Marwane Rezzouki
email: marwane.rezzouki@ims-bordeaux.fr

Guillaume Ferr
email: guillaume.ferre@ims-bordeaux.fr

Performance of Differential Chirp Spread Spectrum in Underwater Acoustic Channel

Keywords: Connected fishing nets, differential chirp spread spectrum, DCSS system, low acoustic noise

In recent years, connecting fishing nets underwater has received much interest in carrying out fishing activities efficiently and protecting the ocean from pollution, especially from ghost fishing. In this paper, we propose an implementation of a system based on the differential chirp spread spectrum (DCSS) technique to connect fishing nets underwater while preserving the biotope from acoustic pollution. This technique is based on differential encoding, making it more robust to Doppler shift. Besides, it exploits the orthogonality of chirps to deal with inter-symbol interference and improve spectral efficiency. Furthermore, an estimation of the channel and equalization processes are used to eliminate the multipath effect which is very present in underwater acoustic (UWA) channels. The performance of our system is evaluated in terms of bit error rate (BER) in a lake trial.

I. INTRODUCTION

The fishery sector plays a central role in food security in many countries. According to the food and agriculture organization, fish consumption has doubled since the 1960s and as of 2019 capture production accounted for 92.5 million tonnes [START_REF]/fao anuario. estadísticas de pesca y acuicultura[END_REF]. This huge production is a result of multiple factors as population growth and the need for resources rich in proteins and vitamins.

The introduction of underwater acoustic communication over the last decades enables diverse applications in civil and military sectors such as connecting autonomous underwater vehicles (AUV), deploying underwater sensor networks (USNs), and navigation [START_REF] Rowan | The role of digital technologies in supporting and improving fishery and aquaculture across the supply chainquo vadis?[END_REF]. In the fishery area, communication would help fishers to conduct efficiently their job. Indeed, by ensuring data link communication the angler could track the areas of fishing by measuring parameters such as salinity and temperature. Moreover, communication could prevent fishers in case of danger by detecting swells and alerting them. However, using a large network in the ocean based on acoustic waves with high power will pollute acoustically the environment and participate in the migration of species as mentioned in [START_REF] Rice | Variation of ocean acoustic environments along the western north atlantic coast: A case study in context of the right whale migration route[END_REF]. In this context, we focused on a particular technique of communication which is based on linear frequency modulation (chirps) to communicate in underwater acoustic (UWA) channels. The proposed technique is called differential chirp spread spectrum (DCSS) and it offers the ability to deploy a less disruptive network for marine animals. By sacrificing spectral efficiency, it will be possible to communicate at low values of signal-to-noise ratio (SNR). Therefore, the transmitted signals in the medium will be almost inaudible for marine animals.

Due to the physical properties of underwater acoustic channels, the transmitted signal may undergo a major degradation. The main characteristics of an UWA channel are multipath propagation because of the reflection of the acoustic wave on the surface and seafloor, severe Doppler shift, and spread, and finally high time variability.

In order to face the aforementioned characteristics of the channel, [START_REF] Rezzouki | Differential chirp spread spectrum to perform acoustic long range underwater localization and communication[END_REF] added to the conventional chirp spread spectrum (CSS) technique processes to make the communication robust such as the differential encoding process to reduce the Doppler shift effect. Besides, channel estimation and equalization are used to eliminate the multipath effect. In this paper, we focus on the implementation of the DCSS system presented in [START_REF] Rezzouki | Differential chirp spread spectrum to perform acoustic long range underwater localization and communication[END_REF] and its performance in a lake trial. The rest of this paper is organized as follows, in section II we introduce the architecture of DCSS and explain each part of it. In section III we introduce the hardware used to test the DCSS system. Section IV is dedicated to measurement results in lake trial and discussion. Finally, a conclusion is provided.

II. DIFFERENTIAL CHIRP SPREAD SPECTRUM A. DCSS technique

At the transmitter, the binary frame is divided into several sub-sequences from the most significant bit, each of the length SF bits to constitute a symbol. Then, the summation of two consecutive symbols is performed to generate the symbols to transmit as mentioned in equation [START_REF]/fao anuario. estadísticas de pesca y acuicultura[END_REF].

S p = m p + S p-1 mod M , p ≥ 1 (1)
where m p ∈ 0, M -1 are the symbols obtained from the binary information, M = 2 SF is the possible number of constellations, SF is the spreading factor and S 0 is fixed at 0 to initiate the process. The association of the symbol S p to a chirp signal defined at time symbol T and within a bandwidth B is done through a temporal cyclic shift to the raw chirp

x ref (n) sampled at T s = 1 B . x ref (n) = e j2π( 1 2M n 2 -1 2 n) , n ∈ 0, M -1 (2)
Consequently, the modulated chirp discrete phase of the p th symbol to transmit at time pT can be expressed as: At the receiver, the transmitted signal is transformed by the impulse response of the UWA channel, and an additive white Gaussian noise is introduced to the signal. However, to understand the demodulation process, we consider only one path signal and we suppose that the received has perfect time and frequency synchronization. Thus, the expression of the discrete received signal at sampling time T s is:

ϕ p (n) =        2π 1 2M n 2 + ( Sp M -1 2 )n for n ∈ 0, M -S p -1 2π 1 2M n 2 + ( Sp M -3 2 )n for n ∈ M -S p , M -1
y(n) = Ns k=1 e jϕp(nT s-(k-1)T ) 1 [(k-1)T,kT ] (n) (3)
with N s is the number of transmitted symbols and 1 x (n) is the indicator function. The first step in demodulation consists in multiplying each symbol period of the received signal by the conjugate of the raw chirp x ref (n). Then, perform the fast Fourier transform (FFT) at every symbol time. Thus, the obtained FFT for each the p th symbol can be expressed as follows:

Y p [k] = 1 √ M M -1 n=0 y p (nT s )x ref (n)e -j2π nk M (4)
where f (n) is the conjugate of the function f (n) y p (nT s ) = y(nT s + (p -1)T ) is the complex envelope of the p th transmitted symbol. Consequently, in a non-coherent receiver, a symbol Sp is obtained by: Sp = argmax k∈ 0,M -1

(|Y p (k)|) (5)
Finally, the original symbol mp can be obtained from the estimated symbol Sp through differentiation using the following equation:

mp = Sp -Sp-1 mod M , p ≥ 1 (6)
The main advantage of using differential encoding is to eliminate the constant frequency amount that could occur because of the Doppler effect or oscillators through differentiation in the frequency domain.

B. Transmitted signal

C. Received signal

The proposed receiver is composed of several processes organized as follows:

1) Detection: Initially, the recorded signal is sub-sampled at time T s and divided into several blocs, each of length M points that correspond to a symbol time. Then, each bloc is multiplied by the conjugate of the raw chirp x ref (nT s ), followed by an FFT operation. Finally, the argmax of the first peak of the FFT will coarsely indicate the first chirp in the preamble.

2) Doppler Estimation: The estimation of the Doppler scale consists of calculating the rate of received chirps. More precisely, a part of the long chirp in the preamble is used in the Fractional Fourier Transform (Frft) domain to estimate the new rate. According to [START_REF] Zhao | Parameter estimation of wideband underwater acoustic multipath channels based on fractional fourier transform[END_REF], the optimal order of Frft corresponds to the rate of the chirp. Using the formula of the new rate and the expression of order, the Doppler scale can be simplified to:

∆ = -cot(p opt π 2 ) B Tc N T 2 s -1 (7)
where N is number of samples, T c is the chirp duration, and p opt is the optimal order.

3) Doppler Compensation: The compensation is made by re-sampling the recorded signal at T s 1+ ∆ using a linear interpolation technique as mentioned in [START_REF] Li | Mobile underwater acoustic communication based on passive time reversal[END_REF].

4) Synchronization: In this process, the raw up and down chirps in the preamble are used to estimate and compensate the amounts of desynchronization in both time and frequency domains [START_REF] Ben Temim | A novel approach to enhance the robustness of lora-like phy layer to synchronization errors[END_REF].

Coarse synchronization: This part consists in multiplying each chirp by its conjugate and calculating the argmax of the FFT as mentioned in equation [START_REF] Zhao | Parameter estimation of wideband underwater acoustic multipath channels based on fractional fourier transform[END_REF]. As raw chirp is expected to be at zero, then the obtained values are the results of the desynchronization amounts. Therefore, combining the argmax of up chirps with argmax of down chirps leads to the expression of frequency and temporal synchronization.

Fine synchronization: At this point the received signal is resampled at rythm 1 2B and only up chirps are used to estimate the fraction part of desynchronization. The fractional part of carrier frequency offset is obtained by de-chirping the signal and calculating the phase. Whereas, the time amount is obtained as an average of argmax of FFT.

5) Channel Estimation:

The channel estimation algorithm used is proposed in [START_REF] De Almeida | Alternative chirp spread spectrum techniques for lpwans[END_REF]. It is based on the received up chirps of the preamble and the raw up chirps in the preamble. Indeed, the raw chirp x ref (n) , n ∈ 0, M -1 is used to constitute the circulant matrix x c (M, M ) and the received chirps are used to calculate the average vector y Avg (1, M ). Thus, the temporal estimation of the channel ĥ can be expressed as:

ĥ = x H c y Avg x H c x c (8)
6) Channel Equalization: The payload is rectified in the frequency domain using the minimum means square error (MMSE) equalizer [START_REF] Huang | Study of frequency domain equalization for chirp spread spectrum systems[END_REF]. Firstly, the signal is divided into several blocs, each of length M depending on SF used to generate symbols. Then the FFT is applied, followed by the multiplication of MMSE function transfer to each bloc. After that, inverse Fast Fourier transform (IFFT) is performed on each bloc. Finally, the estimation of symbols is carried out by applying the following operations of dechirping, calculating the argmax of FFT, and differentiation decoding as mentioned in part II-A.

III. HARDWARE USED TO TEST DCSS COMMUNICATION

To conduct experiments in UWA channels, we developed the system shown in Fig. 2. This system is divided into two parts:

• A transmitter composed of a signal generator, a power amplifier, and a transducer. • A receiver composed of a hydrophone, a voltage preamplifier, and a data acquisition board. The signal generator is based on STM32F746 microcontroller that generates analog signal from stored sampled frame (at a sampling frequency of 100 kHz) as wave files in the micro SD. To drive the transducer BII-7506 we used PAM-8610 module that's amplify 1 V rms output of the board into 15 V rms . Thus, considering the transmitting voltage response of the transducer 157.6 dB 1 µP a/V @1m, the acoustic power of the transmitter is 181.1 dB re 1 µP a @1m. After crossing the channel, the signal is received by means of the hydrophone AS-1 (-208 dBV re 1 µP a). Then, the signal is amplified with a gain of 50 dB using an Low-noise broadband hydrophone amplifier PA-4. Finally, the signal is recorded using USB-6364 National instrument board connected to a laptop. The sampling frequency is programmable and limited to 500 kHz and the resolution of samples is 16 bits. The experiments are conducted in Bordeaux "Bassin a Flot" lake (see Fig. 3) at different ranges. The maximum distance between the transmitter and the receiver was 140 m, and it is chosen after establishing an acoustic link budget adapted to a lake environment and the characterization of the hardware in terms of the power of the transmitter and the sensitivity of the receiver. In addition, The depth of the lake was about 16 m, and both the transmitter and the receiver were fixed at a depth of 4 m. The main parameters used to generate the signal are listed in the table below.

B. Impulse response of the channel

The estimation of the underwater acoustic channel is made using a set of hyperbolic frequency modulation (HFM) signals defined within a bandwidth of 5 kHz at a carrier frequency of 18 kHz, using a spreading factor of 9 and a time length of 120 ms. This technique is proposed in [START_REF] Schmidt | Measurement of impulse response of shallow water communication channel by correlation method[END_REF] and it consists in applying cross-correlation between the raw chirp and the received signal to obtain the variability of the channel and the power delay profile. As depicted in Fig. 4 the channel has three paths that vary slightly over time. As the most significant paths are located in an interval of time no longer than 4 ms, we can consider that the channel is sparse and its delay spread is less than the used symbol duration, which respects the condition of frequency selectivity of the channel.

C. Result of communication

The performance of the DCSS system is presented as bit error rate (BER) for different payload configurations at different ranges. The breakdown of each configuration is presented in Table II. As we can see the communication works perfectly when the distance between the transmitter and receiver was respectively 20 m and 60 m. However, at Consequently, the frequency equalization and demodulation processes are strongly impacted. Therefore, it is possible to enhance the result of this experiment through high acoustic power or a hydrophone with good receiving sensitivity.

V. CONCLUSION

In this work, we present the implementation of the DCSS system and its performance in a lake trial. The proposed DCSS receiver faces the severe characteristics of the UWA channel due to Doppler estimation and compensation in the fractional Fourier transform domain. Besides, channel estimation and MMSE equalization reduce significantly the multipath effect that could occur in such channels. These processes have low complexity and can be implemented in the FPGA board to ensure real-time communication. The experiments are conducted using a limited power amplifier. Driving the transducer with a better amplifier or having a hydrophone with a good receiving sensitivity would make long-range communication possible. Finally, the DCSS technique offers a good data link in the ocean environment because of its ability to demodulate the signal at low values of SNR which would preserve the biotop from acoustic noise. Further experiments will be carried out in diverse environments using different configurations to perform the DCSS system.

Fig. 1 :

 1 Fig. 1: Spectrogram of the transmitted signal in baseband

Fig. 1

 1 Fig. 1 illustrates the spectrogram of the transmitted frame. The signal is composed of a long chirp used to estimate the Doppler scale, a silence time greater than the delay spread

Fig. 2 :

 2 Fig. 2: Hardware of DCSS system

Fig. 3 :

 3 Fig. 3: Setup of the experiment

Fig. 4 :

 4 Fig. 4: Underwater channel characteristics

TABLE I :

 I Parameters of the transmitted signal

	Parameter	Value
	Carrier frequency	18 kHz
	Sampling frequency	100 kHz
	Bandwidth	2.5 kHz and 5 kHz
	Preamble: Long chirp duration	1 s
	Preamble: Number of up chirps	8
	Preamble: Number of down chirps	2
	payload: Double SF	5/6 and 6/7
	Number of symbols	30

TABLE II :

 II Bit error rate

	Range	Preamble Spreading factor Payload	Bandwidth	Bitrate	BER
	20 m	6 6	5 and 6 5 and 6	5 kHz 2.5 kHz	572 bps 286 bps	0 0
		7	6 and 7	5 kHz	338 bps	0
		7	6 and 7	2.5 kHz	169 bps	0
	60 m	6 6	5 and 6 5 and 6	5 kHz 2.5 kHz	572 bps 286 bps	0 0
		7	6 and 7	5 kHz	338 bps	0
		7	6 and 7	2.5 kHz	169 bps	2.56 10 -2
	140 m	6 6	5 and 6 5 and 6	5 kHz 2.5 kHz	572 bps 286 bps	4.16 10 -2 3.33 10 -2
		7	6 and 7	5 kHz	338 bps	1.17 10 -1
		7	6 and 7	2.5 kHz	169 bps	9.87 10 -2
	a distance of 140 m, the obtained values of BER are low
	because the estimated channel presents a high level of noise.


Mazdak Afshar Bakshloo

Safia Yahiaoui

Matthieu Bourderioux

Regis Daniel

Manuela Pastoriza-Gallego

John J Kasianowicz

Abdelghani Oukhaled

Discrimination between Alpha-Synuclein Protein Variants with a Single Nanometer-Scale Pore

Keywords: synuclein, nanopores, Parkinson's disease, protein identification, post-translational modifications 47

Alpha-synuclein is one of several key factors in the regulation of nerve activity. It is striking that single-or multiplepoint mutations in the 140-amino-acid-long protein can change its structure, which leads to the protein's aggregation and fibril formation (which is associated with several neurodegenerative diseases, e.g., Parkinson's disease). We recently demonstrated that a single nanometer-scale pore can identify proteins based on its ability to discriminate between protease-generated polypeptide fragments. We show here that a variation of this method can readily discriminate between the wild-type alpha synuclein, a known deleterious point mutation of the glutamic acid at position 46 replaced with a lysine (E46K), and a post-translational modification (i.e., tyrosine Y39 nitration). KEYWORDS: alpha-

■ INTRODUCTION

Alpha-synuclein (αS) is a protein located primarily in neurons, [1][START_REF] Maroteaux | The Rat Brain Synucleins; Family of Proteins Transiently Associated with Neuronal Membrane[END_REF][START_REF] Taguchi | Brain Region-Dependent Differential Expression of Alpha-Synuclein[END_REF] where it aids in the regulation of synaptic vesicle trafficking and neurotransmitter release. [START_REF] Bendor | The Function of α-Synuclein[END_REF][START_REF] Huang | Soluble α-synuclein facilitates priming and fusion by releasing Ca2+ from thapsigargin-sensitive Ca2+ pool in PC12 cells[END_REF] In dysfunctional states, it is associated with several neurodegenerative diseases (synucleinopathies), including Parkinson's disease (PD), [START_REF] Lee | Mechanisms of Parkinson's Disease Linked to Pathological α-Synuclein: New Targets for Drug Discovery[END_REF][START_REF] Stefanis | α-Synuclein in Parkinson's Disease[END_REF] multiple system atrophy, [START_REF] Graham | Orthostatic Hypotension and Nicotine Sensitivity in a Case of Multiple System Atrophy[END_REF][START_REF] Stefanova | Multiple System Atrophy: An Update[END_REF][START_REF] Wenning | Recent Developments in Multiple System Atrophy[END_REF][START_REF] Laurens | Multiple System Atrophy -State of the Art[END_REF] dementia with Lewy bodies (DLB), [START_REF] Spillantini | α-Synuclein in Lewy bodies[END_REF][START_REF] Kim | Alpha-Synuclein Biology in Lewy Body Diseases[END_REF][START_REF] Simon | α-Synucleinmediated neurodegeneration in Dementia with Lewy bodies: the pathobiology of a paradox[END_REF][START_REF] Marotta | Alpha-Synuclein from Patient Lewy Bodies Exhibits Distinct Pathological Activity That Can Be Propagated in Vitro[END_REF][START_REF] Ayers | Different α-synuclein prion strains cause dementia with Lewy bodies and multiple system atrophy[END_REF] and others. 17,[START_REF] Goedert | The Synucleinopathies: Twenty Years On[END_REF] In these cases, αS, which is intrinsically disordered, [START_REF] Esteban-Martín | Identification of Fibril-Like Tertiary Contacts in Soluble Monomeric α-Synuclein[END_REF] typically accumulates and aggregates into fibril structures [START_REF] Vilar | The fold of α-synuclein fibrils[END_REF][START_REF] Cremades | Direct Observation of the Interconversion of Normal and Toxic Forms of α-Synuclein[END_REF][START_REF] Lorenzen | The N-terminus of α-synuclein is essential for both monomeric and oligomeric interactions with membranes[END_REF][23][START_REF] Guerrero-Ferreira | New Insights on the Structure of Alpha-Synuclein Fibrils Using Cryo-Electron Microscopy[END_REF] in Lewy bodies. [START_REF] Taguchi | Brain Region-Dependent Differential Expression of Alpha-Synuclein[END_REF] It is the latter form that induces cytotoxic effects, which are assumed to be responsible, in part, for the symptoms noted above. Some evidence suggests that αS can interact with relatively short amyloidogenic proteins (e.g., Aβ40 and Aβ42). [START_REF] Mandal | Interaction between Aβ Peptide and α Synuclein: Molecular Mechanisms in Overlapping Pathology of Alzheimer's and Parkinson's in Dementia with Lewy Body Disease[END_REF][START_REF] Chen | Amyloid Beta: Structure, Biology and Structure-Based Therapeutic Development[END_REF] Alpha synuclein's sequence is highly conserved in many species, [START_REF] Uéda | Molecular Cloning of CDNA Encoding an Unrecognized Component of Amyloid in Alzheimer Disease[END_REF][START_REF] Touchman | Human and Mouse α-Synuclein Genes: Comparative Genomic Sequence Analysis and Identification of a Novel Gene Regulatory Element[END_REF][START_REF] Gitler | α-Synuclein is part of a diverse and highly conserved interaction network that includes PARK9 and manganese toxicity[END_REF] and in humans it is composed of 140 amino acids. [START_REF] Xia | Synthetic Heparan Sulfate Standards and Machine Learning Facilitate the Development of Solid-State Nanopore Analysis[END_REF][START_REF] Uversky | Amino acid determinants of αsynuclein aggregation: putting together pieces of the puzzle[END_REF] A rather striking finding is that a point mutation of the guanosine to adenosine at position 209 (G209A) in the SNCA gene encoding for αS, which causes an A53T amino acid change in the N-terminal repeat segment of the protein, is associated with PD. [START_REF] Polymeropoulos | Mutation in the α-Synuclein Gene Identified in Families with Parkinson's Disease[END_REF][START_REF] Ki | The Ala53Thr mutation in the α-synuclein gene in a Korean family with Parkinson disease[END_REF][START_REF] Puschmann | A Swedish family with de novo α-synuclein A53T mutation: Evidence for early cortical dysfunction[END_REF] After the initial study, it was shown that additional missense mutations of αS, including A53E, [START_REF] Pasanen | A novel α-synuclein mutation A53E associated with atypical multiple system atrophy and Parkinson's disease-type pathology[END_REF] A30P, [START_REF] Kruger | AlaSOPro mutation in the gene encoding α-synuclein in Parkinson's disease[END_REF] and E46K, [START_REF] Zarranz | The new mutation, E46K, of α-synuclein causes parkinson and 644 Lewy body dementia: New α-Synuclein Gene Mutation[END_REF] were linked to PD as well.

We previously demonstrated that an ion channel formed by aerolysin (AeL) can discriminate between different proteins based on how their protease-cleaved fragments partition into the channel's nanometer-scale pore and thereby reduce its ionic conductance. 38,39 For example, trypsin-induced frag-fragments are -1 and 0 for the αS variants (αS_wt) 13 and (αS_E46K) 12 , respectively.

Because protein-based nanopores can differentiate between slightly different molecular species, [43][44][45][46][47][48][49][50][51][52][53][54][55][START_REF] Fuller | Real-Time Single-Molecule Electronic DNA Sequencing by Synthesis Using Polymer-Tagged Nucleotides on a Nanopore Array[END_REF][START_REF] Piguet | High Temperature Extends the Range of Size Discrimination of Nonionic Polymers by a Biological Nanopore[END_REF][START_REF] Talarimoghari | Size-Dependent Interaction of a 3-Arm Star Poly(Ethylene Glycol) with Two Biological Nanopores[END_REF][START_REF] Manrao | Nucleotide Discrimination with DNA Immobilized in the MspA Nanopore[END_REF][START_REF] Wang | Determining the Physical Properties of Molecules with Nanometer-Scale Pores[END_REF] including proteins, 38,39,[START_REF] Lucas | Protein Identification by Nanopore Peptide Profiling[END_REF] we used the nanometer-scale pore formed by the protein Aeromonas hydrophila AeL [START_REF] Parker | Structure of the Aeromonas toxin proaerolysin in its water-soluble and membrane-channel states[END_REF][START_REF] Degiacomi | Molecular Assembly of the Aerolysin Pore Reveals a Swirling Membrane-Insertion Mechanism[END_REF] in an attempt to discriminate between the two αS polypeptides in Table 2.

In the protein nanopore-based analytical method, 47 an ion channel is formed in a planar lipid bilayer membrane, and the target species are typically added to one of the two aqueous electrolyte solutions bathing the membrane. Individual molecules that enter the pore transiently reduce the ionic current due to volume exclusion and, in certain instances to the reversible binding of mobile ions to the molecules. 49 The degree by which the single channel current is reduced, and the distribution of residence (or dwell) times for the molecules in the pore provide information about the target molecules' physical and chemical properties. 49 The relatively long dwell times of single polypeptides in the pore are a consequence of the interaction between the two.

We first show how enzymatically cleaved fragments of wildtype αS (αS_wt) and the E46K single-point mutant version f1 (αS_E46K) interact with a single AeL nanopore. Figure 1A illustrates schematically that the LysN-induced cleavage of Scheme 1. Full Length Human α-Synuclein Sequence a a The sequence of 140 amino acids in αS, with the first proteolytically cleaved fragment of interest (highlighted in yellow) and the singlepoint amino acid mutation studied here (αS_E46K, emphasized in red). The protease cleavage fragment in which the point mutation E46K occurs is highlighted in yellow, and the two amino acids are emphasized in red colored text. The three 9-amino-acid-long fragments highlighted in light orange are discussed later in this study. The altered amino acid in the point mutant is highlighted in red colored text. In Figure 1C, there are fewer distinct peaks than one might 129 expect based on the predicted action of the protease on the 130 target protein. There are several hypothetical reasons that 131 might account for that observation. First, proteolytic digestions 132 are generally not 100% efficient in either the complete 133 processing of the target protein or in the production of every 134 polypeptide fragment. Second, it is possible that aggregation of 135 either the target protein or some of the fragments could occur 136 even though the experimental conditions (i.e., a relatively short 137 digestion time of 3 h, the pH was basic at pH 10, and no 138 stirring was applied) are not conducive to that process 139 (aggregated fragments would likely not enter the pore). 140 Third, some of the predicted polypeptide fragments may not 141 enter the pore due to an excessively high entropic cost (i.e., their secondary structures may limit the partitioning of some polypeptides into the highly confined geometry of the nanopore). We are currently investigating this issue experimentally.

The green and red Gaussian fits to the single peaks in the I b / I 0 histogram data (Figures 1C andS1) are located at I b /I 0 = 0.34 ± 0.01 and 0.38 ± 0.01 for the samples derived from fulllength (αS_wt) and (αS_E46K), respectively. Because the only polypeptide fragments that would contain the amino acids that are different in the two full-length proteins are (αS_wt) 13 and (αS_E46K) 12 (Tables 1 and2), it follows that those particular fragments are the likely cause of those two different peaks.

To test that hypothesis, we studied the effects of synthetic polypeptides (αS_wt) 13 and (αS_E46K) 12 individually on the f2 AeL nanopore. Figure 2A (top) shows that there is one peak in the I b /I 0 histogram for (αS_wt) 13 located at 0.34 ± 0.01. The results obtained with (αS_E46K) 12 (Figure 2A, center) show that there are two peaks in its I b /I 0 histogram: a predominant one located at 0.38 ± 0.01 and a secondary peak at 0.51 ± 0.01. Note that the locations of the single peak for (αS_wt) 13 and the more probable peak for (αS_E46K) 12 are situated at the same I b /I 0 values as the Gaussian fit peaks from LysNcleaved full-length (αS_wt) and (αS_E46K), respectively (Figure 1C). Note that the ionic current blockade dwell time (Figure 2B, center) and standard deviation (Figure 2C, center) vs the blockade depth (I b /I 0 ) event plots provide two additional means to discriminate between these two synthetic polypeptides. Lastly, the bottom panels in Figure 2A-C show that the effects of (αS_wt) 13 and (αS_E46K) 12 on the AeL nanopore current are independent of each other, which suggests that the two different polypeptides do not interact significantly with each other in the bulk aqueous phase. The histograms shown in Figure 2, which were produced with equimolar concentrations of (αS_wt) 13 and(αS_E46K) 12 polypeptides, have qualitatively similar blockade event rates. These results suggest that even though these two fragments are only slightly different in sequence, mass, and length (Table 2), the AeL nanopore can easily discriminate between them and thus between the LysN-cleaved versions of the full-length native and (αS_E46K) point mutant proteins (Figure 1).

Although the E46K point mutation correlates with some cases of PD and DLB, not all the patients affected by synucleinopathies present with it. Other reported neurodegenerative cases are associated with certain PTMs of αS. Thus, these PTMs, which include phosphorylation of S129, [START_REF] Miranda | Posttranslational Modifications of Blood-Derived Alpha-Synuclein as Biochemical Markers for Parkinson's Disease[END_REF][START_REF] Levine | α-Synuclein O-GlcNAcylation alters aggregation and toxicity, revealing certain residues as potential inhibitors of Parkinson's disease[END_REF] nitration, [START_REF] Wang | Phosphorylated α-Synuclein in Parkinson's Disease[END_REF] O-GlcNAcylation, [START_REF] Anderson | Phosphorylation of Ser-129 Is the Dominant Pathological Modification of α-Synuclein in Familial and Sporadic Lewy Body Disease[END_REF] sumoylation, or ubiquitination, 66 are also used as biomarkers for PD and DLB.

LysN proteolysis of full-length αS_wt would theoretically produce three unique 9-amino-acid-long polypeptides (Table 1), which we label here as (KE wt), (KG wt), and (Y39 wt). The physical properties of those fragments and those of a Y39 t3 nitration PTM of the latter one (Y39 NO 2 ) are listed in Table t3 3. Given that nanopores have proven useful for discriminating between different size RNA oligonucleotides, 45 synthetic polymers, 46,49 polypeptides, [START_REF] Piguet | Identification of Single Amino Acid Differences in Uniformly Charged Homopolymeric Peptides with Aerolysin Nanopore[END_REF][START_REF] Ouldali | Electrical Recognition of the Twenty Proteinogenic Amino Acids Using an Aerolysin Nanopore[END_REF] and characterizing PTMs in proteins, [START_REF] Rosen | Single-Molecule Site-Specific Detection of Protein Phosphorylation with a Nanopore[END_REF][71][72][73] we tested whether the AeL nanopore can discriminate between these three identical-length wild-type protein fragments and a PTM nitration version. Another relevant biomarker is a phosphorylation on serine 235 residue S129. However, the length of the peptide fragment 236 generated by LysN that includes S129 (Table 1) is longer than 237 the pore's length and therefore not within the detectable and 238 discernible length range for polypeptide discrimination with 239 the AeL nanopore. [START_REF] Piguet | Identification of Single Amino Acid Differences in Uniformly Charged Homopolymeric Peptides with Aerolysin Nanopore[END_REF][START_REF] Ouldali | Electrical Recognition of the Twenty Proteinogenic Amino Acids Using an Aerolysin Nanopore[END_REF] We overcame that limitation by 45,46,51,52,54,[START_REF] Fuller | Real-Time Single-Molecule Electronic DNA Sequencing by Synthesis Using Polymer-Tagged Nucleotides on a Nanopore Array[END_REF] simultaneous 274 detection of several different proteins, 78 discriminating 275 between polymers based on their size, 46,49,53,[START_REF] Piguet | High Temperature Extends the Range of Size Discrimination of Nonionic Polymers by a Biological Nanopore[END_REF]79 and 276 identifying several different proteins from their protease-277 induced fragments. 38,39,[START_REF] Lucas | Protein Identification by Nanopore Peptide Profiling[END_REF] The work described herein repre-278 sents a significant extension of the latter method. Specifically, 279 we used two different proteases (LysN and AspN) and the AeL Table 3. Physical Properties of the Three 9-Amino-Acid-Long Polypeptides Predicted from LysN Cleavage of the Full-Length αS_wt Protein (from Table 1) and of the PTM Y39 Nitration Version a a The polypeptide abbreviations, which are specific to this study, are color-coded to aid interpretation of the electrophysiology data illustrated in Figure 3. We note that not all of the blockade events shown in Figure 1 are necessarily due to polypeptide translocation. Specifically, some of the events might instead be caused by polypeptides 1 and3) and the PTM (Y39) nitration of one of the polymers (Table 3). The plots are histograms of the relative ionic current blockade value, I b /I 0 (left), dwell time-current blockade value event plots (center), and ionic current standard deviation-current blockade value event plots (right) for a successive addition of (A) (KE wt), (B) (KE wt) + (KG wt), (C) (KE wt) + (KG wt) + (Y39 wt), and (D) (KE wt) + (KG wt) + (Y39 wt) + (Y39 NO 2 ). For clarity, the results that correspond to each polypeptide variant are indicated with arrows matching their respective color-code. The data shown is from a single experiment but was highly reproducible for n > 3 replicates. E 294 that enter and leave the pore from the sample side. Also, there 295 are two known processes that can drive polypeptides into and 296 possibly through the aerolysin channel. These include 297 electrophoresis (e.g., as was the case for single-stranded DNA 298 transport through the αHL nanopore) 45 and electroosmosis, 299 which can drive polypeptides with any net charge (positive, 300 negative, or neutral) into and possibly through the pore. 39 301 This method for the label-free identification of mutations 302 and PTMs, which should work for many other proteins, could 303 be a useful tool for rapid diagnoses at the point of care in 304 medical facilities if it is integrated into a low-cost, miniaturized, 305 high-throughput analytical platform. However, there are several 306 technological hurdles and levels of systems integration (e.g., of microfluidics-based protein separation, 80,81 etc.) that will need to be resolved or employed. The 14-amino-acid-long variant, highlighted in yellow, and a phosphorylated variant of it (Table 5) were analyzed with a single AeL nanopore (Figure 4). Table 5. Two Variants (Wild-Type and S129 Phosphorylation) of the Predicted 14-Amino-Acid-Long AspN-Cleaved Fragment from the Full-Length αS_wt Protein KEGVVHGVATVAE, KGVVHGVATVAE, KEGVVAAAE, KQGVAEAAG, KEGVYLVGS, KEGVY(NO 2 )LVGS, DNEAYEMP-SEEGYQ, and DNEAYEMPS(pho)EEGYQ polypeptides (purity ≥ 98%) were purchased from ProteoGenix (Schiltigheim, France), and recombinant αS_wt and αS_E46K (purity ≥ 95%) were purchased from rPeptide (Watkinsville, GA, USA).

Protein Digestion. Recombinant αS_wt and αS_E46K were dissolved in a 0.1 M glycine, 16 mM NaOH buffer at pH 10. The proteins were digested by LysN in a 1:50 ratio (protein/LysN, mass/ mass) for 3 h at 37 °C. LysN cleavage was stopped by quenching the sample using 0.1% TFA. The subsequent fragmented proteins were filtered using a 10 kDa cut-off membrane at 15,000 x g 4 °C for 1 h to withdraw undigested, aggregated proteins, and native LysN protease. The fragmented samples were stored at -20 °C until their use.

Aerolysin Production. AeL is a pore-forming toxin from A. hydrophila produced as a precursor protein, proaerolysin (ProAeL), which forms soluble dimers. Recombinant wild-type ProAeL was produced in Escherichia coli BL21 using the pET22b-PA vector. ProAeL is produced after IPTG induction and localizes into the bacteria's periplasm. The periplasmic fraction containing soluble ProAeL dimers was extracted using an osmotic shock. Because the recombinant protein is C-terminal His-tagged, ProAeL was further purified by affinity chromatography using Ni-Sepharose MiniSpin columns, and elution was made by adding imidazole. The recombinant ProAeL purity (about 99%) was determined by SDSpolyacrylamide gel electrophoresis and Coomassie blue staining. The ProAeL concentration was estimated by optical absorbance at 280 nm. ProAeL (3 μg) was activated by 0.25 units of trypsin-agarose in 25 mM HEPES pH 7.5 for 30 min at 25 °C, as previously reported. 82

In Silico Modeling of Protein Digestion. While it is possible to predict which polypeptide fragments will be produced by LysN by inspection of the protein's sequence, we used an in silico fragmentation model of the αS protein that was calculated using the expasy PeptideCutter software (https://web.expasy.org/peptide_ cutter/). The codes of αS_wt (P37840) and αS_E46K (P37840, VAR_022703) proteins are available in a free Uniprot database (https://www.uniprot.org). Nanopore Recording. A vertical lipid bilayer electrophysiology setup (Warner Instruments, Hamden, CT, USA) was used for all the experiments with AeL. The lipid bilayer was formed by painting and spontaneous thinning a film of diphytanoyl-phosphocholine, DPhPC (Avanti Polar Lipids, Alabaster, AL, USA), in decane (Merck, Darmstadt, Germany) at 10 mg/mL over a 150 μm diameter aperture on a Teflon support separating the cis-and trans-compartments. The aqueous solutions on both sides of the membrane contained 1 mL of 2.5 M KCl 1 M CaCl 2 , 25 mM HEPES at pH 7.5 (Merck, Darmstadt, Germany). Two matched Ag/AgCl electrodes (Alfa Aesar, Ward Hill, MA, USA) were used to apply +80 mV or +50 mV across the membrane and measure the ionic current. The cis-compartment is defined as the virtual ground. After forming the lipid bilayer, activated aerolysin was added to the cis-compartment at ≈ 50 ng/mL final concentration. Once a single AeL nanopore formed, a fragmented αS protein (αS_wt or αS_E46K digested by LysN) or an αS peptide sample was added to the cis-compartment. The final concentration of fragmented protein is 3.5 μM each of αS_wt and αS_E46K. The final concentration of (KE wt), (KG wt), (Y39 wt), and (Y39 NO2) polypeptides is 5 μM and for (S129_wt)AspN, (S129_pho)AspN is 30 μM.

Single-channel current recordings were performed using an Axopatch 200B patch-clamp amplifier (Molecular Devices, Sunnyvale, CA, USA) in the whole-cell mode with a CV-203BU headstage. The signal was filtered using the internal 4-pole Bessel filter at a cut-off frequency of 5 kHz. The data were digitized at 100 kHz and current digital resolution of 30.5 fA/bit state, using a DigiData 1550B A/Dconverter (Molecular Devices) controlled by Clampex 10.2 software (Molecular Devices). The solution temperature was held at 22.0 ± 0.5 °C for all the experiments with a Peltier device controlled by a bipolar

Figure 1 .

 1 Figure 1. Nanopore-based discrimination of protease fragments of wild-type α-synuclein (αS_wt) and a point mutant version of the protein (αS_E46K). (A) Cleavage of either full length αS_wt or αS_E46K by protease LysN produces well-defined polypeptide fragments. Polypeptide fragment samples of either αS_wt or αS_E46K are added to the electrolyte solution surrounding one side (cis) of an AeL nanopore. A transmembrane voltage V drives fragments into the pore and thereby reduces the pore's ionic conductance. (B) Protease-induced fragments of αS_wt or αS_E46K cause short-lived reductions in the ionic current (typical single blockade events for each of the samples are shown); I 0 , I b , σ b , and t b are the mean open current, the mean blocked current, the standard deviation of the blocked current, and dwell time for each event, respectively. (C) Histogram of the I b /I 0 values for the cleaved samples of αS_wt (top) or αS_E46K (bottom). The colored peaks correspond to a Gaussian fit to those segments of the data. All data were recorded at T = 22 °C, [KCl] = 2.5 M, [CaCl 2 ] = 1 M, [HEPES] = 25 mM, pH 7.5, and the transmembrane potential was V = +80 mV. The data shown here are for a single experiment, but the results were highly reproducible (n = 3).

Figure 2 .

 2 Figure 2. Nanopore-based discrimination of the synthetic short polypeptides (αS_wt) 13 and (αS_E46K) 12 (Table 2). (A) Single channel ionic current blockade value histograms, (B) dwell time (t b ) vs current blockade value (I b /I 0 ) event plots, and (C) blocked ionic current standard deviation event plots for (αS_wt) 13 only (top); (αS_E46K) 12 only (middle); or an equimolar mixture of both (αS_wt) 13 and (αS_E46K) 12 polypeptides in the same sample (bottom). Gaussian fits to the predominant single peaks for the (αS_wt) 13 (green) or (αS_E46K) 12 (red) samples are shown. All data were recorded at T = 22 °C, [KCl] = 2.5 M, [CaCl 2 ] = 1 M, [HEPES] = 25 mM, pH 7.5, and the transmembrane potential was V = +80 mV. These data were obtained in single experiments but were highly reproducible in n > 3 replicates.

f3Figure

  Figure 3A-C shows the AeL nanopore electrophysiology data for the three 9-amino-acid-long polypeptide fragments predicted from LysN proteolysis of wild-type αS protein, each produce characteristic and differentiable distributions. The polypeptide fragment (KE wt) produces events characterized with one peak at I b /I 0 = 0.48 ± 0.01 in the relative current blockade value histogram (Figure 3A left). Adding the (KG wt) polypeptide to the sample causes a new peak to appear at I b /I 0 = 0.57 ± 0.02 (Figure 3B left). The subsequent addition of the third fragment type (Y39 wt) caused a broadening of the peak caused by (KE wt) due to an additional peak at I b /I 0 = 0.49 ± 0.02 (Figure 3C left). Finally, adding the Y39 nitration PTM polypeptide (Y39 NO 2 ) caused another distinct peak at I b /I 0 = 0.42 ± 0.02 (Figure 3D left). While the I b /I 0 histogram data allow the discrimination between all four of these polypeptides, their corresponding dwell time (t b ) event plots (Figure 3A-D, center) provide additional discriminatory capability. The latter plots show that the first two polypeptide variants, (KE wt) and (KG wt), have similar dwell time distributions with mean residence times ⟨t b ⟩ ∼ 0.3 and 0.5 ms, respectively (Figure 3B center). Both the third polypeptide variant (Y39 wt) and its Y39 nitration PTM version (Y39 NO2) have mean dwell times that, at ⟨t b ⟩ ≈ 5.4 and 7.9 ms, respectively, are about an order of magnitude longer than those for the other two polypeptides. Moreover, note that the clustered t b event plots for each of the four variants are further distinguishable because their distributions cluster at different I b /I 0 values. Moreover, the standard deviation (σ b ) event plots (Figure 3A to 3D right) for each

  234

  240 changing the protease to cleave the relevant fragment into 241 one that is sufficiently short. Specifically, we used another 242 enzyme, AspN peptidyl-Asp metalloendopeptidase from the 243 Gram-negative bacteria Pseudomonas fragi, 74-77 which cleaves 244 at the amino terminus side of aspartic acid residues. This 245 process should produce the polypeptide fragments listed in 246 t4

247

  Figure 4 illustrates the AeL nanopore electrophysiology data

D

  280 nanopore to discriminate between wild-type α-Synuclein and 281 three different versions of it (i.e., a single-point mutation E46K 282 and two different PTMs, Y39 nitration and S129 phosphor-283 ylation) that are implicated in several neurodegenerative 284 diseases, including Parkinson's and DLB. The method shown 285 here offers the possibility to detect various forms of proteins 286 with a single nanopore through its versatility. This is made possible because of multiple selective proteases allow the precise cleavage of proteins into detectable and discriminable polypeptide fragments of the desired length bearing the mutation(s) or MTP(s) of interest.

Figure 3 .

 3 Figure 3. AeL nanopore-based discrimination of the three 9-amino-acid-long polypeptides predicted from LysN proteolysis of full-length αS_wt (Tables1 and 3) and the PTM (Y39) nitration of one of the polymers (Table3). The plots are histograms of the relative ionic current blockade value, I b /I 0 (left), dwell time-current blockade value event plots (center), and ionic current standard deviation-current blockade value event plots (right) for a successive addition of (A) (KE wt), (B) (KE wt) + (KG wt), (C) (KE wt) + (KG wt) + (Y39 wt), and (D) (KE wt) + (KG wt) + (Y39 wt) + (Y39 NO 2 ). For clarity, the results that correspond to each polypeptide variant are indicated with arrows matching their respective color-code. The data shown is from a single experiment but was highly reproducible for n > 3 replicates.

  His SpinTrap mini columns were purchased from GE Healthcare Life Science (Chicago, IL, USA), IPTG (R0392), HEPES buffer (BP310) from Thermo Fisher Scientific (Waltham, MA, USA), and Vivaspin 10 kDa cut-off filters (VS0101) from Sartorius (Gottingen, Germany). LysN protease (L101) was purchased from ImmunoPrecise Antibodies (Victoria, Canada), trypsin-agarose (T1763), imidazole (104716), potassium chloride (P5405), calcium chloride (223506), trifluoroacetic acid (TFA, T6508), and decane (457116) were purchased from Merck (Darmstadt, Germany). Diphytanoyl-phosphocholine (DPhPC,

Figure 4 .

 4 Figure 4. AeL nanopore-based discrimination of two 14-amino-acid-long polypeptides (αS_wt)AspN 14 and its phosphorylated version (αS_S129)AspN 14 _pho. The single channel ionic current blockade value histograms (left), dwell time (t b ) vs current blockade value (I b /I 0 ) event plots (center), and blocked ionic current standard deviation event plots (right) for (A) (S129_wt)AspN only, (B) (S129_pho)AspN only, or (C) a mixture of both (S129_wt)AspN and (S129_pho)AspN polypeptides in the same sample. For clarity, the results that correspond to each polypeptide variant are indicated with arrows matching their respective color-codes. All data were recorded at T = 22 °C, [KCl] = 2.5 M, [CaCl 2 ] = 1 M, [HEPES] = 25 mM, pH 7.5, and the transmembrane potential was V = +50 mV. The data shown are for single experiments but were highly reproducible in replicate (n > 3) experiments.

  Data analysis was performed using Igor Pro 6.12A 392 software (WaveMetrics, OR, USA) with in-house routines. The 393 approach relies on a statistical analysis of the properties of the analyte-394 induced current blockades, involving at least several hundred (more 395 typically thousands) events. The detection of each individual current 396 blockade in a nanopore current vs time recording is based on a single 397 current-threshold (Th) method. A blockade event is detected when 398 the current magnitude becomes smaller than Th, until it returns to a 399 value greater than Th. The beginning of the blockade is defined as the 400 first point of current increase after having monotonically decreased 401 below Th, and its end as the last point of current decrease before 402 monotonically increasing above Th. This defines the range of points 403 used to compute the characteristic quantities of the blockade, such as 404 dwell time t b , mean residual current value I b , and the standard 405 deviation σ b of the residual current. Here, Th = I 0 -5σ 0 , where I 0 and 406 σ 0 are the mean value and standard deviation of a Gaussian fit of the 407 open-pore current distribution, respectively. 408 Histograms of the relative mean residual current I b /I 0 are 409 constructed with a bin width of 0.002. I b /I 0 values constitute the 410 main criterion to discriminate populations of blockades induced by 411 enzymatically produced polypeptide fragments from the αS protein 412 variants. I b /I 0 population j is defined as the subset of blockades whose 413 I b /I 0 values fall in the range ± σ j are 414 respectively the mean value and standard deviation of a Gaussian fit of 415 the distribution of I b /I 0 values in the corresponding histogram peak. 416 This range includes 95% of the Gaussian distribution.

  operating at 355 nm. Spectra were acquired using 429 FlexControl software (version 3.4 Bruker). The reflectron mode 430 was used with a mass range of m/z 100 to 600. The fixed instrument 431 voltages were ion source 1, 20

Table 1 .

 1 LysN Cleavage Products of Wild-Type αS (αS_wt) a

	a

Table 2 .

 2 Properties of the Two α-Synuclein Fragments Studied Here a

	a

Table 4 .

 4

Table 4 .

 4 Seven Polypeptide Fragments Predicted from AspN Proteolysis of Full-Length Wild-Type αS Protein a

	a

  .00 kV; ion source 2, 17.85 kV; lens,

	7.90 kV; reflector 1, 20.80 kV; and reflector 2, 10.80 kV. All mass	432
	spectra were processed using FlexAnalysis software (version 3.4,	433
	Bruker). Pulsed ion extraction was set to 170 ns. Matrix suppression	434
	cut off mass was set to 500 m/z. Mass calibration was performed using	435
	peptide calibration standard from the Bruker Starter Kit (P/N	436
	8208241).	437
	MALDI Sample Preparation. The 2,5-dihydroxybenzoic acid	438
	(DHB) matrix was prepared at 20 mg/mL in 30% acetonitrile (v/v)	439
	in water with 0.1% trifluoroacetic acid (TFA). Polypeptides were	440
	diluted to a working concentration of 1 μM in 30% acetonitrile (v/v)	441
	in water with 0.1% TFA as well. Samples were mixed 1:1 with DHB	442
	matrix prior to spotting 1 μL on an MTP anchorchip 384 target (P/N	443
	8280790) and allowed to air dry at room temperature.	444
	■ ASSOCIATED CONTENT * sı Supporting Information	445 446

447

The Supporting Information is available free of charge at 448 https://pubs.acs.org/doi/10.1021/acschemneuro.3c00164. 449 Discrimination between αS_wt and αS_E46K proteins; 450 reproducibility of αS_wt protein fragmentation and 451 (αS_wt) 13 identification; reproducibility of αS_E46K 452 protein fragmentation and (αS_E46K) 12 identification;


Stéphane Février

Stéphane Nachar

Lionel Mathelin

Frédéric Giordano

Bérengère Podvin

An overview of aircraft vibration environment prediction using machine learning

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Prediction of aircraft vibration environment using machine learning

  Stéphane Nachar 3 , Frédéric Giordano 4 This work is made possible through funding from Dassault Aviation. • Studying the vibration environment of an aircraft is fundamental to ensure the on-board equipment robustness with respect to vibrations up to 2000 Hz • Challenge: being predictive with the currently available models is a difficult task in the frequency band of interest • Proposed approach: to develop data-driven predictive models, based on flight test data and enhanced by physical models Context • Develop new insights of the data: better understand the vibration environment to improve specifications • Local model: predict the vibration environment at one point of the aircraft depending on the flight parameters • Global model: predict the vibration environment at any point of the aircraft (equipment & structure) Thesis Objectives 1 Université Paris-Saclay, CNRS, Laboratoire interdisciplinaire des sciences du numérique, 91405, Orsay, France 2 Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C, 91190, Gif-sur-Yvette, France 3 Dassault Aviation, Direction Générale Technique, 78, quai Marcel-Dassault, 92552 Saint-Cloud Cedex 300, France 4 Dassault Aviation, Direction des Essais en Vol, Base Aérienne 125, ZI le Tubé, 13800 Istres, France Kinematic lines prediction • Objective: predict engines kinematic lines, transpose ground test data to flight • Methods: gaussian process, physical transposition model • Results: 10% error with noise estimation • Applications: troubleshooting, unbalanced monitoring RMS prediction for a specific accelerometer, along the engine % rpm (left), reconstruction of a kinematic line amplitude (right). Data transformation • Objective: handle the high sample rate temporal data • Methods: Flight phases identification, Power Spectral Density (PSD), Root Mean Square (RMS) frequency bands compression, order analysis • Results: data takes up 0,01% of its original size Data transformations from the temporal domain. Structural propagation • Objective: predict vibrations environment at any point of the aircraft for a given source • Idea: propagation path identification • Methods: FE model + test data hybridization, graph signal processing techniques • Preliminary results: learned connections (graphs) • Future work: extension to new aircrafts (transfer learning) Empirical graph learned from test data (left), kinematic lines attenuation through the structure (right).

  broadband response generated from a high variety of sources, without separating them • Methods: multivariate multi-output ensemble model • Results: 1% (random split) / 10% (extrapolation split) error • Applications : anomaly detection, flight envelope extension RMS prediction for a specific accelerometer, projection along the dynamic pressure (left), reconstruction of a predicted spectrum (right).

Acknowledgments

Measurements from an accelerometer close to an equipment are used to characterize the maximum vibrational levels it needs to withstand.