Two applications of Independent Component Analysis for Non-Destructive Evaluation by Ultrasounds Addisson Salazar1, Jorge Gosálbez1, Jorge Igual1, Raúl Llinares1 1
Universidad Politécnica de Valencia, Departamento de Comunicaciones, Camino de Vera s/n, 46022 Valencia, Spain
[email protected],
[email protected],
[email protected]
Abstract. This paper presents two novel applications of ICA in Non Destructive Evaluation by ultrasounds applied to diagnosis of the material consolidation status and to determination of the thickness material profiles in restoration of historical buildings. In those applications the injected ultrasonic pulse is buried in backscattering grain noise plus sinusoidal phenomena; this latter is analyzed by ICA. The mixture matrix is used to extract useful information concerning to resonance phenomenon of multiple reflections of the ultrasonic pulse at non consolidated zones and to improve the signals by detecting interferences in ultrasonic signals. Results are shown by real experiments at a wall of a Basilica’s restored cupola. ICA is used as pre-processor to obtain enhanced power signal B-Scans of the wall.
1
Introduction
Non-destructive evaluation (NDE) by ultrasounds is a very useful technique applied in fields such as construction, food, and biomedicine. The technique has basically two operation modes: pulse-echo (one sensor as emitter and receiver) and transmission (one emitter and one receiver). An ultrasound pulse is injected in the inspected material and a response of the material microstructure is received [1,2]. The measured signal can contain echoes produced from discontinuities, inhomogeneities, borders of the material, plus material grain noise (superimposition of many small echoes due to the material microstructure). All of this information can be used for quality control and characterization of materials [3,4]. The present study used the pulse-echo technique given the inspected material consisted of a wall with no possible access from opposite sides. This wall was a zone at the cupola of the Basilica de la Vírgen de los Desamparados in Valencia, Spain. This paper includes two novel applications of ICA [5,6] as pre-processor in ultrasound NDE applied to historical building restoration. The first application consists in using the mixture matrix to discern on useful material information of the consolidation process that consists in injecting a product to fill cracks at the wall. The second application is detecting interferences in the recorded signals to cancel them improving the quality of the signals. This procedure was applied to recorded signals for estimating thickness layer profile at the wall.
Interferences can be due to the internal clocks of the measurement equipment, interferences with other equipments, and so on. In many applications, the recording of a high quality raw data is a difficult task, especially in situations where the conditions can not be controlled during the experiment. One difficulty to have the measurements at the cupola was the use of a plastic for covering the transducer to avoid direct contact of the ultrasonic coupling gel with artistic painting on the walls. This kind of measurement produced attenuated signals B-Scans diagrams were used to visualize consolidated and non consolidated material zones to check the quality of restoration and to detect interfaces between different materials in the wall. B-Scan is a 2D representation of a signal set. The evolution in time windows of a parameter such as power or spectrum is calculated for each one of the signals. Then all the calculated information is put together in a representation of the measurement point versus the signal parameter evolution. Figure 1 shows different points of a B-Scan measured by ultrasound at the cupola. M easurement 1 M easurement 2
M easurement 11 M easurement 12
Fig. 1. Ultrasound inspection at the cupola
Following sections describe the ICA model of the problem; the experiments performed, including the equipment setup, a comparison between the B-Scans obtained using or not using ICA as a pre-processor and the sensitivity to detect interferences. Finally the conclusions and future work.
2
ICA Statement of the Problem
The recorded signals are modelled as the superposition of the backscattered signal plus sinusoidal phenomena. This latter sinusoidal contribution should be determined to know if it is due to useful information on the material structure, such as material resonances, or interferences due to the instrumentation during measurement. ICA statement of the problem is: N −1
x k (t ) = s k (t ) + ∑ α ik e j (ωi t +θ ik ) i =1
k = 1...M
(1)
where M is the number of measurements, x k (t ) is the received signal from the material at the position k of the B-Scan, sk (t ) is the backscattering signal that depends on the material microstructure, and α ik e j (ω t +θ ) i = 1K N − 1, k = 1K M are the sinusoidal sources to be analyzed. The backscattering signal, under certain assumptions related to the wavelength of the ultrasonic wave and the scattering size, can be modeled as a stochastic process given by: i
ik
{Z~(x, t )} = ∑ A~ (x) f (t − τ~ (x)) N (x) n =1
n
n
(2)
where x is the transducer location (we obtain different backscattering registers for ~ different transducer locations). The random variable, An , is the scattering crosssection of the nth scatter The r.v. τ~ is the delay of the signal backscattered by the n
nth scatter and N (x) is the number of scatters contributing from this position. The function f (t ) is a complex envelope of the ultrasonic frequency pulse, that is f (t ) = p(t )e jω0t
(3)
where p(t ) is the pulse envelope and ω 0 the transducer central frequency. Backscattering model of equation (2) is composed of a homogeneous nondispersive media, and randomly distributed punctual scatters depicting the composite nature of the received grain noise signal instead of a rigorous description of the material microstructure [7]. In the simplest case consisting of a homogeneous material and only one harmonic of the sinusoidal component, the ICA model of equation (1) is x k (t ) = s (t ) + α k e j (ωit +θ k )
k = 1...M
(4)
As we know, in usual ICA (no prior information ICA model included) we need as many mixtures as sources. In the case of equation (1), a B-Scan of 2 points would be enough. In the proposed applications M = 12 and 10, therefore 12 and 10 mixtures were used in order to include the anomalies of the material and allow a relative high number of interferences. Even more; if we think that there is not enough with the M points registered, the number of sensors can be virtually increased if we record responses to different pulses, considering that the echo is the same and the pulse repetition period is not a multiple of the sinusoid period [8]. Obviously the sinusoidal components have the same frequencies along the B-Scan, with possibly changing amplitude and phase. From a statistical point of view, considering the interference or resonance as a sinusoid with deterministic but unknown amplitude and uniform random phase, it is clearly guaranteed that the backscattering signal and it are statistically independent.
3
Experiments and Results
The objectives of experiments were visualizing non consolidated zones and calculate layer thickness at the wall of the cupola. Ultrasound transducers have a working transmission frequency; the higher transducer frequencies the higher capacity to detect small details, but also lower capacity of material penetration. Therefore using high frequencies is possible to detect smaller details but they have to be closer to material surface. The transducer used for consolidation analysis (application 1) was 1 MHz and transducer used for thickness layer profile was 5 MHz (application 2). This latter was selected because we were interested in obtaining information of the superficial layers. 3.1 Equipment setup The equipment setup used for NDE of the historical building was the following: Ultrasound equipment setup Ultrasound Matec PR5000 Equipment 1 MHz (application 1) Transducers 5 MHz (application 2) Pulse width 0.9 µs Pulse amplitude 80 % 200 kHz – 2.25 MHz (ap. 1) Analog filter 1 MHz – 7 MHz (ap. 2) Tone burst Excitation signal 1 MHz and 5 MHz Operation mode Pulse-echo Amplifier gain 65 dB
Acquisition equipment setup Acquisition Oscilloscope equipment TDS3012 Tektronix 10 MHz and Sampling frequency 250 MHz Sample number 10000 Observation time 1 ms and 40 µs Vertical resolution
16 bits
Dynamic range
± 2.5V
Average PC connection
64 acquisitions GPIB
Table 1. Equipment setup
Due to the temporal structure of recorded signals we selected the Temporal Decorrelation Separation TDSEP algorithm based on simultaneous diagonalisation of timelagged correlation matrices. This algorithm exploits the temporal structure of the signals and can separate more than one Gaussian [9]. The mixture matrix obtained by ICA was used to separate the information concerning to the sinusoidal phenomena. 3.2 Diagnosis of the material consolidation status Figure 2 shows the B-Scan estimated by the signal power using a conventional nonstationary analysis applying a moving window over the 12 ultrasonic recorded signals. Figure 2a shows two zones clearly differentiated; the first corresponds to consolidated zone (low level of signal) and the second corresponds to non consolidated zone (high level of signal). The signal penetrates well into the wall at the consolidated zone and it is attenuated before reflecting any kind of signal. Conversely, the signal
level is increased in a non consolidated zone due to multiple reflections of the ultrasonic pulse, see Figure 2b. Signal is attenuated
Air hole
Multiple reflections are produced giving a higher signal level
2b. Scheme of the wall
2a. B-Scan
Fig. 2. Power signal B-Scan by non-stationary analysis
2
2
4
4
6
6
Signals
Signals
From the spectral analysis, two frequencies (181 and 356 kHz) were found in all the recorded signals. After estimating B-Scan of Figure 2 was not clear enough the origin of those frequencies, they could be interferences or material resonances. Then we applied ICA to obtain more information from the mixture matrix and recovered sources. Figure 3 shows the recorded signals and the recovered sources by ICA; the sample numbers processed were from 600 to 6000.
8
8
10
10
12
12 0
1
2
3
4
5 Time (us)
6
7
8
0
9 -4
x 10
3a. Recorded signals
0.5
1
1.5
2
2.5 3 Time (us)
3.5
4
4.5
5 -4
x 10
3b. Recovered sources
Fig. 3. Recorded signals and recovered sources (the supposed “interference” is highlighted)
Figure 4a and 4b show two B-Scans obtained from the mixture matrix corresponding to x =
12
∑a s , s i =1
i i
12
i
= 0 (i ≠ 2) and x = ∑ a i s i , s i = 0 (i = 2) respectively. The i =1
first B-Scan represents the sinusoidal phenomenon depicting the non consolidated zone thus this phenomenon can be associated with the shape of the material non consolidated zone. The second B-Scan is the complementary information concerning to
the consolidated zone. The diagrams obtained from ICA information depict more precisely the two different zones of the material.
4a. Power B-Scan from sinusoidal components
4b. Power B-Scan from backscattered components
Fig. 4. Power B-Scan after ICA preprocessing
3.3 Thickness material layer profile Figure 5a and 5b show the recorded signals plus an artificial interference added and the corresponding B-Scan calculated by the evolution of the centroid frequency. Following information is represented in the diagram: i.) axis x: transducer position; from position 0 to 10, ii.) axis y: depth axis, and iii.) axis z: depicted by colours that denotes the parameter level at a given position in a given depth. Temporal signals with 1MHz interference 1 2 3
Signals
4 5 6 7 8 9 10 0
0.5
1
1.5
2 Time (us)
2.5
3
5a. Recorded signals
3.5 -5
x 10
5b. centroid frequency B-Scan
Fig. 5. Recorded signals and centroid frequency B-Scan by non-stationary analysis
The depth is obtained by depth = velocity * time / 2 where factor 2 is due to the round trip travel of the ultrasound pulse between the material surface and the layer. The first two layers of the cupola wall were composed of mortar and plaster respectively. For calculation of depth, an average ultrasound propagation velocity of 1600
m/s was used calculated from lab probes. Due to the 1 MHz interference, the B-Scan is not clear enough to represent a profile of a layer. Figure 6a and 6b shows the results obtained by applying ICA on the ultrasonic signals. To assess the sensitivity of the ICA in detecting the interference, a controlled interference was added to the signals, trying with different frequencies and amplitudes of the interference. Figure 6a shows the error in the extraction of the interference versus the ratio power interference to power signal (Pinterference/Psignal ) for different interference frequencies. The higher interference amplitude the better extraction of the interference and the higher interference frequency the worst extraction of the interference. Figure 6b shows the centroid frequency B-Scan of the ultrasonic signals with the cancelled interference. Error between the recovered interference and the real interference (%)
2
10
Interference Interference Interference Interference Interference
freq. freq. freq. freq. freq.
=1MHz =2MHz =3MHz =4MHz =4.5MHz
1
Error (%)
10
0
10
-1
10
0
10
20
30 40 P interference/P signal
50
60
70
6a. Error percentage vs. (Pinterference/Psignal )
6b. centroid frequency B-Scan with cancelled interferences
Fig. 6. Recorded signals and centroid frequency B-Scan by non-stationary analysis
Figure 6b depicts an enhanced B-Scan with a layer clearly defined at 4 mm. corresponding to the mortar layer of the cupola wall.
4.
Conclusions
The ICA model for ultrasound evaluation as the superposition of the backscattered signal plus sinusoidal phenomena has been tested by means of two novel applications. The application of ICA to NDE by ultrasounds has enabled the diagnosis of the consolidation status in restoration of historical buildings. The proposed procedure allowed separating the sources corresponding to the contributions of consolidated and non consolidated zones to the backscattered recorded signals (application 1). The application of ICA to NDE by ultrasounds made possible the determination of the thickness layer profile allowed cancelling interferences from the recorded signals. The enhanced B-Scan allowed determining the first thickness layer of mortar for the analyzed wall. ICA works well when the interference signal has certain level related to the ultrasonic signal.
Enhanced power and centroid frequency B-Scans were obtained using ICA as preprocessor of the non-stationary analysis. Future work is being addressed to apply the ICA for classification and characterization of materials.
Acknowledgements This work has been supported by Spanish Administration under grant TEC 200501820 and Universidad Politécnica de Valencia under interdisciplinary grant 20040900.
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4. 5. 6. 7. 8.
9.
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