Arnaud Malher
email: arnaud.malher@ensta-paristech.fr

Olivier Doaré
email: olivier.doare@ensta-paristech.fr

Cyril Touzé
email: cyril.touze@ensta-paristech.fr

Pseudoelastic Shape Memory Alloys to Mitigate the Flutter Instability: A Numerical Study

A passive control of aeroelastic instabilities on a two-degrees-of-freedom (dofs) system is considered here using shape memory alloys (SMA) springs in their pseudo-elastic regime. SMA present a solid-solid phase change that allow them to face strong deformations (∼10 %); in the pseudo-elastic regime, an hysteresis loop appears in the stress-strain relationship which in turn gives rise to an important amount of dissipated energy. This property makes the SMA a natural candidate for mitigating undesired vibrations in a passive manner. A 2-dofs system is used here to model the classical flutter instability of a wing section in a uniform flow. The SMA spring is selected to act on the pitch in order to dissipate energy of the predominant motion. A simple phenomenological model for the SMA hysteresis loop is introduced, allowing for a quantitative study of the important parameters to optimize in view of an experimental design. Thanks to a simple phenomenological model for the SMA hysteresis loop, a quantitative numerical study is performed in order to exhibit the best tuning of the material parameters for controlling the flutter instability.

Introduction

Aeroelastic instabilities are an important issue in aeronautics, especially regarding the wing motions. Indeed, for a coupled system airflow-flexible structure, like aircraft wing, turbojet or bridge, a limit velocity exists above which the flexible structure cannot evacuate the energy received from the airflow anymore, then giving rise to strong or even fatal deformations. These instabilities, usually described under the generic term flutter instability, result from interaction between aerodynamic, inertia and elastic forces [START_REF] Bisplinghoff | Aeroelasticity[END_REF]. In this contribution, we focus on a passive control device for mitigating the flutter instability by using springs composed of shape memory alloys (SMA). In their pseudo-elastic regime, SMA are known for showing the ability of dissipating an important amount of energy thanks to the hysteresis loop appearing in their stress-strain relationship [START_REF] Moussa | Non-linear dynamic thermomechanical behaviour of shape memory alloys[END_REF], and has thus already been used in numerous applications ranging from civil engineering, aeronautics to medical industry [START_REF] Saadat | An overview of vibration and seismic applications of niti shape memory alloys[END_REF][START_REF] Strelec | Design and implementation of a shape memory alloy actuated reconfigurable airfoil[END_REF]. The goal of this study is, in a first step, not to describe the system as accurately as possible but to exhibit the interest of using an hysteretic phenomenon in the view of controlling an aeroelastic instability and studying the influence of different SMA parameters for the flutter control.

Recent contributions have considered the dynamical responses of SMA springs from the theoretical viewpoint [START_REF] Bernardini | The influence of model parameters and of the thermomechanical coupling on the behavior of shape memory devices[END_REF][START_REF] Lacarbonara | Nonlinear thermomechanical oscillations of shape-memory devices[END_REF][START_REF] Moussa | Non-linear dynamic thermomechanical behaviour of shape memory alloys[END_REF] in order to properly quantify the most prominent features of the vibrations of simple single dof systems. Experimentally, a torsion pendulum has recently been used in order to clearly exhibit the softening effect of SMA oscillators [START_REF] Doaré | Experimental analysis of the quasistatic and dynamic torsional behaviour of shape memory alloys[END_REF].

The aim of this paper is to investigate the effect of a SMA spring on the flutter instability. More particularly, the most relevant parameters of a pseudo-elastic regime on the amplitudes of the limit cycle oscillations (LCO) are analyzed, in order to quantify the effect of the dissipation brought by the hysteresis loop. The airfoil is modeled using the classical 2-dofs system coupling pitch and heave motions [START_REF] Dowell | A Modern Course in Aeroelasticity[END_REF]. In order to exchange energy and create the possibility of a Hopf bifurcation in the system, the minimal model should contain at least a flexural (heave) and a torsional (pitch) mode. The SMA nonlinear behaviour is described by an heuristic model where the prominent parameters are left free to vary. The structural nonlinearities that may appear in the wing motion are here described thanks to the addition of a cubic nonlinearity in the restoring force [START_REF] Ko | Adaptive feedback linearization for the control of a typical wing section with structural nonlinearity[END_REF][START_REF] Lee | Suppressing aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments[END_REF][START_REF] Lee | Suppression aeroelastic instability using broadband passive targeted energy transfers, part 1: Theory[END_REF][START_REF] Platanitis | Control of a nonlinear wing section using leading-and trailingedge surfaces[END_REF]. Numerical simulations are then conducted in order to investigate the effect of the SMA on the LCO. In particular, it is shown that for certain parameter range, the SMA spring can lead to a significant decrease of the amplitude of the LCO.

2DOFs Airfoil Model

Linear Model and Flutter Velocity

The system under consideration is shown in Fig. 1. A Lagrangian formulation is used to express the evolution of the altitude h (heave) and the angle of attack α (pitch) [START_REF] Dowell | A Modern Course in Aeroelasticity[END_REF]. The kinetic energy reads T = 1 2 m ḣ2 + 1 2 I α α2 + S α ḣ α, and the potential energy

reads V = 1 2 k α α 2 + 1 2 k h h 2 .
In these expressions, I α is the inertia moment and S α the static moment which is directly related to the position of the airfoil gravity center and is the cause of the coupling. The source terms F and M (aerodynamic force and moment) are classically derived from the lift coefficient C L such as F = 1 2 ρU 2 SC L and M = eF, where ρ is the fluid density, U the upstream airspeed and S the airfoil section. We assume that the angle of attack remains small, so that the lift coefficient depends linearly on α app the apparent angle of attack, so that C L = (∂C L /∂α)α app (C L | α=0 = 0 because the airfoil is symmetric). A pseudo-static approach is used, i.e. the airfoil speed ḣ is not neglected as compared to the upstream airspeed U and α app = α + ḣ/U [START_REF] Dowell | A Modern Course in Aeroelasticity[END_REF]. Lagrange equations lead to the following dynamical system:

m S α S α I α ḧ α + 1 2 ρU SC L ,α 0 -1 2 eρU SC L ,α 0 ḣ α + K h 1 2 ρU 2 SC L ,α 0 K α -1 2 eρU 2 SC L ,α h α = 0. (1)
In nondimensional form (1) reads

1 x α x α r 2 α y α + μC L ,α 0 -μγ C L ,α 0 y α + 2 μC L ,α 2 0 r 2 α -μγ C L ,α 2 y α = 0, (2)
y = h b , τ = K α t I α , ( ) = d dτ , r α = I α mb 2 , μ = ρbS 2m , x α = S α mb , = U b I α K α , = K h I α m K α , γ = e b .
In order to gain insight on the critical parameter values, the flutter speed f can be derived analytically. Indeed, assuming that the airfoil motion is harmonic, y = ( ỹ exp( pt)) and α = ( α exp( pt)) with ( p, α, ỹ) ∈ C, replacing α and y by their new expressions in (2) it yields

A = p 2 + μC L ,α p + 2 x α p 2 + μC L ,α 2 x α p 2 -μγ C L ,α p r 2 α p 2 + r 2 α -μγ C L ,α 2 .
(3) Equation ( 3) has non trivial solutions p i when det(A) = 0. Using the parameter values of Table 1, the solutions p i versus the flow speed is plotted in Fig. 2. At the flutter velocity f , the real part of one of the solutions p i vanishes. Assuming then p purely imaginary, separating real and imaginary parts in the equation det(A) = 0, and grouping the terms to eliminate p, the following expression is found for which f is solution

(A 1 2 -A 2 )(A 3 2 + A 4 ) = 0, with ⎧ ⎨ ⎩ A 1 = μC L ,α (r 2 α + γ x α ) A 2 = r 2 α x α , thus f = A 2 A 1 = r 2 α x α μC L ,α (r 2 α + γ x α ) . ( 4
)
Using values of Table 1 we find f = 0.87.

SMA Model

The SMA spring is assumed to have pseudo-elastic behaviour, which is briefly recalled in Fig. 3. This nonlinear behaviour is characterized by a solid-solid phase change between two different states. The first one called austenite is stable at large Fig. 3 Pseudo-elastic behaviour of SMA and its microstructure for each phase temperatures and is the natural state of the spring at rest. The microstructure of the austenite phase is also sketched in Fig. 3. When deformed, the microstructure of the SMA turns into a new phase called martensite, energetically stable at small temperatures and for which the microstructure is now oriented. The points in the stress-strain space where the transformations start and finish are usually denoted with the subscripts s (start) and f (finish), so that for instance M f refers to the point where the martensitic transformation has been fully accomplished in the SMA structure. The path followed in the stress-strain relationship is not the same when the material is loaded or unloaded, thus an hysteresis loop appears as illustrated in Fig. 3. This hysteretic phenomena is the most salient feature of the pseudo-elastic behaviour of SMA. The dissipated energy during a cycle is proportional to the area of the hysteresis loop so that the more the loop area is large, the more energy is prone to be dissipated in the device.

The nonlinear behaviour of single dof SMAs can be derived from a general, threedimensional model inferred from thermodynamical laws and then reduced by considering ad-hoc assumptions, see e.g. [START_REF] Bernardini | Non-isothermal oscillations of pseudoelastic devices[END_REF][START_REF] Lacarbonara | Nonlinear thermomechanical oscillations of shape-memory devices[END_REF][START_REF] Moussa | Modélisation du comportement dynamique non-linéaire des structures en matériaux à mémoire de forme[END_REF][START_REF] Moussa | Non-linear dynamic thermomechanical behaviour of shape memory alloys[END_REF]. In this case the model contains, in-built within the oscillator equation, additional equations governing the evolution of the fraction of martensite, the description of heat transfer, and the thermodynamic force, which expression is derived from a pseudopotential of dissipation that can include yields functions in order to express the phase transformations [START_REF] Moussa | Non-linear dynamic thermomechanical behaviour of shape memory alloys[END_REF]. These modeling features are typical of hysteretic systems [START_REF] Visintin | Differential Models of Hysteresis[END_REF] and give rise to a complex formulation which, in turn, induces numerical difficulties for solving the whole system. Contrary to this general approach, we use in this contribution a simple heuristic model instead, as it has the capacity to retrieve the main features of the dynamical behaviour within a light computational framework. It is built following the sketch in Fig. 3 by approximating each part of the diagram by a linear relationship, h l modelize the beginning of the martensitic transformation and H the end of the martensitic transformation. An internal auxiliary variable playing the role of the fraction of martensite is defined so as to keep the memory of the precedent state of the material in a dynamical simulation. For simplification, it is assumed that the slopes of the purely austenitic and purely martensitic phases are equal, as well as the slopes during the reverse or transverse transformations, so that the stiffness of the SMA are defined by K 1 and K 2 , only as shown in Fig. 3. It is also assumed that the behaviour of the spring is symmetric in traction and compression. Internal loops are described following the sketch in Fig. 3 and we call A SM A the area of the maximal internal loop. The area A SM A is completely defined by the four parameters K 1 , K 2 , h l and H with the following relationship

A SM A = h l H 1 + K 2 1 1 + K 2 2 cos(tan -1 (1/K 1 ) + tan -1 (K 2 )).
For the remainder of the study, the four parameters that will be considered are A SM A , K 1 , K 2 and h l (A SM A instead of H as it is more physically meaningful).

After the flutter instability, with the physical parameters from Table 1 the wing experiences large-amplitude motions especially on the pitch mode, whereas the amplitude of the motion of the heave mode remains fairly small. In order to take advantage of the dissipative properties of the SMA, it appears logical to include a SMA spring on the torsional motion, whereas the flexural spring is left unchanged with a linear behaviour law.

Final Model

To ensure a LCO after bifurcation occurs (no matter using SMA or not) a cubic stiffness is added on both modes (ξ y for heave and ξ α for pitch). The final model with a SMA torsional spring is then derived by replacing r 2 α α from (2) with the nonlinear behaviour of the SMA spring f SM A N L depicted in Fig. 3. It reads:

1 x α x α r 2 α y α + μC L ,α 0 -μγ C L ,α 0 y α + 2 μC L ,α 2 0 -μγ C L ,α 2 y α = -ξ y y 3 -f SM A N L (α) -ξ α α 3 .
(5)

Results and Discussion

The aeroelastic parameters for the two-dofs system have been selected according to [START_REF] Dowell | A Modern Course in Aeroelasticity[END_REF], they are listed in Table 1. Equation ( 5) is integrated in time with a fourthorder Runge-Kutta scheme. The initial condition is generally prescribed as a small perturbation on the heave mode. The results shown in Fig. 4 are made for ξ y = ξ α = 0, thus the nonlinearity is exclusively due to the SMA. When < f , the airfoil motion decreases and tends to zero, see Fig. 4a. When ≥ f , the flutter instability occurs and the position at rest is not stable anymore. However, the energy of the LCO can be dissipated by the SMA, so that for a certain range of reduced velocity, the amplitude of the motion saturates thanks to the nonlinear behaviour of the SMA, as illustrated in Fig. 4b. When the motion amplitudes of the LCO are beyond the end of the martensitic transformation, the potential of dissipation of the SMA is reached, so that divergent motions are retrieved. The critical speed above which the motion diverges is denoted c . The first observed and awaited effect of adding the SMA is to increase c thanks to the damping property of the hysteresis loop, an intermediate stage where LCO with small amplitude is present. In a first step the energy evolution is investigated to ensure the LCO is entirely due to the hysteresis loop of the SMA and in a second step, a parametric study of the SMA is made to understand its influence on the LCO.

Energy Exchange

We investigate the energy evolution with time for the case f < < c . The energy contained in the airfoil reads

E tot = T + V = 1 2 m ḣ2 + I α α2 + K α α 2 + K h h 2 + S α ḣ α.
Then the nondimensional energy is

e tot = 1 2 ẏ2 + r 2 α α2 + k α α 2 + 2 y 2 + x α ẏ α. ( 6
)
Its evolution is plotted in Fig. 5 for system with and without SMA. For each cycle the energy increase of the system without SMA corresponds exactly to the energy dissipated by the SMA in its internal loop (for example right after the system with SMA enters in its first internal loop this loop dissipates 1.198 10 -4 and during this time the system without SMA grew 1.189 10 -4 ). Hence in this regime, the energy saturates to a finite value. This clearly shows that the LCO appearing when f < < c is entirely due to the SMA hysteresis loop. We now explore the influence of the SMA parameters on the LCO.

Influence of SMA Parameters

The global effect of the SMA parameters on the behaviour of the flutter instability is studied through the bifurcation diagram for varying flow velocities . Fig. 6 shows such a bifurcation diagram for a given SMA spring (the amplitude of pitch motion LCO is represented versus ). The diagram is obtained numerically by direct integration in time of [START_REF] Dowell | A Modern Course in Aeroelasticity[END_REF]. The flow velocity is increased step by step, one time forward and one time backward, in order to get all the solution branches. When changing to + δ , the initial condition for + δ is selected as the steady state of the previous simulation launched for . The black line in Fig. 6 shows the bifurcation diagram when only a cubic nonlinear restoring force is considered, no SMA is added to the system. In this case the classical supercritical bifurcation is retrieved. The diagram with a given SMA is represented with the red line.

The first striking feature one can observe is that due to the softening effect brought by the SMA, the bifurcation is now subcritical. The gain in using enhanced damping properties thanks to the hysteresis loop is illustrated through the appearance of the points denoted s (flow velocity for which the oscillations enters the loop and thus the enhanced damping capacity is present) and c (the point for which the martensitic transformation is finished so that the damping capacity has been fully exploited). Above c , a jump is observed to a branch parameterized by α J (amplitude at c ) where the LCO amplitudes are larger than without SMA. Hence the advantage of the enhanced damping capacity is here completely lost due to the appearance of this subcritical branch where large-amplitude motions are observed. Finally, the point where this subcritical branch disappears when decreasing the flow velocity, denoted e , defines a dangerous range of flow velocities where the system could jump to the higher branch.

The SMA parameters can be optimized in order to fulfill the following targets:

• decrease the amplitude α J of the secondary branch as much as possible. In the best case, avoid subcriticality, • decrease s so as to bring this point as close as possible to the flutter velocity,

• increase c as much as possible so as to full advantage of the enhanced damping capacity of the SMA, • increase e so as to avoid the large range of subcriticality where the two solution branches coexist.

Numerous simulations have been done to obtain the best parameters h l and K 1 /K 2 , in order to fulfill at best these objectives. Figure 7c sums up some of the results obtained for illustration. One can conclude that in order to decrease the value α J describing the upper branch, one has to select a large value for h l , and in this case

K 1 /K 2 = 2 K 1 /K 2 = 10 K 1 /K 2 = 20 Without SMA K 1 /K 2 = 2 K 1 /K 2 = 10 K 1 /K 2 = 20 h l = 0.05 h l = 0.12 LCO α (c)
it appears then more appropriate to take smaller values for the ratio K 1 /K 2 . One can also observe the advantageous effect of using a small value for K 1 /K 2 when h l has been selected small, as it increases substantially the value of e . Table 2 summarizes the effect of the coefficients with respect to the targeted objectives relative to the different remarkable points s , e , c and α J . A simple plus/minus sign code is used for a quick understanding of the effect of each coefficients: a plus sign indicates an advantageous effect whereas a minus sign indicates a detrimental effect with respect to the target. From this table and Fig. 7c it appears clear that the best choice is a large h l together with a small ratio K 1 /K 2 . Figure 7a, b show the restoring force at two particular points in order to get physical insight in the results obtained. In Fig. 7a, a disadvantageous case is selected and one can observe that the softening effect is the dominating feature of the nonlinear restoring force of the SMA, explaining the enforced subcriticality observed on the bifurcation diagram. This adverse case helps also in understanding that increasing blindly the hysteresis loop area A SM A is not a solution as it may have no effect on the subcriticality. When K 2 is too small, the sudden jump in amplitude observed for a small variation of force is detrimental as the system jumps to large amplitude motions and the energy of this vibratory state is too important. Figure 7b illustrates an advantageous case where the softening effect is not too important and thus leads to an improved global behaviour in the bifurcation diagram.

= = +++ --- e +++ --- --- +++ c - + --- +++ α J ++ -- --- +++
A plus sign shows an advantageous effect, whereas a minus sign indicates a detrimental effect on the targeted behaviour, while an equal sign shows no effect. The number of the sign is proportional to the magnitude of the effect This analysis shows undoubtedly that the best choice would be to have both the case of the hysteresis loop together with a stronger hardening effect at very large amplitude. To fulfill these requests, the full martensite branch should have a hardening behaviour stronger that the one of the reference case (without SMA). Such a configuration is obtained for example with h l = 0.05, K 1 /K 2 = 1.5 and ξ α = 3.4. Figure 8 shows the bifurcation diagram obtained in this case. One can observe that supercriticality is enforced. Secondly a large range of small amplitudes of LCOs are observed between 0.875 and 0.93, where the enhanced damping capacity of the SMA plays its role. Finally the improved hardening effect at large amplitude gives rise to a branch where amplitudes of LCOs are smaller, even when the transformation has been completed.

Conclusion

Whether one wants to harvest energy or avoid devastating intabilities, the control of aeroelastic flutter is a critical issue. An option is discussed here by using SMA springs in pseudo-elastic behaviour, in order to use the potential of dissipation of such materials. A numerical study with a simple heuristic model for the behaviour of the SMA has shown that the amplitude of the LCO after the flutter velocity can be significantly reduced by adding a SMA spring on the pitch mode of the twodofs aeroelastic system. More precisely, the study of the bifurcation diagram clearly exhibits an advantageous effect of using the enhanced damping capacity of the SMA with the appearance of a branch of small amplitudes LCOs. However a detrimental effect appears because of the softening effect created by the solid-solid phase change. The optimized case is obtained by hardening the stiffness of the martensite phase. In this case it has been shown that subcriticality together with small amplitudes LCOs can be obtained.

The next steps of this research is to confront these preliminary findings with experiments. Complicating effects such as the dependence of the hysteresis loop on frequency, asymmetry of the SMA restoring force, aeroelastic nonlinearities due to stall phenomenon, will be studied and included in the model in order to obtain a global picture of the passive control of the flutter instability with SMA springs.

Fig. 1

 1 Fig.1Sketch of the airfoil model as a rigid body in uniform flow U with two dof: pitch (α) and heave (h)

Fig. 2

 2 Fig.2Real (solid lines) and imaginary (dotted lines) parts of the solutions of det(A) = 0, with A defined in[START_REF] Bisplinghoff | Aeroelasticity[END_REF]. Parameters of the problem are listed in Table1

Fig. 4 Fig. 5

 45 Fig. 4 Effect of the SMA on the linear flutter instability (ξ y = ξ α = 0) for three different reduced velocities: a Linear stability case, = 0.86 b Instability case, with LCO due to SMA dissipation, = 0.91 c Instability case where SMA cannot dissipate enough energy, and an exponential growth is observed, = 0.93 ( f = 0.87 and c = 0.926). Blue heave motion y, green pitch α. The curves are normalized to their maximal value

Fig. 6

 6 Fig. 6 Bifurcation diagram of the 2 dof aeroelastic system with cubic stiffness (ξ y = ξ α = 1). Black Without SMA spring. Red With SMA spring (selected values: h l = 0.05, K 1 = 10 K 2 and A SM A = 2.35 × 10 -3 )

Fig. 7 a 10 -

 710 Fig. 7 a LCO amplitude versus flow speed for different SMA parameters (ξ h = ξ α = 1 and A SM A constant). b Corresponding restoring force for = c , on the left h l = 0.05 and K 1 /K 2 = 10 and on the right h l = 0.12 and K 1 /K 2 = 10

Fig. 8 a

 8 Fig. 8 a Bifurcation diagram with h l = 0.05, K 1 /K 2 = 1.5 and ξ α = 3.4. b Restoring force at = 0.95

Table 1

 1

	Nondimensional
	aeroelastic parameters	r α 0.5	μ 1/10π	x α 0.2	0.5	γ 0.4	C L ,α 2π

Table 2

 2 Influence of the SMA constants on the identified points in the bifurcation diagram SMA parameters K 1 /K 2 h l

	Bif. pt	Small	Large	Small	Large
	s

Acknowledgments This work is supported by Direction Générale de l'Armement (DGA) from French Ministry of Defense.


Avid Roman-Gonzalez

Natalia I Vargas-Cuentas

Miguel Hoyos

Joel Diaz

Mirko Zimic
email: mirko.zimic@upch.pe

Brain Computer Interface to Answer Yes-No Questions

Keywords: BCI, EEG, brain-computer interface, communication system, yes-no questions

The aim of this work is to design, implement and validate a primary communication system based on a brain-computer interface. There are people whofor various reasons -are affected in their ability to externalize their communication, however, they receive and process information from different sources. This system would allow basic communication -allowing the user to answer closed questions -through thought. The system was implemented by analyzing and interpreting electrical signals from brain activity, collected through electrodes attached to the scalp. The analog electrical signals were received by a data acquisition system and digitized for computer analysis. We implemented different signal processing techniques, pattern analysis, and classification and discrimination methods. By analyzing these signals and interpreting the electrical patterns, was achieved understand answers to simple questions. The system has been validated testing with healthy volunteers in the laboratory, obtaining good results.

I. INTRODUCTIÓN

HE functions of speech and language have essential importance for humans, both in social relations and intellectual development. When these functions are altered as a result of brain disease, the consequences exceed in severity, other dysfunctions including blindness, deafness, and paralysis. From a broader perspective, language is the mirror of all higher mental activity. Particularly, in the case of patients, speech and language are the vehicles through which patients report their symptoms and medical problems while the means to carry out all their interpersonal relationships [START_REF] Pfurtscheller | Event-related EEG/MEG Synchronization and Desynchronization: Basic Principles[END_REF]. Although speech and language are closely interrelated functions, they are not equivalent. A disorder of language function always reflects an abnormality of the brain, and more specifically, the dominant cerebral hemisphere. A speech condition can have a similar origin, but not in all cases; it can also be caused by certain anomalies in various parts of the brain or extra-brain mechanisms. Language function encompasses the understanding, development and transmission of ideas and feelings through the use of verbal symbols, sounds and gestures adopted and their sequential order by the accepted rules of grammar. The term speaks, on the other hand, refers more to the articulatory and phonetic aspects of verbal expression. [START_REF] Pfurtscheller | Event-related EEG/MEG Synchronization and Desynchronization: Basic Principles[END_REF] There are people who -for various reasons -are affected in their ability to externalize their communication. One reason for this situation is the locked-in syndrome and aphasia. Aphasia is a language disorder as a result of secondary dysfunction of specific brain areas, which are manifested in the form of changes in the spoken or written expression, or a failure to understand the language heard or read. Currently, cases of aphasia or locked-in syndrome end up being people without any capacity for physician-patient interaction for monitoring neurological health. This situation is due to the absence of a communication system allowing interaction with these patients. Additionally, in remote villages it has a limited presence of specialized medical personnel in neurology, which further complicates the evolution of the health of these patients. In recent years, electronics and communications technologies have evolved significantly. Today, it is possible to collect, amplify and analyze electroencephalographic (EEG) signals, to interpret specific stimuli and simple questions. This basic level of communication patient-doctor can have enormous importance for the brain health of these patients. It has been shown that the human has a leading position in the animal world due to two faculties:

1) The ability to develop and employ verbal symbols like words and written, for communicating to other members of the species.

2) The remarkable ease to use their hands. [START_REF] Pfurtscheller | Event-related EEG/MEG Synchronization and Desynchronization: Basic Principles[END_REF] The recording of the brain electrical activity (electroencephalogram -EEG) of the motor area is far from being a simple epiphenomenon of neuronal activity. This recording is the core essence of complex brain function. The potentials of individual neurons vary in sync, and they control the information transfer, generating different types of rhythms. These rhythms include some cortical rhythms that are in the same frequency range of the occipital alpha rhythms (8-13 Hz) distributed mainly in the somatosensory cortex, known as "rhythms Mu". The rhythm Mu is shown when the subject is at rest and blocked with the movement of the contralateral limbs or extremities [START_REF] Kachenoura | ICA: A Potential Tool for BCI System[END_REF]. This particular situation allows us to propose an opportunity to use the pattern of this rhythm that maintains a constant when one registers the activity corresponding to the upper extremity, and through algorithms, generate a type of communication using alternative brain circuits.

T

The use of EEG in such applications has been shown earlier [START_REF] Gonzalez | System of Communication and Control based on the Thought[END_REF], demonstrating its reliability and is reinforced because it is not invasive. This kind of applications makes an impact on the quality of life of patients, especially in initial disease state where they are unable to express their thoughts, generating situations of extreme anxiety. For several years, it has been researching and developing technology to capture electroencephalographic (EEG) signals, process and interpret them to implement a braincomputer interface, or BCI (Brain -Computer Interface). In the first years when these works were developed, they were first designed to provide an interaction channel for handicapped people who for various reasons totally lost motor skills. This type of work can be found for example in [START_REF] Gonzalez | System of Communication and Control based on the Thought[END_REF] where the author develops a method for interpreting EEG signals and move a cursor on a computer screen. In research [START_REF] Tomita | Hemodynamic characteristics for improvement of EEG-BCI performance[END_REF], [START_REF] Hoffmann | Recent Advances in Brain-Computer Interfaces[END_REF] and [START_REF] Gao | The design and implementation of visual braincomputer interfaces[END_REF] the recent developments related to the development of BCI, the pre-processing, processing, feature extraction methods, classification, and interpretation procedures are presented. Over the past few years, the BCI were not only applied to people with motor disabilities; but also were aimed at people with intact motor abilities for different applications. These applications could be games, applications in robotics and aerospace missions among others [START_REF] Hoffmann | Recent Advances in Brain-Computer Interfaces[END_REF] and [START_REF] Ma | Logics in Animal Cognition: Are They Important to Brain Computer Interfaces (BCI) And Aerospace Mission[END_REF]. Recently, research works related to BCI are moving towards applications in communication with people in a vegetative state, or people who are in a coma. These studies could be found in recent work [START_REF] Bekinschtein | Functional Imaging Reveals Movement Preparatory Activity in the Vegetative State[END_REF], [START_REF] Cruse | Bedside Detection of Awareness in the Vegetative State: A Cohort Study[END_REF] and [START_REF] Genari | Perception of BCI assistive technology by post-ischemic stroke patients[END_REF] where the authors show the first advances in this type of application. Currently, there are several procedures and methods for implementing the BCIs, as described in works [START_REF] Hoffmann | Recent Advances in Brain-Computer Interfaces[END_REF], [START_REF] Lecocq | Les Interfaces Cerveau-Machine pour la Palliation du Handicap Motor Severe[END_REF], [START_REF] Wolpaw | Brain-Computer Interfaces for Communication and Control[END_REF] and [START_REF] Lee | Using a Low-Cost Electroencephalograph for Task Classification in HCI Research[END_REF] This work seeks to develop a system to assist patients with neurological damage such as those described above, as works presented in [START_REF] Hill | A practical, intuitive brain-computer interface for communicating 'yes' or 'no'by listening[END_REF] and [START_REF] Roman-Gonzalez | EEG Signal Processing for BCI Applications[END_REF].

In the present study, we develop a brain-computer interface, which is connected to a low-cost laptop located at the patient's bedside. The interface consists of 4 electrodes fixed in a cap which will be placed on the patient's head ensuring that the electrodes make contact with the scalp in the right positions. The EEG signals collected by electrodes of the BCI interface will be captured and amplified by a system of analog-digital conversion to then by an ad-hoc program transmitted to the laptop. A personal ad-hoc individualized recorded a battery of questions for each patient which is expected answers like yes/no. Before starting the process of questions, a brief and clear explanation will be transmitted to the patient to know what to do if the answer is a 'yes' and what to do if the answer is 'no'. Basically, if the patient wants to answer 'yes', he must imagine a right-hand motion; if the answer is 'no', the patient must imagine a left-hand motion. The EEG signals collected from both hemispheres of the brain may be processed to detect the patient intention. After made some questions, the BCI interface will capture patient's EEG signals during a time window (nine seconds). These EEG signals are transmitted from the BCI interface to the laptop. This process is repeated until the total of questions. This information will be treated immediately by a pattern recognition algorithm that is developed in this study. Thus the collected EEG signals in response to each question will be analyzed to identify yes/no answer. Since the answers to each question will be known in advance by the system, a full report on the percentage of matches between the responses interpreted from captured EEG patterns and real answers known in advance is generated. If the patient whether or not respond randomly (probably due to a compromised neurological status), we would expect 50% of matches all issues simply by chance. Instead, by detecting a match rate significantly higher than 50%, it is an indication of some degree of healthy neurological activity which is expected to occur during a favorable outcome in patients with aphasia or locked-in syndrome. Importantly, also, the same system can be used by the treating physicians to interact in a basic way with bedridden patients with this syndrome. The doctor may ask questions to the patient and collect the EEG signals in response to the question. To the extent that the expected answer is 'yes' or 'no', and having explained the procedure to imagine righthand or left-hand motion if the answer is 'yes' or 'no', respectively; the EEG signals can be interpreted in real time by the doctor knowing the patient's response. In these cases the doctor may ask important questions for some time, such as: Do you have pain? Do you have a cold? Do you have any discomfort? To demonstrate the proof of concept of how this integrated system could contribute in a meaningful way in the process of recovery of patients who suffer strokes and have lockedin syndrome and/or expressive aphasia. This system would be a highly cost-effective tool that could help bedridden patients in remote areas where there are not neurologists. Fig. 2 Block diagram for a general BCI System validation will be done by estimating the correlation between real thinking and system interpretation from electroencephalographic signals picked up against questions whose answers are yes/no. For the characterization of the EEG signal, it is crucial to analyze the EEG signal in the frequency domain, precisely the Mu rhythm, which corresponds to the band between 8 and 13 Hz. This rhythm is picked up in the sensorimotor zone located in the central region of the scalp. This rhythm has the peculiarity of presenting an attenuation in its amplitude when some motion is carried out, or what is more important when one intends to make some movement, or only imagining extremities motions. It is precisely this type of behaviour that we must detect through a frequency analysis of amplitude of the Fast Fourier Transform. The classification stage is the final task of the entire process. For the entry to the classification or discrimination algorithm, we have the set of extracted features in the previous stage, and the output is an interpretation of the brain activity developed by the user.

III. RESULTS

For the proof of concept, the system was tested in several laboratory volunteers with normal motor capacity, and in a patient with amyotrophic lateral sclerosis (ALS).

As a result, we show the calculated error at each time instant during the 9 seconds. Figure 3 shows the results of one tests performed on a volunteer with intact motor skills. We can observe that the error decreases and reaches its minimum point of 6.25% in the sixth second approximately. In Figures 6,7, and 8 we can observe the same results for a patient with amyotrophic lateral sclerosis. In Figure 9, we can see a photograph of the system process tested with a laboratory volunteer with regular motor capacity. The system was tested with good results in people with normal motor capacity; the users could dominate the use of the system quickly. However, when testing with a patient with ALS, to dominate the system was more difficult, several tests were performed over several months until an acceptable discrimination between 'yes' or 'no' answer. In spite of this, the patient did not achieve a sustained management of the system, in moments, he came to have good control, but then the error increased. This problem could be due to the mental fatigue generated by the use of the system. The errors obtained of 6.25% for people with standard motor capacity, and 10% for the patient with ALS, represent acceptable values, so, the proposal can be used as a method for essential communication.

  . The first stage is a process for understanding the EEG signals, which is a record of the electrical potentials generated by the brain and obtained by electrodes placed on the scalp surface with the help of conductive pastes and gels. The EEG signals have different rhythms in the frequency domain ([3] [12] [14]) with the following characteristics: Rhythm Alfa or Mu: Low voltage (20-60 microvolts / 3-4mm) with variable morphology. High frequency (8-13 Hz). Rhythm Beta: Low voltage (10-15 microvolts / 1-1.5 mm) with variable morphology. High frequency (13-25 Hz or +). Theta rhythm: High Voltage (50 microvolts / 7mm). Frequency (4-8 Hz). Delta Rhythm: High Voltage (70 -100 microvolts / 9 -14 mm) with variable morphology. Low frequency (4 or -Hz). For the exact location of the electrodes on the scalp, one can use the International Positioning System 10/20 which indicates the different positions to place the sensors, depending on the area and the activity to register.Figure 1 shows these locations.

Fig. 1

 1 Fig. 1 International Positioning System 10/20

Fig. 3

 3 Fig. 3 Classification error of a healthy subjectIn Figure4we can see the separation of the signals representing 'Yes' answers from 'No' answers. Clearly, a difference between the two intentions can be seen.

Fig. 4

 4 Fig. 4 Spectral density of both signals: 'yes' and 'no' In Figure 5, we can see the result of the classification method separating of the signals representing 'Yes' answers from 'No' answers. Classification method can separate both intentions since the fourth second.

Fig. 5

 5 Fig. 5 Result of the classification method

Fig. 6 Fig. 8 Fig. 9

 689 Fig. 6 Classification error of an ALS patient

Acknowledgements

This work was supported by FONDECYT -'01-2013-Fondecyt Financiamiento de Subvención para Investigación Postdoctoral'.


Avid Roman-Gonzalez
email: avid.roman-gonzalez@ieee.org

Natalia I Vargas-Cuentas
email: natalia.i.vargascuentas@ieee.org

Luis Aucapuma

Analysis of Landslide in Chosica Using Satellite Images

Keywords: Floods, landslide, satellite images, Peru, image processing, Sentinel 1

Early in the year, Peru suffered from heavy rains mainly due to the El Niño and La Niña phenomena. As a result of these heavy rains, several cities were affected by floods and landslides. One of the most affected cities was Chosica. On the other hand, the satellite images have many applications, one of them is the aid for a better management of the natural disasters (post-disaster management). In this sense, in the present work, one proposes the use of radar satellite images to make an analysis of the most-affected areas by landslides in the city of Chosica. The results show a significant number of places flooded according to satellite images of March 2017. The satellite images used were from the Sentinel 1 satellite belonging to the European Union.

Introduction

In the months of January, February, and March 2017, there is an intensification of rains in some districts of Lima -Peru. This intensification of rains produces the soaking of lands and the increase of the river level. This increase in the level of the rivers causes overflows, and the overexposure of land to the rains produces landslide called 'Huaycos' in Peru. Due to these effects, we can indicate that the intense rains have damaged urban areas in different districts as Chosica, Chaclacayo, Santa Eulalia, Cañete, Huaral and Huaura in Lima. Several families, from these communities mentioned above, have lost their belongings, their homes, their businesses, and we also can talk about human losses. Due to these disasters, immediate decision-making is needed to define where to take help, the type of support to make, and where to bring it. For this purpose, the use of satellite imagery can be a great help.

A satellite image shows a broader picture of the areas to be analyzed. In this work, we propose to develop satellite image processing algorithms to analyze the areas most affected by landslides. For this purpose, we plan to use both optical and radar satellite imagery because when the area under analysis is covered by clouds, optical images will not help us much, and hence the importance of having radar images whose products are not affected by the climatic conditions. Then it is proposed to apply segmentation algorithms and identify those areas covered by water and sludge.

The continuation of this work is organized as follow: Section 2 shows the applied methodology; in Section 3 one can see the obtained results; finally, one present de discussion.

Methodology

For the present work, it is necessary to apply some physical principles of microwave and remote sensing concepts. The methodology that we used for the analysis of landslides produced by the rains is composed of three main components:

1.-Collection of satellite images 2.-Image processing 3.-Mapping the results

In Figure 2, one can observe a flow diagram for the methodology.

Collection of satellite images

Data collection is the first step in the flow to be follow. Considering that we want to analyze territories that have been affected by landslides caused by rainfall, it is very probable that these areas are covered by clouds, so the use of optical images will not give us much information. In that sense, the best option is the use of radar images. For this work, we have used radar images from the Sentinel 1A and Sentinel 1B satellites. Both satellites are part of the European constellation. To download the pictures that we need, we can access to the Copernicus Open Acces Hub (https://scihub.copernicus.eu).

Sentinel-1 is a part of space mission by the European Union and carried out by the ESA (European Space Agency) within the Copernicus Programme. The payload of Sentinel-1 is a Synthetic Aperture Radar (SAR) in C band. Sentinel-1A was launched on 3 April 2014 and Sentinel-1B on 25 April 2016.

Image processing

After data collection, one applies different image processing techniques, which were applied in this work, consists of 5 stages:

1 In Figure 3, one can observe a block diagram for the image processing step.

The image processing step is the most critical phase of this work. The idea is to extract a much information as is possible from the satellite images, and to achieve a good classification of the image. Fig. 3 Image processing steps

Radiometric calibration

The radiometric calibration is significant in order to make a quantitative interpretation rather than a qualitative interpretation. For this step, one uses the VV polarization.

Speckle filtering

It is necessary to filter the common speckle in the SAR image. For our cases, one use a Gamma Map Filter and apply it to a moving window which across the image. The size of the filter as 5 for both X and Y.

Terrain correction

Another important step is to apply a geometric correction, in this work one apply a terrain correction.

For terrain correction one use SRTM 3secc. For DEM and image, one set the resampling methods as bilinear interpolation. The pixel spacing in metres should be set to 10 m. In this case, one used "WGS84 (DD)" geographical coordinates.

Histogram Analysis

The flood detection methodology chosen to be used in this work relies on the unique backscattering properties of water surfaces. Water surfaces appear dark in SAR images. The retrieval methodology that was used in this work was apply a threshold in order to classify an image into flooded and non-flooded portions.

The threshold value can be determined manually or automatically by histogram analyzing.

Identification of flooded areas.

To identify flooded areas we apply a mask based on the threshold identified in the previous step. For a better visualization, one set the mask with the red color.

Mapping the results

For the results mapping we must analyze a beforedisaster, and after-disaster image, then one can show the difference between both results and identify the affected areas.

Results

Our area of analysis is Chosica. Chosica is the capital city of the Lurigancho-Chosica district of the Lima region. In Figure 3 one can observe a map where it is possible to identify the Lurigancho-Chosica district. After applying the methodology explained before, we have the following results that can be seen in Figure 5 and Figure 6. Figure 5 shows how was identified the threshold using the histogram analysis, after choosing the threshold, one create a mask. In Figure 6 one can observe two images that show the difference between and image before overflows and landslide, and image after overflows and landslides.

Discussion

When the optical images cannot help when the analysis area is covered by clouds, the radar images are the ones that can provide information about the affected areas.

The use of satellite images to analyze affected areas is critical and allows us to do better post-disaster management, helping us to make better decisions. Identify the most-affected areas, determine the contribution to taking, what kind of help to manage and where to get it to the victims.

The shaded areas in red show areas affected by water, you can see a greater covered area in the image of 2017 compared to the picture of 2016.

Fig. 1

 1 Fig. 1 Image of the overflow in Chosica -Peru Among the consequences of this nature fury, we can mention: Huaycoloro Bridge collapsed due to an overflow of the river, Central Highway blocked by a landslide, More than 170 houses and medical centers affected by landslides, Kilometer 66 of Cañete-Yauyos road obstructed by landslides, Fall of public lighting posts and power outages by landslides in Lunahuaná,

Fig. 2

 2 Fig. 2 Methodology used to analyze landslides

  .-Radiometric calibration 2.-Speckle filtering 3.-Terrain correction 4.-Histogram Analysis 5.-Identification of flooded areas.

Fig. 4

 4 Fig. 4 Lurigancho-Chosica district ubication

Fig. 5 Fig. 6

 56 Fig. 5 Satellite image, histogram, and applied mask


Victor Romero-Alva

Avid Roman-Gonzalez

Nanosatellite Vibration Test Equipmentn

Keywords: Vibration test, nanosatellite, cubesat, test equipment, vibration

There is now a considerable increase on the part of universities in the incursion into the development of nanosatellite missions. In the aerospace sector, almost every operation is full of risks and big investments of time and money, and to locate a nanosatellite in orbit, even smaller, is not the exception. Therefore, it is imperative to know if the nanosatellite will be prepared to surpass any critical moment. The rockets or launchers in which the nanosatellites are placed for going to space, produce strong vibrations that can affect the nanosatellite. The primary objective of this work is to design a vibration test equipment that will help determine the resistance of a nanosatellite against the sudden movements that can be experienced within the space launcher. And for that, what is wanted, is that this equipment can generate the vibrations and recreate them as equal as they are in an original launcher. The idea is to guarantee that the nanosatellite will not present problems or failures during the launching and putting in Orbit. This step would be the most critical moment for a nanosatellite, therefore, what is sought with this is to ensure the significant investments of study time and money made by the government or any entity dedicated to the scientific and technological development, since this would have the security that will fulfil the objective for which was planned.

Introduction

Nowadays, the aerospace sector has been taking a lot of field in the research areas and development mainly at academic and commercial level. The aerospace application is very useful regarding communications, observation, tracking, information transfer, monitoring and in general any activity that is related to the communication and information of long reach and distance. Given this space revolution, it is needed to be able to transport these space equipment as satellites, telescopes, soundings, unmanned missions, among others. As a consequence of this need, we had to design and build vehicles that transport space cargo from the Earth to space. These are the so-called "rockets" or space "launchers", which are responsible for placing the different space devices in orbit. These vehicles are currently being presented by companies and the aerospace industry exclusively dedicated to the development of rockets and space launchers. There are different types of launchers, which depend mainly on the application that will be given taking into account the positioning orbit, the weight and dimensions of the apparatus to be transported, and even the cost that will demand the construction depending on the size of the rocket [START_REF] Roman-Gonzalez | Principio y fin de una era espacial[END_REF].

In the academic sector, significant work has been devoted to the research level to obtain the maximum benefit of the applications in aerospace studies. The development of smaller scale space devices has been developing more frequently in recent years since it is feasible to be able to design equipment and prototypes capable of sending information at high altitude from the ground. The most particular and typical case that has been carried out is the development of nanosatellites for different functions and applications oriented to the research environment with more exclusively academic purposes than commercial or business purposes. In fact, its design and manufacture turn out to be of little cost in comparison to an ordinary large-scale satellite that can easily exceed millions of dollars in design, construction, and orbital value. Nanosatellites are satellites of small dimensions in scale in centimeters. These equipment operate in the low orbit, and they contemplate a life between 3 and six months, the reason why the nanosatélites are denominated like disposable equipment with different payloads [START_REF] Gómez | EXPERIENCIAS DE LAS UNIVERSIDADES EN EL DESARROLLO DE PEQUEÑOS SATÉLITES[END_REF]. Since we know the space equipment to be used by specialized institutions or universities, the need to transport them and put them into orbit, we are aware that rocket launchers capable of surpassing the skies and leaving the atmosphere are used, a problem arises in which we will focus hereafter on the present research work. This issue occurs when pitchers, having to have enough power to overcome the gravitational pull of the Earth, cause an excessive vibration from the propellers and the resistance of the air to rise at more than 20000 kilometers per hour. This vibration, directly and indirectly, affects the payload since it is induced by the rocket to the same, being able thus to damage it or in the worst of the cases to destroy it, having as considerable economic losses and invested the time of work.

Having established the general problem of research, we can determine the primary objective of this study and proceed to mention the methodology that will be carried out in the development of the entire work. The central purpose of this work is to design a vibration test equipment to determine the strength and operability of a nanosatellite in the face of the strong vibrations that it experiences in the launcher. In the first place, it is imperative to seek all the information necessary to obtain an overview. Following this important information, the first phase is related to the different space launchers, it is necessary to take into account their technical specifications of operation, and it is determined in which it will be based to reproduce its environment of vibration during the transport and orbit of its load.

Methodology

The methodology used in the present research lies primarily in the search for information such as bibliographical sources, theses, articles or other research related to the subject of interest. That can provide us with the necessary information both in the generation of vibration and in banks vibrator, then run and start with the development of the design having a bright idea that is what we want to accomplish. Following this arduous but necessary first step, we will identify the software programs that will be used to carry out the mathematical modeling, the structure analysis in response, the design of the equipment itself, and the structural and electronic simulation. Firstly, it is necessary to identify and characterize the vibration situations and for this, firstly, different pitchers are compared and then chosen with the one that has the best technical specifications of operation that are suitable for the particular purpose of this research, as mentioned above.

Having selected the appropriate space launcher to be able to shape their vibration situations considering the weight and dimensions of the payload, we proceed to perform the mathematical model of the vibration structure, after having the necessary mathematical model and the respective equations, is established the design of the electrodynamic exciter equipment, the LMS Imagine.Lab Amesin R15 software is used for this after the design the results obtained are analyzed by entering the appropriate values in the machine comparing them with a real electrodynamic exciter.

Finally, we present the results obtained in the present research, the conclusions and recommendations to be proposed mentioning the contributions and the purposes reached of the one whose purpose was the realization of this article.

Identify and characterize vibration situations

For the development of this first part as indicated textually, we have the requirement to identify and describe the critical conditions of vibration, and for this, it is necessary to have the technical data of the same launcher that will carry the payload, in this case, a nanosatellite CubeSat of a unit. In this way and having these references or technical specifications we can focus on a clear perspective of the frequencies that we need in vibration and that allows us to recreate them since they are the same frequencies of the rockets exposed in their manuals by the same manufacturer.

Different launchers will be considered with their respective manufacturers and then select one of them that will be taken as a reference. It will have higher performance or provide a better feature regarding the application, which is to transport a smaller satellite and take it out of the Earth's atmosphere, placing it in the LEO orbit which is where a nanosatellite of these characteristics and specifications usually works.

Soyuz

First, the "Soyuz" rocket of the European space company Arianespace is selected, to analyze its characteristics and work operation. This launcher has its origins in the former Soviet Union since the design was based on an intercontinental missile of that time. In addition to this, this launcher marks a legacy in aerospace history by transporting and locating the first artificial satellite, "Sputnik", in 1957, as well as the first man in space who was Yuri Gagarin in 1961. This vehicle has performed a different range of missions in different orbits as well as in low orbit (LEO), medium orbit (MEO), geostationary orbit (GEO), among others [START_REF]Soyuz at the Guiana Space Centre User's Manual[END_REF].

Figure 1: Soyuz launcher. Source: www.infoset2012.blogspot.pe [START_REF]Info_Set: Transbordadores Espaciales[END_REF] Sinusoidal excitations affect the launch vehicle during the flight to the engine (especially in the atmospheric flight), as well as in some of the transitory phases. The typical duration of this trip is 6 minutes.

For the single configuration spacecraft to meet defined and stated rigidity requirements, it must tolerate the equivalent sine-wave vibration limits at the interface of the craft to the adapter. These levels must be taken into account for the design and dimensioning of the spacecraft. These are shown in the following tables [START_REF]Soyuz at the Guiana Space Centre User's Manual[END_REF]. As we can see in the figure, the scale of the frequency range of random vibration starts at 20 Hz and extends to 2000 Hz, but with different level of power spectral density.

Vega

Secondly, we have the launcher rocket "Vega" from the same aerospace company Arianespace. This launcher has very particular characteristics and necessary to use it in different transports of a small and medium load. The Vega program originated in the early 1990s when studies related to the complement of the Ariane family were carried out, where it was intended to have a small launch vehicle using Ariane technology. El Vega began as an Italian space program of the company BPD Difesa Spazio who proposed in 1988 a space vehicle to the Italian Space Agency (ASI) to replace a US space launcher. By a new one that was based on the Zefiro engine developed from the experience of the Ariane [START_REF]Vega User's Manual Issue 4 -Revision 0[END_REF]. Source: www.esa.int [START_REF]El lanzador Vega / ESA[END_REF] The Vega launcher consists of three stages and mainly of the following components. A lower composite consisting of three solid fuel stages, a payload fairing adapter, a payload dispenser with separation system, a variety of different adapters, distributors and used structures [START_REF]Vega User's Manual Issue 4 -Revision 0[END_REF].

Each stage of the rocket has its propulsion, taking it to the specified orbit. The Vega launcher can carry loads of up to 1500 kg, making it ideal for carrying light loads in generally low operating orbits [START_REF]Vega User's Manual Issue 4 -Revision 0[END_REF].

Sinusoidal excitations affect the launch vehicle during its flight because of the engine (mainly in the atmospheric flight), as well as some of its transitory phases. For the single configuration spacecraft to meet the defined rigidity requirements and avoid dynamic coupling, it must be designed with a structural rigidity that ensures it [START_REF]Vega User's Manual Issue 4 -Revision 0[END_REF]. The random vibrations at the base of the craft are generated by the operation of the propulsion system and by the vibro-acoustic response of the adjacent structure. Given this, maximum levels of excitation are obtained during the flight of the first stage. For payloads above 300 kg, the manufacturer mentions that the broadband vibrations are covered by the acoustic environment [START_REF]Vega User's Manual Issue 4 -Revision 0[END_REF]. Concluding all of the above, it can be determined that the differences between the vibration and frequency parameters in which these launch vehicles operate are not significant since they cover a range from 20 Hz to 2000 Hz with time variant proportional to the increase in frequency. However, the amplitude of vibration between one and the other is affected and mark some distinctions, which can be seen in the spectral graphs, both longitudinally and laterally.

Therefore, we conclude with the purpose of the information process with the selection of the space launcher that will be used as a reference to reproducing the vibrations it produces in the actual flight process. This chosen launcher is the space launcher Vega. It presents better performances and alternatives that are appropriate to the application that would be given, since of the two launchers that were presented in this objective. This vehicle has features oriented to the transport of relatively (up to 1500 kg), which prove to be accurate for sending and positioning a nanosatellite in orbit without problems.

Therefore, the development of following objectives will be realized in function of the vibration generated by a vehicle launcher Vega. [START_REF]Soyuz at the Guiana Space Centre User's Manual[END_REF] [5]

Structural approach and mathematical analysis.

Continuing with the development of the present research, we proceed to select the structural and functional model that will be based on the design to be performed to ensure the purpose set out optimally. Therefore we will be based on an equipment of industrial use but also has a direct application in the aerospace sector. This device turns out to be an "electrodynamic exciter or exciter"since this equipment delivers a variable range of vibration to very high frequencies and can position in different directions, which is very useful.

Electrodynamic stirrer

Electrodynamic stirrers generate motion using the principles of operation of an electric motor. Specifically, the excitation force occurs when a variable current passes through a moving coil placed in a magnetic field.

A constant magnetic field is created by a stationary electromagnet consisting of coils on the ground located on a ferromagnetic base. The stirring head, which is supported by a mounting flex, is also located in a loop. When the electrical excitation signal passes through this excitation coil, the stirring head is set in motion.

This agitator marks its difference from the others to be able to produce a very high vibration of up to 10000 Hz. However, the range that is commonly used practically is between 2000 to 3000 Hz with a displacement of 2.5 cm being able to generate forces up to 450 lbf.

Operation goes back to the passage of current through a coil placed in a magnetic field. That is where a current proportional to the current I (amperes) F (Newtons) force and intensity of magnetic flux B (tesla, occurs 1Kg .s-2.A-1), which accelerates the component placed on the agitator table [START_REF] Silva | [END_REF].

Mathematical model

The mathematical model of the electrodynamic exciter is proposed both in structure and in the electrical part which turns out to be an important variable to consider. Starting from the second law of Newton is obtained. [START_REF] Ricci | Virtual shaker testing for predicting and improving vibration test performance[END_REF] The modal analysis of these equations is performed taking into account the electromagnetic force.

Where the following matrix is obtained. This results in the equation of the second order that has been intended to arrive.

With this factor, we can determine critical parameters such as mass, stiffness, elasticity constant, etc. which will be useful when comparing it to a real driver in operation.

Design of exciter equipment

Continuing the development of this research, the design of mathematical model in LMS Imagine.Labmade Amesin R15 [START_REF] Ricci | Virtual shaker testing for predicting and improving vibration test performance[END_REF] software is presented. Since this way the physical and mathematical representation of electrodynamic exciter shown with an optimal performance that can provide very accurate data and approximations and thus show reliable operating parameters, such as the conditions of acceleration or force concerning time during the oscillatory movement. In the software can be input data from different magnitudes and driving parameters according to a real electrodynamic exciter such as mass, stiffness, elasticity constant, inductance, resistance, voltage, etc., and compare viewing frequency response versus time. In Figure 11 we can see that the design is divided into three parts that will have variable behavior. The first composed by "mb" that corresponds to the body of the exciter and that includes the magnets. The second "mc" corresponding to the mass of the winding and the third "mt" corresponding to the surface where the test weight (nanosatellite) is supported, also the electrical circuit that feeds the coil is added.

Conclusions

You can check and verify that the design complies with the necessary parameters and comparable appropriate characteristics with real electrodynamic exciter regarding authenticity is concerned, since their values as mass and stiffness approximating the actual values that will work. That is, the design shows the optimal working representation of an electrodynamic driver that resembles a real one. So you can set mechanical, electrical and constant coupling parameters according to actual data that you can expect a driver and thus be able to work on the design with the assurance of an efficient operation according to the requirements established at the time of its construction.

FREQUENCY

  BAND (Hz) 1 -5 5 -10 10 -20 20 -30 30 -40 40 -60 60 -100 As next point, we have random vibrations. The random waves at the base of the craft are generated by the operation of the propulsion system and by the vibro-acoustic response of the adjacent structure. Given this, maximum levels of excitation are obtained during the flight of the first stage. The following table shows the frequency vibration levels along the three axes. Table 2: Random Vibration Frequency Bands FREQUENCY BAND (Hz) 20 -50 50 -100 100 -200 200 -500 500 -1000 1000 -2000

Figure 2 :

 2 Figure 2: Random vibration at the base of the spacecraft. Source: Soyuz rocket manual.

Figure 3 :

 3 Figure 3: Vega space launcher.Source: www.esa.int[START_REF]El lanzador Vega / ESA[END_REF]

FREQUENCY

  BAND (Hz) 1 -5 5 -45 45 -110 110 -125 Continuing with the environment, there are random vibrations.

FREQUENCY

  50 -100 100 -200 200 -500 500 -1000 1000 -2000

Figure 4 :

 4 Figure 4: Schematic of an electrodynamic vibrator Source: Rao, 2012 [8]

Figure 5 :

 5 Figure 5: Design of the electrodynamic exciter.

Table 1 :

 1 Vibration Frequency Bands

Table 3 :

 3 Vibration frequency bands.

Table 4 :

 4 Random vibration frequency band.


Natalia I Vargas-Cuentas
email: natalia.i.vargascuentas@ieee.org

Avid Roman-Gonzalez
email: roman-gonzalez@ieee.org

Luis Anthonyaucapuma Muñoz

USE OF SATELLITE IMAGES FOR DROUGHTS STUDYING: THE BOLIVIAN CASE

Bolivia is a country with a high risk of suffering a wide variety of natural disasters, such as forest fires, droughts, floods, earthquakes, and landslides; which may cause life losses, health impacts, property damage, and services, social and economic disruption in the country.

The consequences of a natural disaster usually hinder access to the disaster area to assess the current situation and make a correct decision. It is for this reason that satellite images are a valuable tool to have complete access to the area of the disaster because we can have a full coverage and a greater facility to assess the situation and mobilize the necessary help and assistance.

Due to climate change and human activities, droughts have been occurring in some regions of our planet, making access to water resources difficult for human consumption, animals and agricultural activities.

In 2016, for example, Bolivia experienced the greatest drought in the country for 25 years. There was a big problem with water supply in six of the nine principal cities of the country; the problem was due to several elements such as the long period without rains in the country. In addition, the relevant authorities not had work in a previous plan and could not contain the crisis.

Due to above reason, the present research work has the primary objective of use satellite imagery to generate and promote understanding of these types of natural disasters in the country, to clearly identify areas that are likely to suffer droughts, determine our vulnerabilities, and exposure the potential impact of future drought disasters.

We think that in this way we could reduce the risks and increase the attention to this type of disaster in the country, with better decisions based on satellite information.

I. INTRODUCTION

Climate change and natural phenomena such as 'El Niño' and 'La Niña' which have a global natural climate cycle and are changing the environmental characteristics in the country.

Changes in climatic conditions have a more pronounced effect on changes in ocean currents, sea level rise, floods, droughts, forest fires and the disappearance of ecosystems.

Drought is a climatological anomaly where the water flow is lower than usual in a given area. The lack of water flow is due to the lack of precipitation. During drought the water available in a certain area is below normal levels and the needs of humans, animals and plants cannot be met. [START_REF] Lloyd-Hughes | The impracticality of a universal drought definition[END_REF] There are different types of drought, meteorological, agricultural, hydrological and socioeconomic drought. [START_REF] Wilhite | Understanding the Drought Phenomenon: The Role of Definitions[END_REF] The impact of drought will vary from region to region, as the environmental conditions of one territory cannot be replicated in another territory. The World Meteorological Organization (WMO) has reported that while extreme weather variations have occurred in Mesoamerica and the Caribbean, on the other hand, droughts have occurred in the Southern Cone of America that have affected countries of the region such as: Venezuela, Colombia, Brazil and Bolivia, among others. [START_REF] Cepal | Millennium development goals: advances in environmentally sustainable development in Latin America and the Caribbean[END_REF] Figure 2: South America Drought map 2016 Source: AccuWeater

The greatest consequences of drought include reduced agricultural production, socioeconomic losses, and destabilization of food security, among others.

Years ago in order to identify the occurrence of a drought in a certain area it was necessary to use methods of visual interpretation.

Currently the use of satellite images allows us to obtain data from the earth surface without the need to be in direct contact with it. That's why satellite technology has become a great tool for various applications, because with this technological advance we can determine the environment in which the phenomenon of drought occur.

There are different indicators of the existence of drought, among them we can mention: physical indicators such as the index of precipitation, soil moisture and the existence of water bodies. On the other hand there are also agricultural indicators, such as vegetation indices, the existence of water in the vegetation and others. [START_REF] Bannari | A review of vegetation indices[END_REF] So far there are no mechanisms that can prevent the occurrence of droughts, but it is possible by means of the analysis of the climatic and meteorological parameters, to carry out monitoring and evaluations that allow to prepare plans of prevention of damages and of mitigation of the effects of the drought.

The present project seeks to extract environmental parameters from satellite images and to complement them with the metrorological parameters to be able to identify the main indicators of the existence of drought, so with this proof of concept to be able to realize in the future a system of monitoring and detection of droughts in the country.

II. DROUGHTS IN BOLIVIA

Since 2015 Bolivia has faced declared states of emergency due to the presence of droughts in some departments of the country.

In December 2015, 27 municipalities in the departments of Chuquisaca, Oruro and Cochabamba were declared in a state of emergency due to the drought. [OCHA 2015] In 2016, the situation did not improve at all, as by February 2016 the drought affected more municipalities in the regions of the Altiplano and the Bolivian Chaco.

By May 2016 the drought affected 104 municipalities in the western departments, among which the departments of Oruro and La Paz were most affected.

Finally, on November 21 Bolivia declared a state of national emergency, since the drought had generated a water shortage in large strips of the country and had affected 173 of the 339 municipalities of Bolivia, affecting an average of 133,000 Bolivian families.

[OCHA]

This last drought of the country lived at the end of 2016 is considered the worst drought in the country in four decades and the worst water shortage since 1980. Seven of the nine departments of the country were affected by the decrease of water level in several dams, which triggered the rationing of water in some cities and the cut of water supply in rural areas. From the two meteorological stations selected, data of the minimum, maximum and average temperature were obtained; in addition to the average precipitation data of the study area in the selected period of time.

B. Satellite Images

For this research project we use the satellite imagery from Landsat 8, which is an American terrestrial observation satellite launched on February 11, 2013. It is the eighth and most recent satellite of the Landsat project operated by NASA and the United States Geological Survey (USGS) since 1972.

The Landsat 8 satellite carries two instruments: Operational Land Imager (OLI) and the Thermal Infrared Sensor (TIRS). Of the total of 11 spectral bands, 9 bands are taken by the OLI instrument and 2 bands are taken by the TIRS instrument [START_REF] Roy | Landsat-8: Science and product vision for terrestrial global change research[END_REF], in the next table we can see the specifications: Table 3: Landsat 8 Satellite Sensor Specifications.

Source: USGS-NASA A level 1 scene consists of a radiometrically and geometrically corrected image with 13 files, where 11 files are in GeoTIFF and correspond to each of the 11 recorded bands, one metadata file (MTL) and one more file with a scene quality evaluation (QA).

For download the Landsat 8 images we must enter in the website of USGS (https://earthexplorer.usgs.gov/), for download the satellite images we do not need to use special software, as mentioned above is free and allows you to download the images that you want. Initially we look for our area of interest, in this case Carangas, Oruro, Bolivia:

We can filter the images by different criteria, mainly by year, month, percentage of cloudiness and others.

The selected study months are: January, February, November, and December 2016, due to the fact that on January and February the problem start, and on November and December were the most critical months. [START_REF]After Rwanda: the coordination of United Nations humanitarian assistance[END_REF] Figure 9: Making a shape of the study area.

Source: Own elaboration

As we can see in the previous image, it was decided to create a shape and crop the satellite image in order to obtain the data only from the area of interest.

Image preprocessing

Due to satellite instruments, different effects can occur that can affect the images acquired, which is why, in order to acquire valid information from our satellite images, different types of corrections must be made in the pre-processing stage, since we need correct the errors that our satellite image acquired when it was exposed to different interferences. Source: Own elaboration

The corrections that will be made in the present project will be explained in the following section.

C. Radiometric correction

This correction is the technique to reconstruct the physically calibrated values by correcting the spectral distortions caused by different reasons like: the instrumental effects due to the calibration, the seasonal changes, the type of terrain that influences the radiation, the sunlight that affects the radiometric values and the scattering effects of the atmosphere, among others.

The main purposes of the radiometric correction is to perform a sensor calibration for reduce the vignetting and the red-out effects and improve the sensitivity of the detector, also the calibration wants to reduce the sun angle and topographic effect for reduce the surface slope, finally wants to correct the phenomena caused for the absorption and scattering caused for the Earth's atmosphere.

For this reasons the radiometric correction is really important for this project as we will perform a quantitative image analysis and and we know that the improperly calibrated Landsat 8 images may lead us to a wrong conclusion.

D. Geometric correction

The geometric correction is the technique to reproject the radiometrically corrected image onto a common map projection. Also an important step is to georeferencing each pair of pixel in the image with a geographic coordinate of the map. Finally applying these two techniques we will achieve a geocoded product.

For this project we will need a totally geometrically corrected image, because for this application we required the absolute locations of the data extracted from the image.

E. Atmospheric correction

The atmospheric correction is the technique of evaluate and eliminate the atmospheric and terrain distortions that are introduced in the values of radiance that arrive at the sensor from the Earth's surface.

This with the main objective of recovering the physical parameters of the terrestrial surface including the reflectance of the surface, the visibility of the ground and the temperature. This correction is especially needed for the application of the present project, because it is necessary to compare and analyze images of different dates and taken in different conditions.

Image processing

In the image processing step we will need to extract environmental parameters that are relevant indicators of the triggering of the phenomenon of drought. For this we need to extract from the satellite images the next parameters: Source: Own elaboration

As we can observe we need to compute meteorological, hydrological and agricultural indicators, as the Relative Humidity, Normalized Difference Water Index (NDWI), Normalized Difference Soil Index (NDSI), Normalized Difference Vegetation Index (NDVI), among others. [START_REF] Zargar | A review of drought indices[END_REF] To calculate the parameters mentioned above, an algorithm has been programmed in MATLAB, the general block diagram of the algorithm was as shown in Figure 12.

The programmed algorithm will perform several tasks to finally calculate the parameters of interest, the algorithm first selects the bands of interest, then reads the metadata file from which it will extract certain constants, then perform the calculations with the programmed equations and finally show heat maps and graphics to be able to analyze the behaviour of the environmental parameters in the different areas of the image.

Figure 1 :

 1 Figure 1: Types of drought. Source: Drought concept and space technology

Figure 3 :

 3 Figure 3: Water reservoir in La Paz Source: Infobae 2016

Figure 4 :Figure 5 :

 45 Figure 4: Cut of water supply in La Paz Source: Infobae 2016On the other hand, as a consequence of the drought, there have been losses of many crops in rural areas of

Table 1 :

 1 List of priority attention municipalities. Source: National Program of United Nation Office for the Coordination of Humanitarian AffairsAs we can see in the list most municipalities with high priority of attention belong to the department of Oruro, so we will select the municipalities of Carangas and Corque in the department of Oruro as a study area.

Figure 6 :

 6 Figure 6: Map of provinces of Oruro, Bolivia Source: Military Geographic Institute Bolivia As we can see in the figure, the area selected by the shape in red is our area of interest, where we have two provinces of interest, these are: Carangas and Corque.

Figure 7 :

 7 Figure 7: General block diagram. Source: Own elaborationIn the previous diagram we can observe the sequence of ordered steps that will help us to achieve the objective of the present research project.

Figure 8 :

 8 Figure 8: Location of the weather stations in Carangas -Bolivia Source: National Service of Meteorology and Hydrology -SENAMHI In total there are two meteorological stations located in the provinces of Carangas (according to the SENAMHI website), Opoqueri and Corque SAT as we can observe in the next table:

Figure 10 :

 10 Figure 10: Preprocessing step block diagram. Source: Own elaboration

Figure 11 :

 11 Figure 11: Processing step block diagram. Source: Own elaboration

Source: Own elaboration As can be observed, the environmental parameters calculated from the image processing step and the meteorological data of the SENAMHI stations located in the study area were included.

After the creation of the database, a statistical analysis was performed. The results will be displayed in the next section.

V. ANALYSIS OF RESULTS

The obtained have been analysed by statistical tools using MATLAB. For this purpose one will obtain the correlation coefficient.

The variables included in the analysis are detailed in the following table: Index that represents the water stress of the vegetation Table 4: Definition of the measured variables. Source: Own elaboration

These variables have been calculated to investigate their effect within the droughts during the months of analysis. An important effect to which we gave greater presence is the variation of temperature, for this reason we analyzed the maximum and minimum temperature of the period.

In Figure 14, Figure 15, and Figure 16; one can see the relation between these variables: To analyse the correlation coefficient between all variables, one use the corrcoef command in MATLAB. In Table one can see the results of this analysis.

VI. CONCLUSIONS AND RECOMMENDATIONS

• NDMI, NDSnI, and NDWIleaves shows a similar behaviour to the precipitations and to the minimum temperature. • With this project a proof of concept of the identification of the main indicators of the presence of drought was realized, in order to be able to establish mitigation measures and the planning of early warning actions in the near future.

• A future study will seek to realize a system of automatic detection of the presence of drought in certain area, we consider that this is important for a proper decision making to be able to mitigate the effects of this natural phenomenon. • In a future project it is important to use data from different satellite sensors, to greatly improve the accuracy of the data obtained.