M H Siemann
email: martin.siemann@dlr.de

B Langrand

Coupled fluid-structure computational methods for aircraft ditching simulations: comparison of ALE-FE and SPH-FE approaches

Keywords: Aircraft ditching, Fluid-structure interaction, Arbitrary Lagrangian-Eulerian, Coupled Euler-Lagrangian, Smoothed Particle Hydrodynamics

research documents, whether they are published or not. The documents may come     Copyright Coupled fluid-structure computational methods for aircraft ditching simulations: comparison of ALE-FE and SPH-FE approaches

Introduction

The majority of the air transport occurs over significant bodies of water and thus the emergency landing on water (ditching) represents a fortunately rare but significant safety threat. In order to minimize the risk of immediate injuries to the occupants and to allow for a safe evacuation of the aircraft before it potentially sinks, aircraft manufacturers must demonstrate the structural capabilities within the certification process of novel aircraft types (see [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF][START_REF] Climent | Aircraft Ditching Numerical Simulation[END_REF][START_REF] Toso | Contribution to the Modelling and Simulation of Aircraft Structures Impacting on Water[END_REF] for further details about certification regulations and processes). While ditching analyses are conducted for fixed-wing aircraft [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF][START_REF] Climent | Aircraft Ditching Numerical Simulation[END_REF][START_REF] Benítez Montañés | Ditching Numerical Simulations: Recent Steps in Industrial Applications[END_REF][START_REF] Ortiz | Structural Loading of a Complete Aircraft Under Realistic Crash Conditions: Generation of a Load Database for Passenger Safety and Innovative Design[END_REF] and helicopters [START_REF] Toso | Contribution to the Modelling and Simulation of Aircraft Structures Impacting on Water[END_REF][START_REF] Hughes | Experimental observations of an 8 m/s drop test of a metallic helicopter underfloor structure onto water: part 2[END_REF][START_REF] Hughes | Application of the finite element method to predict the crashworthy response of a metallic helicopter under floor structure onto water[END_REF][START_REF] Hughes | Helicopter crashworthiness: a chronological review of water impact related research from 1982 to 2006[END_REF], the present work considers solely fixed-wing aircraft ditching. The extreme characteristics of ditching constitute great challenges for the numerical simulation. For instance, capturing the fluid dynamics, such as jet and bow wave formation and breakup, separation, and splashing, over typically long time scales is very challenging. Moreover, the involved hydrodynamic effects and the highly transient hydrodynamic pressure acting on the structure pose challenges for the numerical simulation. Furthermore, the nonlinear structural behavior with potential rupture and the complex fluid-structure interaction (FSI) occurring during a ditching constitute additional challenges for the simulation. Other major challenges arise from the multi-scale character of the phenomena involved in a ditching. On the one hand, acting pressures rise and fall within milliseconds requiring very small time steps to be resolved, yet the impact phase lasts several hundred milliseconds. On the other hand, the high impact pressures act over very local zones in the order of millimeters, while the aircraft structure moves several meters throughout the event. These scale differences, which amount to about a factor of one thousand in both time and space, account for major challenges for the computational models that need to resolve the local scales, while remaining computationally efficient to allow covering the complete impact phase.

Due to the challenges addressed above, the state-of-the-art analysis methods are currently limited to comparisons of the novel structural design with aircraft structures that were previously certified for ditching, sub-scale experiments, and (semi-)analytical methods in combination with subsequent, uncoupled finite element analyses of the structure. A detailed description as well as associated advantages and disadvantages are given in [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF][START_REF] Climent | Aircraft Ditching Numerical Simulation[END_REF]. In summary, current means widely lack the ability to be applied to novel and uncommon designs thus limiting progress, they are based on several assumptions and simplifications that cause inaccuracies, and, perhaps more critical, they do not account for the coupled fluid-structure interaction. To the knowledge of the authors, the latter is a topic of research since the 1960s, where effects of structural deformations on hydrodynamic results were studied for purely vertical impact on water, e.g. [START_REF] Bingman | Water Impact Loads on Structures[END_REF][START_REF] Chuang | Investigation of Impact of Rigid and Elastic Bodies with Water[END_REF], and continues to be investigated nowadays, e.g. [START_REF] Panciroli | Hydroelasticity in water-entry problems: Comparison between experimental and SPH results[END_REF][START_REF] Allen | Mechanics of Flexible Composite Hull Panels Subjected to Water Impacts[END_REF]. Also for oblique impact on water at high horizontal velocity, structural deformations were demonstrated to significantly affect the acting hydrodynamic loads [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF]. Thus, it appears to be essential to couple fluid and structure numerical solutions within advanced computational methods in order to correctly predict the structural response and to analyze the structural capacity of novel aircraft designs. Nevertheless, the large computational effort required currently limits the application of advanced, coupled numerical approaches to cases with simple structural models. Furthermore, comprehensive validation remains to be demonstrated as only few validation studies involving deformable structures impacting water at high horizontal velocity were conducted [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF].

The term advanced, coupled numerical approaches comprises approaches that use (a) high-fidelity solutions for both the fluid and the structural domain and (b) a method to couple the fluid and the structural solution in the same computation. Typically, the explicit Finite Element (FE) method is adopted to simulate the structural response, as it is adapted to fast-transient dynamic problems, such as water impact, and it can portray complex 3D geometries and non-linear structural responses with many contacts, whereas fundamentally different computational methods are used to simulate the fluid behavior. Common mesh-based methods are pure Eulerian or Arbitrary Lagrangian-Eulerian (ALE) methods [START_REF] Donea | An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interactions[END_REF][START_REF] Donea | Finite Element Methods for Flow Problems[END_REF][START_REF] Souli | Arbitrary Lagrangian Eulerian and Fluid-Structure Interaction: Numerical Simulation[END_REF]. Common mesh-free methods comprise Smoothed Particle Hydrodynamics (SPH) [START_REF] Gingold | Smoothed particle hydrodynamics -Theory and application to non-spherical stars[END_REF] and Element-Free Galerkin (EFG) [START_REF] Belytschko | Element-Free Galerkin Methods[END_REF][START_REF] Beissel | Nodal integration of the element-free Galerkin method[END_REF] methods.

A general review on hull slamming, which is closely related to ditching, was given by Abrate [START_REF] Abrate | Hull Slamming[END_REF]. The author provided an overview of the computational approaches used for water impact simulations comprising Boundary Element, SPH, FE, and fixed grid methods (Euler) including techniques to detect the interface between the domains (e.g. the water free surface) such as Cubic Interpolated Pseudo-particle, Volume of Fluid, and Level-Set method. For a test case of pure vertical water impact, a comparison of different methods to simulate the fluid has been carried out by Anghileri et al. [START_REF] Anghileri | Survey of numerical approaches to analyse the behavior of a composite skin panel during a water impact[END_REF]. The authors compared experimental and numerical simulation results of four different methods, i.e. FE, ALE, SPH, and EFG. They point out a dependence of the ALE results on the FSI coupling parameters and that finding a proper SPH discretization fineness is not trivial and thus time-consuming. The results of FEM simulations were found to give proper results only as long as fluid deformations are small and the EFG solution was computationally very expensive. Hughes et al. [START_REF] Hughes | From Aerospace to Offshore: Bridging the Numerical Simulation Gaps-Simulation advancements for fluid structure interaction problems[END_REF] presented an insight into recent work using FE, ALE, SPH, and EFG methods, yet with a focus on the application of the SPH method.

Guo et al. [START_REF] Guo | Effect of pitch angle on initial stage of a transport airplane ditching[END_REF] employed the ALE method investigating the effect of the initial pitch angle on the aircraft motion during the ditching. The ALE method was also used by Qu et al. [START_REF] Qu | Study of ditching characteristics of transport aircraft by global moving mesh method[END_REF], who refer to their approach as global-moving-mesh method, to study the ditching characteristics of a generic aircraft fuselage rigid body model, NACA2929 A-body [START_REF] Mcbride | Experimental investigation of the effect of rear-fuselage shape on ditching behavior[END_REF]. Pentecôte and Kohlgrüber [START_REF] Pentecôte | Full-scale Simulation of Aircraft Impacting on Water[END_REF] compared the capabilities of both FE and SPH method to simulate the ditching of a transport aircraft rigid body model. They concluded that the high horizontal velocity of the aircraft together with the considerable duration of the event leads to large mesh distortions that result in a severe drop of the critical time step and eventually to an early termination of the simulation. Another application of the SPH method to a ditching simulation was reported by Ortiz et al. [START_REF] Ortiz | Structural Loading of a Complete Aircraft Under Realistic Crash Conditions: Generation of a Load Database for Passenger Safety and Innovative Design[END_REF], who simulated a deformable Airbus A321 model impacting water and reported the feasibility of the method yet with extremely large runtimes. Climent et al. [START_REF] Climent | Aircraft Ditching Numerical Simulation[END_REF] presented the ditching analysis of a military transport aircraft applying both the FE and the SPH method. Toso [START_REF] Toso | Contribution to the Modelling and Simulation of Aircraft Structures Impacting on Water[END_REF] employed the SPH method to simulate the water impact of a generic aircraft fuselage rigid body model, NACA2929 A-body [START_REF] Mcbride | Experimental investigation of the effect of rear-fuselage shape on ditching behavior[END_REF]. Groenenboom and Siemann [START_REF] Groenenboom | Fluid-structure interaction by the mixed SPH-FE method with application to aircraft ditching[END_REF] simulated the water impact of generic panels of the guided ditching experimental campaign (cf. Sec. 3.1) using the SPH method. The authors furthermore presented modeling techniques that permit a significant efficiency increase.

In summary, the large mesh distortion due to the presence of a high horizontal velocity renders the use of Lagrangian mesh-based methods, such as the FE method, impractical if not impossible. Furthermore, to the knowledge of the authors there exists no application of the EFG method to water impact cases with horizontal velocity. Therefore, the two most used methods, ALE and SPH, are further investigated in this work.

The main objective of this work is to compare and to assess the capabilities as well as the limitations of the two most commonly used, yet fundamentally different, coupled numerical approaches, ALE-FE and SPH-FE, based on a recent benchmark experiment for ditching analysis involving both quasi-rigid and deformable structures. This work employs two explicit software packages, which provide a wide range of structural modeling capabilities that have been demonstrated to work within various applications.

The remainder of the article is organized as follows: Section 2 provides a brief description of the adopted numerical approaches, which serves as a basis for the later comparison and assessment. The selected benchmark experiment and the developed simulation models are presented in Section 3. Section 4 compares experimental and numerical results, followed by a discussion of the capabilities and limitation of the computational approaches investigated. Finally, conclusions are drawn and directions for future research are outlined.

Numerical Approaches

The Lagrangian formulation is classical in solid mechanics and structural analysis. The mesh and the material points are tied and the mesh and material deformations are consequently linked. Sliding between material (structure) and mesh is not allowed. Loads and boundary conditions can easily be applied to the material points (nodes). The Lagrangian description tracks easily the free surfaces and interfaces between different materials. However, when the structure is severely deformed, Lagrangian elements become similarly distorted since they follow the material deformation. Therefore, in those cases the accuracy and robustness of the Lagrangian simulations decrease severely.

The Eulerian formulation is classical in fluid mechanics. The mesh is fixed and the material flows through the mesh. Equations are modified with respect to Lagrangian formulation in order to take into account the convective terms. The treatment of moving boundaries and interfaces is difficult with Eulerian elements. The Eulerian formulation cannot be used in many cases where the boundaries of the domain move.

In the Arbitrary Lagrangian-Eulerian (ALE) formulation, the material flows through an arbitrary moving mesh. Both the material and the mesh move with respect to the laboratory. It looks like a combination of Lagrangian and Eulerian formulations. Grid velocities and displacements are arbitrary. In practice, built-in algorithms determine smooth grid deformation according to displacements of the ALE domain boundaries. Several algorithms are available, e.g. Donea et al. [START_REF] Donea | Arbitrary Lagrangian-Eulerian Methods[END_REF]. Note that the ALE formulation can be degenerated in Lagrangian (the grid velocity is equal to the material velocity) or in Eulerian (the grid velocity is set to zero).

Common between the regarded approaches, the structure is discretized using the Finite Element method. For the fluid domain, however, there are several methods available. This section describes the fundamentals of fluid and structural modeling as well as the fluid-structure interaction. The formulations presented in this section use the explicit approach for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations.

Fundamentals of Fluid Modeling

The fundamental system of differential equations to be solved within the fluid domain comprises the so-called Euler equations:

conservation of mass dρ dt = -ρ∇ • v , (1)
conservation of momentum

dv dt = - 1 ρ ∇p + g , (2)
conservation of energy

du dt = - p ρ ∇ • v . (3)
Above symbols refer to density ρ, time t, velocity vector v, pressure p, vector of accelerations resulting from external body forces g (i.e. gravitation acceleration), and specific internal energy u. The Euler equations neglect effects of fluid viscosity, surface tension, and temperature. These effects are of minor importance for water impact at high velocity, which is dominated by inertial and pressure forces [START_REF] Toso | Contribution to the Modelling and Simulation of Aircraft Structures Impacting on Water[END_REF][START_REF] Abrate | Hull Slamming[END_REF][START_REF] Faltinsen | Hydrodynamics of High-Speed Marine Vehicles[END_REF].

The fundamentals of the adopted computational methods to simulate the fluid are not repeated here; the reader can refer to [START_REF] Donea | An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interactions[END_REF][START_REF] Donea | Arbitrary Lagrangian-Eulerian Methods[END_REF] and to [START_REF] Monaghan | Particle methods for hydrodynamics[END_REF][START_REF] Monaghan | Simulating Free Surface Flows with SPH[END_REF] for the ALE and the SPH formulations respectively. Both formulations are based on the Euler equations for the fluid modeling.

Fundamentals of Structural Modeling

Typical modeling techniques used within the field of aeronautical engineering crash simulations are adopted. The thin walled structure of the aircraft is discretized using thin bi-linear shell elements. In order to portray nonlinear structural deformations, elastic-(visco)plastic material models in conjunction with an appropriately refined discretization able to capture the transient response of the structure are commonly employed. The failure of the material can be modeled in different ways, from the basic element erosion technique to the advanced extended FE method.

Modeling Fluid-Structure Interaction

There are several possibilities to couple the fluid and the structural solution such as coupling based on constraint equations, where fluid and structural nodes must obey kinematic constraints, or penalty contact formulations, where a small amount of penetration is permitted and subsequently a repulsive force is generated.

Coupled Euler-Lagrange Method

Among the different methods described by Casadei and co-workers to couple fluids and a structure [START_REF] Casadei | An algorithm for permanent fluid-structure interaction in explicit transient dynamics[END_REF][START_REF] Casadei | Permanent fluid-structure interaction with nonconforming interfaces in fast transient dynamics[END_REF][START_REF] Casadei | Coupling finite elements and finite volumes by Lagrange multipliers for explicit dynamic fluid-structure interaction[END_REF], the coupling between fluids and structure relies, in the computations presented in the paper, on an immersed interface also referred to as embedded interface. The structure and the fluids are meshed in a completely different manner and the structure mesh is immersed within the mesh of the fluids [START_REF] Casadei | Coupling finite elements and finite volumes by Lagrange multipliers for explicit dynamic fluid-structure interaction[END_REF]. An unstructured fluid mesh (conforming or non-conforming) is no longer necessary. With this technique, the fluid mesh can be even regular. In this case, an ALE formulation is no longer necessary in the fluid sub-domains that can be Eulerian so than the fluid mesh will never entangle (fixed mesh). The immersed interface allows slave nodes (material grid) belonging to the Euler or ALE fluid media to interact with the master surfaces of the Lagrange solid medium. The coupling forces are computed using the penalty method that depends on two parameters: the contact height h C and the contact stiffness k C that are defined by Eq. ( 4) and ( 5) respectively. This interface was applied to deal with vertical water impact problems such as presented in [START_REF] Delsart | Evaluation of an Euler/Lagrange coupling method for the ditching simulation of helicopter structures[END_REF] for rotor-craft.

h C ≥ 1.5 • l F (4) k C = ρ F v 2 h C A S (5)
where l F is the fluid cell size (Euler or ALE), ρ F the fluid density, v is the relative velocity between the fluid and the structure in the impact direction (here the norm of the horizontal and vertical velocity components), and A S is the area of the structural elements. The factor of 1.5 is needed to maintain contact once it is established. If the mesh size of the fluid and the structure are both homogeneous in the interaction area, the fluid structure coupling can be easily defined with one interface only.

When the fluid penetrates the contact area, a contact force is applied to the degrees of freedom (DOF) of the fluid material as well as to the DOF of the fluid grid. This contact force is proportional to the penetration depth.

Coupled SPH-FE Method

A weak coupling using a node-to-surface penalty contact algorithm is typically adopted. Therein, the particles represent the slave nodes and the structural elements are the master segments. The contact algorithm checks for any penetration of slave nodes into the contact zone around the master segments, which is defined by an offset commonly referred to as contact height h C . This contact height is chosen in relation to the thickness of the structure t S and the particle spacing d F as

h C = 0.5 (t S + d F ) . (6)
Upon penetration, a repulsive force is applied to the particle and, in order to conserve momentum, the force magnitude is distributed to the element's nodes in opposed direction. The contact force magnitude is proportional to the penetration depth and to the contact stiffness. Additionally, a velocityproportional damping is included to dissipate numerical oscillations.

Benchmark Simulations

Benchmark Experiment

The present study uses selected benchmark test cases from the guided ditching experimental campaign, which was conducted by CNR-INSEAN3 as part of the EC-funded research project SMAES 4 . A detailed description of the guided ditching facility, the experimental campaign, as well as analyzes of uncertainties and results can be found in [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF][START_REF] Iafrati | Experimental investigation of the water entry of a rectangular plate at high horizontal velocity[END_REF][START_REF] Iafrati | High-speed ditching of a flat plate: Experimental data and uncertainty assessment[END_REF]. Subsequently, a brief insight is given.

The guided ditching experimental facility comprises a large water tank and a guide structure, which features five height-adjustable bridges holding the guide track. A trolley carrying the test specimens is attached to the guide track, which permits only a motion in the direction of the guide track. In addition, there is a catapult-like acceleration system that accelerates the specimens to the high impact velocities characteristic for fixed-wing aircraft ditching at quasi-full-scale. The design of the facility permits to vary the guide track inclination, i.e. the ratio of vertical to horizontal impact velocity, in a range representative of realistic full-scale aircraft ditching conditions. All specimens analyzed within this experimental campaign measured 1000 mm in length and 500 mm in width, yet their thickness, material, and transverse curvature were varied. In total, 22 test cases with typically two to three repeats were investigated. Two selected test cases were repeated ten times in order to demonstrate the repeatability of the experiments, which proved to be high [START_REF] Iafrati | High-speed ditching of a flat plate: Experimental data and uncertainty assessment[END_REF]. The experimental campaign produced a comprehensive set of highly repetitive, high-quality data, which are used for the purpose of comparison and assessment of the numerical methods within the present work.

For the present work, three test cases with flat specimens of different thickness (15 mm, 3 mm, and 0.8 mm noted as case 1122, 2122, and 3122, respectively) made of aluminum alloy Al2024 were selected. The three specimens were tested with identical impact conditions of 6 • pitch angle, 40 m/s initial horizontal, and -1.5 m/s initial vertical impact velocity. The specimens were attached to quasi-rigid, L-shaped frames, reducing the unsupported area to 850 × 350 mm (case 1122) and 900 × 400 mm (cases 2122 and 3122). The total mass undergoing the impact was 840 kg, 834 kg, and 832 kg for the case 1122, 2122, and 3122, respectively.

The complete instrumentation was presented in [START_REF] Iafrati | Experimental investigation of the water entry of a rectangular plate at high horizontal velocity[END_REF][START_REF] Iafrati | High-speed ditching of a flat plate: Experimental data and uncertainty assessment[END_REF]. Here results from load cells measuring forces acting in normal direction of the panel, biaxial strain gauges, and pressure probes are used. Experimental results were sampled at 20 kHz except pressure results that were sampled at 200 kHz due to the highly transient nature of the hydrodynamic pressure.

Simulation Model

In this section, the fluid and structural models employed are described along with an overview of the hardware and the computational settings adopted for the simulations in Tab. 1. The material behavior of the fluids is modeled using the hydrodynamic viscous fluid law given in Eq. ( 7) and ( 8)), which has been specifically designed to model liquids and gases.

s ij = 2ρν ėij (7) p = C 0 + C 1 µ + C 2 µ 2 + C 3 µ 3 + (C 4 + C 5 µ) E n with µ = ρ/ρ 0 -1 (8)
where C i and E n are material constants, s ij is the deviatoric tensor, ν the kinematic viscosity, and ėij the deviatoric strain rate tensor.

For a quasi-incompressible medium like water, Eq. ( 8) is simplified to

p = C 0 + C 1 µ , (9)
where C 0 is the hydrostatic pressure computed for the given depth and C 1 =ρ 0 c 2 =2.25 GPa (with density ρ 0 =1•10 -6 kg/mm 3 and speed of sound c=1500 m/s). In addition, a minimum pressure (p min ) can be introduced in the hydrodynamic viscous fluid law to take cavitation effects into account.

For water, this minimum pressure is set to 1•10 -23 GPa.

The air is assumed to behave like an ideal gas. Thus, for air Eq. ( 8) is simplified to

p = (C 4 + C 5 µ) E n . (10)
The material constants are totally defined as functions of the perfect gas constant γ and the hydrostatic pressure p 0 as C 4 =C 5 =γ -1 and E n =p 0 / (γ -1).

With values of γ = 1.4 and p 0 =0.1•10 -3 GPa for the air, C 4 =C 5 =0.4 and E n =0.25•10 -3 J. Furthermore, the air density is set to ρ 0 =1.2•10 -9 kg/mm 3 .

In order to initialize the fluid domain with the hydrostatic pressure (p 0 = ρ 0 gh, with h being the depth of water and g the gravitational acceleration), the water domain is split in the vertical direction into layers and a specific material model is applied to each layer with the constant C 0 in Eq. ( 9) set to the depth-dependent hydrostatic pressure p 0 (h). The hydrostatic pressure field is balanced by the gravitational acceleration at the step zero of the computation and does not require preliminary computational steps.

To move the fluid domain with the translational velocity of the structure, ALE links are used between the nodes of the fluid domain (slaves) and one node of the structure (master), for which the center of gravity node of the given structure is selected. With the translational velocity of the master and slave nodes being assigned to the same value, the computation only requires the fluid volume surrounding the structure since the fluid domain (grid) translates with the global displacement of the structure. On the one hand, it is possible to reduce considerably the size of the fluid domain, which is very interesting for ditching applications, and to adapt the fluid mesh in the FSI zone to improve the computation accuracy. Consequently the number of fluid elements and the computational cost are reduced. On the other hand, it is necessary to implement inlets and outlets in the computation to inject and eject fluid material when the fluid domain translates with the structure. Inlet and outlet are used as boundary conditions of the fluid domain. Generally the following elementary boundary conditions are used:

• For inlet, flux is imposed using imposed velocities (density and energy are imposed as constants). Continuity is imposed for pressure (display purposes only).

• For outlet, continuity is imposed for all variables except pressure. When using the silent boundary option, a value for sound speed and a typical relaxation length are provided, which must be greater than the largest wave length of interest.

To avoid any interaction between the inlets/outlets and the impact zone, it is advised to insert some fluid elements between the inlets/outlets and the impact zone: ahead the structure, more than the length of the structure, and behind the structure, more than twice the length of the structure. The fluid domain (air and water) is modeled using 3D hexahedron finite elements (8 nodes) and the ALE formulation is considered. Figure 1 shows the fluid model and provides its dimensions. The mesh size in the impact zone is about 5 mm (lower than the mesh size of the structure, in order to load the shell FE with more than a single fluid hexahedron FE). The length of the structure being about 1000 mm, the distance between the impact zone and the inlets is 1600 mm (more than 1000 mm) and the distance between the outlets and the impact zone is 2600 mm (more than 2000 mm). In order to reduce the total number of elements while keeping a good resolution in the impact zone, the mesh size is increased in all directions with a growth rate of about 10% outside the impact zone. The total length of the fluid domain is 5800 mm leading to a total volume of 4.06•10 9 mm 3 . The total number elements is about 1.27 million and 3.68 million for air and water respectively. Figure 1 displays the ALE fluid model. The fluids are initially at rest and gravity is applied.

Fluid Model: SPH-FE

For the SPH simulations, the Tait equation of state [START_REF] Panciroli | Hydroelasticity in water-entry problems: Comparison between experimental and SPH results[END_REF], which models a weakly-compressible fluid, is adopted. It reads

p(ρ) = p 0 + ρ 0 c 2 γ ρ ρ 0 γ -1 (11)
with hydrostatic pressure p 0 =0, density ρ 0 =1•10 -6 kg/mm 3 , speed of sound c 0 =500 m/s, and adiabatic exponent γ=7 for water. Reducing the speed of sound, thus increasing the compressibility, is common practice for SPH simulations where bulk flow velocities remain well below the artificial speed of sound, e.g. below 10% [START_REF] Monaghan | Simulating Free Surface Flows with SPH[END_REF]. It effectively reduces the strength of numerical pressure fluctuations. Computed pressure values below a defined minimum pressure are cut-off accounting for the effect of cavitation.

In contrast to the ALE fluid model, air is not accounted for in the SPH-FE simulations due to the large number of particles additionally required. Nevertheless, the modeling of air and water in one simulation is technically possible. It requires, however, adapting the SPH scheme, i.e. by using another formulation for the pressure term in the momentum and energy equations that copes with the large density gradient of approximately 1.2/1000 at the air-water interface 5 .

The SPH-FE fluid model adopts a hybrid approach combining the SPH method in the impact zone with the FE method (3D hexahedron finite elements, 8 nodes) in the surrounding far field. Selecting this modeling approach is motivated by the significantly higher computational cost of the SPH method in comparison to that of the FE method for an equivalent reference volume. Therefore, this hybrid modeling approach permits increasing the efficiency of the simulation model by far. Moreover, it was proven to work stable and robust within simulations of vertical water impact of simple, generic structures, helicopters, and rigid body fixed-wing aircraft [START_REF] Climent | Aircraft Ditching Numerical Simulation[END_REF][START_REF] Toso | Contribution to the Modelling and Simulation of Aircraft Structures Impacting on Water[END_REF][START_REF] Pentecôte | Full-scale Simulation of Aircraft Impacting on Water[END_REF][START_REF] Kohlgrüber | Numerical simulation of a composite helicopter sub-floor structure subjected to water impact[END_REF].

In order to further increase the efficiency of the computation, the translating active domain feature is employed. It defines a rectangular domain that moves with the impacting structure in reference to a selected node of the structure, which in the present cases is the trolley's rigid body reference node. Particles located within the active domain are considered within the SPH algorithm, whereas particles located outside of it are skipped. This increases the efficiency of the simulation by a factor approximately proportional to the ratio of the total number of particles to the number of active particles. For the present fluid model, this factor is approximately equal to 2.75.

Figure 2 shows the fluid model and provides its dimensions, which are constant among all test cases. Particles are initially arranged in a hexagonal pattern with a spacing of 10 mm. This particle spacing is defined in accordance with the shell element size of the structure that should be larger than the particle spacing to avoid an unphysical loading of the structure. The surrounding FE mesh size is about 30 mm. The cross-section of the SPH-FE fluid domain is larger than that of the ALE fluid domain because there are no outlets; therefore, the fluid domain must be larger to avoid any influence due to the fixed boundaries (e.g. pressure wave reflections). Nevertheless, the size of the SPH domain equals that of the ALE water domain with constant mesh size (1600 mm × 600 mm × 200 mm). The total length of the fluid domain is 4400 mm resulting in a total volume of 9.68•10 9 mm 3 . In total there are about 1.06 million particles and 358000 volume elements composing the fluid domain. The fluid is initially at rest and gravity is applied.

Structural Model

The structural model contains the trolley box structure, the L-frame, and the panel as shown in Fig. 3. The trolley box structure and the L-frame form one rigid body. All structural parts are modeled using thin shell four-node bi-linear elements with a full-integration rule in the element plane and five integration points through the thickness. The characteristic element size on the panel is 10 × 10 mm. The panel is connected to the L-frame by means of point link elements with realistic stiffness in normal and shear directions calculated using the Huth-formula [START_REF] Huth | Influence of Fastener Flexibility on the Prediction of Load Transfer and Fatigue Life for Multiple-Row Joints[END_REF].

In order to reduce the code-specific differences between the simulation models to a minimum, the structural model was simplified. On the one hand, the guide structure is not modeled although small deformations were measured during the experiment [START_REF] Iafrati | High-speed ditching of a flat plate: Experimental data and uncertainty assessment[END_REF]. On the other hand, the trolley model only contains the box structure and the L-frame, whereas the upper part of the trolley is not modeled. Furthermore, the box structure and the L- frame are defined to be rigid. Effects of these simplifications are discussed in Sec. 5.3. The material behavior of the specimens uses an isotropic, elastic-plastic model with the isotropic hardening defined with the Ramberg-Osgood equation: σ y = σ 0 + Kp n . The elastic modulus E = 71 GPa, Poisson ratio ν = 0.32, initial yield stress σ 0 =0.328 GPa, hardening modulus K=0.768 GPa, and hardening exponent n=0.5805 were obtained from experiments performed by Onera on sheet metal plates of Al2024-T351. A Newton iterative algorithm available in both software packages is applied to compute the plastic variables. The density was set to ρ=2.8•10 -6 kg/m 3 in the computations.

Boundary conditions are prescribed to the rigid body reference node of the structural model. The structure is free to move only along the path defined by the resulting vector of horizontal and vertical impact velocities, whereas all other degrees of freedom are constrained. In addition, the initial velocity used in the experiments is prescribed. All parts of the structure are subject to gravity. At the beginning of the impact, the structure is positioned with the specimen trailing edge at a distance of X=100 mm from the rear of the ALE fluid domain with constant mesh size or the SPH active domain, respectively.

The total mass of the impacting structure is adjusted to match the experiments, e.g. 840 kg, 834 kg, and 832 kg for test cases 1122, 2122, and 3122, respectively. This is done by adding a concentrated mass to the rigid body reference node that accounts for parts not modeled such as the acquisition system.

Validation of Structural Model

In order to validate the structural model adopted within each software package, its response to a predefined pressure load is compared using the test case shown in Fig. 4. The structural model contains solely the lower portion of the rigid L-frame and the panel. For the present cases, the Lframe is fixed in space and the panel is loaded with a predefined pressuretime history. The applied pressure loading on the panel is composed of a sinusoidal ramp, f p , over 5 ms up to a constant pressure of 1•10 -3 GPa, which is arbitrary, yet in the order of the peak pressures measured in the experiments, until the end of the simulation at 20 ms. The sinusoidal ramp is defined as f p = 0.5 × (1 + sin((1 + t)π)) and scaled accordingly.

For the purpose of validation, maximum deformations normal to the panel surface and in transverse direction as well as strain distributions and time histories are compared. Table 2 provides the maximum deformations and their relative differences, which are up to about 3%, 17%, and 7% for cases 1122, 2122, and 3122, respectively.

Figure 5 shows the upper surface strain distributions in x-direction (ε xx ) for the test cases 2122 and 3122. The strain distributions obtained by the different software packages for the same test cases show a good agreement. Small differences can however be observed near the boundaries, where joints connect the panel to the L-frame and contacts take place between both parts. Figure 6 shows strain time histories for the gauge located at location S 2 of the three test cases. Strains are given in x-and y-direction at the same location. Gauge location S 2 , which is located at 325 mm from the trailing edge on the center line, was selected to facilitate the comparison and assessment of the numerical methods-the main objective of the present work-and to avoid spurious effects induced by structural model boundaries, e.g. the contacts between the panel and the L-frame. The strain time histories at gauge S 2 agree well. Minor differences are found in terms of oscillation amplitudes in case 2122, which are attributed to the different natural time steps used in the simulations. Yet, mean strain values in the phase of constant pressure show differences of 11.3%/0.7% (case 2122, x/y) and 1.2%/4.0% (case 3122, x/y) from their common mean strain values.

These discrepancies are attributed to the code-specific differences in the computation of shell elements, link elements, contacts, and plasticity variables, which are inevitable. Based on a further simplification using a fully clamped panel, where the only differences of the models are the exact shell element formulation and the computation of plasticity variables, it was demonstrated that differences from their common mean strain values already occur. At the gauge location S 2 differences are 0.93%/0.16% (case 2122, x/y) and 3.1%/2.9% (case 3122, x/y).

Simulation Results

Having validated the structural models with reported differences, ALE-FE and SPH-FE simulations for the three selected test cases of the benchmark experiment were conducted. In this section, the simulation results are compared to experimental data from the guided ditching experimental campaign (cf. Sec. 3.1).

Pressure

Being the source of the structural loading, pressure time histories are evaluated first. Figure 7 provides results for pressure probes P 4 and P 12 located on the center line (y=0 mm) at x=125 mm and x=400 mm, respectively, from the trailing edge of the panels. These results are representative for the effects observed at all 18 pressure probe locations. Experimental pressure results were recorded only in test case 1122. Common for both numerical methods, pressure results uncover the strengths as well as the limitations of the fluid models. The employed methods both capture the delaying effect of the structural deformations on the pressure results. This delay grows while the panel immerses into the water, which shows as a growing difference in timing comparing pressures at probes P 4 and P 12 . The ALE solution shows an excellent timing compared to the experimental data of case 1122. In the other cases, the pressures in the ALE solution advance slower compared to the SPH solution. With the latter advancing faster in time, a growing time discrepancy arises as the specimens immerse into the fluid. This behavior is attributed to the lack of air and related phenomena such as air cushioning and ventilation, which are both expected to lower the acting hydrodynamic loads [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF][START_REF] Ma | Pure and aerated water entry of a flat plate[END_REF] and thus delay the impact.

In general, the use of weakly-compressible schemes, i.e. employing an equation of state, results in numerical pressure oscillations that arise due to the "stiffness" of the EOS, which already for small density variations yields large pressure variations. The oscillations are generally stronger in the SPH solution than in the ALE solution, which is attributed to two main aspects. On the one hand, the particle volume is significantly larger compared to the cell volume, i.e. 720 mm 3 for SPH versus 125 mm 3 for ALE. On the other hand, the Lagrangian nature of SPH leads to an increasingly irregular particle distribution, which adversely affects the accuracy of the SPH algorithm.

Just after the decay of the peak pressure, the pressure in the ALE simulations shows strong oscillations, which however quickly decay. In addition, the pressure measurement technique is affecting the oscillations recorded by the numerical pressure gauges: whereas in the ALE simulations, the gauges evaluate the pressure from one ALE cell, in the SPH simulations passive SPH particles (gauge particles) probe the pressure over a number of neighbor particles located inside their compact support domain [START_REF] Siemann | Pressure Evaluation at Arbitrary Locations in SPH Water Impact Simulations[END_REF], which leads to a variation in the number of particles used for the evaluation. While the major shape of the pressure response is captured by both simulation methods, there are distinct differences in the ability to capture the highly transient pressure peak with its sharp rise and quick decay as well as the post-peak pressure level. In the ALE method, the contact stiffness affects the pressure peak values: a higher stiffness yields larger pressure peak values. ALE results show the characteristic pressure peak as observed in the experiments. In contrast, the measured SPH pressure results do not portray such sharp pressure peaks and also the measured pressure values are lower compared to ALE predictions and experimental data. This is assumed to be related to the employed pressure measuring technique in the SPH On the one hand, the size of the compact support of the gauge particles (i.e. the sampling domain) and, in addition, the present particle resolution are both considerably larger than the sensible element of the pressure probes used in the experiment. This leads to a smoothing effect and a lower measured pressure, while the local pressure acting on the structure may reach higher values. On the other hand, the gauge particles probe the pressure in a spherical region, which therefore also includes particles farther away from the surface of the structure, where due to the pressure gradient in normal direction to the structure the local pressure is lower. The latter could be circumvented by using a more complex pressure measurement technique, as for instance the one presented by Oger et al. [START_REF] Oger | Two-dimensional SPH simulations of wedge water entries[END_REF], that permits limiting the sampling domain also in normal direction to the structure's surface. Yet, this should not compromise the computational efficiency as it involves computations of surface normals.

Normal Force

Normal force time histories are shown in Fig. 8. They provide a measure of the overall load resulting from the fluid-structure interaction. The force time histories generally are in good qualitative agreement with the experimental data. Both numerical methods predict the initial slope, its reduction after the flow field has been established, and the abrupt decay after the leading edge immersion. Common for both numerical methods, normal force oscillations are lower for test cases with deformable specimens as structural deformations act as a filter of the highly transient and oscillating pressure that is acting on the structure. Another observation related to the occurrence of structural deformations is the local force peak just before the leading edge immersion that is predicted by both simulation methods for the cases with deformable panels. As shown by Siemann [START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF], this force peak is caused by the FSI at the front of the panel, where the structural deformation results in a negative local pitch angle of the panel. The timing of normal force results follows the observations made for pressure results, i.e. the SPH solution advances faster in time, whereas the ALE solution shows an excellent timing compared to the experimental data. This is particularly visible at the instant when the leading edge immerses into the water causing the normal force to decay rapidly. Normal force magnitudes are lower in the ALE solutions, which is attributed to leakage problems that can appear when the fluid flow moves nearly tangential to the structure. This is particularly true when the FSI is computed based on a penalty method as done in this work. There, the normal force acting on the water may be underestimated thus leading to leakage.

Strain

Strain time histories are evaluated in order to assess the accuracy of the structural response. Figure 9 shows the responses at gauge location S 2 . Common for all test cases, the strain rate is lower for the ALE solution, which results from the underestimated rate of the pressure loading, i.e. the pressure rises too smooth and thus the structural loading lags. Both solutions considerably underestimate the experimental strain magnitude in test case 1122, which is attributed to the effects of model simplifications that will be discussed in Sec. 5.3. In test case 2122, both solutions capture the strain response with good agreement to the experimental data. Strain magnitudes at gauge location S 2 reach the upper elastic region. Yet, there is a time lead of the SPH solution and, in contrast, a time lag of the ALE solution. Large discrepancies are observed in test case 3122, where strains reach the plastic region. Both simulation results show a high strain rate in x-direction at the instant when the jet root passes the gauge location, whereas the experimental data features a smooth and steady rise of the strain. This observation is ascribed to the lack of capturing the detailed jet root shape in the simulations, which would require a further refinement of the fluid domain. Hence, in the simulations the pressure is applied more rapidly compared to the experiments, where the jet flowing along the structure already causes a loading before the arrival of the high-pressure zone located at the jet root.

Discussion

Effects of Plasticity Computation Method

Validation simulations indicated a noticeable effect of the algorithm used to compute the plastic variables on the strain results. Due to its availability in both software packages, a Newton iterative algorithm was adopted for the comparative studies. Nevertheless, effects of the plasticity computation method on the simulation results were investigated based on additional ALE-FE simulations using the radial return algorithm. Strain results recorded at the gauge locations did not show noticeable effects as they remained within the elastic range. Contour plots, however, revealed larger plastic strains, which were affected by the algorithm used to compute the plastic variables, occurring concentrated at the interface of the specimen and the L-frame. Hence, this change in the structural response did not lead to significant differences in the simulation results. Nevertheless, the use of the radial return algorithm should be favored as it is more accurate compared to the Newton iterative algorithm [START_REF] Simo | Computational Inelasticity[END_REF].

Effects of Air

In order to investigate the effects of air on the simulation results, an ALE-FE simulation of case 1122 with a modified air material was conducted. Therein, the air density was decreased by a factor of one thousand to an artificial value of 1.2•10 -12 kg/mm 3 . Although the simulation became unstable towards the end of the computation, several observations could be established. Pressure time histories were very similar to the ones in the simulation with the initial air density. They generally showed no effect on the timing, yet lower peak values followed by a phase with significantly lower and even negative relative pressures caused by local instabilities due to a decrease of the density to very small values near zero that were unphysical. This later led to the premature termination of the computation caused by a negative density in one ALE cell. Due to the changes of the pressure acting on the structure, the normal force was lower during the first 25 ms of the impact, whereas afterward the normal force time histories were quasi-identical until the termination that came along with growing oscillations of the normal force. Consequently, the lower normal force yield very similar strain time histories yet with reduced peak values. In summary, the pursued way to investigate effects of air did not permit observing the anticipated results due to air cushioning, such as lower peak pressures, lower normal force, and smaller strain magnitudes.

Effects of Model Simplifications

The absence of the guide structure in the model, which was discarded to avoid additional differences in the structural model due to the use of two software packages, resulted in additional discrepancies with respect to the experimental results. In order to quantify these discrepancies, SPH-FE simulation using a structural model including the guide structure and an elastic trolley model were conducted. Figure 10 compares numerical results for the two models, i.e. with and without the guide structure, against experimental results for all three test cases. The discrepancies of the normal force magnitudes were in the order of 8% to 12% for the regarded test cases. Normal forces were generally larger when there was no guide structure because the evasive motion observed in the experiment was suppressed and thus the acting vertical velocity remained larger. Furthermore, the timing of the numerical results was slightly worse without using the guide model. This can be explained by the absence of the reduction of the vertical velocity, which delayed the immersion in the cases with the guide model. Despite the reduced correlation due to the absence of the guide structure, the superimposed oscillations were lower for all simplified models, which is attributed to the use of the rigid body trolley model. Strain time histories are presented in Fig. 11 for gauge S 2 . For case 1122 strain magnitudes were highly affected by the model simplification. In particular, the rigid trolley model was responsible for the differences of the structural response near the interface of the specimen and the L-frame. In contrast, no significant differences occurred in case 2122. Finally, case 3122 showed minor differences, yet the strain magnitudes were smaller in the simulation with the model simplification. Overall, strain results indicated the importance of the structural modeling that affected the structural response depending on the stiffness of the specimen.

In addition, the effects due to the use of a simplified, rigid trolley model were investigated. Therefore, further ALE-FE simulations with an elastic trolley model were conducted. Results showed no effect on the normal force. In comparison with above findings, the observed sensitivity of the normal force on the model simplifications can therefore be ascribed to the presence of the guide structure. However, there was an important effect on the strain time histories in case 1122 as shown in Fig. 12. Similar to the observations in Fig. 11, strain magnitudes were found to be sensitive to the stiffness of the trolley model. Future studies could further address the sensitivity of the structural response to the discretization of the trolley and in particular the L-frame as well as the joint modeling.

Further Aspects

The resolution of the structural model was identical for both computational methods. It defines the resolution of the ALE fluid domain, which must be smaller than the structural resolution to warrant proper functionality of the coupling; however, the resolution of the SPH fluid domain could not be refined as much because of constrains regarding the related computational effort. Consequently, a comparison of the computational effort between the two computational methods cannot be established. Furthermore, the pressure measurement in each method is affected by the difference in fluid domain resolution as well as the measurement technique. These points could be addressed in further parametric studies regarding a similar yet two-dimensional water impact test case and evaluating local as well as global results.

The present study also indicated coupling effects between fluid and structure in the ALE simulations. When the fluid material motion is tangential to the structure, leakage may occur because contact forces can be underestimated. Additionally, the contact height was found to affect the rate of the pressure acting on the structure. The latter could be further investigated based on above-mentioned parametric studies concerned with the fluid domain resolution or by using Lagrange multipliers for the fluid-structure coupling.

This study was limited to one impact condition, i.e. the combination of impact velocities and pitch angle, with limited structural deformation and no failure. For impact conditions leading to higher loads, however, findings may vary as the structural failure in terms of material or joint failure could develop. Hence, future studies could compare the computational methods in terms of their capabilities and limitations when structural failure occurs.

Conclusion

This work investigated the capabilities and limitations of two coupled fluid-structure computational methods, namely ALE-FE and SPH-FE approaches. The use of different software packages for simulations based on each method impeded the present study, but the comparison was concentrated as far as possible on the fluid methods. Therefore, the similarity of the structural models in each software package was extensively studied and finally demonstrated with the reported accuracy. Results of benchmark simulations of guided ditching experiments demonstrated that both approaches were capable of simulating the fluid as well as the structural response of quasi rigid as well as deformable specimen impacting water under conditions representative of aircraft ditching. The ALE-FE and the SPH-FE approaches were able to handle large fluid displacements in conjunction with rapidly moving structures undergoing significant structural deformations.

Despite continuous advances in computing technologies, e.g. high performance computing, advanced modeling strategies, etc., the main limitation for both approaches is their large run time. In order to apply these approaches to large realistic aircraft structural models, a further speed-up is required.

Figure 1 :

 1 Figure 1: Illustration of ALE fluid domain. All measures are in millimeters.

Figure 2 :

 2 Figure 2: Illustration of hybrid SPH-FE fluid domain with translating active domain feature. All measures are in millimeters.

Figure 3 :

 3 Figure 3: Illustration of structural model. Partially elements are hidden for clarity of illustration. All measures are in millimeters.

Figure 4 :

 4 Figure 4: Validation test case for structural models. The horizontal portion of the L-frame is fixed in all degrees of freedom.

Figure 5 :

 5 Figure 5: Comparison of upper surface strain distributions (ε xx ) for simulations with ALE-FE software (top) and SPH-FE software (bottom) at t = 20 ms. Contours are given in [mm/mm]. Structures refer to test cases 2122 (left) and 3122 (right). Half of the panel is shown to help the comparison.

Figure 6 :

 6 Figure 6: Comparison of strain time histories at gauge location S 2 for simulations with ALE-FE software (green solid lines and square markers) and SPH-FE software (red solid lines and triangle markers). Structures refer to test cases in the order 1122, 2122, and 3122 from top to bottom.

Figure 7 :

 7 Figure 7: Comparison of pressure time histories of probes P 4 (left) and P 12 (right) for ALE-FE (green solid lines and square markers) and SPH-FE (red solid lines and triangle markers) simulations against experimental data (black solid lines without markers). Test cases refer to 1122, 2122, and 3122 from top to bottom.

Figure 8 :

 8 Figure 8: Comparison of normal force time histories for ALE-FE (green solid lines and square markers) and SPH-FE (red solid lines and triangle markers) simulations against experimental data (black solid lines without markers). Test cases refer to 1122, 2122, and 3122 from top to bottom.

Figure 9 :

 9 Figure 9: Comparison of strain time histories at gauge location S 2 for ALE-FE (green solid lines and square markers) and SPH-FE (red solid lines and triangle markers) simulations against experimental data (black solid lines without markers). Test cases refer to 1122, 2122, and 3122 from top to bottom.

Figure

  Figure 10: Comparison of normal force time histories for SPH-FE simulations without (green solid lines and square markers) and with (red solid lines and triangle markers) model simplification against experimental data (black solid lines without markers). Test cases refer to 1122, 2122, and 3122 from top to bottom.

Figure 11 :

 11 Figure 11: Comparison of strain time histories at gauge location S 2 for SPH-FE simulations without (green solid lines and square markers) and with (red solid lines and triangle markers) model simplification against experimental data (black solid lines without markers). Test cases refer to 1122, 2122, and 3122 from top to bottom.

Figure 12 :

 12 Figure 12: Comparison of strain time histories at gauge location S 2 for ALE-FE simulations with rigid (green solid lines and square markers) and elastic (blue solid lines and triangle markers) trolley model against experimental data (black solid lines without markers). Test case 1122.

Table 1 :

 1 Overview of hardware and computational settings used for ALE-FE and SPH-FE computations.

		ALE-FE simulations	SPH-FE simulations
	Cluster system	Linux CentOS 6.5	Linux Ubuntu, Beowulf
	Processor type	2 × Intel Ivy-Bridge 2 × Intel Xeon E5540
		E5-2667v2 (8-core,	(4-core, 64-bit, 2.53 GHz)
		64-bit, 3.3 GHz)
	Number of CPUs 32	8
	RAM per node	16 GB	24 GB
	Computing mode Distributed memory, Shared memory,
		single precision	single precision
	3.2.1. Fluid Model: ALE

Table 2 :

 2 Maximum deformations for structural model validation test case at t = 20 ms.

	∆Y max		∆Z max
	Case ALE SPH Difference [%] ALE SPH-FE Difference [%]
	1122 0.021 0.022	2.09 2.46	2.61	2.90
	2122 3.590 5.030	16.71 33.60	41.66	10.71
	3122 2.890 3.350	7.37 56.62	54.48	1.93

Consiglio Nazionale delle Ricerche -Istituto Nazionale per Studi ed Esperienze di Architettura Navale

SMart Aircraft in Emergency Situations, 2011-2014

Further information is given in[START_REF] Siemann | Numerical and Experimental Investigation of the Structural Behavior during Aircraft Emergency Landing on Water[END_REF].

Assessment of Ditching and Water Impact, 2015-2017

Acknowledgement

This work was performed as part of the common research project ADAWI 6 , which was supported by Onera and DLR.


Tristan Cazenave
email: cazenave@lamsade.dauphine.fr

Jialin Liu
email: jialin.liu@essex.ac.uk

Fabien Teytaud
email: fabien.teytaud@lisic.univ-littoral.fr

Olivier Teytaud

Learning opening books in partially observable games: using random seeds in Phantom Go

Many artificial intelligences (AIs) are randomized. One can be lucky or unlucky with the random seed; we quantify this effect and show that, maybe contrarily to intuition, this is far from being negligible. Then, we apply two different existing algorithms for selecting good seeds and good probability distributions over seeds. This mainly leads to learning an opening book. We apply this to Phantom Go, which, as all phantom games, is hard for opening book learning. We improve the winning rate from 50% to 70% in 5x5 against the same AI, and from approximately 0% to 40% in 5x5, 7x7 and 9x9 against a stronger (learning) opponent.

I. INTRODUCTION

A. Offline learning in games

Offline learning in games can be e.g. endgame table building [START_REF] Nalimov | Kqqkqq and the kasparov-world game[END_REF], opening book construction by self-play [START_REF] Gaudel | A principled method for exploiting opening books[END_REF], or parameter estimation [START_REF] Chaslot | Parameter tuning by cross entropy method[END_REF]. We propose the use of Random-Seed-portfolios (Section III-A) for offline learning in games for which randomized AIs perform well. This approach will essentially, though not only and not explicitly, learn at the level of the opening book. Learning opening books is particularly hard in partially observable games, due to the difficult belief state estimation; therefore, this recent approach by random seeds is particularly suitable in this case.

The random seeds approach has already been proposed for the game of Go, but the present paper is, to the best of our knowledge, the first application to partially observable games, and our resulting algorithm outperforms by far the original algorithm, which is at the current top level in Phantom Go, including its traditional board sizes. This is mainly obtained through opening book learning -which is a hard task in partially observable games.

B. Randomized artificial intelligences

1) Why randomizing AIs.: There are games in which optimal policies are randomized and, beyond that, in many cases the state of the art is made of randomized algorithms, in particular since the advent of Monte Carlo Tree Search [START_REF] Coulom | Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search[END_REF], [START_REF] Kocsis | Bandit based Monte-Carlo planning[END_REF]. Randomized AIs are also required when the AI should be robust to "overfitting" by an opponent -i.e. when we do not want an opponent to be able to learn, by repeated games, a simple winning strategy. A deterministic AI is certainly not suitable in such a case, e.g. for playing on a server or for the pleasure/education of a human opponent. Still, we point out that our approach makes sense in terms of pure performance against the baseline algorithms.

2) The original Monte Carlo approach.: The Monte Carlo approach in games goes back to [START_REF] Bruegmann | Monte-carlo Go[END_REF]. The basic idea is to evaluate a position thanks to random simulations. The value at a state s is obtained by averaging the result of hundreds of games played randomly from this state s. This is compliant with partially observable games by randomly sampling the hidden parts of the state. With ad hoc randomization, this approach is the state of the art in Phantom Go.

3) Improvements of the original Monte Carlo approach.: The original Monte Carlo method for games has been vastly improved [START_REF] Bouzy | Associating domain-dependent knowledge and monte carlo approaches within a go program[END_REF], [START_REF] Bouzy | Bayesian generation and integration of knearest-neighbor patterns for 19x19 go[END_REF]. For fully observable games it was outperformed by Monte Carlo Tree Search [START_REF] Coulom | Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search[END_REF], which adds a tree search to the Monte Carlo evaluation principle. For fully observable puzzles (one player games), nested Monte Carlo often outperforms Monte Carlo [START_REF] Cazenave | Nested monte-carlo search[END_REF], [START_REF] Méhat | Combining uct and nested monte carlo search for single-player general game playing[END_REF]. In partially observable games with large hidden state, Monte Carlo remains at the top of game programming [START_REF] Cazenave | A phantom-go program[END_REF], [START_REF] Cazenave | Golois wins phantom go tournament[END_REF].

C. Boosting randomized artificial intelligences and learning opening books

Randomized AIs can be seen as random samplers of deterministic policies. A random seed is randomly drawn, and then a deterministic AI, depending on this seed, is applied. The choice of the random seed is usually considered of negligible importance. However, a recent work [START_REF] Saint-Pierre | Nash and the Bandit Approach for Adversarial Portfolios[END_REF] has shown that random seeds have an impact, and that the bias inherent to the use of a given randomized AI (which has an implicit probability distribution on random seeds) can be significantly reduced by analyzing the impact of random seeds. We here extend this work to a more challenging case, namely Phantom Go.

Section II describes our testbed for experiments. Section III describes our approach for boosting random seeds. Section IV presents experimental results.

II. PHANTOM GO

The game of Phantom Go is a two-player game with hidden information. It consists in playing Go without seeing the other player's moves. Each player does not see the board of the other player. In addition, there is a reference board that is managed by a referee and that the players do not see either. On each player's turn, the player proposes a move to the referee. If the move is legal on the reference board, it is played on the reference board and it is the other player's turn. If the move is illegal on the reference board, the referee tells the player that the move is illegal and the player is asked to play another move. The referee is in charge of maintaining the reference board and of telling illegal moves to the players. The game is over when the two players pass.

Monte Carlo methods have been used in Phantom Go since 2005. The resulting program plays at the level of strong human Go players. Monte Carlo Phantom Go was one of the early success of Monte Carlo methods in Go and related games. The principle of Monte Carlo Phantom Go is to randomly choose a "determinization" (i.e. a filling of the unknown parts of the state space) consistent with the previous illegal moves before each playout. For each possible move, the move is simulated, followed by a determinization and a random playout. Thousands of such determinizations and playout sequences are played for each move and the move with the highest resulting mean is played.

This simple method has defeated more elaborate methods using Monte Carlo Tree Search in the former computer Olympiads. Using a parallelization of the algorithm on a cluster our program won five gold medals and one silver medal during the last six computer Olympiads. When winning the silver medal, the program lost to another program using the same method. The program also played three strong Go players in exhibition matches during the 2011 European Go Congress and won all of its three games.

III. RANDOM SEEDS AND THEIR BOOSTING

A. Seeds in games

We consider a randomized artificial intelligence (AI), equipped with random seeds. Our experiments will be performed on a Monte Carlo approach for Phantom Go, though the method is generic and could be applied to any randomized algorithm such as those cited in Section I-B.

We can decide the seed -and when the seed is fixed, the AI becomes deterministic. The original (randomized) algorithm Algorithm 1 The BestSeed algorithm for boosting a randomized AI. There is a parameter K; K greater leads to better performance but slower computations. The resulting AI is deterministic, but it can be made stochastic by random permutations of the 8 symmetries of the board. Require: K, and a randomized AI.

1: for i ∈ {1, . . . , K} do 2:

for j ∈ {1, . . . , K} do 3:

Play a game between

• an AI playing with seed i as Black;

• an AI playing with seed j as White.

4:

M i,j ← 1 if Black wins, 0 otherwise 5:

end for 6: end for

7: i 0 ← argmax i∈{1,...,K} K j=1 M i,j 8: j 0 ← argmin j∈{1,...,K} K i=1 M i,j 9:
return The (deterministic) AI using seed i 0 when playing Black and j 0 when playing White.

can be seen as a probability distribution over these deterministic AIs.

A Random-Seed-portfolio (RS-portfolio) consists in optimizing the probability distribution on random seeds. Such an algorithm has been proposed in [START_REF] Saint-Pierre | Nash and the Bandit Approach for Adversarial Portfolios[END_REF]. We recall below the two algorithms they propose, namely Nash and BestSeed. In both cases, the learning of the probability distribution is based on the construction of a K ×K binary matrix M , where M i,j = 1 if Black with random seed i wins against White with random seed j, and M i,j = 0 otherwise. This matrix is the learning set; for validating our approach in terms of performance against the original randomized algorithm, we use random seeds which are not in this matrix, and distributed as in the original randomized algorithm.

B. Strategies for choosing seeds

We describe here two methods for choosing a probability distribution on rows i ∈ {1, 2, . . . , K} and a probability distribution on columns j ∈ {1, 2, . . . , K}. These probability distributions are then used as better probability distributions on random seeds at the beginning of later games.

1) BestSeed approach.: BestSeed is quite simple; the probability distribution for Black has mass 1 on some i such that j∈{1,...,K} M i,j is maximal. We randomly break ties. For White, we have probability 1 for some j such that i∈{1,...,K} M i,j is minimum. The BestSeed approach is described in Algorithm 1. This method is quite simple, and works because

lim K→∞ 1 K K j=1 M i,j (resp. lim K→∞ 1 K K j=1 M j,i )
is far from being a constant when i varies.

2) Nash approach.: This section describes the Nash approach. It is more complicated than the BestSeed approach, but it is harder to "exploit", as detailed in the experimental section. First, we introduce constant-sum matrix games, and then we explain how we use them for building portfolios of random seeds.

a) Constant-sum matrix games: We consider constantsum matrix games; by normalizing matrices, we work without loss of generality on games such that the sum of the rewards for player 1 and for player 2 is one. Consider the following game, parametrized by a K × K matrix M . Black plays i. White is not informed of Black's choice, and plays j. The reward for Black is M i,j and the reward for White is 1-M i,j .

It is known [START_REF] Neumann | Theory of Games and Economic Behavior[END_REF], [START_REF] Nash | Some games and machines for playing them[END_REF] that there exists at least one Nash equilibrium (x, y) such that if Black plays i with probability x i and White plays j with probability y j , then neither of the players can improve its expected reward by changing unilaterally his policy. More formally:

∃(x, y), ∀(x , y ), x t M y ≤ x t M y ≤ x t M y ,
where x, y, x and y are non-negative vectors summing to one. Moreover, the value v = x t M y is unique -but the pair (x, y) is not necessarily unique.

It is possible to compute x and y in polynomial time, using linear programming [START_REF] Stengel | Computing equilibria for two-person games[END_REF]. Some faster methods provide approximate results in sublinear time [START_REF] Grigoriadis | A sublinear-time randomized approximation algorithm for matrix games[END_REF], [START_REF] Auer | Gambling in a rigged casino: the adversarial multi-armed bandit problem[END_REF]. Importantly, these fast approximation algorithms are mathematically proved and do not require all the matrix to be available -only O(K log(K)/ ) elements in the matrix have to be computed for a fixed precision > 0 on the Nash equilibrium.

b) Nash portfolio of random seeds: Consider (x, y) the Nash equilibrium of the matrix game M , obtained by e.g. linear programming. Then the Nash method uses x as a probability distribution over random seeds for Black and uses y as a probability distribution over random seeds for White. The algorithm is detailed in Algorithm 2. We also tested a sparse version, which gets rid of pure strategies with low values. The algorithm depends on a parameter α, and it is detailed in Algorithm 3.

C. Criteria

We now give two performance criteria, namely performance against the baseline (which is the original randomized algorithm) and performance against an agent which can choose its seed with perfect rationality among a finite randomly drawn set of a given cardinal -the second criterion is harder, and simulates an opponent who has "learnt" how to play against us by optimizing his seed.

1) Performance against the baseline.: The first criterion is the success rate against the original AI, with its randomized seed. This is precisely the criterion that is optimized in BestSeed; but, obviously, we perform experiments in crossvalidation, i.e. the performance obtained by BestSeed and displayed in Section IV is the performance against seeds which were not used in the learning phase.

Algorithm 2 The Nash method for boosting a randomized AI. There is a parameter K; K greater leads to better performance but slower computations. The resulting AI is stochastic. It is outperformed by BestSeed in terms of winning rate against the original (randomized) algorithm, but harder to overfit. Require: K and a randomized AI.

1: for i ∈ {1, . . . , K} do 2:

for j ∈ {1, . . . , K} do 3:

Play a game between

• an AI playing with seed i as Black;

• an AI playing with seed j as White.

4:

M i,j ← 1 if Black wins, 0 otherwise 5:

end for 6: end for 7: Let (x, y) be a pair of probability distributions over {1, . . . , K}, forming a Nash equilibrium of M . 8: return The (stochastic) AI using seed

• i 0 randomly drawn with probability distribution x when playing Black • and j 0 randomly drawn with probability distribution y when playing White.

Algorithm 3

The SparseNash method for boosting a randomized AI. Compared to Algorithm 2, there is an additional parameter α.

Require: K α and a randomized AI. 1: for i ∈ {1, . . . , K} do 2:

for j ∈ {1, . . . , K} do

3:

Play a game between

• an AI playing with seed i as Black;

• an AI playing with seed j as White.

4:

M i,j ← 1 if Black wins, 0 otherwise 5:

end for 6: end for 7: Let (x, y) be a pair of probability distributions over {1, . . . , K}, forming a Nash equilibrium of M . 8: x max ← max 1≤i≤K x i 9: y max ← max 1≤i≤K y i 10: For all i ∈ {1, . . . , K}, if x i < αx max , then x i ← 0. 11: For all i ∈ {1, . . . , K}, if y i < αy max , then y i ← 0. 12: x ← x/ K i=1 x i 13: y ← y/ K i=1 y i 14: return The (stochastic) AI using seed

• i 0 randomly drawn with probability distribution x when playing Black • and j 0 randomly drawn with probability distribution y when playing White. 2) Performance against an opponent who learns.: The second criterion is the success rate against an opponent who plays with the original randomized AI, but can test K randomly drawn random seeds and can select the best of these seeds. This modelizes the case in which the opponent can choose (perfect choice) one policy among K policies. We here consider K policies, each of them obtained by fixing the random seed to some random value. We do this choice among K policies for Black, and K policies for White as well, so that we have indeed the worst performance against K × K policies. This becomes a very tough criterion when K increases -our opponent can basically test (K ) 2 openings and choose the one for which we are the weakest.

Obviously, all experiments in the present paper are performed with separate seeds for the learning and the validation experiments, so that no overfitting can explain the positive results in Section IV.

IV. EXPERIMENTAL RESULTS

We perform experiments on the Phantom Go testbed. Our randomized AI is Golois [START_REF] Cazenave | A phantom-go program[END_REF], [START_REF] Cazenave | Golois wins phantom go tournament[END_REF]. In all our results, we use cross-validation; we test performance against seeds which were not used during the learning phase. We consider values of K ≤ 400. We use the two criteria described in Section III-C, i.e. winning rate against the original randomized algorithm and worst of the winning rates against K × K deterministic policies obtained as described in Section III-C2. All presented winning rates are the average between the winning rate as Black and the winning rate as White.

We observe in Figure 1 (also Table I):

• The BestSeed approach clearly outperforms the original method in 5x5, 7x7 and 9x9. The performance is excellent in 5x5, greater than 71%; around 67% in 7x7; it is still good in 9x9 (54%). • The Nash approach reaches 64% in 5x5, 58% in 7x7. This is already reasonably good for a very randomized game such as Phantom Go; in partially observable games like Phantom Go, Poker, or many card games, several games are usually required for knowing the best among two players. In 9x9, we got only 52% -not very impressive. • The SparseNash approach outperforms BestSeed in terms of success rate against the original randomized AI, in 5x5 (Figure 2 (top), summarized in Table I). Results are however disappointing on larger board sizes (Figure 2 (middle and bottom); also presented in Table I).

These two methods were tested directly on the original algorithm, without using the symmetries of the game or any prior knowledge. All results are obtained with proper crossvalidation. Standard deviations are shown on figures and are negligible compared to deviations from 50%. The approach has a significant offline computational cost; but the online Board Method Winning rate (%)

K = 1 K = 2 K = 4 K = 8 K = 16
5x5 Baseline 50 30.5 ± 0.9 12.5 ± 0.7 0. 1). α is the sparsity parameter (cf. Algorithm 3). The experiments are repeated 1000 times. The standard deviations are shown after ±. K = 1 corresponds to the original algorithm with randomized seed; K = 2 corresponds to the original algorithm but choosing optimally (after checking their performance against its opponent) between 2 possible seeds, i.e. it is guessing, in an omniscient manner, between 2 seeds, each time an opponent is provided. K = 4, K = 8, K = 16 are similar with 4, 8, 16 seeds respectively; K = 16 is a very strong opponent for our original algorithm (our winning rate is initially close to 0), but after Nash seed learning we get results above 40% in 5x5, 7x7 and 9x9.

computational overhead is zero. The offline computational overhead is K 2 times the cost of one game, plus the Nash solving. The Nash solving by linear programming is negligible in our experiments. For large scale matrices, methods such as [START_REF] Grigoriadis | A sublinear-time randomized approximation algorithm for matrix games[END_REF] should provide much faster results as the number of games would be O(K log(K)/ 2 ) instead of K 2 for a fixed precision .

V. CONCLUSIONS

We tested various methods for enhancing randomized AIs by optimizing the probability distribution on random seeds. Some of our methods are not new, but up to now, they were only tested on a fully observable game, without opening book, whereas in fully observable games building an opening book is far less a challenge. We work on Phantom Go, a very challenging problem, with the program which won most competitions in recent years. The three tested methods provide results as follows:

• With BestSeed, we get 71%, 67%, 54% of success rate against the baseline in 5x5, 7x7 and 9x9, just by "managing" the seeds. • The Nash approach provides interesting results as well, in particular strongly boosting the performance against stronger opponent such as K = 2, K = 4, K = 8, K = 16, reaching 40% (in 5x5, 7x7 and 9x9) whereas our original algorithm was close to 0% winning rate for K = 16. This means that the opening book we have learnt is robust against stronger opponents than the ones used for the self-play involved in our learning. • Using the Nash approach with sparsity, with the exponent α = .75 recommended in earlier papers on sparsity, maybe not the best for each case separately, but outperforming the baseline in all cases.

The method has no computational overhead online -all the computational cost is an offline learning. As a consequence, the method looks like a free bonus: when your randomized AI is ready, apply Algorithm 2 and get a better AI. The BestSeed method is the best performing one, but it can be overfitted. The Nash approach is less efficient against the original AI, but more robust, i.e. more difficult to overfit.

Further work

We propose the following further works:

• The approach is quite generic, and could be tested on many games in which randomized AIs are available. For the BestSeed approach, the game does not have to be a two-player game. • Our work does not use any of the natural symmetries of the game; this should be a very simple solution for greatly improving the results; in particular, it would be much harder to overfit BestSeed if it was randomized by the 8 classical board symmetries. • Mathematically analyzing the approach is difficult, because we have no assumption on the probability distribution of E j M i,j for a randomly drawn seed i -how many i should we test before we have a good probability of having a really good one ? Bernstein inequalities [START_REF] Bernstein | The Theory of Probabilities[END_REF], [START_REF] Hoeffding | Probability inequalities for sums of bounded random variables[END_REF], [START_REF] Chernoff | A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations[END_REF] for the BestSeed approach, and classical properties of Nash equilibria for the Nash approach, provide only preliminary elements. • Computing approximate Nash equilibria (using [START_REF] Grigoriadis | A sublinear-time randomized approximation algorithm for matrix games[END_REF] or [START_REF] Auer | Gambling in a rigged casino: the adversarial multi-armed bandit problem[END_REF]) should strongly reduce the offline computational cost. The computational cost was not a big deal for the results presented in the present paper, but performance might be much better with K larger. Approximate Nash equilibria do not need the entire K × K matrix; they only sample O(K log(K)/ 2 ) elements of the matrix for a precision . • This last further work opens some problems also in the algorithmic theory of Nash equilibria. We have done the present work in a not anytime manner; we know K a priori, and we do not have any approximate results as long as the K 2 games are not played. However, we might prefer not to choose a priori a number K of games, and get anytime approximate results. To the best of our knowledge, [START_REF] Grigoriadis | A sublinear-time randomized approximation algorithm for matrix games[END_REF], [START_REF] Auer | Gambling in a rigged casino: the adversarial multi-armed bandit problem[END_REF] have never been adapted to an infinite set of arms. Also, adversarial bandit approaches such as Exp3 [START_REF] Auer | Gambling in a rigged casino: the adversarial multi-armed bandit problem[END_REF] have never been parallelized. [START_REF] Grigoriadis | A sublinear-time randomized approximation algorithm for matrix games[END_REF] is parallel, but possibly harder to adapt in an anytime setting.

Fig. 1 :

 1 Fig.1: Winning rate for Phantom Go 5x5 (left), 7x7 (middle) and 9x9 (right). Top: BestSeed; bottom: Nash. X-axis: K such that we learn on a K × K matrix M . Y-axis: winning rate. The training is performed on a K × K matrix. The testing is performed on K × K strategies, i.e. K strategies for Black and K strategies for White. K = 1 corresponds to a randomized seed -this is therefore the original randomized AI, and performance greater than 50% for K = 1 means that we outperformed the original randomized AI. K > 1 corresponds to the best performing AI, for each color, among K randomly drawn seeds; this is a very difficult opponent, who can try K 2 strategies and keep only the best of their results. The black dashed curve refers to a winning rate= 50%. The experiments are repeated 1000 times. The standard deviations are shown in the plots.

Fig. 2 :

 2 Fig. 2: Winning rate for Phantom Go 5x5 (top), 7x7 (middle) and 9x9 (bottom) using sparse strategy with different sparsity parameter α. X-axis: parameter K (size of the learning set). Y-axis: performance in generalization against the original algorithm (K = 1) and against the learning opponent (see Section III-C2; K = 2 to K = 16).

TABLE I :

 I Winning rate for Phantom Go 5x5, 7x7 and 9x9 with K = 380 (cf. Figure


Ariane Pinche

Bruno Bureau

Christian Nicolas

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

digital edition project

Hyperdonat is a digital project created to deal with complex textual tradition. Born in Lyon, in the HiSoMA laboratory, from the collaboration of B. Bureau and C. Nicolas, Latin professors, Hyperdonat project was first a digital edition of Donat's commentaries which have a complex philological history that led editors to dedicate most of their 'paper' edition to the apparatus making the Latin text mostly unreadable. The project had as first aims to offer the first complete critical edition and a way to visualise those texts easily with its apparatus through the uses of new technologies.

Complex corpus

Difficult to read

Difficult to find informations

Too much apparat

Finding Another Way

To build a new information architecture, the Hyperdonat project tries a new path : digital editions using TEI-P5, XSLT, and web interface. Its aim is to provide tools and guidelines to structure a clear and precise ancient text edition, with a deep focus for those whose tradition is both complex and unreadable on paper because of the amount of informations to show in the apparatus. For these purposes, digital editions are a better way to give access to these texts where specialists can get philological informations and a larger public the text.

Setting Up of an Encoding Protocol

The scope of the project includes Donat but was never limited to it : it had to be useful, adaptable, and sustainable for any future edition. In this regard, Hyperdonat is both TEI conformant and documented. We set up a rationalised collation method to provide consistent encoding practices so that a unique transformation pipeline for web rendering would be shared across editions. To avoid the influence of other encoded witnesses, we chosed to use an external double endpoint apparatus based on a textual hub (text of a preceding edition for example) to whom each manuscript, encoded separately, refers to. It allows a really close mark-up of the text word by word and a really strict way to put the mark-up completely documented in an ODD. After that, the files of all the different manuscripts are reunited to create one single external apparatus in XML where each reading can be linked word for word to the tokenize 'hub' text through the use of xml:id. Using this apparatus and the 'hub' text, you can generate multiple views of an edition with different XSLT transforming XML in HTML.

-apparatus « structure » notifies places where a complete part of the text have been moved;

-apparatus « substantive » includes all the reading with semantics variants;

-apparatus « layout » notifies the textual layout in the manuscript;

-apparatus « graphic » allows you to signal all the graphic alternatives in witnesses.

Example :

<app type='layout' from='#w165'»> <rdg wit='#C' rend='normal'> <app type='graphic' from='#w165'> <rdg wit='#C'> <w corresp='w165'>ꝓconsule</w> <pc>;</pc> </rdg> </app> </rdg>

An interface with the multi-level apparatus

You can see the text with the complete multi-level apparatus or choose what level you want to see with a tool box

• Easy to use, it help to read the text with or without the apparatus.

• Useful for editor to check different versions of the text • Easy to read for students

An interface for each witness

You can see the text with a representation of its layout in the manuscript.

• Useful for editor to understand some variants in the tradition • Easy to read for students • useful to teach paleography

An Interface to Create Your Own Virtual Witnesses

You can see the 'hub' text and choose your reading by clicking on a word. When you have finished, you can download your edition in XML-TEI and eventually add it as a variant of the text in your project.

• Useful for editor to make its own critical edition because it creates the new apparatus automatically by transforming the chosen reading in lemma and the rejecting lemma in a reading.

• Pedagogic interface to understand what the editor's work is.

• Useful for new kinds of projects :

• Making hypotheses about a lost witness,

• trying to reconstructing a step in the tradition, etc.

A Comparison Interface

This interface allows you to see at the same time the edited text with apparatus on the left, and two witnesses on the right. Here, you choose the apparatus sections to display as well as which witnesses you want to compare it to, available as facsimile or as diplomatic translations.

• Useful for editor to check their own critical edition by confronting it with witnesses.

• Useful to confront witnesses or two different families of witnesses in the tradition.

• Useful when the problem in the tradition comes from the layout of glosses.

• Pedagogic interface to understand what the editor's work is.

  HiSoMA) Université Jean Moulin Lyon 3 Faculté des Lettres et Civilisations 18 rue Chevreul 69362 LYON 07l Christian Nicolas UMR 5189 (HiSoMA) Université Jean Moulin Lyon 3 Faculté des Lettres et Civilisations 18 rue Chevreul 69362 LYON 07l Ariane Pinche PhD Student in medieval literature, Région Rhône-Alpes-Auvergne Arc 5 scholarship UMR CIHAM Université Jean Moulin Lyon 3 Faculté des Lettres et Civilisations ariane.pinche@univ-lyon3.fr Creation of a scientific edition with multiple views