·Table of Contents
A New Advanced Multitechnique Data Fusion Algorithm for NDTNathalie FRANCOIS
EDF/Etudes et Recherches
6, Quai Watier
78400 Chatou, France
E-mail : firstname.lastname@example.org
|Fig 1: BE-Mistral project Partners|
« Mistral » stands for « Multi sensor Inspection System for component Testing: toward more Reliable non destructive testing AppLications». The objectives were to develop new multitechniques tools for improved NDT of components from the energy and chemical industries. Two kinds of developments were performed: multitechnique probes, combined acquisition procedures, and data fusion algorithms.
In this paper we focus on the description of a data fusion algorithm developed and tested for the Mistral project.
1.1. Presentation of the Dempster-Shafer Theory
The Dempster-Shafer theory offers a model to the knowledge about one or more hypothesis. This model enables to quantify such concepts as imprecise measurements or uncertainty. The parameter used to perform this description is the evidence mass associated to each event.
The Dempster-Shafer theory enables also to calculate a unique evidence mass for a hypothesis by combining the evidence masses associated to this hypothesis by various sources or operators. This calculation is performed via the « combination rule », also called « orthogonal sum ». This unique evidence mass represents and quantifies the global knowledge we have on a hypothesis from various points of views (for example, various sensors) that we call sources.
If we note m(1) the evidence masses calculated from the data from source 1, and m(2) those calculated from source 2, the combination rule is written m(1Å 2)=m(1)Åm(2).
The evidence mass attributed to an element C belonging to 2Q , space of the elements of our workspace Q, is calculated the following way:
1.2. Application of the Dempster-Shafer theory to a NDT problematic
The problematic we want to solve is the 3D reconstruction of a volume in a component that we inspect with two techniques: radiography and ultrasound measurement. The data fusion should enable us to take advantage of the particularities of both techniques. Therefore we are going to calculate the evidence mass associated to each technique and then fuse them to obtain the global evidence mass representing the global knowledge we have about the inspected component.
On each voxel of the reconstruction volume we consider two hypothesis:
Hence we dispose of three evidence masses calculated from the measurements from each technique (radiography, ultrasound inspection) and we apply the combination rule in order to obtain a final set of three evidence masses on each voxel of the reconstruction volume. We call evidence volume the reconstruction volume where each voxel has been attributed the relevant set of evidence masses.
The architecture of the algorithm can therefore be presented as in Figure 2 .
|Fig 2: Architecture of the Data Fusion Algorithm|
2.1. Data Repositioning
The data that we have to fuse need to be accurately positioned in the same system of reference. A step of repositioning is therefore needed before any other processings. As the measurements are performed according a combined acquisition procedure (dedicated to the simultaneous acquisition of radiographs and ultrasound data with an objective of data fusion), this step is minimised and simplified by the presence of common markers used for both techniques.
2.2. Single-Technique Processings
We first proceed to the processing of the two kinds of data separately. We are trying to calculate the set of evidence masses from each technique for each voxel of the volume we want to reconstruct. The calculation of these evidence masses is based on an evaluation of the certainty of presence or absence of flaw given by the measurements we dispose of.
2.2.1 Evidence calculation from Ultrasound data:
In the case of the ultrasound data, the first step is a 3D-reconstruction of the A-scans. We are not going to detail this step in this paper. We therefore consider that we are working on 3D reconstructed data. The method used for the calculation of the evidence masses is based on a comparison between the local and global amplitude distribution around the considered voxel. The concept of «local» corresponds here to the definition of a neighbourhood of the voxel. We typically use a neighbourhood constituted of 26 voxels (one neighbour along each direction). The «global» concept includes all the voxel belonging to the reconstruction volume.
Fig 3: Presentation of the neighbourhood of the voxel|
The calculation stages are the following:
|Fig 4: Determination of evidence masses|
Effectively the certainty that the considered voxel is flawed (positive evidence) increases if the local amplitude average is high compared to the global amplitude average. In parallel, the certainty of an absence of flaw (negative evidence) decreases. Moreover, the standard deviation around the local average corresponds to a certain noise that we interpret as an uncertainty (doubt).
2.2.2. Evidence calculation from XR data:
The same kind of calculation is performed for the determination of the evidence masses issued by the XR data. In this case, the concept of «local» refers to the pixels associated by backpropagation to the considered voxel: these are the pixels which are an image of the considered voxel, on the radiogram, seen from the XR source position. The concept of «global» includes every pixel from the radiogram (in the limit of the «image» of the reconstruction volume by backpropagation).
|Fig 5: Determination of the «local» pixels by projection|
The determination of the evidence masses is then performed as described previously on the amplitudes (grey level intensities) of the pixels associated by projection to the considered voxel, as compared to the amplitudes of the pixels on the whole film (in the limits of the projection, on the film, of the volume we are trying to reconstruct).
2.3. Multitechnique Data Fusion
We then fuse the sets of evidence masses calculated by the single processings with the Dempster-Shafer combination rule. We can also use this formula in order to combine the evidence masses obtained from various homogeneous data (for instance several radiograms or several ultrasound reconstructions).
If we note Psource, Nsource and Dsource the positive evidence, negative evidence and doubt (respectively) calculated with the data of type source, and Pf, Nf, Df the final positive, negative and doubt evidence resulting from the fusion, the combination rule is written as follows:
Pf=(PXR ´PUS +PXR ´DUS +DXR ´PUS )/(1-K)
Nf=(NXR ´NUS +NXR ´DUS +DXR ´NUS )/(1-K)
|Df=DXR ´DUS /(1-K)
K=PXR ´NUS +NXR ´PUS
The factor K measures the contradiction between the various sources. The more K is near to the value 1, the greater contradiction there is between the various sources. When the evidence masses related to each source are very dissimilar (K very near to 1), we may have to reconsider the result of the combination. Therefore we introduce a «modified combination rule»:
Pf=(PXR ´PUS +PXR ´DUS +DXR ´PUS )|
Nf=(NXR ´NUS +NXR ´DUS +DXR ´NUS )
|Df=(PXR ´NUS +NXR ´PUS +PXR ´DUS )|
|Fig 6: Presentation of mock-up 1|
The results on these mock-ups show that data fusion enables to obtain:
We can therefore conclude that we gain knowledge on the defect via the fusion of data.
We present some results from mock-up 1 on one flaw, in order to illustrate these conclusions:
(For the XR results, five shots were performed and utilised).
|Mock-up 1||Real||US results||XR results||Fusion results|
|Thickness||-||15 mm||2 mm||2 mm|
|Length||15 mm||> 20 mm||14 mm||14.5 mm|
|Depth||3 mm||6 mm||14 mm||3 mm|
|Fig 7a: Positive evidence, XR results||Fig 7b: Positive evidence, US results||
Positive evidence, Fusion results
Example of results, mock-up 1, Positive evidence (Slice)|
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