NDT.net - October 2002, Vol. 7 No.10 |
The utilization of multi-layered materials has increased dramatically in the past decade. These engineered materials have been used extensively for their improved barrier properties combined with good mechanical strength and reduced weight. Process and quality control requirements have resulted in the need for high-precision and high-resolution nondestructive thickness measurements. Ultrasonic pulse-echo methods have been very successful in measuring the thickness of layered materials as well as the quality of the bond interface between them. However, for very thin layers, the resulting echoes overlap in time, limiting the minimum thickness that can be resolved using conventional pulse-echo time-of-flight techniques. In this work, we will describe a signal-processing algorithm that has been developed to overcome this problem. The paper will describe the algorithm and present experimental and simulation results as applied to thin multilayers in automotive fuel tanks.
The application of multilayered materials has increased in past decade due to their excellent
engineering properties [1, 2]. In many cases, the thickness of the layers has to be controlled
and measured very accurately. For this, a variety of methods had been developed to
measured thickness of thin multilayers such as X-ray, optical microscope, magnetic induction
and eddy current [3, 4]. Ultrasonic time-of-flight (TOF) thickness measurements have been
extensively used in process control environments. The time delay associated to the wave
propagating between the two boundaries of the layer can be used to estimate the thickness of
the layer. Unfortunately, as the thickness of the layer decreases, the arrival of the second
echo can partially overlap the first. In order to reduce this overlap, higher frequency
ultrasound has been used. However, there is a limit on the highest ultrasonic frequency that
can be used for a particular measurement. This limit is due to several factors such as:
A model-base estimation has been proposed recently [8, 9], which uses a space-alternating generalized expectation-maximization algorithm (SAGE) to model the ultrasonic echo signals and estimate the thin layers thickness with high precision, accuracy and computational efficiency. The method is based on modeling the ultrasound as a superposition of Gaussian wavelets. Consequently, the multilayer signal can be represented by a sum of amplitude modulated and time delayed Gaussian echoes [10]. The advantage of this approach is that it translates a complex N-echo estimation problem into a series of one- echo estimation problems thus providing computational versatility and flexibility. We will present the algorithm and experimental results on the measurement of the thickness of an embedded thin barrier in a multilayers plastic fuel tank.
With the development of ultrasonic digital instruments, a lot of work has been focused on extending the measuring capabilities of the instruments by means of digital signal processing and algorithms. The ultrasonic signals are digitized and the resulting signal is processed in real-time to provide the measurement result. Therefore, the ultrasonic measurement can be described mathematically using system engineering techniques [11]. The ultrasonic signal traveling through a multilayer can be modeled using a series of impulses [12], whose amplitude are the reflection coefficients at the interfaces and the position in time is the time- of-flight between the interfaces (Figure 1).
Fig 1: (a) Block diagram of the ultrasonic measurement of a multilayered sample, and (b) equivalent model. |
In ultrasonic pulse-echo technique, a single transducer is used for both transmitting and receiving, and we can model the material response using the block diagram in figure 1. The measurement technique uses a transducer with a delay line and in many cases the multilayer is embedded in the material. The echo generated by the transducer travels through the delay line and is partially reflected at the delay line/material interface. We will represent this echo as h(t). The transmitted version of h(t) travels through the top layer and reaches the multilayer. We will refer to this signal as h(t). The top layer is modeled as a lossy material with a time delay and attenuation being a function of frequency. Because of this the each will change in amplitude and shape as it travels through the top layer. The propagation can be modeled as a linear system in figure 1b.
Fig 2: Model signals representing two echoes reflected from a barrier layer embedded in a fuel tank. From the top to the bottom signal, the thickness of the barrier is 50, 200 and 500µm, respectively. |
The frequency response of the top layer is thus represented by M(w) [10]:
(1) |
where x is propagation distance (x = 2d, where d is the thickness of the top layer), a(w) is
material attenuation, and
V_{p}(w) is material phase velocity. If d = 0, the multilayer is at the
front surface of the sample and then h(t) = h_{r}(t). In the case of High-density Polyethylene
(HPDE), the frequency dependent attenuation has been reported to be of the order of 0.5
dB/mm/MHz, hence the overall attenuation at 12 MHz is about 50 dB for a typical top layer
thickness of 6 mm. The layers thickness are determined by time of flight (TOF) sequence of
the echoes at the interfaces, t_{1},t_{2},…,t_{N}. For thick layers, echo signals are separated on time
scale therefore we can estimate the TOF by detecting the location of each of them [6, 10].
For thin layers, the echoes are overlapping therefore the TOF cannot be detected by the
standard method. In this analysis, we assume that the propagation loss and dispersion in the
thin multilayers are negligible. Figure 2 illustrates simulated echo signal from an ethylene
vinyl alcohol (EVOH) barrier with different thickness that is embedded under a high-density
polyethylene layer in a multilayers plastic fuel tank [4]. In the case of the top signal in figure
2, the two multiple echoes cannot be resolved in the time domain, this is the case of a thin
layer. As the layer thickness increases, for example above 200 µm, the two echoes separate
in time. This is the case of thick layers. Using the reflection coefficients, the backscattered
signal y(t) from the N layers can be represented by a superimposition of N+1 echoes [10]:
(2) |
Fig 3: Block diagram of the signal-modeling algorithm to determine the thickness of N layers. (a) Case in which the h(t) is determined; (c) h(t) is estimated using h_{r}(t). |
Equation 2 represents the relationship between the input signal h(t) and the output signal y(t) in figure 1b. Assuming that we know the input signal h(t); the coefficients An and t n can be obtained using inversion-deconvolution algorithms such as Wiener filtering [5] Another approach is to utilize a Least Square Minimization search algorithm to calculate the coefficients A_{n}, t_{n} (n = 0, .., N) that minimize the model error in equation 2. This is a multi- dimension optimization problem with heavy computational load and potential poor convergence. In this paper, we present a solution based on model-estimation algorithms [8, 13]. The approach here presented is based on the decomposition of the multilayer echo y(t) in terms of Gaussian wavelets, this approach results in a faster and more robust convergence.
The echo h(t) is modeled as a superimposition of M Gaussian shaped echo wavelets [10, 11]:
(3) |
where f_{m} is the center frequency, a
_{m} is bandwidth factor, c_{m} is the amplitude, f_{m} is the phase,
l_{m} is the time delay of Gaussian echo wavelet m, and M is model order. Each wavelet is thus
represented by a vector of 5 parameters,
q_{m} = [f_{m} a_{m} c_{m} f_{m} l_{m}], and we can write equation 2 more compactly as:
(4) |
Fig 4: (a) Acquired h_{r}(t) signal (top curve) and (b) Gaussian wavelets calculated as basis for the description of h_{r}(t). |
The optimal choice of the number of wavelets M is calculated using the minimum description length (MDL) principle [8]. Once the parameters q_{m} are defined, we can now rewrite equation 2 in terms of the Gaussian wavelets:
(5) |
where the q_{m} (m = 1,2,..M) are assumed known, and A_{n},t _{n} (for n = 0,1,…N) are the unknown variables.
The basic advantage of equation 5 resides in the fact that the basis functions { f(q_{m};t)} well-behaved, noise-free Gaussian wavelets. This results in enhanced stability and faster convergence in comparison of using the signal h(t) in equation 2.
The proposed algorithm can thus be described using figure 3. The ultrasonic signal h(t) that is used to characterize the multilayer is decomposed in a series of Gaussian wavelets. The output of this first stage is thus the parameters of the wavelets. These parameters are then held constant and used for the analysis of the acquired multilayer echo y(t). In this second decomposition, the only variable parameters are the amplitude and time delay associated with the N+1 back-scattered echoes from the multilayer.
Fig 5: Comparison for the calculated and experimentally determined h(t). |
The algorithm thus requires the acquisition of two signals, h(t) and y(t). Recalling figure 1, we can easily determine that if the top layer is not present, h(t) is equivalent to h_{r}(t), and it thus can be determined by measuring the reflected echo at the end of the delay line. In the case that the multilayer is embedded in the material, we can still measure h_{r}(t), and by means of equation 1, we can estimate the signal h(t). Hence in the case of an embedded multilayer, the proper algorithm is defined in figure 3b, where the extra step of using equation 1 is introduced. It has to be noted that the correction for the lossy propagation in the top layer is applied to the Gaussian wavelets and not to the acquired signal h_{r}(t).
The algorithm here presented was implemented and utilized to measure the thickness of thin barrier layers made of Ethylene Vinyl Alcohol (EVOH) sandwiched between two or more layers of HDPE. The experimental data was acquired using Panametrics 25Multi Plus with a high frequency delay line transducer. The top signal in figure 4 represents the ultrasonic echo reflected from the end of the delay line. The same signal was then decomposed into a sum of 4 Gaussian wavelets, displayed in the bottom part of figure 4 and labeled W1 to W4. As it can be easily seen, the amplitude ratio between the first and fourth component is about 25:1 (-28 db). The signal reconstructed using the 4 wavelets is not displayed but the overlap is practically perfect.
To verify that the lossy propagation model is accurate, we acquired an echo h(t) using a HDPE sample of 6 mm in thickness, and compared the experimental curve with the one calculated using the wavelet components of h_{r}(t) and equation 1, as shown in figure 4b. The comparison of the two curves is given in figure 5. The dotted curve represents the experimental signal, and the continuous line, the estimation using the wavelets of figure 4 and equation 1. The agreement is quite good and acceptable for our analysis of the barrier layer thickness.
Fig 6: Experimental and calculated model fit signals for 70 and 205 µm thick EVOH barriers embedded in a 6 mm thick top HDPE layer. |
The next step is to determine the thickness of a barrier layer, embedded in a 6 mm thick HDPE material. The thickness of the top layer is about 4.5 mm. We obtained an experimental signal for a barrier layer of thickness 70 µm. The signal is shown in the bottom of figure 6 as a dotted line. Using the wavelets W1 to W4 signal, the algorithm returned an estimation of the two echoes back-reflected at each interface of the barrier layer; these echoes are plotted in the top part of figure 6, and labeled Echo1 and Echo2. Echo1 represents the echo reflected at the top layer-barrier interface, while Echo2 the one reflected at the barrier- substrate layer interface. In most practical applications for fuel tanks, the substrate layer is made of the same material as the top layer; i.e., HDPE. For this reason, Echo1 and Echo2 are signals of similar amplitude, delayed and shifted by 180 degrees. The signal reconstructed using Echo1 and Echo2 is also displayed in the bottom of figure 6 as a continuous line and compared with the experimental signal. Again, the agreement is quite good and deemed acceptable for the determination of the barrier layer thickness. The accuracy of the thickness measurement obtained using the proposed algorithm was verified both with simulated and experimental signals. Result are shown in figure 7, and compared with Wiener deconvolution results. The standard deviation of the proposed algorithm is about 8 µm. For comparison, the Wiener algorithm has yielded 12 µm accuracy.
An algorithm based on the model estimation of ultrasonic signals was presented. The method is based on modeling the ultrasound as a superposition of Gaussian wavelets, hence the multilayer signal can be represented by a sum of amplitude modulated and time delayed Gaussian echoes. We have presented the algorithm and experimental results on the measurement of the thickness of an embedded thin barrier in a multilayers plastic fuel tank.
Fig 7: Comparison between the actual and estimated thickness measurements for a thin EVOH barrier embedded in HDPE. |
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