Mohamed Kharrat
email: mohamed.kharrat@femto-st.fr

Emmanuel Ramasso

Vincent Placet

L Boubakar

A signal processing approach for enhanced Acoustic Emission data analysis in high activity systems: application to Organic Matrix Composites

Keywords: Continuous AE signals, CFRP, Quasi-static tests, Wavelet denoising, Hit detection, Pattern recognition

A signal processing approach for enhanced Acoustic

Emission data analysis in high activity systems: application to Organic Matrix Composites

Introduction

Carbon Fiber Reinforced Plastics (CFRP) materials are increasingly used in aeronautical and automotive industries as well as in civil engineering thanks to their high material properties [START_REF] Wu | Acoustic emission detection and position identification of transverse cracks in carbon fiber reinforced plastic laminates by using a novel optical fiber ultrasonic sensing system[END_REF][START_REF] Xu | An acoustic-optical fiber NDE technique for interfacial debonding detection in FRP retrofitted structures[END_REF][START_REF] Silversides | Acoustic emission monitoring of interlaminar delamination onset in carbon fibre composites[END_REF]. Since the integrity of CFRP structures needs to be regularly assessed, the Acoustic Emission (AE) technique is widely used to detect and localize eventual damages [START_REF] Berthelot | Acoustic emission in carbon fibre composites[END_REF][START_REF] Unnthorsson | Acoustic emission based fatigue failure criterion for CFRP[END_REF][START_REF] Sause | Simulation of acoustic emission in planar carbon fiber reinforced plastic specimens[END_REF][START_REF] Silversides | Acoustic emission monitoring of interlaminar delamination onset in carbon fibre composites[END_REF]. AE is a non-destructive method able to ensure in-situ monitoring of the structure through a network of distributed sensors, and can be used to detect damages at a very early stage well before the structure becomes completely failed [START_REF] Grosse | Acoustic emission testing[END_REF]. When the structure is subjected to mechanical, thermal or chemical solicitations, a stress field is generated in the material. As a consequence of the repetition of these solicitations, the material degrades. The appearance of defects leads to the creation of elastic ultrasonic waves that propagate through the material. This wave propagation involves surface vibrations, which are measurable using appropriate sensors. AE consists hence in a transient elastic energy release in materials when microstructural changes occur. It is dependent on some basic deformation and damage mechanisms. In CFRP composites, major damage mechanisms are delamination, matrix cracking, debonding, fiber cracking, and fiber pull-out [START_REF] Gay | Matériaux composites[END_REF].

Three types of AE transients can be distinguished: bursts, continuous and mixed [START_REF] Scruby | An introduction to acoustic emission[END_REF][START_REF] Holroyd | The Acoustic Emission & Ultrasonic Monitoring Handbook, Machine & systems condition monitoring series[END_REF]. Bursts are generated by defects according to the damage mechanisms and have shorter durations than the other types of transients. Continuous AE transients are created when multiple signals emitted from different emission sources overlap in such a way that the amplitude do not fall below the threshold level. The original transients are often hardly recovered and assigned to their emission sources. The background noise and rubbing in the structure are the main sources of continuous emission. Relevant AE information might be buried by noise preventing the identification of particular damages. Mixed AE transients combine bursts and continuous signals. They can be provoked by damage growth and accumulation and are often superimposed with ambient noise and rubbing [START_REF] Harris | Fatigue and accumulation of damage in reinforced plastics[END_REF][START_REF] Mouritz | Non-destructive evaluation of damage accumulation, Fatigue in Composites[END_REF]. This latter type of AE transients is frequently encountered in CFRP structures under complex loading, where the material can be subjected to various solicitations simultaneously (multi-axial stresses, frictions between the clamping jaws and the specimen...) [START_REF] Harris | Fatigue in composites: science and technology of the fatigue response of fibre-reinforced plastics[END_REF]. A high AE activity can be encountered hence, especially when the material is solicited at a high loading rate as well as when its geometry is complex. On one hand, a high loading rate is produced particularly when the cycling frequency is high. Some experimental tests have demonstrated that the AE-hit-rate increases not only with the total number of load cycles but also with the cycling frequency [START_REF] Hahn | An algorithm for life time prediction of fatigue loaded CFRPstructures derived from the rate of acoustic emission[END_REF]. For highest rates, transients emitted from different emission sources can be superimposed. On the other hand, the inhomogeneity of such a material (fibers, matrices, multiple plies...) engenders anisotropy in the wave velocities. The wave reflections and attenuation (dispersion, geometric spreading...) are also added to the complexity. Complications include steering of the direction of the group velocity caused by the anisotropy of the material, wave attenuation due to damping by the matrix and wave scattering engendered by the fibers [START_REF] Lowe | Properties of guided waves in composite plates, and implications for NDE[END_REF].

Under in-service conditions, the background noise is sometimes so important that it cannot be neglected. Several sources of perturbation can be the cause. In this study, the noise generated by the hydraulic system of mechanical testing machines is assimilated to a source of perturbation in real operating conditions. The hydraulic fluid is increasingly hot in such machines when the duration of test is long. Irregular flow characteristics and pressure waves propagate through the fluid. A lot of fluidborne noise can be so generated leading to force fluctuations. These result in a vibration, known as structureborne noise, transmitted through the structure [START_REF] Corporation | Noise Control in Hydraulic Systems[END_REF]. The AE signals can be affected by this noise when it hides them partially or, in many cases, completely. When the level of noise is permanently exceeding the AE detection threshold, which is the case in continuous emission, the AE system is obliged to terminate the hit after a predefined maximum duration. This latter is configured in the AE system in order to avoid recording long signals.

As the threshold is permanently exceeded in such a situation, the AE signal is entirely recorded without a correct hit separation. The consequent AE features can be so affected and the footprint of the noise is not negligible. Most of the commercial parameter-based AE systems employ the conventional threshold-based technique for hits detection and determination. The AE features are calculated without an efficient consideration of noise variations that can mislead the interpretation of real AE events happening in the material. The AE systems also employ predefined band-pass filters in order to avoid the impact of external perturbations. However, if the noise is generated at frequencies that are comprised within the frequency band of the filter, it cannot be suppressed. Thus, the conventional threshold-based technique could not be suitable when dealing with continuous emission, without a further signal processing.

The approach proposed in this study is based on denoising the recorded AE signals prior to the hits determination. The Discrete Wavelet Transform (DWT) is one of the powerful methods that has been widely employed for signal denoising, which has been useful for improving the signal-to-noise ratio much better than using signal filtering, as well as for signal processing to detect multiple defect signatures [START_REF] Lin | Feature extraction based on morlet wavelet and its application for mechanical fault diagnosis[END_REF][START_REF] Song | Wavelet based noise suppression technique and its application to ultrasonic flaw detection[END_REF][START_REF] Wang | Enhancement of signal denoising and multiple fault signatures detecting in rotating machinery using dual-tree complex wavelet transform[END_REF]. The DWT is based on the Wavelet Transform (WT) theory [START_REF] Taha | Wavelet transform for structural health monitoring: a compendium of uses and features[END_REF][START_REF] Baleanu | Advances in wavelet theory and their applications in engineering, physics and technology[END_REF], which provides relevant information about non-stationary signals in the time-frequency domain. The WT has been used in many studies related to the Structural Health Monitoring (SHM) field [START_REF] Abbate | Application of wavelet transform signal processor to ultrasound[END_REF][START_REF] Hou | Wavelet-based approach for structural damage detection[END_REF][START_REF] Kim | Damage detection of structures by wavelet analysis[END_REF][START_REF] Marec | Damage characterization of polymer-based composite materials: Multivariable analysis and wavelet transform for clustering acoustic emission data[END_REF][START_REF] Chen | Fault feature extraction of gearbox by using overcomplete rational dilation discrete wavelet transform on signals measured from vibration sensors[END_REF][START_REF] Kharrat | Pipeline inspection using a torsional guided-waves inspection system. Part 1: Defect identification[END_REF]. Some other studies have reported on the use of the WT on AE signals for a denoising purpose [START_REF] Grosse | Signal conditioning in acoustic emission analysis using wavelets[END_REF][START_REF] Feng | Discrete wavelet-based thresholding study on acoustic emission signals to detect bearing defect on a rotating machine[END_REF][START_REF] Chiementin | Effect of the denoising on acoustic emission signals[END_REF][START_REF] Satour | Acoustic emission signal denoising to improve damage analysis in glass fibre-reinforced composites[END_REF].

This work proposes a signal processing approach for the purpose of conditioning AE signals issued from continuous emission caused by ambient noise and high AE-hit-rate. The efficiency of the proposed approach is evaluated on experimental AE signals obtained from PLBs performed on CFRP specimens in a noisy environment with different levels, and from a quasi-static test at a high speed of solicitation under a high noise level. The improvement in the AE data analysis by the proposed approach is emphasized.

Description of the AE signal processing approach

Figure 1 describes the proposed approach as implemented using a Matlab code. The entire AE signal is postprocessed through several steps. It is either handled one shot if it is small in size, or partitioned into equal time-segments when its size is large. Massive data signals can be encountered at a high sampling rate with a long acquisition duration. Signals are then denoised using the DWT with appropriate denoising parameters to enhance the signals quality. The conventional process of hits determination and AE features extraction is thereafter performed. The final step is the data clustering, which involves classifying the AE hits into groups (clusters) representing the AE sources.

Signal Denoising (Wavelet Transform)

Hit Determination

Feature Extraction

Signal Segmentation

Continuous emission

Wavelet

Decomposition

Level N Thresholding rules Threshold

Timing parameters

Segment duration

Data Clustering

Clustering parameters

Sequence of clusters (damages)

Figure 1: Principle of the proposed AE signal processing approach.

Wavelet signal denoising

Denoising using wavelets is based on the WT theory, which uses a family of wavelets to obtain inner products of the signal to be denoised s(t). A family of wavelets consists of a series of son wavelets generated by dilating and translating a mother wavelet. The wavelet transform W(a, b) gives the so-called wavelet coefficients, which can be considered as functions of translation b (shift or time location) with each fixed scale factor a. They give information about the signal s(t) at different levels of resolution and also measure the similarity between s(t) and each son wavelet. In fact, the WT is the convolution between s(t) and the wavelet function, i.e. a wavelet can be used for feature discovery if the chosen wavelet is similar to the feature components hidden in the signal.

The procedure of DWT signal denoising used in this work includes three steps. Firstly, the signal is decomposed up to a defined decomposition level N. The detail coefficients are thus obtained. Secondly, a thresholding is performed on the N signal details using a threshold selection rule (fixed form, Stein's Unbiased Risk Estimate principle...) and either a soft or hard thresholding [START_REF] Donoho | Ideal spatial adaptation by wavelet shrinkage[END_REF][START_REF] Donoho | De-noising by soft-thresholding[END_REF], by considering a basic model of the noise. Finally, the signal is reconstructed using the original approximation coefficients of the N th level and the modified detail coefficients of all levels.

The selection of the wavelet function in many engineering applications has been based on trial and error [START_REF] Taha | Wavelet transform for structural health monitoring: a compendium of uses and features[END_REF]. On one hand, when choosing the wavelet function for SHM applications, it is important to consider its ability to perform the DWT. On the other hand, no unique choice can be recommended for all SHM applications. Some functions might be better used in certain situations than others. The choice of the wavelet function is application dependent and requires careful scrutiny in its use and its results.

Hits determination

In the parameter-based AE systems [START_REF]PCI-2 based AE system user's manual[END_REF], the hits detection is performed by comparing the signal to a defined threshold, which is set beforehand above the noise level. The threshold is either fixed during the test (stationary noise), or floating within a defined range (under conditions of high and varying background noise) [START_REF] Barat | Intelligent AE signal filtering methods[END_REF][START_REF] Barat | Detection of AE signals against background friction noise[END_REF]. In the conventional threshold-based method, whenever the signal surpasses the threshold, the hit detection and determination are carried out by considering three timing parameters: Peak Definition Time (PDT), Hit Definition Time (HDT) and Hit Lockout Time (HLT). The hit determination involves, defining the time-start, the true peak and the time-end of the detected hit. The AE features can be then extracted from a given AE signal s(t) [START_REF] Grosse | Acoustic emission testing[END_REF]38]. The conventional features include Amplitude, Duration, Counts, Counts-to-peak, Rise time, RMS, ASL, PAC-Energy, Signal Strength and Absolute Energy. Frequency features are Average Frequency, Frequency Centroid, Peak Frequency, Initiation Frequency, Reverberation Frequency and Partial Power features. Hereinafter, the definitions of some AE features whose the expressions have not been explicitly provided in the literature:

• PAC-Energy (E PAC ) [µV.s]: A scaled version of Signal Strength to match the analog AE systems with 20 dB of gain. It is also called MARSE energy (Measured Area under the Rectified Signal Envelope). The sum of the signal envelope is calculated over the duration of the AE hit and converted into counts at 100kHz/V. PAC-Energy is expressed as:

E PAC = t |H[s(t)]| • ∆t • 100 • 10 6 , ( 1
)
where H is the envelope -calculated by the Hilbert Transform -of the signal above the threshold.

• Signal Strength (S tr) [pV.s]: It is the integral of the rectified voltage signal over the duration of the AE hit and can be defined as:

S tr = L t=1 |s(t)| • ∆t • 10 12 . (2)
• Absolute Energy (E abs ) [aJ]: The integral of the squared voltage signal above the threshold divided by the reference resistance (10kΩ) over the duration of the AE hit.

E abs = L t=1 |s(t)| 2 • ∆t/R • 10 18 .
(3)

Data clustering

The clustering algorithm used in this study has been previously proposed by the authors [START_REF] Ramasso | Unsupervised consensus clustering of acoustic emission time-series for robust damage sequence estimation in composites[END_REF]. It is based on the idea that several parameterizations may be suitable for a given dataset but it is difficult to precisely find an optimal one. Therefore, the user can provide to it multiple parameterizations: type of algorithm (e.g. Kmeans, FCM, Gustfason-Kessel, Hidden Markov Models), parameters of those algorithms (e.g. type of distance, fuzziness parameter), all possible (and relevant) combinations of features, and so on. Given those parameterizations, a criterion is optimized based on the entropy of the cumulated appearance of clusters which allows getting a subset of relevant parameterizations. The partitions (sequence of clusters) obtained with those parameterizations are then combined. The number of clusters is finally optimized based on an information-theoretic criterion called Normalized Mutual Information NMI [START_REF] Strehl | Cluster ensembles-a knowledge reuse framework for combining multiple partitions[END_REF]. This clustering fusion algorithm is also able to quantify the uncertainty around the estimation of the clusters. This algorithm has been studied with different clustering methods (Kmeans, GK and Hidden Markov Models) on simulated and real datasets. It has been shown that the GK algorithm [START_REF] Gustafson | Fuzzy clustering with a fuzzy covariance matrix[END_REF] provided more relevant results. It accounts for its use in the present paper.

Experimental procedure

Materials and methods

A unidirectional CFRP ring with an outer diameter of 124 mm, a thickness of 1.5 mm and a width of 16 mm is used in the experiments (see Figure 2). The mounting is performed according to the ASTM D2290 standard test procedure for apparent hoop tensile strength of plastic or reinforced plastic pipe by split disk method. The ring is fixed using two clamping jaws consisting of two separate half-cylinders. Four Micro80-type (Mistras Group Ltd.) sensors are mounted directly on the clamping jaws using spring clamps to ensure a permanent contact. Sensors 1 and 4 are on the upper half-cylinder, whereas sensors 2 and 3 are on the lower one. It was decided to deport the sensors away from the composite ring in order to avoid their deterioration during the test. Indeed, unidirectional CFRP have highly energetic failure that can damage the sensors if they are placed on the specimen. Thus, acoustic waves pass through the interface between the specimen and the jaws before being captured by the sensors. Potential wave reflections should be so expected. The AE sensors are wide-band and have an operating frequency-range of [200-900 kHz] and a resonant frequency of 325 kHz. The AE system settings are shown in Table 1. The aim is to recover AE transients from simple and complex signals. To this end, simple AE bursts are firstly generated using Pencil Lead Breaks (PLBs) on the outward surface of an intact specimen under low and high noise levels created by the hydraulic system of the testing machine. As the hydraulic system is located at the bottom of the machine, sensors 2 and 3 are intended to be more affected by the generated background noise. A PLB is the Hsu-Nielsen source frequently employed to simulate an AE event. The fracture of a brittle graphite lead generates an intense acoustic signal, quite similar to a natural AE source, that the sensors detect as a strong burst [START_REF] Hsu | Characterization and calibration of acoustic emission sensors[END_REF]. These simple AE signals are created in the material while the machine is at rest (no applied loading). A comparison is then addressed between raw and denoised signals in order to demonstrate the efficiency of the approach. The footprint of the noise on the AE features is studied. Thereafter, a tensile test at a high loading rate under a high noise level is performed on the same specimen until its total failure. The tensile force is applied using a hydraulic jack linked to the lower clamping jaw. This experimental configuration is then complex as it involves a multi-axial stress state at the level of the gap between the half-cylinders, frictions between the specimen and the clamping jaws, as well as the consideration of the deported sensors. This results in complex AE signals with a high hit-rate similar to that obtained under in-service conditions. By synthesizing the experiments, three types of signals will be considered:

• Simple AE signal 1: a PLB under a low noise level.

• Simple AE signal 2: a PLB under a high noise level.

• Complex AE signal: a high loading-rate tensile test under a high noise level.

The effectiveness of the implemented approach is assessed by comparing some AE features determined by the algorithm to those obtained by a commercial AE system.

Simple AE signal 1: PLB-burst with a low noise level

As the channels 2 and 3 are mounted closer to the hydraulic system than channels 1 and 4, they are subjected to a higher perturbation . Under a low noisy environment, the AE signals received by the four channels are not noticeably impacted, as the threshold is higher than the noise level. Figures 3 and4 show the Duration-Amplitude graphs and time-signals, respectively, of the hits detected by channels 2 and 3. A further analysis of the measured signals from all channels and their corresponding Duration-Amplitude graphs can be found in a previous publication of the authors [START_REF] Kharrat | A signal processing method for hits detection and separation in high ae activity systems: Application to composite materials under fatigue tests[END_REF].

For the purpose of reducing the impact of noise, the raw signals of channels 2 and 3 are denoised using the DWT before performing the hit detection. The parameterization of the denoising procedure is important to enhance the quality of the denoising process [START_REF] Donoho | Ideal spatial adaptation by wavelet shrinkage[END_REF] and is application-dependent. When dealing with unknown noise level, it would be convenient to adopt a soft thresholding with a selection rule of the universal threshold (denoted 'sqtwolog') equal to 2 log(n), where n is the total number of wavelet coefficients, and by considering a non-white noise model [START_REF] Donoho | De-noising by soft-thresholding[END_REF]. This has been confirmed by testing this parameterization on our experimental signals. Another important issue is the choice of the mother wavelet and its order as well as the decomposition level. The Daubechies wavelet [START_REF] Daubechies | The wavelet transform, time-frequency localization and signal analysis, Information Theory[END_REF][START_REF] Daubechies | Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising[END_REF] is found to be efficient to reduce the noise level in the recorded signals processed in this work. Various orders of the Daubechies wavelet with different decomposition levels (DL) are thereafter tested on the raw signals. In order to evaluate the performance of the signal denoising, the number of detected hits (N hits ) and the signal-to-noise ratio (S NR) between the obtained denoised signal and the residual noise removed from the raw signal are calculated for each tested parameterization. Table 2 summarizes the obtained values for the signals of channels 2 and 3. In order to choose the best parameterization, N hits and S NR must be as small as possible. Indeed, by applying a single PLB, generally one hit or at most few hits should be detected. Besides, the higher is the extracted noise from the raw signal, the lesser is the S NR. For the sake of simplicity, the same parameterization is adopted for denoising the signals of both channels 2 and 3. The best parameterization enhancing the quality of these signals is obtained with the "db8" wavelet and 8 decomposition levels. As we can see in Figure 4, the noise level is reduced under the threshold for the channels 2 and 3. Consequently, the number of the detected hits is decreased to only one hit for each channel (Table 2).

Simple AE signal 2: PLB-burst with a high noise level

When the hydraulic fluid reaches an important fluctuations' activity, a high noise is generated in the testing machine. Another PLB is created near sensor 1. As we can see in Figure 5, all the hits detected by the AE system are saturated at a duration of 200 ms, which corresponds to the predefined maximum duration. Thus, the hits separation and the calculated AE features performed by the AE system are erroneous. The raw time-signals corresponding to the four channels (see Figure 6) show that the recorded bursts are so noisy that the amplitude never drops below the threshold during the acquisition period, especially for channels 2 and 3. Figure 3: PLB bursts under a low noise level: Duration vs. Amplitude graphs of the detected hits by the AE system (•) and by the proposed approach ( * ). This figure shows that the number of AE hits on channel 2 and 3 is much higher than expected due to the noise level. Each channel's signal is denoised using various orders of the Daubechies wavelet with different decomposition levels in order to find the best parameterization. The performance evaluation of the denoising is presented in Table 3 as performed in the last subsection. The results for channels 2 and 3 are presented here as they are more affected by the noise than channels 1 and 4.

Consequently, a good quality of denoising can be obtained using the "db45" wavelet with 14 decomposition levels for both channels. This parameterization is also applied on the signals of channels 1 and 4. Figure 6 shows a comparison of the raw and denoised signals of the four channels. As we can see, a considerable improvement of the signals' quality is made, especially for channels 2 and 3. The waveform of the PLB burst is well recovered from the noise. The resulting Duration-Amplitude graphs are represented in Figure 5 where it can be remarked that the saturation of the hits at the predefined maximum duration is now eliminated and the PLB bursts can be identified.

Another issue can be also addressed here, which is the footprint of the noise on the AE features. For that purpose, the frequency contents of the detected hits in both raw and denoised cases are examined. Figure 7 shows the timefrequency diagrams -obtained by the Wavelet Transform (WT) -of the raw and denoised signals of channel 2. As we can see, the frequency content of the hit associated to the PLB-burst in the raw signal is very affected by the noise. We can point out that the denoising process has considerably eliminated the noise contribution in the frequency content of the signal, whereas that of the PLB-burst is kept. Figure 7(a) allows to distinguish between the noise footprint and the PLB-burst (comprised mainly within the range 20-50 kHz) that has been efficiently conserved after denoising, as we can observe in Figure 7(b). Accordingly, the frequency features (such as average frequency, centroid frequency ...) of a noisy signal are potentially altered, which may give erroneous information about the AE data and falsify further interpretations. The eventual alteration of the non-frequency AE-features is also studied. Table 4 shows some calculated AE features for raw and denoised signals of channels 1 and 4, as their raw PLB-bursts are available. It can be noted that the signal amplitudes are conserved and not altered by the denoising process. Obviously, the raw-signal durations are erroneous as they are equal to the predefined maximum duration (200 ms), those of the denoised signals would be more correct. However, the number of counts of the PLB-bursts is very affected by denoising, as they are superimposed with the number of counts of the noise-signals. PAC-Energy is almost divided by two; the alteration of the duration and the number of counts is compensated by a conservation of the amplitude.

Complex AE signal: a high loading-rate tensile test under a high noise level

A tensile test at a high loading-rate is performed on the same specimen. This test is performed after that of the PLB with a high noise level, so this latter is expected to be the same or higher. This configuration simulates an inservice-like loading under severe working conditions and results in complex experimental signals where continuous signals and AE transients could be superimposed. Practically, the test consists in applying an increasing tensile force (a ramp function) on the composite ring through the clamping jaws until the total failure. The applied force is going from 0 N to 60 kN at a loading rate of 625 MPa/s [START_REF] Kharrat | Acoustic emission in composite materials under fatigue tests: Effect of signal-denoising input parameters on the hits detection and data clustering[END_REF].

AE raw data

Signals acquisition is launched before the beginning of the loading and is stopped after. The AE software records all the detected events produced in the material and determines all eventual hits. Features obtained by the AE system are presented hereafter and compared to those calculated after post-processing the signals by the proposed approach. Since channels 1 and 4 have quite similar responses (and similarly for channels 2 and 3), only the responses of channels 1 and 2 are considered hereinafter. A selection of features determined by the AE system is presented in Figure 8.

Figures 8(a) and 8(b) show the amplitude of the detected hits and the applied force exerted by the machine on the specimen over time. First of all, as we can note, the amplitude increases with force, which begins to rise a little before the 4 th second; then it falls again when the force tumbles down shortly before the 7 th second with the complete failure of the ring. The hits detected outside the period of loading would correspond to noise as there was no other emission source in the material. We also remark that the level of their amplitudes is reduced after the rupture of the specimen. Indeed, on one hand, the noise generated by the hydraulic system is related to the applied force. When this latter falls, the fluid turbulence decreases, and therefore the noise level is reduced. On the other hand, the contact between the upper and lower clamping jaws is broken. So, channel 1 (analogously channel 4) is less impacted by noise after the failure of the composite ring. It should be also mentioned that the amplitude of the "noise hits" in channel 2 is higher than that in channel 1 since the level of noise is higher in channel 2, as shown also in the previous section. The next figures can prove this interpretation. Hits' durations obtained using the AE software are represented as a function of time (Figures 8(c) and8(d)). For channel 1, all the hits recorded until the total failure of the specimen have durations equal to the maximum duration (200 ms). After the total failure of the specimen (end of loading), various hits are detected. Concerning channel 2, all the detected hits are equal to the maximum duration. This is a total saturation of the AE system throughout time. In the Duration-Amplitude graphs (Figures 8(e) and 8(f)), we note a saturation of hits at the maximum duration. As it was explained previously, the AE software has considered a number of signal segments with a duration of 200 ms as detected hits because the amplitude is stagnated above the threshold during a certain period within the test. These hits can be thus poorly separated. This potentially erroneous hit separation may be caused either by noise or by damage accumulation in the material leading to a high AE activity. This phenomenon is quite significant in channels 2 and 3 as they are more impacted by the generated noise. Figure 9 shows time signals of channels 1 and 2 as retrieved from the streaming file in order to be processed by the algorithm.

Signal denoising

The recorded time signals are post-processed and the resulting AE features are compared to those calculated by the method of the AE system. Initially, the signals of each channel are taken entirely; so that the denoising as well as the hit determination and separation are performed on each signal after loading it one shot. This strategy has the drawback of requiring a lot of computer memory when treating massive data files as the size of each acquisition is large due to the sampling rate, which is generally from 2 to 5 MS/s in this kind of tests. Time signals of the four channels are denoised using different Daubechies wavelets, decomposition levels and threshold selection rules [START_REF] Donoho | Ideal spatial adaptation by wavelet shrinkage[END_REF][START_REF] Donoho | De-noising by soft-thresholding[END_REF], in order to find a suitable method efficiently applicable to this kind of tests. Table 5 summarizes the employed denoising parameters. Figure 10 shows a comparison of the Amplitude and Duration of both raw and denoised signals of channels 1 and 2. By comparing the different denoising methods, we remark that the hits obtained using 'DenPar1' are not well denoised; whereas 'DenPar3' is better than 'DenPar2' since it eliminates more efficiently noise hits detected before the loading. When increasing the decomposition level to 14, no better improvement in signal denoising is noticed. Since increasing the decomposition level is time consuming, there is no need to adopt 7 levels. Accordingly, the best adjustment of the denoising process is obtained using the "db45" wavelet , 7 decomposition levels, a soft thresholding with a selection rule of the universal threshold 'sqtwolog', and considering a non-white noise model.

Moreover, from Figures 10(a) and 10(c) (channel 1), we can note that the hits detected before and after the effective period of loading in the raw signal are now eliminated as they were representing the noise. As shown in Figures 10(b) and 10(d) (channel 2), although the noise hits are eliminated after the rupture of the ring, the amplitude of those detected before the start of the loading is reduced by about 10 dB. Another important observation can be also taken from Figures 10(a) and 10(b): the amplitudes of the hits detected during the loading, which are associated to various AE evolving sources, are approximately conserved. So that the denoising process did not alter the effective AE information. Besides, in Figures 10(c) and 10(d) the hidden information by the effect of noise is now considerably revealed in channel 1 and especially in channel 2. However, some continuous emission still persists: about twelve hits during the loading have a duration equal to 200 ms (the Maximum Duration), which can be also observed in Figures 10(e) and 10(f) showing the Duration-Amplitude graphs.

Signal segmentation

In order to overcome the problem of loading heavy signal files and trying to totally eliminate the hits saturation, a signal segmentation is adopted. The signal to be processed is thus divided into short segments having equal durations of 0.5 s. Then, each signal segment is successively denoised and potential hits are determined. This strategy has the advantage of surmounting the limitation of computer memory. The obtained results are presented in Figure 11 where the amplitude and duration of the hits detected after the signal segmentation are compared to those obtained previously by processing the entire signal using 'DenPar3'.

The most important ascertainment is that the saturation phenomena is now eliminated. All the separated hits have so a duration less than the pre-defined maximum duration. For channel 2, the hits detected before loading are greatly reduced. In fact, if the AE signal is processed entirely, the wavelet denoising procedure constructs an estimation of the noise model based on the full length of the signal, which could not be fairly accurate. Whereas, if the AE signal is segmented, the noise variation in each segment is less important than that in the entire signal. So, the noise model is updated in each segment and is estimated more accurately, especially when dealing with non-stationary noise characteristics. It can be concluded that a blockwise wavelet denoising is more accurate to cope with highly non-stationary noise encountered in AE. An example of a signal-segment extracted from the response of channel 2 during the loading is shown in Figure 12. The raw, non-segmented denoised, and segmented denoised signals are compared. It can be remarked that the signal obtained after segmentation is better denoised than that resulting after a one-shot denoising.

Voltage (V) Time (s) A deep observation of the hits' shapes that can be extracted by the algorithm leads to classify these hits into three categories whose samples are shown in Figure 13: a piece of hit, a typical burst of a natural AE source, and a relatively long hit exhibiting more than one waveform-packet that may be engendered by the superimposition of multiple AE hits. The separation of the first and the last hits seems to be not properly performed.

The hits belonging to the first category (Figure 13(a)) have a low number of counts and short durations; whereas the other two categories have medium and large number of counts, and medium and long durations. As shown in Figure 14, the truncated hits, which are located between 0 and 10 counts approximately appear as straight lines; that is to say multiple hits with equal counts are detected. This seems to be unlikely due to the complexity of the involved damage mechanisms, but may be engendered by a residual noise, wavelet artifacts, as well as a bad hits separation caused by inappropriate timing parameters (HDT, PDT and HLT). The proportions of the truncated hits are estimated at 40% for channel 1 and 49% for channel 2. The rest of the data would then contain the other two categories of hits (Figures 13(b) and 13(c)). The pattern recognition could be used here to regroup the truncated hits within a specific cluster. This issue is addressed in the next step of the proposed approach.

Data clustering

The AE data obtained after the above-mentioned denoising procedures using two processing parameterizations, namely one-shot with 'DenPar1' and segment-based with 'DenPar3', are analysed by the pattern recognition approach proposed in [START_REF] Ramasso | Unsupervised consensus clustering of acoustic emission time-series for robust damage sequence estimation in composites[END_REF] and described in section 2.3. The clustering algorithm is used to determine the sequence of clusters in both cases. A number of clusters K=7 is found to be the optimal value (based on the NMI criterion). Figure 15 presents the obtained sequences of clusters, where the vertical axis corresponds to the decimal logarithm of the cumulative occurrence of AE hits in a given cluster (called CSCA). These graphs allow locating the time of occurrence of each cluster, and following the temporal evolution of its activity. In Figure 15(a) obtained by using the one-shot denoising strategy, the four first clusters appear at the very beginning while the loading has not been applied yet (see the loading profile in Figures 8(a) and 8(b)). Furthermore, several clusters are highly activated later after the specimen failure. The damage scenario suggested by this sequence is thus unlikely. The sequence obtained in Figure 15(b) using the segment-based strategy is different. A first cluster starts at the same time as the AE acquisition (without loading) which is coherent with the activation of an AE source related to the 'structureborne' and 'fluidborne' noises. This cluster represents 62% of the total number of hits and may regroup those associated to external emission sources as well as other meaningless hits. The first category of hits that was mentioned in the previous section, namely the truncated hits, is found to be included in this cluster after verification. Clusters 2, 3 and 4 start at the same time as the loading and are activated throughout the test. These clusters are thus associated to the activation of AE sources related for example to the friction between the specimen and the clamping-jaws. This friction is also observed after the specimen failure.

The remaining clusters 5, 6 and 7 are probably associated to the material damage mechanisms as they appear during the specimen loading period. In CFRP composites, major damage mechanisms are matrix cracking, delamination, debonding, fiber cracking and fiber pull-out [START_REF] Gay | Matériaux composites[END_REF]. It can be concluded that the proposed algorithm leads to a better identification of the natural clusters in acoustic emissions and improves the interpretation of damage mechanisms.

Conclusion

The problem of continuous AE in CFRP was addressed in this paper. Continuous signals produced by in-servicelike environment are post-processed. The proposed approach includes successive steps allowing the denoising of raw signals, hits determination, and AE features extraction. In order to assess its efficiency, the approach was tested on AE signals derived from experimental procedures. They firstly consist in a PLB applied on the surface of a composite ring under low and high noise levels. A complex AE signal is also created after a high loading-rate tensile test under a high noise level until the total failure of the specimen.

The proposed approach was able to improve the signals quality under different working conditions if the denoising parameters were properly set. It was also found that the extracted AE features that had been erroneous due to the noise, became coherent and exploitable. Moreover, it was also shown that the frequency features of a noisy signal are altered by the noise, which engenders erroneous information about the AE information. Using the proposed approach, the denoising process has eliminated considerably the noise contribution in the frequency content of the signal; whereas the frequency content of the PLB-burst was kept. The process of signal segmentation was able to substantially improve the hit determination and eliminate the hit saturation, especially when dealing with non-stationary noise in large signals recorded during high loading-rate tests. Besides, the signal segmentation was found to be of interest for pattern recognition. An appropriate hit detection algorithm leads to a better identification of natural clusters in AEs and improves the interpretation of damage mechanisms. In order to assess its reliability, the proposed approach can be applied on AE signals retrieved for example from fatigue tests with cycling loading performed on the studied composite ring. Such test case will be addressed in future works.

Figure 2 :

 2 Figure 2: Configuration of the tests performed on a CFRP ring: (a) a photograph of the mounting on the testing machine; (b) a basic diagram of the mounting.

Voltage

Figure 4 :

 4 Figure 4: [Color representation] Comparison of the raw and denoised signals of channels 2 and 3 after a PLB under a low noise level. Denoising using the "db8" wavelet and 8 decomposition levels. ( ) Raw signals; ( ) denoised signals; and ( ) threshold level.

Figure 5 :

 5 Figure 5: [Color representation] PLB bursts under a high noise level: Duration vs. Amplitude graphs of the detected hits by the AE system (•) and by the proposed approach ( * ). The figures show that the saturation is eliminated.

Figure 6 :

 6 Figure 6: [Color representation] Comparison of the raw and denoised signals of the four channels after a PLB under a high noise level. Denoising using the "db45" wavelet and 14 decomposition levels. ( ) Raw signals; ( ) denoised signals; and ( ) threshold level.

Frequency

Figure 7 :

 7 Figure 7: [Color representation] Comparison of the WT diagrams of raw and denoised signals of channel 2 (PLB test under a high noise level).

Figure 8 :

 8 Figure 8: [Color representation] A selection of features retrieved from the AE data acquisition file of the tensile test for channels 1 and 2: (a) and (b) Amplitude and force over the acquisition time; (c) and (d) Duration over time; (e) and (f) Duration vs. Amplitude.

Figure 9 :

 9 Figure 9: Raw time-signals obtained from channels 1 and 2 during the tensile test.

Figure 10 :

 10 Figure 10: [Color representation] Comparison between the detected hits in the raw data (•) and those detected after denoising with different parameters. Signals processed entirely one-shot for channels 1 and 2. (a) and (b) Amplitude over the acquisition time; (c) and (d) Duration over the acquisition time; (e) and (f) Duration vs. Amplitude.

Figure 11 :

 11 Figure 11: [Color representation] Comparison of the detected hits for channels 1 and 2 after a denoising using the parameters 'DenPar3': (•) Signals processed entirely one-shot ; ( * ) signals segmented into 0.5 s-long segments. (a) and (b) Amplitude over the acquisition time; (c) and (d) Duration over the acquisition time; (e) and (f) Duration vs. Amplitude.

Figure 13 :Figure 14 :

 1314 Figure 13: Main three types of the extracted hits. ( ) threshold level. Channel 1

  Signals denoised entirely one-shot using the parameter 'DenPar1'. The sequence of damages is unlikely since some clusters start too early or activate later with respect to the loading phase (4-7s). Signals segmented and denoised using the parameter 'DenPar3'. The sequence of damages is enhanced as some clusters start and evolve during the loading phase.

Figure 15 :

 15 Figure 15: [Color representation] Clustering sequences obtained using two processing parameterizations on the AE signals of all channels.

Table 1 :

 1 Settings of the AE system.

	Threshold	40 dB
	Pre-Amplifier	20 dB
	Analog Filter	20 kHz -1 MHz
	Sampling Rate	2 MS/s
	PDT	60 µs
	HDT	120 µs
	HLT	300 µs
	Max. Duration	200 ms

Table 2 :

 2 Denoising performance evaluation of the signals of channels 2 and 3 affected by a low noise level, with "dbx" standing for the x-order of the Daubechies wavelet and "DL" for the decomposition level.

			Channel 2	Channel 3
			N hits S NR[dB] N hits S NR[dB]
	Raw signals	1772 -	2020 -
		DL = 4 61	3.387	1	1.169
	db4	DL = 6 1	2.316	2	0.706
		DL = 8 1	2.296	2	0.698
		DL = 4 66	3.396	1	1.180
	db6	DL = 6 1	2.313	1	0.706
		DL = 8 1	2.299	1	0.699
		DL = 4 51	3.398	1	1.187
	db8	DL = 6 1	2.308	1	0.707
		DL = 8 1	2.297	1	0.701

Table 3 :

 3 Denoising performance evaluation for signals channels 2 and 3 affected by a high noise level, with "dbx" standing for the x-order of the Daubechies wavelet and "DL" for the decomposition level.

			Channel 2	Channel 3
			N hits S NR(•10 -4 )[dB] N hits S NR(•10 -4 )[dB]
		DL = 6	237	8.80	532	4.41
	db8	DL = 10 30	8.16	250	3.89
		DL = 20 34	-2.81	215	-88.92
		DL = 10 14	8.06	215	3.81
	db10	DL = 14 13	7.99	202	3.73
		DL = 20 22	-25.25	159	-44.63
	db20	DL = 10 10 DL = 14 10	7.68 7.60	77 63	3.18 3.10
	db30	DL = 10 6 DL = 14 6	8.07 7.99	26 21	2.95 2.87
		DL = 7	7	8.31	35	3.15
	db45	DL = 10 5	8.02	11	2.84
		DL = 14 5	7.95	10	2.76

Table 4 :

 4 Effect of denoising on non-frequency AE features.

		Channel 1	Channel 4
		Raw	Denoised Raw	Denoised
	Amplitude [dB]	91	91	92.5	92.3
	Duration [µs]	2.10 5	3832	2.10 5	4421
	Counts	28792 528	31333 605
	PAC-Energy [µV.s] 2350	1294	2400	1200

Table 5 :

 5 Denoising parameters tested on the raw signals obtained for the tensile test under a high noise level.

	Denoising parameters Wavelet Decomp. levels Threshold selection rule
	DenPar1	db10	7	minimax (ch.1) / heursure (ch.2)
	DenPar2	db10	7	sqtwolog
	DenPar3	db45	7	sqtwolog
	DenPar4	db45	14	sqtwolog

Acknowledgment

This work was supported by the Laboratory of Excellence ACTION through the program "Investments for the Future" managed by the National Agency for Research (references ANR-11-LABX-01-01) and by BPI France and the Franche-Comté Region through the project "Smart Composites".


B Brazey

R Dahmouche
email: redwan.dahmouche@femto-st.fr

J A Seon
email: ja.seon@femto-st.fr

M Gauthier
email: michael.gauthier@femto-st.fr

Experimental Validation of In-Hand Planar Orientation and Translation in Microscale

This paper presents the experimental validation of automatic dexterous in-hand manipulation of micro-objects. Currently, precise handling of micro-objects is still a challenge especially when large rotations are required. Indeed, the current dexterity of microgrippers is still very low and only some small range rotations have been shown. Although, the robotic hands in the macroscale have better capabilities, they are not able to manipulate micro-objects. The proposed approach extends the capabilities of dexterous macrohands to the microgrippers enabling dexterous micro-manipulation. Design rules of the microhand fingers and trajectories enabling micro-manipulation are proposed. The developed methods are validated by simulation and on an original experimental prototype having three fingers (7µm in diameter). Half turns of 220µm square objects demonstrates the relevance of the approach which opens the way to new advanced in-hand micro-manipulation and micro-assembly methods.

I. INTRODUCTION

The development of microtechnologies in fields such as biomedical instrumentation, watch industry and optical microsystems, in which several technologies has to be merged in a unique system, has increased the applicative interest of micro-assembly in micromanufacturing. However, most of micro-assembly operations are still done manually because of the lack of automated systems able to perform complex operations especially when orientation positioning is critical.

The first challenge for micro-assembly mentioned in a large majority of papers in the literature deals with the adhesion forces (mainly van der Waals, electrostatic and capillary forces) which are larger than volume forces (weight and inertia). The manipulation strategies in microscale have to take this constraint into account.

The development of microassembly methods is also limited by the lack of precision of multi-axes rotation systems which are currently not able to provide sufficient positioning accuracy for precise micro-assembly [START_REF] Savia | Contact micromanipulation-Survey of strategies[END_REF], [START_REF] Clevy | Micromanipulation and microassembly systems[END_REF]. The classical structure of an industrial robot consisting in bodies, joints and actuators linked in serial or parallel architecture are not efficient in microscale. Indeed, the eccentricity error of a conventional joint (e.g. several microns) becomes comparable to the request manipulation precision when manipulating a micro-object. The use of a serial robotic structure composed of several rotational stages is only possible for large microobject having a size down to 100µm [START_REF] Tamadazte | CAD Model-based Tracking and 3D Visual-based Control for MEMS Microassembly[END_REF]. Moreover the rotation of a whole robot to manipulate only microparts significantly increases the moved mass and thus reduces the potential throughput. The last drawback is the high volume needed to achieve the rotations which limits the application of this solution especially in confined environments (Scanning Electron Microscope, for instance). To work around this problem, self-assembly techniques have been developed [START_REF] Savia | Contact micromanipulation-Survey of strategies[END_REF], [START_REF] Arai | Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments[END_REF]. However, these techniques have limited application cases.

Increasing the dexterity of the microgrippers is one of the most studied solutions to overcome the precision lack in rotation. Indeed, in-hand manipulation allows to perform local rotations without using conventional rotation stages. Previous works have demonstrated the feasibility of automatic and semi-automatic handling using two [START_REF] Kim | Design, fabrication and testing of a serial kinematic MEMS XY stage formultifinger manipulation[END_REF]- [START_REF] Xie | Development of a flexible robotic system for multiscale applications of micro/nanoscale manipulation and assembly[END_REF], three [START_REF] Wason | Dextrous manipulation of a micropart with multiple compliant probes through visual force feedback[END_REF] or four [START_REF] Krishnan | A multi-fingered micromechanism for coordinated micro/nano manipulation[END_REF] probes having several degrees of freedom (DoF). However, the manipulated objects were limited to microspheres except in [START_REF] Wason | Dextrous manipulation of a micropart with multiple compliant probes through visual force feedback[END_REF] where more complex objects have been manipulated using three probes having 6 DoF (two mobile fingers and a static one). In [START_REF] Zhou | Automatic dextrous microhandling based on a 6 dof microgripper[END_REF] an integrated dexterous gripper with 2 fingers having 3 DoF each was also used for micro-parts inspection. In all these works, no regrasping strategy was considered during the manipulation and the contact points between the gripper and the manipulated object were kept as stable as possible which limits the manipulation to small rotation adjustments. In [START_REF] Shimada | Prototyping millirobots using dextrous microassembly and foldings[END_REF]- [START_REF] Fearing | Apparatus and method for manipulation of an object[END_REF], large object rotations have been performed thanks to two compliant microtweezers. However, the manipulation process requires placing the manipulated object on a specially designed shape for object regrasp which limits the versatility of the approach. To enhance the dexterity in micro-manipulation, multiple fingers, having multiple DoF, are needed to enable online regrasping.

In this paper, we propose a new approach of automatic multi-fingers dexterous micro-manipulation using rolling contacts and finger gaiting strategies. Based on our knowledge, this work represents the first in-hand manipulation performed in microscale, which allows 180 • positioning range. The experimental validation of the concept is performed on several micro-objects of different sizes (from 120µm to 400µm).

The next section describes the proposed manipulation strategies and formalizes the dexterous micro-manipulation problem. Section III details the finger gaiting trajectory generation and the kinematics behind it. Finally, section IV describes the experimental setup and shows the obtained results in micro-objects reorientation, followed by a conclusion and perspectives. Fig. 2: The main dexterous manipulation steps. After the initial grasping, the manipulated object is reoriented using two fingers until the stability limit is reached, whereupon the object regrasp using the third finger is performed. The reorientation and regraping operations are repeated until the desired orientation is reached. Finally, the object is released, inserted or assembled.

II. HANDLING PRINCIPLE AND PROBLEM DEFINITION

A. MANIPULATION APPROACH

The approach of the proposed dexterous manipulation method is to translate, in the plane (x and y axes), N compliant beams which will act as fingers to handle microobjects (as depicted in Fig. 1). The fingers will apply a bending force on the manipulated object to move it along a reference trajectory. To perform pick-and-place operations using dexterous micro-manipulation approach, the handling sequence is decomposed into four major steps (see Fig. 2):

1) Grasping the object from the substrate 2) Translation of the fingers and in-hand rotation of the object 3) Finger gaiting and in-hand regrasping of the object (and eventually going to step 2) 4) Release or assembly of the object Each step will imply several constraints to take into account in order to perform a stable handling. In absence of force sensors able to measure grasping force in microscale, fingers compliance will be exploited to control the grasping forces. The next subsection focuses on the three first steps and presents their characteristics.

B. NOTATIONS AND HYPOTHESES

The notations of this section are illustrated in Fig. 3. In accordance with our experimental device, we focus on the case where cylindrical fingers are used to manipulate an object with opposite edges. We assume that all the fingers have identical shapes and mechanical behaviors. The main parameters and their definition are summarized in Table I.

Frames and points:

We consider compliant fingers whose base is translated along 2 DoF, and which are in contact with a square shaped object. L defines the length of the edge of the object.

The origin of the object frame R o ={O,(x,y,z)} is chosen as the center of the closest object surface to the actuation as depicted in Fig. 3.a. The x & y axes are parallel to the object edges.

B i =

x b i y b i is the projection of the i th finger base center on the (Oxy) plan.

C i = x c i y c i R o
is the contact point between the i th finger and the object on the (Oxy) plan. F i is the intersection between the i th finger central axis and the (Oxy) plan.

Geometrical and material properties:

The parameters describing the end-effectors (fingers) are: the radius R d , the flexure stiffness k (defined by the Euler-Bernoulli formula), the Young Modulus E and the mechanical yield R e . The contact between the object and a finger is considered as a punctual contact, with a friction coefficient µ. H d defines the distance between the contact point and the finger base.

Grasping force control:

A contact between the i th finger and the object induces a bending --→ F i B i which is proportional to the applied force on the object

--→ R i/o ext : --→ R i/o ext = F i/o x F i/o y = k --→ F i B i = k ε x i ε y i . (1)
The bending --→ F i B i is the distance from the tip to the base of the finger in projection in the (Oxy) plan (see Fig. 3.b). ε defines the bending amplitude: ε = ε 2

x + ε 2 y . As we consider in the study that the contacts are on parallel edges, F i/o

x and F i/o y will always respectively represent the tangential and normal component of applied forces. Knowing the fingers stiffness, the forces applied on the object can be controlled through the fingers bending thanks to the fingers bases positions which can be calculated as a function of the contact points distance. The case in which the fingers are in contact with the edges parallel to -→ x is not detailed in this paper but is similar to the previous case.

The influence of the adhesive frictional contacts:

In microscale, volume forces such as weight can be considered negligible compared to the blocking forces applied by the fingers. Adhesion forces (van der Waals, electrostatic, capillarity...) will then have a significant influence on the manipulation and have to be considered. As the manipulation strategy implies rolling without sliding, the finger trajectory will ensure that no slippage will occur during the manipulation. This means that the sliding limit defined by a friction cone will not be exceeded. Let F s/o ad be the adhesion force amplitude between the substrate and the considered object (pull-off force) and F f /o ad the adhesion force amplitude between a finger and the object.

The adhesion will increase the contact force between a finger and the object, and between the object and the substrate. In other words, adhesion improves the stability during the in-hand manipulation but induces difficulties during the pick-up from the substrate. Nevertheless, adhesion amplitude is highly variable and unpredictable due to its dependence on the characteristics of the contact surface between the considered objects (tribology of surfaces, applied forces, etc.). This stochastic behavior will imply different hypotheses on adhesion during the four main manipulation steps considering always the worst case.

C. MANIPULATION STABILITY

The effect of adhesion forces in microscale requires particular care to guarantee stable in-hand micro-manipulation process. We propose to study the stability of the steps required for successful manipulation: grasping, reorientation and regrasping.

Initial grasping and pull-off:

We assume that the parts to handle are initially laid on a planar surface (the substrate). For the successful pick-up of the object using two fingers (Fig. 4), it is necessary to overcome pull-off force F s/o ad between the object and the substrate (plan/plan contact). During this step, the critical case corresponds to the maximal possible value of the pulloff force F s/o ad , and the minimal adhesion force between the fingers and the object. We consequently assume that there is no adhesion between the fingers and the object. Considering that the two fingers have a friction coefficient µ, to pick-up the object, the normal force to apply by each finger is:

--→ F 1/o x = --→ F 2/o x ≥ 1 2µ .F s/o ad (2)
The minimum admissible grasping force applied by each finger is then given by:

F grasping = ( --→ F 1/o x 2 + --→ F 1/o y 2 ) 1 2 ≥ 1 2 (1 + 1 µ 2 ) 1 2 F s/o ad (3)
Object reorientation:

During the in-hand reorientation, the displacement of the contact points on the object and the evolution of the forces directions applied by the pair of fingers modifies the orientation equilibrium of the object which makes it Fig. 4: Representation of the grasping forces exerced by 2 fingers to detach an object from the substrate. The condition to achieve the object pick-up is that the exerted grasp forces overcome the pull-off force. Fig. 5: Finger rolling while handling an object: rolling induces a contact point variation that must be considered to ensure a stable grasp. rotate as shown in Fig. 5. The most critical situation which is considered during this step is when the adhesion forces that contribute to stabilise the grasp are null. In absence of external forces (the gravitation force being neglected), the grasp stability while rotating the object is ensured when the applied forces remain in the friction cone. Let us consider the Newton's law applied at the center of the object:

   F 1/o x + F 2/o x F 1/o y + F 2/o y L 2 (F 2/o y -F 1/o y ) -F 2/o x y c 2 -F 1/o x y c 1    R o = - → 0 , (4)
As only two forces are applied on the object respectively in C 1 and C 2 , we can show that both forces are parallel to

--→ C 1 C 2 .
Consequently, the ratio between the tangential and normal forces depends on the contact points positions. Thus, the grasp stays stable as long as: Fig. 6: Example of regrasping using 3 fingers. Geometry of the different elements should enable both initial and final configuration to be stable by applying forces remaining in the friction cone.

| y c 2 -y c 1 L | ≤ µ (5)
Considering that the fingers can roll on the object without sliding during the reorientation, equation 5 can be expressed as a function of the initial contact points positions 1 y c i and the object rotation amplitude ∆θ as follows:

| 1 y c 2 -1 y c 1 -2R d ∆θ L | ≤ µ, (6)
Let us consider an initial grasping in which contact points C 1 and C 2 are in front of each other ( --→ C 1 C 2 is the normal of the grasped object edges). The maximal achievable angle ∆θ without regrasping is:

|∆θ| ≤ µ L 2R d (7)
Regrasping:

If the required rotation angle is larger than the achievable one using two fingers, the object regrasping using a third finger is needed to continue the rotation (see Fig. 6).

The regrasping can be performed if both finger 1 & 2 and finger 1 & 3 represent stable grasps. Considering both geometrical conditions (5) for each grasp and the fact that the minimal distance between finger centers is 2R d , the finger gaiting can be done only if:

R d ≤ L µ (8)
This inequality shows that the regrasping feasibility does not depend on rotation amplitude but only on the relative dimensions between the end-effectors and the object. During the transition between the two configurations, the pull-off forces between the removed fingers and the object may also disturb the grasp. A detailed study of the impact of pull-off force on finger gaiting is presented in [START_REF] Seon | Trajectory planner for dexterous in-hand micromanipulation taking into account adhesion forces[END_REF].

To conclude this section, adhesion is a phenomenom that contributes to stabilize the grasp during in-hand rotation but disturbs pick-up and regrasping operations. Consequently, hypotheses about adhesion are:

• Pull-off F s/o
ad is maximal and adhesion between the object and the fingers F f /o ad is zero during the pick-up.

• F f /o ad is minimal for fingers grasping the object and maximal for the finger to detach. This microscale particularity were considered for the design of the finger. The equations ( 2) to (8) define a compromise to reach regarding the geometry of the fingers. Indeed, a tradeoff has to be found between both conditions. This point will be tackled in section IV.B.

III. MOTION PLANNING

In this section, we are going to propose a formulation of finger trajectories enabling the different manipulation steps.

Initial grasping:

During the intial grasping step, the fingers are translated from their initial position to the pick-up grasping configuration where two opposite fingers are used (Fig. 7.a). Knowing the stiffness of the fingers, the fingers bases positions are calculated to generate the required blocking force F grasping allowing to overcome the pull-off force as defined in (3). After reaching the required positions, the object is moved up to a position above the substrate.

Rotation:

Once the object is detached from the substrate, a first rotation is performed by the two fingers used during the pickup step. The fingers trajectories are generated to enable the rolling of the fingers on the object sides. In the case presented here, the center of rotation is chosen as the center of mass of the object as shown in Fig. 5. For a given initial contact points 1 y c 1 and 1 y c 2 , the fingers base positions are defined by:

x b 1 y b 1 R o = --→ OB 1 = -R d -L 2 + ε x 1 1 y c 1 + R d ∆θ + ε y 1 (9a) x b 2 y b 2 R o = --→ OB 2 = R d + L 2 -ε x 2 1 y c 2 -R d ∆θ -ε y 2 (9b)
The symmetry of the forces induces a symmetry of the bending:

ε = ε 2 x 1 + ε 2 y 1 = ε 2 x 2 + ε 2 y 2 .
The positions of the fingers bases expressed in the object frame R o are thus given by: , where s = sign(y c 2y c 1 ).

  x b 1 y b 1 1   R o =       -R d -L 2 + ε 1+( 1 yc 2 -1 yc 1 -2R d ∆θ L ) 2 1 y c 1 + R d ∆θ + sε 1+( L 1 yc 2 -1 yc 1 -2R d ∆θ ) 2 1       (10a)   x b 2 y b 2 1   R o =       R d + L 2 - ε 1+( 1 yc 2 -1 yc 1 -2R d ∆θ L ) 2 1 y c 2 -R d ∆θ - sε 1+( L 1 yc 2 -1 yc 1 -2R d ∆θ ) 2 1       (10b)
These equations describe the base centers B 1 and B 2 coordinates expressed in the object frame R o . The fingers trajectories can be expressed in the working frame by simply applying the transformation matrix between both frames:

w X = T o X, (11)
where w X and o X are respectively the homogeneous positions of the fingers in the work frame and the object frame and T the transformation matrix between both frames depending on the object pose.

Regrasping:

When the contact point positions between the fingers and the manipulated object reaches the stability limit or one of the object corners, a regrasping is needed (Fig. 7.b →Fig.7.d).

The new grasp will be stable if and only if the applied forces are in the friction cone. Finger 3 can then be placed on the object respecting the stability condition. The direction of rotation and the fingers accessible workspace will impose the side on which the finger will be placed on (Finger's 1 or Finger's 2 side). The approach trajectory of Finger 3 satisfying the stability condition and the application of desired force is given by:

  x b 3 (ε) y b 3 (ε) 1   R o =       R d + L 2 - ε 1+( 2 yc 2 -2 yc 1 L ) 2 2 y c 3 - sε 1+( L 2 yc 2 -2 yc 1 ) 2 1       , ( 12
)
where 2 y c 1 and 2 y c 3 are respectively the initial positions of Finger 1 and Finger 3, before detaching Finger 2. At last, Finger 2 is detached from the object and the object rotation is resumed. The two previous sections provided us all the mathematical formulations needed to generate stable trajectories during the three manipulation steps studied. The criteria (3), ( 7) and ( 8) respectively define the stability limit of the grasping, in-hand rotation and finger gaiting, while the equations ( 10), ( 11) and ( 12) enable to generate the trajectories.

IV. SIMULATION AND EXPERIMENTAL RESULTS

A. EXPERIMENTAL SETUP

The role of the 6-DoF dexterous manipulation system, shown on Fig. 8, is to demonstrate the experimental viability of our approach. The experimental system is composed of:

• The actuation system: 6 Smaract SLC-1730 piezoelectric actuators controlled in closed-loop. Travel: 18mm, repeatability: 1.5µm. • The fingers:

3 carbon fibers (Fig. 8 & Fig. 10). Diameter: 7µm, approximate length: 350µm (more details on the fibers will be given in the next section). • The vision system: Two 1024 x 768 pixels cameras with CCD sensors, a front camera and a side one placed at 45 • , both equipped with a x5 zoom. • Initial positioning of the fingers:

Three Newport M-DS40-XY manual linear stages with 1µm sensitivity. The architecture of the whole system is presented in Fig. 9.

The fingers are carbon microfiber beams which can be translated independently of each other in the plane (Oxy), thanks to the stick-slip actuators. We ensure beforehand that all fingers bases have the same depth by adjusting their position along the z axis using the manual linear stages.

The crystallographic quality of the fibers enables large elastic deformations. The fibers are fixed on the tip of a silicon triangle, as shown in Fig. 10. This part has been manufactured from a silicon wafer with a diamond saw and glued on a polymer support. The geometry of the silicon part has been designed to prevent collision during 180 • rotation of the object.

B. DESIGN OF THE FINGERS

Objects from 100 to 500µm in length & width and about 100µm in thickness have been considered. The fingers have to be dimensioned in order to satisfy stability criteria enounced in section II, for all considered object sizes. They also have to be rigid enough to reach a sufficient force able to overcome the pull-off forces and sufficiently compliant to allow the control of the forces exerted on the manipulated object. Thus, their dimensions have to allow to:

• Overcome the pull-off force between the object and the substrate during the initial grasping:

To avoid breaking the fingers by applying an excessive force and to prevent collision between the fingers supports (bending higher than the half of the object edge length), we consider the analytical formulation of strain and bending while applying a force on the fingers:

   σ(F grasping ) ≤ R e ε(F grasping ) ≤ L 2 , ( 13a
) ( 13b
)
where σ is the internal strain induced by the bending ε of the carbon fibers. We consider that the maximum pull-off force is proportional to the surface force f s/o ad and the contact surface of the widest manipulated object S contact :

F s/o ad = f s/o ad S contact (14)
This equation enables to define the theoretical maximum pull-off force value. The minimum blocking force applied by fingers to ensure a stable initial grasp is calculated from (3):

F grasping ≥ 1 2 (1 + 1 µ 2 ) 1 2 f s/o ad .S contact (15)
The maximum finger lengths are calculated from the bending and strain formulas for an Euler-Bernoulli beam:

         H d ≤ ( 3 E π R 4 d L 4 F grasping ) 1 3 H d ≤ π R e R 3 d 2 F grasping (16a) (16b)
• Perform rotations with the highest possible amplitude, without sliding: As defined in (Fig. 7), the amplitude of the rotation ∆θ is a function of the end-effector radius R d . Moreover, collision due to fingers supports will also limit the rotation amplitude to approximatively π 2 . We choose to maximize the available rotation and to define a R d enabling to perform the maximal rotation π 2 . From ( 7), R d verifies:

R d ≤ µ L min π , (17)
where L min is the minimum length of manipulated objects.

Fig. 8: The dexterous micro-manipulation station. 3 cylindrical fingers are mounted on a support and translated by the actuation system to perform manipulations. Two cameras allow to calibrate and visualise the 6 DoF micro-manipulation system.

Fig. 9: Blok diagram describing the interactions between the different elements of the setup and the user. Thanks to the interface, the user can send trajectories to the actuation system. Fingers will thus be translated to execute the commanded task. A visual of micro-object manipulation is given back by the cameras.

• Perform stable in-hand regraspings: From the stability criterion which was introduced in ( 8) we can deduce that:

R d ≤ L min µ
Both criteria ( 8) and (17) define a minimum value for R d . The criterion ( 8) is less restrictive than the (17), and only the second one ( 17) is thus considered.

The Modulus E of the carbon fibers used in the experimental setup may vary between 200 and 600GPa, and their yield R e between 2 and 7GPa. We consider a medium value to define an order of magnitude of the applied forces and the internal stress: R e = 4.5GPa, E=400GPa. Pull-off and friction values cannot be known a priori. We assume the following values of adhesion between the substrate and the

f s/o
ad < 10kPa, µ > 0.25. The experiments will confirm the order of magnitude of these parameters. The table II summarizes all the parameters of the experimental setup which satisfy the requirements expressed in ( 13) to (16).

C. CALIBRATION OF THE SYSTEM

Each finger being moved independently by its own translation stages (2 DoF motion), we need to express their positions in the same frame. The front camera is used to calibrate the system thanks to the homography matrices. Each finger is moved to pre-defined positions sequence (grid like positions). The corresponding positions in the image are measured which enables computing the homography matrix between the actuators and the camera frames:

  x i y i 1   = H i   X i Y i 1   (18)
The coordinate in each actuator reference frame is simply obtained by inversing the homography matrix:

  X i Y i 1   = H -1 i   x i y i 1   (19)
The calibration precision will directly influence the fingers trajectory accuracy and the success of the manipulation operations.

D. SIMULATION AND EXPERIMENTAL RESULTS

Before performing the experimental validation of the proposed dexterous micro-manipulation method, the proposed approach was validated in simulation. Existing simulators developed for dexterous manipulation in macroscale are not fully usable in micro-manipulation. Indeed, none of the current simulators enables to simulate flexure, adhesive contact and rolling at the same time. Thus, a simulator was developed for in-hand micro-manipulation. The simulator's features and architecture is described below.

Simulator description:

• Fingers bases coordinates generation Extraction of the fingers coordinates is achieved thanks to sampling functions associated to the trajectory. The initial sampling step can be given by the user or generated automatically. An adaptive sampling is then used when the system is close to an unstable state (sliding, adhesive contact loss). All parameters, and in particular adhesion forces, can be set randomly from their nominal value, in order to validate the method robustness.

• Contact detection

Contact detection enables measuring the contact position of the finger on the object. Initial contact detection is done by projecting the finger base on the object plane. Once the fingers and the manipulated object are in contact, the contact position is updated at each step. Sliding or contact loss can be known by calculating the normal and tangential components of the contact forces. Adhesion is calculated as described in the previous sections. Rolling is calculated from the object angle variation and fingers radius.

• Equilibrium position resolution

Fingers are modeled as springs that apply forces which are proportional to the deformations. The distance between the fingers base and the contact point corresponds to the spring deformation, enabling to determine the applied force -→ F ext on the object in the x and y directions. The equilibrium position -→ P is computed by inversing the stiffness matrix K built from the springs stiffness:

- → P = -inv(K) -→ F ext (20)

Simulation results:

The example of the simulation of a 180 • rotation of a 220µm silicon square is presented in Fig. 11. The fingers trajectories and forces are respectively described in Fig. 11.a and Fig. 11.b. This grasping sequence consists in the following steps:

• Initial approach (t 0 → t 1 )

The three fingers come in position to begin the manipulation.

• Pick-up (t 1 → t 2 )
Finger 2 & Finger 3 perform the initial grasping without sliding thanks to a high force F grasping = 450µN that ensures to overcome the pull-off force between the object and the substrate. The peak on each force curves along the y axis represents the half of the simulated pull-off force. • First rotation (t 2 → t 3 )

The grasping forces applied by Fingers 2 and 3 are reduced to F r = 225µN and a 90 • rotation of the object is performed. • Regrasping (t 3 → t 4 ) In this step, Finger 1 takes over from Finger 3. The peak on the Finger 2 force appears when Finger 1 takes position on the object. The applied force F r is set to a significant lower value than F grasping in order to guarantee that the force is always lower than F grasping despite this force peak. However, the force F r during in-hand manipulation must be high enough to guarantee a grasping stability despite the potential adhesion disturbance that appears when Finger 3 is removed. In our experiments, F r = 225µN is sufficient to change the fingers without disturbing the grasping stability. • Rotation continuation (t 4 → t 5 )

The second rotation is performed following the same procedure as the first one with Fingers 1 and 2. • Object release (t 5 → t 6 )

The object is released on the substrate while making the fingers sliding on the object edges. This explains the last peak on Fingers 1 and 2 force curves.

Experimental results:

The manipulation trajectories tested in simulation have been validated experimentally (see Fig. 12). After aligning the fingers and the object thanks to the manual z linear stages and calibrating the setup, the computer generates the planned trajectories to square objects, with a length of 120µm and 220µm for the silicon ones and 400µm for the SU8 ones.

The object is initially laid on a planar surface made of glass (see Fig. 12.a). The fingers positions trajectories validated in simulation are executed thanks to the positioning stages controllers. No vision feedback is exploited which enables to show the robustness of the proposed method against uncertainties.

The pick-up step was successfully achieved which means that hypotheses about the frictions and the pull-off were Fig. 12: Experimental in-hand manipulation of a 220µm silicon square using 3 fingers. The object is firstly detached from the substrate (a→c). Then a first rotation is performed (c→e). After the in-hand regrasping (e→g), a second rotation (g→i) enables to generate the tested 180 • reorientation for finally replacing the object on the substrate (i→j). satisfied. A residual rotation of the object about the z axis appears during the initial grasping. This is a consequence of calibration errors and fingers orientations defaults (the fingers being not exactly parallel). Positioning errors due to calibration imply that one finger comes in contact with the object before the other one. The orientation defaults of the fibers imply that the contact point is not located on the center of the object side, creating a pivot. However, we can see that the object realigns with the fibers during the manipulation. Rotations and regrasping operations were performed successfully for all object lengths. No apparent sliding has been observed during the 180 • object reorientation as shown on the images sequence of Fig. 12.

The stages displacement ranges and the time required in the execution of the whole manipulation sequence (Fig. 12.b→Fig.12.j) are given in Table III. Note that the presented trajectories execution time was not optimized and further experiments have to be done to define the velocity limit.

V. CONCLUSIONS AND PERSPECTIVES

This paper has presented a new micro-handling method that exploits dexterity provided by a 3-compliant beams manipulation system. A detailed study has been performed to manipulate micro-objects having parallel edges. Manipulation procedure includes the grasping step, the in-hand rotation and the finger gaiting. The stability of each step has been studied considering the worst case. The trajectory planning associated to the defined steps and the fingers design methods have been also provided. Automatic translations and rotations over 180 • degrees of objects with sizes down to 120µm have successfully been performed. This demonstration shows that this approach has a high potential in micro-assembly.

Based on the proof of concept presented in this paper, an automatic 3D handling methods associated to an enhanced setup will be developed. More complex object shapes will be handled thanks to the trajectory planner developed in [START_REF] Seon | Trajectory planner for dexterous in-hand micromanipulation taking into account adhesion forces[END_REF]. Furthermore, rotations about additional axes will be studied enabling out of the plane rotations. Integrated dexterous Fig. 13: 20.3µm in diameter polystyren sphere sticked on a fiber tip. The punctual contact between the micro-sphere and the manipulated object would allow 3D dexterous micromanipulation. piezoelectric microgrippers will be used to perform assembly tasks. More DoF will be integrated to the manipulation system and a fourth finger will be added. To guarantee punctual contact between the fingers and the manipulated object, micro-spheres will be fixed to the fingers tips and used as end-effectors as shown in Fig. 13. This will result in better estimation of the contact point's positions and enables 3D motion control of the manipulated micro-object. Another ambitious perspective is to perform dexterous manipulation at the nanoscale.

Fig. 1 :

 1 Fig. 1: Proposed in-hand manipulation principle : the manipulated object is rotated using 3 microfingers moving in a plane. Each finger has a 2DoF translation motion.

Fig. 3 :

 3 Fig. 3: The proposed dexterous micro-manipulation solution (a) illustrated in 3D and (b) its 2D projection. Compliant beams are used as fingers to grasp and manipulate the object by rolling without sliding. The desired forces are obtained by controlling the fingers bending thanks to the fingers bases positions calculated as a function of the contact points distance.

Fig. 7 :

 7 Fig. 7: Dexterous manipulation using rolling without sliding and finger gaiting techniques: the 180 • rotation of the object is obtained by performing a succession of rotations (a→b, d→e) and regraspings (b→d, e→g).

Fig. 10 :

 10 Fig. 10: Scanning Electron Microscope (SEM) photograph of a 7µm in diameter carbon fiber glued on a silicon tip.

Fig. 11 :

 11 Fig. 11: Simulation of the handling of a 220µm silicon square. Elaborated trajectories are generated (a) and then introduced in the handling simulation block that returns applied forces (b).

TABLE I :

 I Main parameters used in the problem formulation.

TABLE II :

 II Parameters of the experimental setup object, and friction between the fingers and the object:

TABLE III :

 III Manipulation range and execution duration between the initial grasping and the pose of the object.

ACKNOWLEDGMENT

This work has been supported by: Labex ACTION project (contract "ANR-11-LABX-0001-01"), Equipex ROBOTEX project (contract "ANR-10-EQPX-44-01"), French RENAT-ECH network and its FEMTO-ST technological facility, Region of Franche-Comté, Percipio Robotics SA Company.