Methods for the automated detection of acoustic multiplets and their hierarchical classification according to the similarity of their emission mechanisms
Note : originally, this method has been developped to study acoustic multiplets from fatigue of materials. However, as general AE method, acoustic multiplets from other fields can also be detected.
See publications on this topic for more details [1] and [2].
This package was created and documented by Théotime de la Selle. Any contributions are very welcomed.
This work was supported by the french ANR project e-Warnings (ANR-19-CE42-001).
Copyright ©️ 2024 Théotime de la Selle
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.
No installation is needed. Just download the codes and their dependencies (functions).
(See graphic for more details of the Method architecture.pdf)
- AE : acoustic emission.
- WF : digitized waveform of an individual AE signal (generally around hundreds of microseconds,sampled between 1 and 5 MHz).
- TOA : time of arrival of a single WF. In AE field, TOAs are commonly defined as threshold crossings.
- PDM : Partial Dissimilarity Matrix, see graphic and [1].
- MultiDetec() : identifies multiplets in an AE waveform dataset and establishes the dissimilarity structure between them (dendrogram).
Multiplets or clusters of multiplets analysis :
- DendroCut() : plot colored dendrogram (pre-computed ; Ward' method) and calculate clusters of multiplets from it according to a user-selected level of dissimilarity.
- MultiCentroid() : Determine the centroid iteratively by calculating cross-correlation maximum between each waveforms of a multiplet and the centroid steps ; then plot the resulting centroid.
- WFSuperposed() : align and plot all waveforms of a multiplet or cluster of multiplets (also compute and plot the centroid). /!\ could be long to compute
Sub-functions of MultiDetec() :
1.1 PartialDissimiMat() : compute the partial dissimilarity matrix of a waveform dataset part by finding the maximum of the cross-correlation function between specific pairs of waveforms.
1.2 Threshold() : estimate automatically a dissimilarity threshold from the distribution of partial dissimilarity matrix coefficients.
-> 1.2.1 Distribution() : compute distribution of some matrix coefficients from its diagonals.
1.3 MultiPeriod() : (optionnal) give a measure of the multiplets signals emission time period.
1.4 MultiAssembly() : assembles (or delete) pre-clusters, obtained by application of DBSCAN on partial dissimilarity matrices, into multiplets by cutting a dendrogram (centroid linkage), obtained by hierarchical clustering of pre-clusters centroids. The mean of dissimilarity thresholds is used to automatically select the cutting level.
-> 1.4.1 MultiCentroid() : same as 3, but on pre_clusters (no plot of centroid).
Entries :
-
WF(s,n) : array of all n individual AE waveforms composed of s points, ordered by increasing time of arrival.
-
Toa(n) : list (sorted) of n Time Of Arrival associated to each waveforms of WF.
-
dtmax : (float number) time limit for partial dissimilarity matrix calculation (see Content description).
-
PDM(n,n) (optionnal) : previously computed partial dissimilarity matrix (see How to use).
Returns :
-
Multiplets(n) : list of multiplets assignations (identified by numbers) of each n waveforms, ordered by increasing time of arrival.
-
Dendrogram : array of multiplets links and respective levels of recomputed dissimilarity metric (Ward' method). Used to plot dendrograms and perform clustering.
Multi-Detec, to be user-friendly as possible, has been developped upon 3 categories of parameters. According to your expertise and Multi-Detec usage, you will set only one or all of the 3 categories.
Operator parameter is a function parameter (in MultiDetec) while cross-correlation and super-user parameters has to be set directly in MultiDetec code, into the structure variable para.
(parameter for all)
dtmax : defines the maximum gap between TOAs of 2 WF to perform dissimilarity measure of them (i.e. a PDM coefficient). Note that dtmax is not used by the code if a PDM is provided.
- In case of periodically emitted multiplets signals (MultiPeriod function activated), dtmax has to reach a value to accurately detect multiplets. However, above this value, a large dtmax increases time complexity as more PDM coefficients are computed.
- In case of non-periodically emitted multiplets signals (MultiPeriod function disactivated), dtmax defines totally PDM and thus the multiplets detection. dtmax has to be chosen according to the context.
(parameters for ajusting the dissimilarity metric based on cross-correlation function)
- pretrig_cut : (boolean) keep (0) or not (1) the WF pretrigger during calculation of dissimilarity between WF.
- pretrig_length : (integer) size of pretrigger in points.
- window : (integer) size of the cross-correlation window in pts.
(all are integers)
- minsize : minimal nomber of WF in each multiplets (clusters composed of less WF are deleted).
- d : multiplets density parameters (see [1]).
- mat_size : defines PDM size.
- degree : factor for selecting number of diagonals in Threshold function.
- minpts : a DBSCAN parameter, see [1] or DBSCAN definition.
[1] Théotime de la Selle, Jérome Weiss, Stéphanie Deschanel, Acoustic multiplets detection based on DBSCAN and cross-correlation, Mechanical Systems and Signal Processing, Volume 211, 2024, https://doi.org/10.1016/j.ymssp.2024.111149.
For more information about physical sources of multiplets :
[2] Théotime de la Selle, Julien Réthoré, Jérôme Weiss, Joël Lachambre, Stéphanie Deschanel, Signatures of fatigue crack growth from acoustic emission repeaters, Engineering Fracture Mechanics, Volume 309, 2024, https://doi.org/10.1016/j.engfracmech.2024.110388.