Transient Vibration Signal Analysis for Bedload Transport Monitoring Systems

Transcription

1 Tranient Vibration Signal Analyi for Bedload Tranport Monitoring Sytem Gabriel Vaile, Guy D Uro, Elena Lungu To cite thi verion: Gabriel Vaile, Guy D Uro, Elena Lungu. Tranient Vibration Signal Analyi for Bedload Tranport Monitoring Sytem. MTS/IEEE North American OCEANS conference (OCEANS 7), Sep 27, Anchorage, United State. < <hal-59349> HAL Id: hal Submitted on 26 Sep 27 HAL i a multi-diciplinary open acce archive for the depoit and diemination of cientific reearch document, whether they are publihed or not. The document may come from teaching and reearch intitution in France or abroad, or from public or private reearch center. L archive ouverte pluridiciplinaire HAL, et detinée au dépôt et à la diffuion de document cientifique de niveau recherche, publié ou non, émanant de établiement d eneignement et de recherche françai ou étranger, de laboratoire public ou privé.

2 Tranient Vibration Signal Analyi for Bedload Tranport Monitoring Sytem Gabriel Vaile Grenoble-Image-Peech-Signal-Automatic Lab CNRS / Univ. Grenoble Alpe Grenoble Cedex, France, F-3842 gabriel.vaile@gipa-lab.grenoble-inp.fr Guy d Uro Electricité de France EDF R&D, STEP Chatou, France, F-784 guy.duro@edf.fr Elena Lungu SIGnal INformatic TEChnology SIGINTEC Nîme, France, F-3 elungu@igintec.fr Abtract Thi paper propoe a novel framework for detecting and localizing the tranient correponding to the hock created by ediment impact on a teel plate. Baed on unupervied hierarchical agglomeration of complex vibration pectra, the derived claification i available for bedload tranport monitoring tation in underwater environement. I. INTRODUCTION Underwater bedload tranport urvey i important for aeing tability iue uch a reervoir ilting or channel elfcleaning. To thi purpoe, ediment trap are currently ued to derive the ediment balance. For example, the Birkbeck ampler ha become one of the preferred method for in itu bedload meaurement. An alternative nonintruive bedload monitoring intrument i the buried geophone tation [], [2], [3]. Under protection of teel plate, everal geophone can provide continuou and automatic meaurement, even during large flood. Every tone paing the teel geophone equipped plate generate an impule recorded by the ignal acquiition board. Uing a calibrated voltage threholding cheme the grain impact are recorded and counted. In [4], Bogen and Moen ued piezoelectric acoutic tranducer for bedload monitoring tation in Norway. Recently, we have propoed, the coupling of ultraound (US) tranducer and with piezoelectric accelerometer for bedload tranport monitoring tation. The reult obtained in a controlled laboratory environment provided intereting enitivity capabilitie, in accordance with the ground truth. The main objective of [5] were to increae the operating frequency of the acoutic tranducer, to provide conitent calibration and proceing and to evaluate the uncertainty of the derived meaurement. To purue thee objective, an experimental platform, illutrated in Fig. - ha been developed and teted in the GIPSA-Lab controlled tank ytem. The following enor have been employed: four ultraound contact tranducer PAC R5 (EM, R2, R3, R4), 2 calibrated piezoelectric accelerometer Endevco 233E (A, A), geophone R.T. Clark (G). Fig.. Multi-enor bedload tranport monitoring platform: general view, etup of the acoutic enor on the top teel plate. The EM US tranducer ha been excited uing the ENI 2L power amplifier and the Picotet G5A arbitrary ignal generator. The received ignal from A, A2, R3, R4 have been conditioned uing the Nexu low noie amplifier and recorded uing the PXIe-82 NI ytem. Thi paper propoe a new framework for detecting and localizing the tranient (in the paive configuration) correponding to the hock created by ediment impact on the teel plate. The propoed algorithm i baed on hierarchical agglomeration of complex vibration pectra. The multivariate egmentation algorithm propoed in [6] i elected: the multimodal ignal are analyzed by exploiting the aymptotic ditribution of the covariance matrix of the complex pectra. The paper i tructured a follow. Section II illutrate in everal tep the general framework of hierarchical agglomeration of complex vibration pectra, while Section III preent both qualitative and quantitative performance aement. Section IV conclude the paper.

3 II. HIERARCHICAL AGGLOMERATION OF COMPLEX VIBRATION SPECTRA The firt tage of the propoed egmentation cheme i preproceing. A each acquiition i triggered on the amplitude level of the enor exhibiting the fatet repone time (the accelerometer in our cae), the obtained tranient ignal i not ymmetric. In order to improve the pectral repreentation, each received ignal i circularly hifted to the right and filtered in the common bandwidth. The complex pectrum i obtained by applying the Fat Fourier Tranform (FFT) on each ignal. One advantage of thi repreentation reide in the fact that it i independent of the time of arrival of each tranient. A. SIRV pectral etimation In the next tep, a multivariate random vector i obtained by concatenating all the complex pectra of the available ignal. For each enor, let k be the m complex target vector correponding to the ame frequency range. One way to model the tatitical propertie of thi multivariate random vector lead to Spherically Invariant Random Vector (SIRV) [7]. It i defined a the product of a quare root of a poitive random variable τ (variation in power) with an independent circular complex Gauian vector z with zero mean and covariance matrix [M] = E{zz H } (Gauian kernel): k = τ z, () where the upercript H denote the complex conjugate tranpoition and E{ } the mathematical expectation. SIRV repreentation i not unique, o a normalization condition i neceary. Indeed, if [M ] and [M 2 ] are two covariance matrice uch that [M ] = α[m 2 ]. Then {τ, [M ]} and {τ 2 = τ /α, [M 2 ]} decribe the ame SIRV. In thi paper, the trace of the covariance matrix i normalized to p the dimenion of target cattering vector (p = 3 for the reciprocal cae) [7]. The ML etimator of the normalized covariance matrix under the determinitic texture cae i the olution of the following recurive equation : [ ˆM] F P = f([ ˆM] F P ) = p N N i= k H i k i k H i [ ˆM] F P k, (2) i with T r([ ˆM] F P ) = p. It aymptotic ditribution can be aimilated to the Wihart Probability Denity Function (PDF) [7]. In thi way, each random vector i decribed by it normalized covariance matrix, which i independent on the total power at the reception. Thi will form the feature pace for the tranient egmentation algorithm. B. Hierarchical egmentation The hierarchical egmentation algorithm from [6] i adapted to the vector of complex pectra. The egmentation algorithm i a claical iterative merge algorithm. At each iteration, the two egment which minimize the Stepwie Criterion (SC) are merged. The baic principle of the hierarchical egmentation algorithm can be divided into three tep : ) Definition of an initial partition (which i formed by the acquired buffer, in our cae). 2) For each egment pair, SC i computed. Then, the two egment which minimize the criterion are found and merged. 3) Stop if the maximum number of merge i reached, otherwie go to tep 2. C. Similarity meaure At each iteration, merging two egment yield a decreae in the log-likelihood function. The tepwie criterion i baed on thi conideration. The hierarchical egmentation algorithm merge the two egment S i and S j which minimize the lo of likelihood of the partition (which i defined a the um of likelihood of partition egment). The tepwie criterion (SC i,j ) can be expreed a: SC i,j = MLL(S i ) + MLL(S j ) MLL(S i S j ), (3) where MLL( ) denote the egment maximum log-likelihood function. It i the log-likelihood of the egment (ample in each egment are conidered independent realization) with repect to the aumed probability denity function (the Wihart ditribution in our cae) whoe parameter are etimated in the maximum likelihood (hence, the name) ene. It expreion i given by: MLL(S) = ( ) ln p k (k i θ S ), (4) i S θ S repreent the et of ditribution parameter (normalized covariance matrix in our cae). ) Generalized Maximum Log-Likelihood (GMLL): In general, the normalized covariance matrix i unknown. One olution conit in replacing the SIRV parameter by their etimate. After replacing the covariance matrix [M] by it repective ML etimator, the tepwie criterion become: SC i,j = GMLL(S i ) + GMLL(S j ) GMLL(S i S j ), (5) where GMLL(S) i the generalized maximum log-likelihood function for egment S. 2) For the Wihart PDF: the generalized maximum loglikelihood function for egment S i: { GMLL(S) = pn ln(π) N ln [ ˆM } ML ] (6) where [ ˆM ML ] i the ML etimator of [M ML ] for egment S (2). D. Stop criterium The ue of the L-method [8] ha been conidered in thi paper. Thi method employ the very error (quality) function that i ued to perform cluter merging during the hierarchical egmentation algorithm, pecifically the Log-Likelihood Function (LLF) of the partition (i.e. the um of the MLL value for all the egment of the partition). A thi i readily computed

4 during the propoed method, no further computational effort i required. The knee of thi error function i identified and the optimal number of cluter i choen at that point. The knee of a curve i omewhat imilar to the point of maximum curvature. III. RESULTS AND DISCUSSION The propoed experimentation were carried in the GIPSA- Lab controlled tank ytem. Fig. 2 and 3 illutrate the tranient ignal obtained from the four enor (accelerometer and ultraound) in paive configuration, after right circular hift and common band pa filtering. Accelerometer A [dbv] [dbv] Accelerometer A Frequency [KHz] Ultraound tranducer R Frequency [KHz] -.5 Fig. 3. Senor recording pectra in paive configuration, buffer triggered by A: accelerometer A (up) and ultraound tranducer R2 (down) Accelerometer A Ultraound R Ultraound R Fig. 2. Senor recording in paive configuration, buffer triggered by A: accelerometer and ultraound tranducer. In order to build the data bae, five metallic ball with different diameter have been elected for the experiment. For each ball, 25 independent impact have been recorded uing the bedload tranport monitoring platform from Fig.. The ball have been manually releaed form the urface of the water at approximately the ame poition on the metallic plate. An independent buffer ha been recorded for each impact with the four enor imultaneouly and coherently. After concatenating the 25 5 buffer, Fig. 4 how the derived ignal ued to tet the propoed hierarchical agglomeration algorithm. The obtained reult are preented in the confuion matrix from Tab. I. There are at leat two fact to be noticed. Firtly, the diagonal tructure of the confuion matrix reveal a rather good claification accuracy. Secondly, the L-method toped the egment merging at 8 clae. Thi i explained by the fact that the impact of the ball have been plitted in two clae, while ome impact from and generated two additional clae. Thi i in agreement with the ubjective viual aement of the ignal from Fig. 4. TABLE I QUANTITATIVE PERFORMANCE ASSESSMENT: CONFUSION MATRIX. SC (FROM TO 8) ARE THE CLASSES OBTAINED BY THE PROPOSED ALGORITHM, WHILE TC (FROM TO 5) ARE THE GROUND TRUTH BASED CLASSES. TC TC 2 TC 3 TC 4 TC 5 SC 25 8 SC SC SC SC 5 SC 6 9 SC 7 4 SC 8 2 Finally, an overall quantitative indicator of the performance of the propoed algorithm i the claification accuracy A,

5 B Accelerometer A B Accelerometer A B Ultraound R B Ultraound R Fig. 4. Senor recording in paive configuration, buffer triggered by A: accelerometer and ultraound tranducer. defined a: 5 i= A = T P Bi + 5 i= T N Bi, (7) 5T with T P Bi the true poitive for the metallic ball Bi, T N Bi the true negative and T = 25 the total population. After fuing the clae SC 5 and SC 6, SC 2 and SC 8, SC 4 and SC 7, we can compute the total claification accuracy according to Eq. 7. The obtained value i A = 9.9%. IV. CONCLUSION Thi paper propoed a new framework for detecting and localizing the tranient correponding to the hock created by ediment impact on the teel plate. The propoed claification trategy i baed on hierarchical agglomeration of complex vibration pectra: the multimodal ignal were analyzed by exploiting the aymptotic ditribution (SIRV) of the normalized covariance matrix. Qualitative and quantitative performance aement ha been carried out uing vibration ignal recorded by the multi-enor bedload tranport monitoring platform form the GIPSA-Lab. Future work will enroll in two main direction. Firtly, we will try to explore a much a poible all the benefit of the propoed claification algorithm in real life cenario. Secondly, we will continue with improving the decription of tranient vibration ignal by uing non-tationary timefrequency repreentation intead of the Fourier tranform. REFERENCES [] D. Rickenmann, J. M. Turowki, B. Fritchi, A. Klaiber, and A. Ludwig, Bedload tranport meaurement at the Erlenbach tream with geophone and automated baket ampler, Earth Surface Procee and Landform, vol. 37, no. 9, pp., 22. [2] D. Rickenmann, J. M. Turowki, B. Fritchi, C. Wy, J. B. Laronne, R. Barzilai, I. Reid, A. Kreiler, J. Aigner, H. Seitz, and H. Haberack, Bedload tranport meaurement with impact plate geophone: comparion of enor calibration in different gravel-bed tream, Earth Surface Procee and Landform, vol. 39, no. 7, pp , 24. [3] R. Hilldale, W. Carpenter, B. Goodwiller, J. Chamber, and T. Randle, Intallation of impact plate to continuouly meaure bed load: Elwha river, Wahington, USA, J. Hydraul. Eng., vol. 4, no. 3, pp. 6423, 25. [4] J. Bogen and K. Moen, Bedload meaurement with a new paive acoutic enor, in Eroion and Sediment Tranport Meaurement in River: Technological and Methodological Advance, 23, pp [5] G. Vaile, G. d Uro, R. Charlatchka, and E. Lungu, Calibration of an active ultraound bedload monitoring ytem for underwater environment, in Proceeding of the MTS/IEEE North American OCEANS conference, Wahington, DC, USA, 25, pp. 4. [6] L. Bombrun, G. Vaile, M. Gay, and F.C. Totir, Hierarchical egmentation of polarimetric SAR image uing heterogeneou clutter model, IEEE Tranaction on Geocience and Remote Sening, vol. 2, no. 46, pp , 2. [7] G. Vaile, F. Pacal, J.P. Ovarlez, P. Formont, and M. Gay, Optimal parameter etimation in heterogeneou clutter for high-reolution polarimetric SAR data, IEEE Geocience and Remote Sening Letter, vol. 8, no. 6, pp. 46 5, 2. [8] S. Salvador and P. Chan, Determining the number of cluter/egment in hierarchical clutering/egmentation algorithm, in 6th IEEE International Conference on Tool with Artificial Intelligence, ICTAI 24, 24, pp