domain: spi phys math info

text:
Xavier Olive
email: xavier.olive@onera.fr

Jérôme Morio
email: jerome.morio@onera.fr

Trajectory clustering of air traffic flows around airports

Keywords:

Trajectory clustering of air traffic flows around airports

Introduction

Identifying air traffic flows is a topic of interest [START_REF] Sidiropoulos | Identifying significant traffic flow patterns in multi-airport systems terminal manoeuvring areas under uncertainty[END_REF][START_REF] Chida | Topology design for integrating and sequencing flows in terminal maneuvering area[END_REF][START_REF] Jiening | Visualizing air traffic flow management alert information using squarified treemaps[END_REF] with room for improvement in regard to several applications such as traffic analysis [START_REF] Rocha Murça | A robust optimization approach for airport departure metering under uncertain taxi-out time predictions[END_REF], load balancing on sectors monitored by air traffic controllers [START_REF] Chang | Models for single-sector stochastic air traffic flow management under reduced airspace capacity[END_REF]; anomaly detection of events [START_REF]Spatial-temporal traffic flow pattern identification and anomaly detection with dictionary-based compression theory in a large-scale urban network[END_REF] or diverging behaviours that have a higher risk of leading to traffic incidents (loss of separation, runway excursion, etc.).

A way to assess rare aircraft incidents (e.g., runway excursion) is to identify contributing factors (e.g., late braking, long landing, inappropriate flare, unstable approach) and to build a dependency tree (e.g., long landing may be the result of an unstable approach not followed by a go around) that describes the causality between these factors. Probabilities are then fed into such models in order to evaluate the assessed risk. Identifying air traffic flows is a key issue in such treatment as it contributes to identify and estimate the probability to observe an aircraft with a non standard behaviour. In other words, we aim at detecting trajectories that do no fall in a common flow of trajectories. We can then place them in context in order to understand and model what makes them outliers. The understanding we get from this kind of study should provide insight and improve our models of contributing factors.

Trajectories are mathematical objects used to describe the evolution of a moving object. They are described by a state vector with parameters (x(t), y(t), • • • ) that evolve in time. In practice, this state vector is only known at some sampled times. The term (x i , y i , • • • ) represents the state vector at time t i . For clarity con- cerns, we will name trajectory a sequence of recordings associated to a moving object. The explosion of recorded (and sometimes, available) data makes the study of trajectories a popular topic and opens new fields of research in data mining common patterns and identifying outliers from recorded trajectories [START_REF] Zheng | Trajectory data mining: an overview[END_REF].

The literature in trajectory clustering addresses the issue in various ways; the relevancy of each method is highly dependent on the nature of the moving objects tracked and on the kind of information we want to extract from the data. Lee et al. [START_REF] Lee | Trajectory clustering: a partition-and-group framework[END_REF] present a clustering method based on the identification of common sub-trajectories and apply their techniques to the study of hurricanes. Gariel et al. [START_REF] Gariel | Trajectory clustering and an application to airspace monitoring[END_REF] address the specificity of aircraft trajectories around San Francisco airport: they perform a clustering on turning points of trajectories followed by a sequence mining on these clusters. However, the spatial distribution of all turning points on our set of data does not separate well into clusters. Puechmorel et al. [START_REF] Puechmorel | Entropy minimizing curves with application to flight path design and clustering[END_REF] manipulate trajectories as purely mathematical functional objects: they warp trajectories so as to highlight more intelligible tracks and define distances as a minimum energy necessary to bundle trajectories. However as their approach modifies the data records, it may not be appropriate for safety analysis.

The key to a proper clustering of trajectories lies in the proper definition of a distance. Jeung et al. [START_REF] Zheng | Computing with Spatial Trajectories[END_REF] present different popular metrics, like the Hausdorff distance but it does not apply well on converging air traffic flows. Li [START_REF] Li | Anomaly detection in onboardrecorded flight data using cluster analysis[END_REF] or Conde [START_REF] Rocha Murca | Trajectory clustering and classification for characterization of air traffic flows[END_REF] consider resampling trajectories so as to transform them into n-dimensional vectors on which Euclidean distances are computed. This approach is relevant in some applications but can be problematic as an aircraft being put on holding stacks before landing may see this part of the trajectory trimmed out after resampling. In general, it is rather difficult to define a meaningful distance that separates trajectories well, generalises on full trajectories and computes in a reasonable time.

We present a different approach to identify patterns in landing with two objectives: understand how controllers schedule landing on a specific airport, then analyse outlier trajectories with respect to the risk of runway excursion. The proposed algorithm computes a clustering on subsets of significant points of trajectories while keeping a dependency tree of their temporal chaining (Section 3); then associates trajectories to root-to-leaf paths in the dependency tree based on the clusters they cross (Section 4). The full process is rather quick, efficient and robust, and detects outlier trajectories calling for further analysis (Section 5).

The dataset

ADS-B is a cooperative surveillance technology for air traffic control. An aircraft determines its position via satellite, inertial and radio navigation and periodically emits it (roughly 1 Hz) with other relevant parameters to ground stations and other equipped aircraft. A decent ADS-B receiver antenna can receive messages from cruising aircraft located up to 400 km far away (Fig. 1); the range is lower for aircraft flying in low altitude.

We present in this paper the result of three weeks of ADS-B recording from 5 to 30 December 2016. 1 Apart from positional messages, aircraft also emit a callsign, i.e. an 8-character identifier (like "EZY62FN") for a flight (the EasyJet flight from Berlin-Schönefeld and scheduled to land in Toulouse-Blagnac at 19:30). After filtering out all flights not landing in Toulouse, we simplified trajectories as they enter the TMA through a Douglas-Peucker algorithm [START_REF] Douglas | Algorithms for the reduction of the number of points required to represent a digitized line or its caricature[END_REF][START_REF] Sim | 3D UAV flying path optimization method based on the Douglas-Peucker algorithm[END_REF] as on Fig. 3, with ε = 1 km (i.e. roughly: remove points less than ε far from a straight line) and reduced about 5 GB worth of data to less than 200 kB for 1991 trajectories. Most trajectories now consist of 5 to 7 points, but can reach 20 points for aircraft being put on holding stacks. Fig. 2 displays all trajectories we consider in this paper, as they are trimmed within the TMA. We can already remark that the traffic bound for Toulouse airport is heavily unbalanced, with its major 1 The dataset has been made available at the following link: https://doi .org /10 . 5281 /zenodo .891468. Aircraft may land from the South-East (QFU32, or 323 • ) or from the North-West (QFU14, or 143 • ). QFU is a Q-letter code naming the magnetic direction (or number) of the runway to be used. Air traffic management concertedly determines a QFU based on wind.

Clustering and sequencing significant points

Fig. 4(a) represents Toulouse-Blagnac airport with the last airborne positions recorded for each flight. The quality of the reception is variable; yet, we can distinguish two main clusters according to the direction of landing. Fig. 4(b) looks one step backward and displays all one-before-last stored points for aircraft landing on QFU14. The cluster that pops out corresponds to the moment aircraft aligned with the runway, also called roll-out point.

Again, we select the points in all trajectories that fall in the area delimited by our cluster, look one step backward and filter out points that are in the current cluster. Fig. 4(c) links the new resulting clusters (full lines) to previous cluster (dashed lines) in our backward-looking process. A basic recursion (to be formalised further) builds a full dependency tree of common trajectory segments as reflected on Fig. 5.

We compute clusters with a standard dbscan algorithm and select points that lie within a cluster through Kernel Density Estimation. Density-Based Spatial Clustering of Applications with Noise (dbscan) is a common density-based clustering algorithm [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF][START_REF] Berkhin | A survey of clustering data mining techniques[END_REF].

It finds clusters based on a density criterion ε and a minimum sample value n: the cluster forms from core elements having at least n neighbours within an ε distance, and grows by finding new neighbours to the clusters until no other element can be added. Outliers are elements that do not belong to any cluster.

dbscan could predict whether a new point falls inside an existing cluster, but as we will need more than a yes/no answer further in our presentation, we use Kernel Density Estimation to evaluate the distribution of samples inside a cluster. Let u 1 , • • • u n be a set of independent and identically distributed random samples in dimension d with unknown Probability Density Function (pdf) f . We can estimate f with a Kernel Density Estimator (kde) as:

f h ( u) = 1 Nh d N i=1 K u -u i h , ( 1
)
where K is a multivariate kernel (a non-negative symmetric function that integrates to one) and h a parameter called bandwidth. We set the same bandwidth parameter for each of the two dimensions of u, namely the x, y coordinates (conformal conic projections from latitudes and longitudes). There are many available kernels (e.g., Gaussian, uniform, sigmoid, etc.); we prefer here the Epanechnikov kernel that is appropriate with bounded support distributions:

K( u) ∝ 1 -u T • u 1 ( u T • u≤1) (2)
We fit a pdf on all core elements from each cluster, with h = ε (that is the density criterion from dbscan). Since all elements of a cluster fall within distance ε of one of the core elements, the domain delimited by this cluster is defined as:

(x, y) ∈ R 2 s.t. f ε (x, y) > 0 (3)
We may now formalise the proposed clustering method of this article in Algorithm 1. We name the set of all (x, y)-coordinates that constitute our full set of trajectories; and a sequence of pdf f i built through recursion.

Algorithm 1 Dependency tree of trajectory segments function grow_tree(clusters, )

for all c ∈ clusters do fit density f to all (x i , y i ) ∈ core elements of c add f as a new child node to the tree

S ← (x i , y i ) ∈ s.t. f (x i , y i ) > 0 S ← (x i , y i ) ∈ s.t. (x i+1 , y i+1 ) ∈ S

Labelling trajectories

Algorithm 1 produces a tree whose root node is the airport and all paths to leaf nodes describe a potential flow of aircraft following landing procedures. Fig. 5 plots a geographical representation of this tree. A potential pattern p is therefore described as a suite of pdf f p i , i ∈ {0, • • •n p }, n p being the depth of the leaf node associated to p.

As our algorithm considers segments of trajectory, we shall keep in mind that some dense segments may emerge as part of a set of flights that gets more sparse in later parts of the trajectory. We insist on this aspect as we study the outliers in Section 5. Therefore, there may be a number of leaf-to-root paths in our tree that do not result in clusters.

We represent all trajectories t in as a sequence of u j = x j , y j , j ∈ {0, • • •n}. In addition, we describe every possible path p by a sequence of f p i , i ∈ {0, • • •n p }. We define as m p t the following (n p , n)-matrix:

m p t ij = f p i u j ij (4)
that is, a probability for each point of the trajectory to fall within one of our cluster. A square and diagonal matrix m p t with ∀i, f p i u i > 0 and ∀i = j, f p i u j = 0 would mean that our can- didate trajectory passes through all gates of the candidate path, and that for each gate, exactly one point of the trajectory falls into that gate.

⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ • • • 0 • • • 0 • • ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ • • 0 • 0 0 0 0 0 0 • • ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ • 0 • 0 0 • 0 0 • 0 0 • 0 • ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 0 • • 0 • • • 0 • • ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
A gate is a nice metaphor to describe a node of our tree as part of a procedure, i.e. a candidate leaf-to-root path. We say a point of a trajectory falls into a gate if the evaluation of its associated pdf is strictly positive, that is the trajectory goes through one of the bubbles of Fig. 5. A gate can be compared to a distribution probability centred around a procedure point that the aircraft must fly over before landing.

In practice, those matrices are not square, so it may happen that a point falls into two consecutive gates, or that several consecutive points of a trajectory fall into the same gate. Yet if all points of the trajectory fall in the right order into each gate of a possible leaf-to-root path, we can assert that the trajectory flies according to this path and may form a cluster with other trajectories meeting this criterion.

Fig. 6 shows possible patterns for matrix m p t . Pattern a) is an extension of the diagonal matrix described here above: some consecutive points of the trajectory fall in the same gate. Pattern b) is representative of trajectories that fly only through gates of a path, yet miss one of its gates p i . Pattern c) is a trajectory which follows a path, yet has one point outside the gates. It cannot match the path as the trajectory is too distorted compared to the set of other trajectories matching this path.

Pattern d) is similar to c) but must be considered as matching. From the structure of the tree represented on Fig. 5, some leaf nodes do not reach the border of the TMA: the origin of the trajectories converging to this node is not dense enough to form clusters. However, we can bundle all these trajectories as long as they fly through all the gates of the path.

Based on this analysis, we associate a numerical score s p t from m p t : flights of 5). The structure of traffic becomes clear, with several directions of incoming flights and different ways to align on both QFU. We added to this plot two types of information: two outlier flights in dashed lines complete the picture for flights coming from the South; crosses and dotted lines reflect standard arrival procedures (STARs) ruling approaches at Toulouse airport.

s p t = ⎧ ⎪ ⎨ ⎪ ⎩ 0 i f∀i ≥ 0, j m p t i, j = 0 0 i f∃t ≥ 0 s.t. ∀ j ≥ t, i m p t i, j = 0 i max j m p t i, j otherwise (5)
The dense traffic from the North and bound for QFU 14 splits into several clusters showing how aircraft are scheduled according to a pattern of linear hold: aircraft are scheduled by timing their turn into final approach so as to land no less than two minutes apart. One of the clusters is formed from trajectories being warped even further in order to respect tight scheduling constraints; on the other hand, a cluster forms from flights from the North which get clearance from the ATC to shortcut the entry point to the TMA and align directly into final approach.

These two emerging clusters show how STAR procedures published by eAIP 2 are not sufficient to describe traffic flows around airports. To sum up, it is interesting to see how official procedures somehow emerge from the clustering we produce, and how the picture is also completed with common practices used to regulate the traffic, i.e. giving aircraft the best approaches for their direction of travel according to the current traffic and weather conditions.

From a performance point of view, the building of the dependency tree described in Section 3 took few seconds to compute with the implementation of dbscan provided by scikit-learn (Intel Core i5 2.40 GHz). The labelling was the most intensive part as it took about 6 minutes with our pure Python implementation to label all trajectories.

A study of the outliers

Our clustering of trajectories yields about 30% of outliers. The study of the outliers is interesting as these trajectories may contain information about the circumstances under which a landing procedure may differ from the norm and result in dangerous behaviour, or worse, traffic incidents.

With our procedure for attributing a label to a trajectory, we outcast by default those that lack data around landing. Fig. 8 plots all trajectories for which the last recorded points do not end in one of our original clusters above the runways (refer to Fig. 4(a)). We find on the lower left-hand side a series of trajectories which 2 https://www.sia .aviation -civile .gouv.fr/. do not seem to land at Toulouse airport. After investigating this anomaly, we found that the callsigns associated to these trajectories correspond to flights from Nantes or Bordeaux, which land in Toulouse before taking off again and flying further to their final destination (here Tenerife, Canaries and Agadir) with the same callsign. As we made this mistake in the preprocessing of our trajectories (the trajectories should have been trimmed after the aircraft landed) in good faith, 3 we mention them here as they demonstrate that the method we present was robust enough to keep them out of any cluster.

Fig. 9 plots trajectories being put on holding stacks of various orientations and positions. We remark that the northernmost hippodrome could be dense enough to form some kind of cluster. However, as no clear way out of this pattern emerges (linear holds are pushed to extremes in such saturated situation), our algorithm will not make a pattern out of these trajectories. It could be interesting to study their distance to statistically standard landings once they are back on a regular track. More generally, some trajectories enter the TMA from areas of lesser density, yet still match existing clusters on the latter part of the landing; we could craft a refined way to match a trajectory to a cluster and use this degree of matching to evaluate some degree of risk in an approach.

The outlier trajectory on Fig. 10 is associated to callsign AF526KB on December 26. This flight started its approach for QFU 32 but changed halfway and aligned on QFU 14. Indeed, a QFU change at the turning point of this trajectory is consistent with the landing history of that day. If we look more closely on Fig. 11, we can see that the altitude profile (pale dashed lines) is not surprising, yet there seems to be a sudden change in ground speed (full line) and vertical speed (dotted-dash) at 20:52 on that day, about 50 seconds before the aircraft changes its trajectory.

As sudden as the change may look, the aircraft managed to align properly on QFU 14.

A late QFU change may lead to unstable approaches, which may lead to a late touchdown on the runway (long landing), which is a potential risk of runway excursion. In practice, the estimation of the different conditional probabilities involved in the estimation of the risk of runway excursion (like the probability of an unstable approach for flights subject to a late QFU change), may only be 3 Institutions like Eurocontrol try to enforce using a different Globally Unique Flight Identifier (GUFI) for each leg of this kind of flights rather than callsigns that are subject to such misinterpretations. GUFIs would still be helpless with rerouted flights. roughly evaluated by experts since those events are not properly recorded or reported by airlines. A good analysis of outlier trajectories yielded from a bigger amount of data could improve the estimation of such conditional probabilities, hence improve the estimation of such risks.

Conclusion and future works

We presented a new method to cluster aircraft trajectories before landing and compared the resulting clusters to official STAR procedures for Toulouse airport: the clustering complements the procedures well as it adds insight concerning common practices of the ATC in charge of approaches. Then we explained how the study of outliers may nurture a more precise risk assessment analysis. In the specific case of outlying trajectory we address, we find a late QFU change to a shorter STAR procedure: a further analysis on a larger time scale of trajectories subject to a late QFU change could be a valuable result. More generally, we believe that a source of data with a global view on traffic (such as ADS-B) in addition to other data from flight data managers (owned by airline operators) announces promising perspectives as it considers each aircraft in context, with information about how other aircraft fly in the same environment.

Future works may include a validation on other airports with various runway configurations, a better metric measuring a deviation from a trajectory cluster core. A study of the evolution of traffic patterns over the seasons, correlated with meteorological reports (METAR) would also be precious, as weather (gale, fog, etc.) has a strong impact on how traffic in the TMA is regulated and on how aircraft fly before landing. The use of other available data like vertical speed, indicated airspeed, roll, track, or heading angles would also be of interest; as well as a coupling with ACARS messages aircraft send shortly before landing with information about required maintenance operations.

Fig. 1 .

 1 Fig. 1. An instant view of traffic as seen by a Radarcape antenna.

Fig. 2 .

 2 Fig. 2. The full dataset: three weeks of recorded trajectories. The border delimits the convex hull of the TMA.

Fig. 3 .

 3 Fig. 3. Douglas-Peucker simplification of two sample trajectories (in red) with ε = 1 km. The dashed lines connect the points selected by the algorithm. A trajectory put on holding stack yields more points than a regular approach. (For interpretation of the colours in the figure(s), the reader is referred to the web version of this article.) part coming from the North-East side of the map. Unbalanced density is a common difficult pattern in clustering that we propose to address with our algorithm.Aircraft may land from the South-East (QFU32, or 323 • ) or from the North-West (QFU14, or 143 • ). QFU is a Q-letter code naming the magnetic direction (or number) of the runway to be used. Air traffic management concertedly determines a QFU based on wind.

UFig. 4 .

 4 Fig. 4. Recursive clustering of significant points on recorded trajectories.

  look backward for all f ∈ do see dashed lines on Fig. 4(c) S ← S -(x i , y i ) ∈ S s.t. f (x i , y i ) > 0 end for if card S > threshold then grow_tree(dbscan(S), ∪ { f }) Now we start the recursion grow_tree(dbscan(last positions), = { })

Fig. 5 .

 5 Fig. 5. Dependency tree (map view to the left, unfolded view to the right) as produced by grow_tree algorithm of Algorithm 1. Latin (resp. Greek) letters label nodes for aircraft landing on QFU 14 (resp. QFU 32).

Fig. 6 .

 6 Fig. 6. Patterns for matrix m p t ; a • means f p i u j > 0.

Fig. 7 .

 7 Fig. 7. Resulting clusters for traffic in Toulouse TMA; significant trajectories for every cluster are in full lines, two outliers complete the picture in dashed lines. Crosses and dotted lines reflect official procedures currently implemented.

Fig. 8 .

 8 Fig. 8. Outliers with respect to our clustering of trajectories: incomplete trajectories.

Fig. 9 .

 9 Fig. 9. Outliers with respect to our clustering of trajectories: trajectories on holding stacks.

Fig. 10 .

 10 Fig. 10. Trajectory clusters and outlier flight AF526KB (bold) on December 26.

Fig. 11 .

 11 Fig. 11. QFU change appears in speed plots on outlier flight AF526KB on December 26, 20:52.

Conflict of interest statement

None declared.


text:
Julien Marzat

Hélène Piet-Lahanier

Sylvain Bertrand

Cooperative fault detection and isolation in a surveillance sensor network: a case study

Keywords: cooperative fault detection and isolation, sensor network, intrusion detection, performance evaluation

This work focuses on Fault Detection and Isolation (FDI) among sensors of a surveillance network. A review of the main characteristics of faults in sensor networks and the associated diagnosis techniques is first proposed. An extensive study has then been performed on the case study of the persistent monitoring of an area by a sensor network which provides binary measurements of the occurrence of events to be detected (intrusions). The performance of a reference FDI method with and without simultaneous intrusions has been quantified through Monte Carlo simulations. The combination of static and mobile sensors has also been considered and shows a significant performance improvement for the detection of faults and intrusions in this context.

INTRODUCTION

Two main applications of sensor networks are usually considered, namely environmental monitoring (continuous sensing) and event detection (surveillance, target tracking). The scenario considered in the EuroSWARM * project is the persistent monitoring and surveillance of a large area in order to protect a high value asset from intruders in a battlefield context. This paper is thus dedicated to event detection networks, whose particular features are the non-persistence of the excitation signals, limited sensor ranges, and possibly sparse coverage. Cooperative FDI can be very useful to avoid sending manned troops or unmanned vehicles from the military basis for intrusion confirmation in the case of a faulty event detection when no intrusion is present or of wrong localisation in the case of an intrusion. In the first case where no intrusion is reported, this also helps the maintenance of the network by replacing faulty nodes without the need for a systematic strategy. This would entail cost saving and security improvement.

For reliable sensor fusion and an enhanced possibility of detecting faults in a cooperative manner, the network should locally present a high density of (possibly heterogeneous) sensors. Otherwise, information gathered on possible intrusions will only be based on scarce measurements, and the lack of possibility of comparison with other sources of information makes it difficult to distinguish between true events and faults without a human intervention. Heterogeneity increases complexity, since it is hard to compare measurements between sensors of different natures and this turns out to be possible only with high-level preprocessed data.

As indicated by [START_REF] Ni | Sensor network data fault types[END_REF], sensor network data is expected to be correlated in both the spatial domain and * https://euroswarm.wordpress.com temporal domain and this is the main assumption at the basis of FDI methods. In surveillance networks, what is defined as a fault may also characterize an event under some conditions. The main difficulty for FDI in event detection sensor networks is thus the coupling between an event that should be detected and a fault. There are two critical situations: (1) No event is present but signals are produced by some faulty sensors and (2) An event is present but is not detected by some faulty sensors. To differentiate between a fault and an event, a training phase may be utilized to determine a model of a specific interesting event, or this could also be distinguished through the exploitation of the spatial and temporal correlations in the measurements.

In this paper, a classification of faults that can affect sensor networks and a review of the main FDI techniques are first given in Section 2. In Section 3, the design and results of extensive simulations of a reference FDI method [START_REF] Choi | A distributed adaptive scheme for detecting faults in wireless sensor networks[END_REF]) applied on the specific case of the area monitoring scenario are provided. In particular, the performances of both FDI and intrusion detection are quantified with a Monte Carlo approach, so as to provide recommendations for the design of surveillance sensor networks. A preliminary study has also been conducted on the combination of a static network and a fleet of mobile sensors for such a mission, which shows significant improvement of the overall performance. Conclusions are discussed in Section 4.

LITERATURE REVIEW

Definition of faults in a sensor network

Classifications of sensor fault types in sensor networks and of associated FDI methods have been proposed in [START_REF] Ni | Sensor network data fault types[END_REF]; [START_REF] Muhammed | An analysis of fault detection strategies in wireless sensor networks[END_REF]; [START_REF] Mahapatro | Fault diagnosis in wireless sensor networks: A survey[END_REF]; [START_REF] Jurdak | Wireless sensor network anomalies: Diagnosis and detection strategies[END_REF]; [START_REF] Fang | In-network sensor data modelling methods for fault detection[END_REF]; [START_REF] Rassam | Advancements of data anomaly detection research in wireless sensor networks: a survey and open issues[END_REF]. These references have been analyzed to propose the following synthesis. A fault is an unpermitted deviation of at least one characteristic property or parameter of the system from acceptable/usual/standard conditions. A fault may lead to a failure, which is a permanent interruption of the system ability to perform a required function under specified operating conditions. There are two classical approaches to define faults in sensor networks, which can be more or less appropriate depending on the context. Frequently there may not be a clear explanation on the cause of a fault (e.g. outliers), and hence it may be easier to describe some faults by the characteristics of the data behaviour. This is the data-centric view, which is the most relevant from the diagnosis point of view. The second systemcentric approach covers physical malfunctions or degraded operational conditions on sensors and describes what type of features this could exhibit in the data collected. These two approaches are therefore complementary: data-centric faults are usually caused by system issues. Monitoring certain aspects of the hardware, such as battery life, may thus help to understand when and why a fault may occur. The data-centric perspective has been adopted in this work, i.e. how faults can be detected by investigating the data of the sensor nodes. It should although be kept in mind that some major hardware faults that are at the root of these data faults can sometimes be self-detected by a node itself (loss of connection to the network, battery end-of-life). In this case, cooperative FDI is not mandatory and the node can just be excluded from sensor fusion for event detection or target tracking.

Data-centric faults:

(1) Outlier: very common fault represented by isolated samples in the temporal or spatial sense. To model an outlier, the most common feature to consider is the distance from other readings. (2) Spike: a rate of change much greater than expected over a short period of time (inconsistent gradient). In some cases, this may represent an event (intrusion) that should be detected. (3) Offset (or bias): deviation in sensed data by an additive constant. (4) Gain (or scaling): the rate of change of the sensed data is affected by a scale factor. (5) Drift: a time-varying signal (linear or not) is added to the measurements, independently from the measured phenomenon. (6) Stuck-at (or locked): some series of data values present no variation over a given period of time. The monitoring of gradients and variances is relevant to detect this kind of fault. (7) High noise: unusually high noise may be due to hardware failures, battery issues or environmental disturbances. (8) Data loss: sensed data is not received during a significant time interval.

System-centric faults:

(1) Calibration error: this is the root cause of faulty data in many cases, leading for example to the presence of offset, gain and drift.

(2) Connection or hardware failures: this causes hard faults, with loss of data. (3) Low battery: may influence sensor readings, creating outliers, spikes or other signal distortions. (4) Environment out-of-range: the sensitivity range of the sensor is exceeded due to current conditions. This may be due to inappropriate calibration or a wrong choice of sensor. (5) Clipping: this saturation phenomenon can be a consequence of environment influence or misuse of the sensor, and can lead to the stuck-at type of fault.

The faults can be persistent or intermittent, therefore the history of events should be stored to discard sensor nodes that repeatedly present an anomalous behaviour.

Techniques for FDI in sensor networks

Fault detection is the determination of the presence of faults in a system and of their times of occurrence. It is generally followed by fault isolation to determine the type and location of the faults. Fault identification (or estimation) aims then at determining the magnitude and time-varying behaviour of the faults. The complete process is usually called either FDI or fault detection and diagnosis (FDD), the latter including identification. These tasks generally involve the generation of residuals, which are fault indicators based on discrepancies between measurements and model-based computations. Residuals should remain small as long as there is no fault, and become sufficiently large to be noticeable whenever faults occur [START_REF] Marzat | Model-based fault diagnosis for aerospace systems: a survey[END_REF]). Emphasis will be put on cooperative processing and detection of faults affecting the collected data. [START_REF] Zhang | Outlier detection techniques for wireless sensor networks: A survey[END_REF] consider specifically detection techniques of outliers. The following generic remarks are of particular interest:

• Two variations for outlier identification exist in sensor networks. One is that each node identifies the anomalous values only depending on its historical values. The alternative is that in addition to its own historical readings, each sensor node collects readings of its neighboring nodes to collaboratively identify the anomalous values. • Outlier detection techniques need to make use of data of neighboring nodes and spatial similarity of the sensor data. This is based on the fact that the sensor faults are likely to be spatially unrelated, while event measurements are likely to be spatially correlated.

FDI techniques can be classified in the following three main categories.

Statistical and model-based

These methods represent spatial or temporal links between data via statistical models. Different types of parametric probability distributions can be employed (Gaussian, Poisson, Rayleigh, uniform), several estimation techniques have been proposed (averaging, median, maximum likelihood, Kalman filtering, Bayesian inference) and various statistical decision tests can be applied (three-sigma test, likelihood ratio). There also exist non-parametric statistical methods using other distance measures (histograms or kernel functions). [START_REF] Franco | Distributed fault diagnosis using sensor networks and consensus-based filters[END_REF] described a distributed FDI methodology based on a bank of Kalman filters and a Bayesian con-sensus decision scheme. The detection procedure is based on the analysis of residuals computed as the innovations of a Kalman filter using a nominal model of the system to be monitored; once a fault is detected, a multiple model estimation scheme is called upon to achieve fault isolation. The distributed algorithm of [START_REF] Ji | Distributed fault detection for wireless sensor based on weighted average[END_REF] computes a spatial weighted average for each node using its pre-defined set of neighbors, with a simple decision mechanism using a fixed threshold (set to zero in the case of binary data). The weights represent the confidence associated to each sensor, depending on its prior probability of becoming faulty.

Neighborhood and clustering

These methods compute some measure of distance between data instances of neighbor nodes, on spatial or temporal windows. Neighbors are defined using criteria of number, distance, connection or overlapping range. The main underlying assumption is that neighboring measurements of the same phenomenon should be correlated and of very similar values. Some basic statistical quantities (similar to those from the first class of methods) can be computed using these data, and consensus mechanisms are applied (usually majority voting, possibly weighted with some prior knowledge) to identify faulty nodes, most often in a decentralized way. This category also includes nearest-neighbor clustering rules and decision processes. [START_REF] Choi | A distributed adaptive scheme for detecting faults in wireless sensor networks[END_REF] proposed a fault detection scheme based on the comparison of sensor readings between neighbors in a homogeneous network with deterministic measurements. An iterative procedure is designed to create clusters and determine if the node is healthy. The node degree and matching threshold are adjusted at each iteration until all the nodes have been classified as healthy or faulty. A distributed fault detection scheme for sensor networks has been proposed in [START_REF] Chen | Distributed fault detection of wireless sensor networks[END_REF]. It uses local comparisons with a modified majority voting, where each sensor node makes a decision based on comparisons between its own sensing data and those of neighbors on successive time instants, while considering the confidence level of its neighbors. This requires two successive exchanges of information between neighboring nodes to obtain a local consensus. The detection criterion was improved in [START_REF] Jiang | A new method for node fault detection in wireless sensor networks[END_REF] in the first level of exchange to avoid misclassifying sensor nodes as faulty.

Classification and learning This set of methods builds classes from a measurement database either in a supervised way (i.e. with the help of an expert) or in a semisupervised manner (i.e. putting in the same class elements of the database that are deemed close to one another, and relying on an expert only to label the classes). A classifier (Neural Network, SVM, Bayesian Network) is then trained with respect to these classes to assign the newly measured variables to classes that represent healthy or faulty behaviors. This category also includes spectral approaches such as Principal Component Analysis (PCA), which builds a learning model by using redundancy in the process history to predict the values of variables and generate residuals by comparing predictions to measured values. [START_REF] Harkat | An improved PCA scheme for sensor FDI: Application to an air quality monitoring network[END_REF] used PCA to detect sensor faults and also additionally estimate their magnitude on a single node by computing the difference between a measurement of one variable and its reconstruction using the PCA projection matrix and the measurements of all the other variables. This technique was applied to supervise an air quality monitoring network.

Performance metrics

The following performance metrics are usually employed to evaluate the FDI methods:

• Detection Accuracy (DA): ratio of correctly detected faulty nodes in the total number of faulty nodes. • False Alarm Rate (FAR): ratio of non-faulty nodes detected as faulty in the total number of fault-free nodes. • Delay of detection (mean and variance can be computed on all nodes detected as faulty).

The trade-off between Detection Accuracy and False Alarm Rate can be represented graphically by a ROC (receiver operating characteristic) curve (see e.g. Figure 3).

Main trends and remarks

Main trends Most of the methods are based on statistical assumptions and data comparison in a neighborhood of sensor nodes, which can be easily decentralized. Decentralized approaches are either explicitly hierarchical with specific gateways and pre-defined cells in the network, or on the contrary implicitly self-organizing where each node exploits the knowledge from its neighbors without rank.

The second design choice is more generic and adaptable to failures. Statistical models are very often employed, in either centralized or neighbor-based approaches. This is quite natural, regarding the usual assumptions on the spatial and temporal distributions of sensor measurements. Majority voting is probably the most employed consensus mechanism. It has the potential to enhance the detection performance from both detection accuracy and false alarm rate perspectives. It should however be noted that the performances of these techniques are worst affected by low average node degree, i.e., these techniques are topology dependent. Learning techniques are cumbersome, due to the need for a large database of data samples to train the algorithms and high computation complexity for the training step. The most used technique is to rely on a single healthy class and to detect outliers. However this strategy does not allow the identification of the type of fault.

Limitations of existing studies

The majority of existing works does not take into account multivariate data and assumes the sensor data is univariate. Many of the neighbor coordination approaches only consider the spatio-temporal correlations between sensor data of neighboring nodes and ignore the dependencies among the attributes of the sensor node itself. Many of the approaches adopt a predefined threshold to detect faults. However, an optimal threshold is not always easy to determine. Rigorous analyses can be obtained under statistical assumptions. Little work has been done on diagnosing intermittent and transient faults. Most often, persistent failures are assumed. This is an important issue in practice. Little work has been done on distinguishing between events and faults. Many of existing techniques simply regard outliers as errors. Since a commonly accepted notion is that errors should be removed from the data set, important information about hidden events may be lost.

Remarks Combining static and mobile sensors for event detection is still an open issue that has not been extensively studied in the literature (a few existing references are [START_REF] Datta | Distributed localization in static and mobile sensor networks[END_REF]; [START_REF] Wang | Probabilistic field coverage using a hybrid network of static and mobile sensors[END_REF]; [START_REF] Mohamed | Using mobile sensors to enhance coverage in linear wireless sensor networks[END_REF]), and collaborative fault detection in this context is all the more challenging. A simple way to address the problem would be to add (when they are available) the mobile sensor measurements along with their localization information to the static ones and use the same fusion and fault detection algorithms. Even if the dynamics of the vehicles would not be fully exploited in this framework, this would still add important information to excite the system for fault detection purposes. This is the approach evaluated in Section 3.5. The security of sensor networks (in particular robustness to attacks) is beyond the scope of this study. Some elements can be found in [START_REF] Chen | Sensor network security: a survey[END_REF], where physical protection, software and network security or secure location and data aggregation are addressed.

FDI IN A SURVEILLANCE SENSOR NETWORK: A CASE STUDY

In this section, the application of a FDI technique from the literature to a sensor network representative of a persistent surveillance task is analyzed through simulation results.

Scenario and simulation conditions

The simulations consider the surveillance of a sub-area of a larger protected zone. The considered dimensions are 20 m × 20 m, this metric unit is just an example, since the obtained results are not sensitive to this value and remain valid if all parameters are modified with the same scale. The sensor network is composed of a large number of cheap omnidirectional sensors with limited ranges (3 m and 4 m have been considered), which are representative of seismic sensors or magnetometers (listed as relevant for the application considered). Several measurement models of increasing complexity can be considered:

• Binary measurements (as in e.g. [START_REF] Arora | A line in the sand: a wireless sensor network for target detection, classification, and tracking[END_REF]) on the full sensor range, which corresponds to a local detection by each sensor using its own information. This is a representative model for imprecise sensors (such as the seismometers and magnetometers considered). • Position of the intruder in the sensor field of view, with possibly an associated uncertainty (which can be very large for cheap sensors). This might lead to slightly better performance than binary measurements (but this is not guaranteed). • Spatial field mapping of the probability of presence defined at each position. This can be easily built from position measurements.

In this case study, the first measurement model has been considered for evaluating the methods. This is a representative situation in practice, and this was deemed sufficient to assess FDI performance. The surveillance mission considers intrusion detection with no prior knowledge: in the nominal case without any intruder present, a sensor should return the value 0, while it should measure 1 if an intruder is present in its field of view. No particular assumption is made on any sensor fusion algorithm for more advanced high-level recognition or combination of sensor information. The FDI algorithm will thus try to detect faulty nodes by comparing the measurements of the nodes. For this purpose, a redundancy in spatial and temporal coverage between nodes is mandatory, since this is the main assumption at the basis of all cooperative FDI approaches for sensor networks. Various percentages of faults in the network have been considered, from 0 to 50% of the nodes (randomly chosen in the simulations).

A relevant operational scenario is to consider that some faulty sensors are stuck to 1, which means an undesired false detection of the presence of a target. The two cases of such a fault occurring in absence or in presence of a true event (intrusion) are considered.

(1) Persistent faults (sensor stuck to 1) in the case of no intrusion in the area. (2) Persistent faults (sensor stuck to 1) in the case of a simultaneous intrusion in the area. Distinguishing faults from true events is known to be a difficult issue in FDI for sensor networks [START_REF] Zhang | Outlier detection techniques for wireless sensor networks: A survey[END_REF]).

The placement of the nodes in the area has been carried out by Latin Hypercube Sampling (LHS). This method generates a near-random space-filling design of N points by dividing each axis of the space in intervals of equal length, and then by sampling randomly with a uniform distribution in only one square per line and per column. This provides a better distribution of samples in the space than grid sampling or pure direct random methods [START_REF] Mckay | Comparison of three methods for selecting values of input variables in the analysis of output from a computer code[END_REF]), especially in high dimensional spaces. This placement does not provide the optimal coverage but still ensures a good spreading in the area with a limited computational cost (see e.g. [START_REF] Balesdent | A multilevel optimization approach for the planning of heterogeneous sensor networks[END_REF] for more advanced considerations). Two sensor nodes are defined as neighbors if their fields of view intersect. Several numbers of nodes in the area have been considered so as to obtain more or less large and dense networks (see Table 1). This yields a collection of average numbers of neighbors for each node, which is one of the main parameters with a strong impact on FDI performance and reliable intrusion detection. All the results presented have been obtained via extensive Monte-Carlo simulations (1000 for each result data point) on the network sampling so as to compute metrics that are independent of the particular disposition of the network.

All the cases from Table 1 have been processed in this context. The intruder has been modelled as a random walk on a duration of 200 time steps, where each subsequent step is chosen using a zero-mean Gaussian distribution with standard deviation 0.5 m. The initial position has been randomly chosen with a uniform distribution in a rectangle centered in the middle of the area and of side equal to half the length of the space.

FDI method for performance evaluation

The method described in [START_REF] Choi | A distributed adaptive scheme for detecting faults in wireless sensor networks[END_REF] has been selected for performance evaluation on the described intrusion detection scenario, since it is representative of the decentralized methods based on neighborhood and clustering that have been extensively studied and which reported the best diagnosis performances in the literature.

This approach uses an iterative procedure to create clusters and determine if the node is healthy. The node degree and matching threshold are adjusted at each iteration until all the nodes have been classified as healthy or faulty.

The method is a good summary of the main features of cooperative FDI techniques: it is decentralized (each node computes its own status using only its neighbors), spatial correlation in data is exploited, a consensus is performed between neighbors and propagated inside the network, and temporal aspects are also taken into account by modifying iteratively the table of neighbors and the detection thresholds. The detailed algorithm is as follows.

For each node i, to determine its status F i (0: good, 1: faulty, 2: undetermined) do

(1) Create the Neighbor Table (N T ) and set F i to 2 (undetermined) (2) Gather measurements of the neighbors of i (3) Determine k i the number of matching neighbors (same measured value in the binary case) (4) If k i > θ i then set F i to 0 (5) Repeat l times for undetermined nodes:

If one of its matching neighbors is determined to be healthy, then set F i to 0 (6) The remaining undetermined nodes are considered to be faulty (F i ← 1) (7) Update N T (remove faulty sensors) (8) Compute threshold θ i for the next time step

The threshold θ i chosen as θ i = max δ, di 2 where d i is the number of neighbors of node i and δ the minimum number of neighbors required to make a decision. Following the recommendations of [START_REF] Choi | A distributed adaptive scheme for detecting faults in wireless sensor networks[END_REF], the value of l has been fixed to 1 and the value of δ to 2.

Persistent detection of some sensor nodes with no intrusion

In this case, all the nodes should normally return the measurement 0 to indicate that no intrusion is currently in process. Therefore, faulty nodes that return 1 should be identified with the proposed method. The results of the Monte-Carlo simulations are presented in Figure 3, for all variations of parameters (sensor range, number of nodes, and percentage of faulty nodes). The perfect performance is represented by a DA indicator equal to 1 and a FAR equal to 0. It clearly appears that the most important parameter impacting FDI performance is the average number of neighbors, which is a consequence of the relation between the total number of nodes and the sensor range. Of course, for the same number of nodes there are more neighbors per node in the case of a larger range. The results show that a good FDI detection performance (DA > 0.95 and FAR < 0.05) can be obtained for a percentage of faulty nodes up to 25% only if the average number of neighbors (also known as the node degree) is larger than 4 (as a reminder, see Table 1 for the relations between those parameters). These results and the level of performance reached are consistent with those obtained in the literature with similar parameters (but not for intrusion detection scenarios, see [START_REF] Paradis | A survey of fault management in wireless sensor networks[END_REF]; [START_REF] Chen | Distributed fault detection of wireless sensor networks[END_REF]; [START_REF] Ji | Distributed fault detection for wireless sensor based on weighted average[END_REF]). This shows that such a method is well qualified in the targeted application, if a sufficient number of nodes can be deployed to satisfy the condition on the number of neighbors per node. For very cheap sensors, this should be possible. Moreover, the percentage of simultaneous faults should not reach very high levels since sensors can be deactivated or replaced as soon as they are detected as faulty. Figures 1 and2 display a few examples of fault detection and identification results for different network parameters.

Persistent detection of some sensor nodes in presence of intrusion

When the same type of faults (sensor measurement persistently stuck at value 1) is considered in the presence of an intrusion, the situation is more complex and there are several possible consequences. The sensor fault can trigger false alarms in locations where there is no actual presence of an intruder and therefore result in a false detection of multiple intrusions on the overall area, which can lead to a bad use of military resources and this should be detected beforehand. If the persistent sensor fault appears where the intruder is located, it does not degrade performance of detection, but only healthy nodes can be reliably taken into account for an intrusion to be confirmed. Finally, another well-known issue with faults in sensor networks that should detect this kind of event is the difficulty to distinguish faults from intrusions, especially if there is a limited number of neighbors for each node. The simulations in the case of an intrusion provide interesting information on all these situations. Results presented in Figure 5 show that the simultaneous occurrence of faulty nodes and intruders degrade the overall performance of FDI. Detection Accuracy slightly decreases and False Alarms are more frequent because sometimes the event is treated as a fault by the consensus mechanism, especially when there are very few neighbors per node. It is however interesting to note that the network is more robust to this kind of confusion between events and faults when the sensor range is larger, even for comparable node degrees. This is because the intrusion can be better captured by multiple neighboring nodes since their overlapping area has more chances to be larger. The FDI performance remains acceptable (DA > 0.85, FAR < 0.15), as long as there is still more than 4 neighbors per node.

So far, only the performance of the FDI algorithm when there are at the same time faults and actual intrusion has been discussed. However, another important operational consideration in this scenario is whether the correct detection of the intrusion can still be achieved even in the presence of such faults. The intrusion is determined to be correctly identified if a healthy node, i.e. one that has not been classified as faulty by the FDI algorithm, detects the target at least once during the time interval studied. The rates of correct intrusion detection for the same simulations have been computed and are reported in Figure 6. In the simulation conditions considered, a meaningful result is that the rate of correct intrusion detection increases with the percentage of faults. This is again mainly because in the case of only a few faults and a reduced number of nodes, events are sometimes treated as faults (in the specific case of the stuck-at fault considered here) and if the percentage of faults increases then some nodes are not detected as faulty and can contribute to detecting the event. When the number of nodes increases (and thus the number of neighbors), the performance of both fault detection and correct intrusion detection is significantly improved. More than 7 neighbors per node are thus required here to guarantee a sufficient level of correct intrusion detection (at least 0.8 to 0.9).

Network of static and mobile sensors

Another possible improvement to the network is to consider a fleet of mobile vehicles, equipped with the same small-range sensors (4 m range) than the static network, which follows a predefined trajectory covering the entire monitored area. These sensors communicate with the static ones (no loss or delay assumed) and can thus help to detect faults and events on the monitored area. We consider the case of a small fleet of 6 sensors, which are non-faulty for the entire duration of the mission but which could be detected as faulty by the FDI algorithm. Figure 7 presents successive screenshots of the mission. Note that in the result figures, the number of nodes is the one of the static network.

FDI performances with simultaneous intrusion are presented in Figure 8 and Figure 9. The detection accuracy remains at a similar level than the original static network, but false alarms have been drastically reduced thanks to the mobile fleet. Regarding intrusion detection, the performance of the combined mobile and static network is excellent. The impact of employing fleets of mobile sensors together with static sensors is thus beneficial in terms of intrusion detection even in the presence of faulty sensors. What is even more interesting is that high level of performances are reached with a smaller number of static nodes (15 are sufficient here, in spite of the corresponding small static node degree). The addition of mobile sensors is thus an efficient way to increase dynamically the network node degree. To implement cooperative FDI, there is a need for redundancy in the sensor network: at least 2 to 3 neighbors are required for voting schemes and much more to be able to distinguish between faults and events (i.e. the intrusion that should be detected). It has been shown that a good level of performance (high detection accuracy and few false alarms) can be attained with more than 4 neighbors per node, without simultaneous intrusion in the monitored area. Existing methods are efficient if the percentage of faulty nodes in the network is limited (less than 25%). This is a reasonable assumption since confirmed faulty nodes can be deactivated or replaced through systematic maintenance.

To obtain a good performance of correct intrusion detection, with simultaneous faults, there should be more than 7 neighbors per node. Otherwise, if there are a lot of faults in the network, they will be detected but a true intrusion could also be classified as a fault. It should be noted that these results have been obtained without considering advanced sensor fusion techniques, which might improve fault and event detection performances and thus reduce the necessary minimum node degree. Performances of both FDI and correct intrusion detection are improved by considering both static and mobile sensors in the process, this type of architecture should thus be further investigated.

This study has obtained progress beyond the state of the art by applying a reference method for FDI in a sensor network to the specific case of intrusion detection in a surveillance mission, and by analyzing simultaneously the performance of these two distinct capabilities. Moreover, this has been extended by combining the static network with a fleet of mobile vehicles and evaluating the resulting increased performance.

Fig. 1 .

 1 Fig. 1. Example of good FDI in a sensor network (20 nodes, 10% faults, no intrusion)

Fig. 3 .

 3 Fig. 3. Performance of FDI method with various sensor ranges and network configurations (case without intrusion, sensor ranges of 3 m (up) and 4 m (down))

Fig. 4 .

 4 Fig. 4. Illustration of FDI results in presence of intrusion (30 nodes with 5% faulty, intruder trajectory in red)

Fig. 6 .

 6 Fig. 6. Performance of intrusion detection in presence of faults

Fig. 8 .

 8 Fig. 8. FDI results in the sensor network with the help of a fleet of mobile sensors (with intrusion)

Table 1 .

 1 Average numbers of neighbors depending on number of nodes and sensor ranges

	Number of nodes	15	20	25	30	40
	Sensor range 3 m	2.43 3.50 4.57 5.64	7.79
	Sensor range 4 m	4.24 5.97 7.69 9.41	12.86

ACKNOWLEDGEMENTS

This work has received funding from the European Union under the Pilot Project on Defence Research managed by the European Defence Agency under grant agreement No PP-15-INR-01 05 EuroSWARM ("Unmanned Heterogeneous Swarm of Sensor Platforms"). This work reflects only the author's views. The European Commission and European Defence Agency are not responsible for any use that may be made of the information it contains (Art. II.9 of the Model Grant Agreement).


Jacques Moret-Bailly

Introduction of spatial, optical coherence in astrophysics

Coherent, collinear, Raman interactions of a perfectly, temporally incoherent ray with low pressure cold H gas "redshift" ray frequencies and heats background radiation. In space, quasar radiated UV light pumps H atoms by Lyman alpha absorptions, thus redshifts light until previously absorbed Lyman beta or gamma line reaches alpha frequency. Redshift may slowly restart by Lyman beta absorption. This redshift is an alternative of Hubble's law, by which many strange hypothesis (dark matter and energy ...) are not anymore needed.

1-Introduction.

In 1917, Einstein showed that propagation of light in a low pressure pure gas is spatially coherent. This means that a light beam propagating at a resonant frequency in a low pressure gas generates and amplifies dipoles with equal phases in wave surfaces, increasing their quadratic energy emission. In other directions, there is no coherence of emissions. Superradiance, emitted perpendicular to wave surfaces becomes generally into other directions super-absorption. Huygens's theory is complicated ! 2 -Redshifts in quasar spectra.

2.1-H atoms produce so-called "cosmological redshifts".

Karlsson formula.

The proof of this title results from many equivalent observations of quantized redshifts which lead to H spectrum : for instance superposition of lines of H having different redshifts (Petitjean [START_REF] Petitjean | Le contenu baryonique de l'univers révélé par les raies d'absorption dans le spectre des quasars[END_REF]). Burbidge [START_REF] Burbidge | The distribution of redshifts in quasi-stellar objects, N-systems and some radio and compact galaxies[END_REF] and Karlsson [START_REF] Karlsson | Possible Discretization of Quasar Redshifts[END_REF][START_REF] Karlsson | Quasar redshifts and nearby galaxies[END_REF] studied redshifts (relative frequency shifts) of light emitted by stars. Karlsson's formula shows that redshifts are often quantized, with values given by formula Z(n)= nK, where n is an integer of serie 3, 4, 6, ..., and K is Karlsson's constant 0.062. This result for n=3 or 4 is verified using Rydberg's formula:

Z(β,α) = (ν β-ν α )/ν α = [(1-1/3 2 )-(1-1/2 2 )]/(1-1/2 2 ) ] ~ 5/27 ~ 0.1852 ~ 3*0.0617; Z(γ,α) = (ν γ-ν α )/ν α = [(1-1/4 2 )-(1-1/2 2 )]/(1-1/2 2 ) ] = 1/4 = 0,25 = 4*0.0625.

The simplest explanation of these quantized redshift is: A redshift stops, (so that sharp gas lines are visibly absorbed) if an absorbed line reaches Lyman alpha frequency: Thus redshift requires Lyman alpha absorption. However, spectra show that redshift restarts slowly as long as it is energy at Lyman beta frequency, absorption of which produces a weak redshift.

-Gas absorption spectra in quasars.

To compute the frequencies of lines absorbed while redshifts stop in a gas of mainly H atoms: -i) Compute the spectrum of all molecules able to absorb light.

-ii) Search the lowest absorbed frequency ν σ larger than ν α . It may be absorbed by any molecule. If it fails, exit.

-iii) Multiply all spectrum frequencies by ν α /ν σ .

-iv) return to ii)

In this first approximation, frequencies are multiplied by a constant, as in a Doppler redshift. To obtain a better result, it is necessary to multiply the result by a dispersion function, close to 1.

Mechanism of redshifts.

Emissions of light in collisionless gas.

Free molecules in a very low pressure gas cannot emit light without an external excitation as a resonant electromagnetic field, or an accidental collision. Thus, molecules excited in high atmosphere by solar wind of electrons and protons, are only d-excited when an accidental collision between two molecules initiates a light emission, then an enormous amplification which produces a polar flare, a polar aurora. This is also observed during degassing of a vacuum bell by high voltage electrical currents.

Coherent light-gas interactions.

A lot of experiments show coherent exchanges of energy between laser beams, for instance to exchange energy between ordinary and extraordinary rays in crystals, or in an optical fiber. These exchanges are qualified "Coherent Raman".

Star light is white, perfectly temporally incoherent: studied by traditional spectrometers, it contains all light frequencies without phases correlations.

Interstellar gas is often made of collisionless H atoms, temperature of which being roughly between ~3500K and ~40000K. H atoms, mainly in their ground state, are pumped by Lyman alpha absorption to a 2P 1/2 or 2P 3/2 state.

Interactions of light with very low pressure H atoms are spatially coherent (Einstein 1917). In an excited gas, the atoms located on a wave surface of an exciting ray emit energy by a Huygens process, amplifying possibly the previously existing ray. Thus, exciting ray is amplified without disorders produced by an emission by collision.

A quantum q at any frequency of a stellar light beam in optical domain may excite an atom in a 2P state, subtracting by Raman interaction, from its energy q, a quantum hν at a resonance frequency in 2P (ν=10.9 GHz for fine structure transition 2P 1/2 →2P 3/2 , or ν=1,06 GHz for Lamb shift 2P 1/2 →2S 1/2 ). Shifted frequency q/h -ν may amplify a frequency of the ray because all frequencies exist in the stellar ray of white light. Energy absorbed by atoms is transferred to background radiation, so that entropy increases.

Variation of frequency of quantum is of the order of 1 GHz, like the hash noise of thermal light. Thus, interaction with a single atom cannot be observed. But a lot of interactions reduce visibly all spectral frequencies. This reduction has a chromatic dispersion because the probability of interaction depends on frequency of quantum q.

Hubble law.

Hubble law does not evaluate distances of sources, but the column density of atomic hydrogen in 2P states. Hot stars generate much UV radiation able to pump H atoms to 2P state. Thus usual Hubble law increases distances. Spiral galaxies become less distant, smaller, stable without dark matter.

Hot stars inflate bubbles in maps of galaxies … 3. Quasar spectra.

Propagation of light in atomic hydrogen.

Lyman alpha absorption by H atoms described in section 2, generates H 2P atoms able to redshift spectral frequencies of stars.

As in a polar aurora, an accidental emission initialized, for instance, by an accidental collision of atoms, produces a superradiant flare observable close to the quasar. Superradiance results from a coupling of dipoles by incident light, increasing quadratic energy emission. In most directions, incoherence of these interactions generates a super matter-absorption which, for instance, led to use pink rubies in laser sources, allowing a propagation of a fraction of exciting light to axis of ruby cylinder, thus a laser emission in this axis. This relaxation process of flare emissions is stable enough to absorb strongly observed quasar light at equidistant distances in spectrum generated by the redshifts: It is a "Lyman forest". This process stops when redshift pushes a previously absorbed line to alpha frequency (section 2).

Propagation of light close to quasars.

Only a few words: is not in topic of this paper, but optical coherence seems useful.

The interactions of light in relatively dense regions are variable: For instance, in "noisy quasars", it seems that a system similar to an Heaviside region is source of electromagnetic emissions.

In very dense regions of star, hydrogen atoms seem bound by pressure into crystal like media, allowing coherent exchanges of energy between X rays as inside the Sun …

Strömgren's regions : Overview of matter-light interactions around stars and planets.

Stars emit "stellar winds" mainly made of protons and electrons. Expansion of this gas cools it, generating excited hydrogen atoms on a "Strömgren's sphere".

Free protons and electrons do not interact with light. Thus, light does not interact with matter inside the sphere, except close to planets.

In a "Strömgren's shell", outside Strömgren's sphere, density of gas, thus spectroscopic absorption parameters are decreasing functions of distance r to center of star. Thus, rays have the largest interaction with excited gas if they are tangent to Strömgren's sphere: they show limbs of sphere which may be so weak that they are detected by amplification of light of background stars, or so strong that an efficient competition of modes splits the circles into sets of bright points. Spectroscopy of these modes is very difficult because there are many types of atoms often very excited ... The most powerful beautiful, varying observed Strömgren's shell is in SNR1987A: almost all star light energy is transferred to ring. Planets or smaller matter ate energy in an equatorial plane, reducing the radius of Strömgren's sphere in this plane, so that the star had three circular limbs.

Conclusion.

The elementary knowledge of spectroscopy of coherent interactions of light with low pressure gas avoids construction of fantastic theories. This paper shows only that there is a great need for work to introduce optical coherence in astrophysics.


P Gasnier
email: pierre.gasnier@cea.fr

M Boucaud

M Gallardo

J Willemin

S Boisseau

A Morel

D Gibus

M Moreau

A 120°C 20G-compliant vibration energy harvester for aeronautic environments

This paper reports the design, fabrication and testing of a piezoelectric energy harvester operating at 90°C and withstanding 120°C and 20G of acceleration. This harvester, along with its dedicated power management circuit, has been designed to supply a 3-channel Acceleration Measurement System (AMS) for the structural health monitoring of an aircraft engine. This aeronautic-compliant bimorph harvester outputs 6.83mW at 1G, up to 246mW at 8G of acceleration and exhibits a maximum Normalized Power Density of 15.3kg.s.m -3 at 90°C.

Introduction

Autonomous wireless sensors nodes operating in harsh environments, especially at high temperatures, are of particular interest for aerospace and aeronautic sectors particularly. Indeed, Structural Health Monitoring (SHM) at various locations of an aircraft engine may help identifying and estimating structural faults or ageing phenomena (e.g. bearings). But some locations on/inside the engine can be very difficult to monitor, either because of their accessibility or because their temperatures are too high for a battery to operate. Particularly at small-scale, vibration energy harvesting has revealed a great innovation potential to supply wireless sensors nodes in such harsh environments. In this work, we use the piezoelectric principle to convert the engine's vibrations into electricity in order to supply a 3channel Acceleration Measurement System (AMS) used to monitor the vibration level of the engine.

The performance of piezoelectric vibration energy harvesters have already been studied as a function of temperature for MEMS and macro scale devices and for various piezoelectric materials [START_REF] Arroyo | High temperature performance of a piezoelectric micro cantilever for vibration energy harvesting[END_REF][START_REF] Kim | Temperature effects on output power of piezoelectric vibration energy harvesters[END_REF] . In this work, we present the design, from a system point of view, of a cm-scale energy harvester and its dedicated power management circuit operating in moderately-harsh environments (<120°C).

Design and fabrication of the harvester and its power management electronics

Vibration energy harvester

Our harvester is based on a piezoelectric bimorph cantilever (figure 1) tuned on a constant engine rotation frequency (≈70000 rpm, 1167Hz). A 2-degree-of-freedom (2-DOF) analytical model was used to design the harvester. It enabled to optimize the dimensions (piezoelectric and substrate thicknesses and lengths) to reach the best global electromechanical coupling while respecting the constraints of our application (resonant frequency, volume, output power, 20G acceleration).

We used Finite Element Methods (FEM) simulation in 3D (COMSOL) on the best geometry to check the validity of our optimization. We made some slight adjustments to tune the resonant frequency to 1167Hz at 90°C and to limit the maximum stress to 10MPa at 20G, i.e. far below the depolarization stress of the piezoelectric material. A tuning screw was added at the end of the beam to easily tune the resonant frequency after the assembly. If the resonant frequency is too high, the screw shifts the center of gravity of the mass to decrease the frequency. A carter surrounds the active part (the beam) to protect the harvester from unexpected shocks which may occur during the installation.

The final prototype was fabricated with an electrical discharge machining (EDM) process and dimensional controls were performed after its fabrication. A photograph of the device is shown in figure 2. A non-conductive epoxy (EPO-TEK 353ND) was used to glue the piezoelectric patches to the substrate and conductive spacers (60µm) enable the electrical contact between these two elements.

The key dimensions of the harvester, its tolerances and the chosen materials are listed in table 1. We performed an identification of the harvester parameters by using optimization methods to get the best match between the harvester admittance (measurements) and its theoretical model [START_REF] Badel | Nonlinear Conditioning Circuits for Piezoelectric Energy Harvesters Nonlinearity in Energy Harvesting Systems[END_REF]. The device exhibits a squared electromechanical coupling coefficient k 2 around 4.1%. Its modified coupling coefficient km 2 is around 4.3% and its mechanical quality factor Qm is around 33.

Power management electronics

A dedicated power management circuit (PMC) has been designed and fabricated (figure 3). This batteryless circuit, uses capacitors as storage elements and a two-path architecture [START_REF] Gasnier | Power conversion and integrated circuit architecture for high voltage piezoelectric energy harvesting 10[END_REF][START_REF] Gasnier | An autonomous piezoelectric energy harvesting IC based on a synchronous multi-shots technique[END_REF] to operate. During the cold start, a "non-optimized path" fills the capacitor Cstart by the mean of a normally-on MOSFET Kd. When Cstart has reached an acceptable voltage value, the harvester is then discharged through an "optimized path", by applying a Unipolar Synchronous Electric Charge Extraction (USECE) technique [START_REF] Brenes | Unipolar synchronized electric charge extraction for piezoelectric energy harvesting Smart[END_REF] which fills the capacitor Cbuff through a Flyback topology. This technique takes advantage of the MOSFET body diode (at the primary) which plays a quasi-similar role to diode half-wave shunt rectifiers. In this way, the piezoelectric element is discharged only once per mechanical period. For device having large km 2 Qm excited at resonance, this strategy yields higher power delivered by the piezoelectric generator compared to the classical SECE. Finally, so as not to overdamp the mechanical system at resonance, our circuit implements a tunable SECE, extensively described in [START_REF] Lefeuvre | Analysis of piezoelectric energy harvesting system with tunable SECE interface Smart[END_REF] : when the piezoelectric voltage reaches a maximum value, the energy stored in the piezoelectric capacitor is not entirely transferred to the primary inductor Lp. This technique is relevant when the factor km 2 Qm is greater than π/4, which is our case (km 2 Qm=1.42). The control parameter β of the tunable SECE technique has been empirically set to about 25%, which means that the piezoelectric element is discharged from its maximum voltage Vmax to β·Vmax.

As depicted in figure 3, the "Power Management" block controls the LDO which supplies the WSN. A "Discharge disable" block may disable the optimized mode when Vbuff reaches a too high value, i.e. when the WSN's consumption becomes lower than the harvested power.

Measurement results and ageing tests of the vibration harvester

Tests were performed in a vibration chamber for various acceleration values at 90°C. As depicted in figure 5, the harvester exhibits the following power performances: 6.8mW@1G, 36.1mW@3G, 70.7mW@5G and 135mW@8G when excited at the engine frequency (1167Hz). The WSN (a 3-channel AMS) which consumes around 40mW, can be powered from 3.5G of acceleration when the aircraft engine is in steady state operation (frotation =1167Hz, T°<90°C). One can notice that the resonant frequency decreases when increasing the base acceleration. It is probably caused by the nonlinear elastic properties of the soft piezoelectric materials used in the harvester [START_REF] Leadenham | Modeling and identification of nonlinear electroelastic and dissipative parameters for PZT-5A and PZT-5H bimorphs: a dynamical systems approach[END_REF].

The output powers at each resonance are 6.83mW@1G, 45.9mW@3G, 112mW@5G and 246mW@8G. It corresponds to a maximum Normalized Power Density (NPD) of 15.3 kg.s.m -3 which is a good result at 90°C and for a highly constrained design (120°C and 20G compliant). The NPD is the ratio Pmax/(A 2 .V), where Pmax is the maximum harvested power, A the input acceleration [m.s -2 ] and V the volume of the beam [m 3 ]. Two ageing tests at 20G were also performed at 90°C and then at 120°C: the harvester was excited for 10 7 cycles (2h) on its first resonant mode. The frequency of this mode at 90°C dropped by 3% after the first ageing, 1% after the second one and stabilized after a third ageing (120°C, 2h). For each acceleration value, the maximum power value is constant from 27°C to 90°C whereas it strongly decreases (-85%) from 90°C to 120°C at resonance (figure 6), due to the reduction of both the piezoelectric coefficients and the mechanical quality factor of the structure. From 90°C to 120°C, the resonant frequency of the harvester drops by around 5.5%.

Operation of the complete autonomous system in real environment

Finally, we validated the operation of the complete system (harvester, PMC, AMS) which was successfully tested on a real engine's bench where acceleration measurements of 3 aeronautic-compliant accelerometers were performed autonomously (figure 7). To the best of our knowledge, this autonomous system is the first one in prior art implementing a high acceleration (20G) and temperature (120°C) compliant piezoelectric harvester tested and validated in real conditions.

Figure 1 .

 1 Figure 1. 3D schematic of the harvester with its dimensions.

Figure 2 .

 2 Figure 2. Photograph of the assembled harvester.

Figure 3 .

 3 Figure 3. Schematic of the power management circuit showing the optimized and non-optimized paths.

Figure 4 .

 4 Figure 4. Photograph of the whole electronic circuit.

Figure 5 .

 5 Figure 5. Electrical power as a function of the input frequency on an optimal resistive load for various acceleration values at 90°C.

Figure 6 .

 6 Figure 6. Electrical power as a function of the input frequency on an optimal resistive load for various acceleration values at 90°C and 120°C.

Table 1 .

 1 Key dimensions, tolerances and materials of the piezoelectric harvester.

	Parameter	Value	Tolerance
	Piezo thickness	1 mm	+/-0.01mm
	Piezo length	30 mm	+/-0.01 mm
	Beam thickness	2.7 mm	+/-0.01 mm
	Beam length	36 mm	+/-0.02 mm
	Beam width	22 mm	+/-0.02 mm
	Mass length	9.5 mm	+/-0.02 mm
	Mass height	5.5 mm	+/-0.02 mm
	Piezo material	NCE51 Noliac (PZT-5)
	Substrate material	XC75 steel


domain: spi phys

text:
Julien Decours

Biel Ortun

Joëlle Bailly

Yves Delrieux

Raphaël Fukari

Frédéric Guntzer

Racer

RACER aero-acoustic propeller design and analysis

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.

I. Introduction

The RACER propellers (Figure 1) correspond to a very specific design since they assume a part of the aircraft propulsion in cruise in addition to the anti-torque function in hover. The propellers are wing tip mounted on a nacelle, very close to the wings and the main rotor and they directly blow the tail unit. Such a complex integration problem has been studied by ONERA with different level of accuracy methods in order to propose a new blade design and to take advantage of all complex aerodynamic interactions.

In the following paper, we will first focus on the propeller blade design methodology used by ONERA to increase the performance while reducing the noise penalty. The second part of this paper will be dedicated to the major aerodynamic interactions comprehension that occurs while the RACER is flying.

II. Propeller design

To meet the wide range of performance objectives from hover to cruise flight conditions, a specific airfoils family has been identified and optimized in order to allow the specific blade designed for the left and right propellers.

A. Airfoils optimization

Specific airfoil family has been designed for the Airbus Helicopters RACER propellers with ONERA in house optimization tools. An airfoil is considered to be the addition of a thickness and a camber laws along the chord and ONERA managed to modify those two laws with the help of Bezier control points. Many airfoils can be generated by this method and their performance quickly evaluated by a simple code considering Euler equations with a boundary layer development. Thus, the Bezier control points defining the airfoil are optimized maximizing the lift over drag ratio of the airfoil for 3 operating conditions, corresponding to a Mach number velocity and lift coefficient. Considering not only one operating condition but 3 allows ensuring high performance for a wide range of Mach numbers and lift coefficients.

This airfoil optimization exercise can be done for several relative thicknesses, but this could lead to relatively different camber laws while varying the relative thickness. Such different camber laws could lead to surface bumps along the blade span. That is the reason why we chose a single airfoil, for example located at 70% of the blade span, to be optimized for a wide range of operating conditions. Then, this optimized airfoil is distributed along the blade span conserving the same camber law and only scaling the thickness law. Each airfoil performance is also evaluated by the mean of 2D CFD simulations with the elsA software co-owned by AIRBUS, SAFRAN and ONERA for a wide range of Mach number and angle of attack (Figure 2).

Finally, 2 airfoil families have been optimized for both left and right propellers, since they assume the antitorque function in hover. Thus, in hover a propeller is generating positive thrust while the other propeller operates in reverse mode. The camber law has been significantly reduced for the airfoil family operating in reverse mode in hover condition.

B. Blade design

Blade design can be done considering the previously described airfoils families. We are dealing with the chord, twist, sweep, dihedral and thickness laws along the blade span. But the aerodynamic blade surface has to be designed with respect to the internal structural and manufacturing constraints. Within the frame of the Clean Sky 2 NACOR project, the preliminary design of the propeller blade relies on natural composite material, that is to say wooden propeller. Even if aerodynamic and acoustic considerations would lead to a thin blade, internal structural and manufacturing constraints were high and lead to a thick blade, especially in the root region, in order to avoid any flutter and guaranty the wooden blade to support the aerodynamic and inertia loads.

Nevertheless, ONERA respect those structural constraints and was able to define many blade laws. A blade performance can be quickly evaluated by the in house code PUMA, based on the lifting line theory with an unsteady wake method. The ONERA in-house unsteady free-wake plus lifting-line code PUMA uses the previously computed airfoil lookup tables and is able to take into account a flow field perturbation such as a wing tip vortex. In addition, the PUMA code gives access to physical quantities along the blade span in the aerodynamic reference frame, for example lift and drag coefficients. This allows the design to be adapted in order to present the best induced efficiency with the airfoils operating at their best lift-to-drag ratio.

L/D C L

A PUMA simulation result could be also used as an entry for acoustic analysis. The loads along the lifting line can be distributed in chord with different model in order to obtain a blade surface pressure coefficient distribution. This surface pressure coefficient is then analyzed with the ONERA in house KIM code based on integral methods (Kirchhoff or Ffowcs-Williams Hawkings) to produce noise levels and spectra.

When a blade candidate is identified with good performance in both hover and cruise, a blade surface geometry can be drawn and grided in order to perform 3D CFD simulations. Many blade shapes have been evaluated by the mean of CFD in cruise and hover (forward and reverse thrust) with a pitch variation, thus the Chimera technic was very helpful in saving time (Figure 3). CFD blade surface pressure distribution can also be used for a detailed acoustic analysis with the KIM code.

Finally, this design procedure allows about 2% power consumption reduction in cruise, more than 5% in hover and up to 3dBA in hover. It also allows showing the loss of efficiency due to the blade root thickness in addition to vortical structures coming from a blade root flow separation. A blade structure allowing a thickness reduction could provide more efficiency and less noise emissions.

C. Blade optimization

In parallel of the iterative designs method, an optimization method has been used in order to evaluate the possibility of improving the design based on PUMA multi-objective optimization. The PUMA code has been used for this optimization process since a simulation restitution time is far smaller than for a CFD simulation. Two main optimization platforms have been used in the framework of this study, DAKOTA and OTOOL.

DAKOTA is a commercial software, which contains among others the CONMIN gradient-based optimizer used for the Cruise configuration. This optimizer is based on the feasible directions method. The main advantage of this method is its low CPU time consumption, but the eventuality to reach a local optimum point is non negligible especially when the objective function is multi-modal. The CMA-ES evolutionary optimizer has been used for the Hover configuration. This optimizer is supposed to reach the global optimum, but a large number of evaluations is required (2500 for example).

OTOOL, is an ONERA in house optimization platform, which contains, among others, the KORRIGAN Kriging surrogate model (developed at ONERA), coupled with a conventional genetic algorithm optimizer.

The first step of this methodology consists in building the Design of Experiment (DoE). The research domain limited by the lower and upper values of the design variables is discretized using the Latin Hypercube Sampling (LHS) methodology, which allows a homogeneous sampling of the domain. Low Fidelity (LF) computations are performed with the PUMA code, on 128 sampler points. 126 points are correctly converged for the Cruise configuration, and 58 points for the (rather severe) Hover configuration.

The second step consists in the enrichment of the data base to update and improve the accuracy of the Kriging model. Two steps are performed, first to determine the minimum point of the model (thanks to a classical genetic algorithm), and then evaluate the real value of the objective function of this point by a PUMA simulation. Secondly, to determine the maximum Expected Improvement (EI) point, thanks to an Efficient Global Optimization (EGO) methodology, and then evaluate the real value of the objective function of this point by a PUMA simulation.

The research and the evaluation of the minimum point and the maximum EI point are performed 100 times twice (which is a choice of the user). Two objectives have been defined for this study, first to determine the design that will provide the best performance in Cruise and in Hover separately. Secondly to validate the optimization procedure using the Kriging surrogate models in Cruise and in Hover. Those models have been used in the framework of the multi-objective optimization procedure in a second part of this study, to define the Pareto front between the two flight configurations.

It has been concluded that the Kriging surrogate model for the Cruise configuration is expected to be as accurate as the PUMA code. But, for the Hover configuration, due to the difficulty to obtain PUMA converged results, some lack of accuracy can occur for the corresponding Kriging surrogate model. Nevertheless, these two surrogate models will be used in the multi-point optimization procedure, in order to replace the PUMA evaluations. More details will be given in the final paper on the multi-objective optimization procedure and results obtained.

III. Aerodynamic interactions analysis

Installation effects are fundamental to the aerodynamic and acoustic performance of the installed propellers of the RACER configuration. Many effects have been deeply investigated within the frame of the Clean Sky 2 project NACOR.

For example, in cruise conditions, the total power consumed by the two propellers varies by more than 10% depending on whether they rotate counter or co-with respect to the wing tip vortex (Figure 4). This trend has been confirmed by 3D CFD simulations.

In forward flight, the main rotor can increase the efficiency of the propellers under certain circumstances. This phenomenon has been investigated with PUMA free-wake simulations. Many simulations allow showing that propeller thrust is linked to the variations in axial velocity induced by the main rotor wake. Axial velocity is slowed beneath the main rotor wake and increased above it; decreases in axial velocity increase propeller thrust. Tangential velocities induced by the main rotor also affect propeller thrust; tangential velocity tends to have an outboard direction.

Trailing edge to propeller distance effect has also been investigated. The objective of this investigation was to quantify the noise mitigation that can be obtained by increasing the spacing between the wing trailing edge and the propeller. The interaction between the propeller and the viscous wake of the wing is a source of noise. The further aft the propeller is placed, the more the viscous wake of the wing is dissipated, thus reducing the strength of this source of noise.

The aerodynamic interaction of the main rotor, the propellers and the tail unit of the aircraft has also been deeply investigated. The propellers were modelled by body-force source terms through an elsA-PUMA coupling and are trimmed in thrust according to the specifications given by Airbus Helicopters (Figure 5). Detailed acoustic analysis of these simulations have been done and main results will be presented in the final paper (Figure 6).

Finally, wind tunnel test have been performed by Airbus Helicopters, modeling the propeller with and without wings in order to quantify precisely these interactions and evaluate the impact on acoustic measurements. This configuration has been simulated by the mean of 3D CFD in order to make precise comparisons with the wind tunnel test results (Figure 5). More details will be given in the final paper.

IV. Conclusion

The final paper will first present in detail the methodology used within the frame of the Clean Sky 2 project NACOR for blade design and aero-acoustic optimization. This design will lead to important improvements in terms of performance but also in terms of acoustic emissions for both cruise and hover flight conditions. A second part will detail complex aerodynamic interactions studied with different methods developed by ONERA. The final proposed design will takes advantage of these interactions. A far better understanding of the complex physical phenomenon happening while the RACER is flying will also be presented thanks to numerous simulations performed with different levels of accuracy.

V. Acknowledgments

These activities were carried out jointly with the DLR as part of a call for tender won in the ITD AIRFRAME of the CleanSky2 platform. The DLR was in charge of the aerodynamic performance of the wing, and of the horizontal stabilizers, as the acoustic analysis is done jointly with ONERA. The particularity of the project was to work on each component individually, taking into account the many aerodynamic interactions between wing/propeller, propeller wing, rotor/propeller/wing /tail parts, requiring numerous and frequent exchanges between the partners.

ISOLATED PROPELLER PROPELLER + MAINROTOR

Figure 1 :

 1 Figure 1: Airbus Helicopters RACER.

Figure 2 :

 2 Figure 2 : CFD 2D lift-to-drag ratio for relative thickness from 4% to 12% airfoils at Mach number = 0.4.

Figure 3 :

 3 Figure 3 : Example of blade shapes evaluated by the mean of 3D CFD (left), vertical structures coming from a blade root flow separation (right).

Figure 4 :Figure 5 :

 45 Figure 4 : Propeller rotation direction effect compared to the wing tip vortex in cruise by PUMA simulations (left) and 3D CFD simulations (right).

Figure 6 :

 6 Figure 6 : Example of acoustic analysis, directivity of the isolated propeller (left) and in the presence of the main rotor (right) depending on the flight configuration. Sphere centered on the propeller, in the near field.

Research Engineer, Aerodynamics, Aeroelasticity, Acoustics Department.

Engineer, Airbus Helicopters