, which have specific loads, suitable protection algorithms should be provided by discrete wavelet transform, Clarke transform, S transform and ... for power transformer 3-In all differential protection studies, a differential current signal component is used to distinguish between internal errors from external errors and magnetic inrush current. For this purpose, instead of current signals, it can be uses the voltage components between the primary and secondary coils of transformer (the ratio of transformer power transform) and define the appropriate criteria for distinguishing between transient phenomena.

2 II 3 -

 23 are ground tide currents, air tide one, and air tide two, and, respectively, are current of phases a, b, c respectively. It should be emphasized that Clarke transform can be applied to instantaneous quantities, such as phasors,[START_REF] Vázquez | Transformer Differential Protection Using Principal Component Analysis[END_REF]. In the next step, the input signals are analyzed by the extraction information of S transform from the transient signal in both time and frequency domains. If one of the three-phase differential currents is greater than or equal to the activation current, frequency information is considered by the help of S transform and the following steps are performed to distinguish between internal errors, external errors, and magnetic inrush current:

  mentioned above, by transforming S, the energy of coefficients of ground tide current (I0) is obtained in different experiments and in different transient phenomena. The energy of coefficients of ground tide currents (I0) related to internal errors is considered as the threshold and is defined as the following equation: the energy of coefficients in the experiments and in different phenomena, the minimum and maximum energy of the ground tide coefficients are related to the internal errors. In this algorithm, 1060 experiments have been carried out in various phenomena, including magnetic inrush currents, internal and external errors, and the energy of signal of ground tide currents is obtained in various experiments.

  the standard deviation of vector D in experiments and different phenomena, the minimum and maximum standard deviation of vector D related to internal errors. In the proposed algorithm using Clarke transform and S transform, internal errors are distinguished from external errors and magnetic inrush current. MATLAB and PSCAD software have been used for simulation. The transform S is coded with MATLAB software. 1060 experiments have been carried out in various phenomena including internal and external errors and magnetic inrush current. In the inrush current phenomenon, the type of residual fluctuation events, the change in the angle of conduction and the change in key switching time, and in internal and external errors, the type of residual fluctuation events, load variation, resistivity of error, the change in the angle of conduction and change in the time of occurrence of error are considered.

  , the output characteristics of the transform S are presented. In this figure, the number of frequency voice, the estimated simulation time, the minimum and maximum frequency, the sampling rate of time and frequency, and the number of samples in the information window obtained in simulation are shown. 500 experiments are considered for external errors and 500 experiments for internal errors. In external and internal errors, various experiments have been performed on residual flux change, change of load level, change of conduction angle, change time of occurring error, and change error resistance. In Figures 3 to 7, the differential currents are shown due to external errors in different modes and the frequency range obtained from the output of S transform during the window time of information that is considered semicircle. Error is occurred in 0.2 seconds in external simulated errors. In these figures, the differential current and frequency rage resulting from the output of transform S are shown due to change in the resistance of error, change in the conduction angle, change in residual flux, change in the time of occurring error, and change in the load level associated with external errors. Error is occurred in 0.2 seconds in external errors.

Figure 1 :

 1 Figure 1: Simulated electrical network for analysis of internal and external errors

Figure 2 Figure 3 :

 23 Figure 2: output of S transform

Figure 4 :

 4 Figure 4: Differential Currents and Frequency Range obtained of Output of S transform related to three-phase external error due to change of load

Figure 5 :Figure 6 :

 56 Figure 5: Differential Currents and Frequency Range obtained of Output of S transform related to external error two-phase to ground due to change of time of occurring error

Fig. 7 :

 7 Fig. 7: Differential Currents and Frequency Range obtained of Output of S transform related to phase to ground external error due to change of conduction angle

Figure 8 :Figure 9 :

 89 Figure 8: Differential Currents and Frequency Range obtained of Output of S transform related to three-phase internal error due to change of error resistance

Figure 10 :Figure 11 :

 1011 Figure 10: Differential Currents and Frequency Range obtained of Output of S transform related to two-phase internal error due to change of time of occurring error

Figure 12 :

 12 Figure 12: Differential Currents and Frequency Range obtained of Output of S transform related to phase-to-ground internal error due to change of conduction angle

Figure 13 :Figure 14 :Figure 15 :

 131415 Figure 13: Differential Currents and Frequency Range obtained of Output of S transform related to inrush current due to change of switching time

Table 1 :

 1 Minimum and maximum energy of ground tide coefficients and standard deviation of Dvector in phenomena and in various experiments

	Type of phenomenon	The minimum	The	Minimum	Maximum standard
		energy of	maximum	standard	deviation of vector
		coefficients	energy of	deviation of	D
			the	vector D
			coefficients
	Magnetic inrush current	5.0151E-6	3.478E-5	2.0552	25.73881
	Phase-to-ground internal	0.41855	0.81911	10.9025	14.377
	error (AG)
	Phase-to-phase internal	0.66410	1.0748	22.8205	33.46675
	error (AB)
	Phase-to-phase to ground	0.32693	0.90161	21.4863	31.7934
	internal error (ABG)
	Three-phase internal error	0.73112	2.67647	62.4266	114.4823
	(ABC)
	Three-phase to ground	0.50608	2.20601	62.5553	120.70921
	internal error (ABCG)
	Phase-to-ground external	2.4757E-6	6.5018E-3	0.61434	1.09706
	error (AG)
	Phase-to-phase external	0.28387	1.19706	4.0667	6.48270
	error (AB)
	Phase-to-phase to Ground	0.84021	1.23814	3.6746	5.97275
	External Error (ABG)
	Three-phase external error	1.15395	1.43581	4.9259	10.11144
	(ABC)
	Three-phase to ground	1.0617	1.34051	8.5061	10.25384
	external error (ABCG)


Negative constraint: A piece-unifier has to map at least one piece of the query to the rule head Piece-unifier of a query Q with a rule R:

¬ (∃X B[X]) or ∀X (B[X] → ⊥) « B[X] must not be found » Positive constraint: ∀X ∀Y ( B[X, Y] → ∃Z H[X, Z] ) « if B[X,Y] is found then H[X,
• a substitution s of frontier(R) by frontier(R) + constants(Q + head(R))

• a homomorphism h from Q' ⊆ Q to s(head(R)) s.t. Q' is

  Abstraction in first-order logic ∃x( parentOf(a,b) ∧ parentOf(a,c) ∧ parentOf(c,x) ∧ F(a) ∧ M(b) ) à ∃ z (parentOf(z,x) ∧ parentOf(z,y))) § Same as Tuple Generating Dependencies (TGDs) § See also Datalog+/- § Same as the logical translation of Conceptual Graph rules § Generalize Description Logics used for OBDA (DL-Lite, EL) Ontology: Existen<al Rules Simplified form: siblingOf(x,y) à parentOf(z,x) ∧ parentOf(z,y) « Value Invention » ∀X ∀Y ( B[X, Y] → ∃Z H[X, Z] ) ∀X ∀Y ( B[X, Y] → ∃Z H[X, Z] ) ∀x ∀y (siblingOf(x,y) à ∃ z (parentOf(z,x) ∧ parentOf(z(a,b) Then h(head) can be « added » to F Value Inven<on R = ∀x ∀y (siblingOf(x,y) à ∃ z (parentOf(z,x) ∧ parentOf(z,y))) F'= ∃ z0 (siblingOf(a,b) ∧ parentOf(z0,a) ∧ parentOf(z0,a)) h ={(x,a), (y,b)} h: body à FA rule bodyà head is applicable to a fact F if there is a homomorphism h: body à F

nynFF

  Conceptual graphs introduced in [Sowa 76] [Sowa 84] n Specific research line by Montpellier's group since 1992 « Graph-based » knowledge representation and reasoning « Graph--Based Knowledge RepresentaKon: ComputaKonal FoundaKons of Conceptual Graphs », Chein & M…, Springer, 2009 Conceptual Graph Vocabulary: 1. parKally (pre--)ordered set of concepts [screenshots from CoGui, http://www.lirmm.fr/cogui] Conceptual Graph Vocabulary: 2. parKally (pre--)ordered set of rela<ons with their signature [any relaKon arity allowed] Logical transla<on (Φ) of the vocabulary: very simple rules p < q ∀x 1 …x k ( p(x 1 …x k ) → q(x 1 …x k ) ) Signature of r ∀x 1 …x k ( p(x 1 …x k ) → t i1 (x 1 )…t ik (x k )) Basic Conceptual Graph Allows to represent facts and conjunc<ve queries Logical transla<on (Φ): existen<ally closed conjunc<on of atoms [total order on the edges incident to a relation node] ∃x ∃y (Girl(Eva) ∧ Child(x) ∧ Toy(y) ∧ Train(y) ∧ sisterOf(Eva,x) ∧ playWith(Eva,y) ∧ playWith(x,y)) Eva x Logical soundness [Sowa 84] and completeness [Chein M… 92]: there is a homomorphism from Q to F iff Φ(Q) is entailed by Φ(F) and Φ(vocabulary) Query Q Fact F The Basic CG fragment restricted to binary relaKons is equivalent to RDFS [Baget ISWC'05] [Baget+ ICCS'10] Homomorphism (with concept/rela<on preorders integrated) Richer Fragments (nested graphs, rules, constraints, + nega<on, …) ¢ Rule: pair of basic conceptual graphs ∀x ∀y (Human(x) ∧ Human(y) ∧ siblingOf(x,y) à ∃ z (Adult(z) ∧ parentOf(z,x) ∧ parentOf(z,y))) ¢ Sound and complete forward chaining and backward chaining [Salvat M… 1996] ¢ Several ways of combining rules and constraints [Baget M… JAIR 2002] The existential rule framework can be seen as a fragment of CGs with a flat vocabulary Outline n Existential rules: a logic-and graph-based framework n Decidability and algorithmic issues § Focus on: tree-shaped saturation in forward chaining piece-based unification in backward chaining n A (graph) tool for combining decidable classes of rules Basic Problem Given a KB K = (F, R) and a (Boolean) conjunctive query Q, is Q entailed by K ? Entailment is not decidable n Many decidable classes exhibited in databases and KR n Three generic kinds of properties ensuring decidability: -Saturation by Forward Chaining halts (« finite expansion set », fes) -Query rewriting by Backward Chaining halts (« finite unificaKon set », fus) -Saturation by Forward Chaining may not halt but the generated facts have a tree-like structure (« bounded treewidth set », bts) None of these properties is recognizable [Baget+ KR 10] but they provide generic algorithms Width of a tree decomposiKon = max number of nodes in a bag (minus 1) Treewidth of a graph = min width over all decomposiKon trees of this graph r a p(a,b) q(b,z0) r(a,b,t0) p(b,t0) q(t0,z1) r(b,t0,t1) p(t0,t1) DecomposiKon tree: 1) each node (term) appears in a bag 2) each hyperedge (atom) has all its nodes in a bag 3) for each node x, the subgraph induced by the bags containing x is connected The decidability proof does not provide a halting algorithm (relies on the bounded treewidth model property [Courcelle 90]) R is bts if FC with R generates facts with bounded treewidth i.e., for any fact F, there is an integer b s.t. any fact R-derived from F has treewidth bounded by b Bounded Treewidth of the Derived Facts (bts) EssenKally [Cali Go)lob Kifer KR'08] fes (finite saturation) is included in bts (bound given by the number of terms in the finite « saturated fact ») y) ∧ r(y,z) ∧ s(x,y,z) à r(y,u) ∧ r(z,u) r(x,y) ∧ r(y,z) ∧ r(x,z) à r(z,u) r(x,y) ∧ r(y,z) à r(y,u) ∧ r(z,u) datalog These classes are moreover « greedy bts » => a halting algorithm [Baget+ IJCAI'11]Greedy bts R1 = p(x,y) à p(y,z) R2 = p(x,y) ∧ q(x,z) à r(x,y,t) ∧ p(y,t) , for each rule application, frontier variables not being mapped to initial terms are jointly mapped to variables occurring in atoms added by a single previous rule application F h(H) 1. Bag pattern = { homomorphisms from part of a rule body to « current fact » that use some terms of the bag } à A rule is applicable to the current fact iff a bag pattern contains its body à FC can be performed on the decorated tree 2. Equivalence relation on bags Only one bag per equivalence class is developed The other nodes are blocked Bounded number of equivalence classes à finite « full blocked tree » T* Build a finite decomposition tree that encodes a potentially infinite fact " Given a subset T of its variables, a set of atoms is partitioned into pieces. all atoms linked by a « path » of variables not belonging to T Basic notion for unification in backward chaining, dependency between rules, decomposition of a rule into equivalent rules, … Key No<on: « Piece » p(u,v) p(v,w) p(w,u) s(u,u) Piece 1 = { p(u,v) p(v,w) p(w,u) } Piece 2 = { s(u,u) } x Q = p(u,v) ∧ p(v,w) ∧ p(w,u) ∧ s(u,u) unifier has to map at least one piece of the query to the rule head R = q(x,y) ∧ q(y,x) à p(x,z) ∧ p(z,x) ∧ p(z,z) ∧ r(z)

  a set of pieces according to s and h Piece--Unifica<on (3) u [Salvat M… 1996] F,R |= Q iff there is a sequence of piece-unifications that empties Q (considering facts as rules with an empty body) u [Baget+ IJCAI 2009] for fus existenKal rules F,R |= Q iff one of the piece-based rewritings of Q maps to F IniKally [Salvat M… ICCS 1996] on conceptual graphs Outline n Existential rules: a logic-and graph-based framework n Decidability and algorithmic issues § Focus on: tree-shaped saturation in forward chaining piece-based unification in backward chaining n A (graph) tool for combining decidable classes of rules

  R1 iff there is a « piece-unifier » of body(R2) with head(R1)[Baget KR 2004, Baget+ IJCAI 2009, AIJ 2011] R1 R2 : R1 « may trigger » R2 (R2 depends on R1) Rules Combining Decidable Classes with the Graph of Rule Dependencies Combining Decidable Classes with the Graph of Rule Dependencies If GRD(R) is without circuit then R is both fes (thus bts) and fus fes = finite fact saturation fus = finite query rewriting bts = (possibly infinite) tree-shaped saturation Datalog with the Graph of Rule Dependencies If all strongly connected components of GRD(R) are fes then R is fes [Baget 2004] The same holds for fus (but not for bts) with the Graph of Rule Dependencies If all strongly connected components of GRD(R) are fes then R is fes [Baget 2004]The same holds for fus (but not for bts) 〉R 2 be a partition of R s.t. no rule of R 1 depends on a rule ofR 2 n If R 1 is fes and R 2 is bts, then R is bts n If R 1 is bts and R 2 is fus, then R is decidableConclusion n An emerging rule-based framework for OBDA § simple § expressive § flexible n Logic-based and Graph-based n Currently: § A quite clear picture of decidable classes and their complexities § First implementations -often for very specific subclasses n Next challenge: scalability

Union of Decidable Sets of Rules

  ., there exists a fact F s.t. R1 is applicable to F but R2 is not and there is an application of R1 to F leading to F'

	n Next question:
	is the union of two decidable sets of rules still decidable ? R2 depends on R1 if applying R1 may trigger a new application of R2
	practically: i.e
	n can we safely merge several decidable ontologies ?
	n can we build a decidable hybrid language from two languages whose Body Head semantics can be expressed by decidable subsets of rules ? h 1 1
	n Bad news: Almost all classes are pairwise incompatible Body F 2
	n Next question:
	which conditions on the interactions between rules ensure compatibility ?

s.t. R2 is applicable to F'

Effective computation of dependencies with a piece-unification test: