The initial attempt of Split Spectrum Processing (SSP) was to improve the signal-to-noise ratio (SNR) of radar ultrasonic signals. Split Spectrum Processing is able to diverse signal's frequency by splitting the spectrum of the received echo instead of transmitting at different frequencies. In this research study, Split Spectrum Processing improve the SNR of the echo spectrum and distinguished the existence of air pockets in concrete pipes easily.
The Split Spectrum Processing procedure has five steps as shown in Figure 1.
Figure 1. Split Spectrum Processing Procedure |
A: Data Acquisition
Figure 2. Measurement setup for Pulse-Echo Mode |
The experimental setup for pulse-echo mode is illustrated in Figure 2. Pulse-echo mode can transmit and receive signals with an ultrasonic transducer. A JSR PR-002 pulse generator was used to produce the electrical impulses to drive the ultrasonic transducers. The settings for the pulse generators are the following:
- Pulse repetition frequency: 1 KHz
- Energy level: Max (approximately 250 V peak voltage) - Receiver Attenuation: 0 dB
Three kinds of transducers were used and tested initially with
the
received signal, as follows:
- Gamma Transducer, center frequency 0.5 MHz, diameter 1.0"
- Alpha Transducer, center frequency 1.0 MHz, diameter 1.0"
- Alpha Transducer, center frequency 2.25 MHz, diameter
1.0"
The 0.5 MHz Gamma transducer, which has the least scattering and non-overlapping received echo, was used in this study.
The received echo signals were converted to digital data by LeCroy 9400 Digital Storage Oscilloscope (DSO) with a sampling frequency of 100 MHz which transferred to a computer. A software program called "Ultrasonic Measurement System" is used to record echo data which will input to Matlab for split spectrum processing.
In our study, since the echo signals received from the concrete are located within the transmitting signals, back wall echo signals could be observed by subtracting air by water samples. In addition, two different sets of water sample data were acquired and the difference was recorded for later comparison.
B: Fast Fourier Transform (FFT)
A typical ultrasonic signal can be represented by
Equ. 1
where m(t) is the received signal, n(t) is the noise signal and T is the total time duration of the ultrasonic signal. The spectrum of the received echo was obtained by performing Discrete Fast Fourier Transform. Zero padding of the signal in the time domain was used before the SSP to increase frequency resolution.
C: Filter
Figure 3. Filtering scheme of split spectrum processing |
The procedure of SSP splits the spectrum into
different
frequency bands as shown in Fig.3 . It has been shown that the optimum frequency separation of the filters' is:
Equ. 2
Theoretically, a time limited signal produces an infinite bandwidth. However, because of the frequency response of the transducer, the only usable spectrum is limited to a frequency band B Hz. Thus, the number of uncorrelated frequency bands N of the bandwidth B is
Equ. 3
So the actual number of filters N that could be used
is
Equ. 4
In SSP, Gaussian filter is introduced whose function is defined
by
Equ. 5
where m is the mean and 
2 is the variance of the Gaussian filter.
As shown in Fig.3, Gaussian bandpass filters with different mean (f1, f2,---, fN) and constant variance of ~f/2 were used to split the spectrum into several overlapping bands so that none of the frequency components of the original signals are lost in the processing.
D: Inverse Fast Fourier Transform (IFFT)
At this point, echo signals were already converted to frequency domain. Different split spectrums were then produced by passing through overlapping Gaussian filters with different center frequencies. The time domain signal of each individual frequency bands can be found by computing Inverse Fast Fourier Transform.
E. Processor
The signals from each individual frequency band were then passed into a Processor and output was produced. In this research study, the output of the Processor determine the existence of air pockets inside a specific sample (metal or concrete).
The nonlinear method of summing local peak voltages of each individual signal with distinct frequency was used in the Processor. Since air has a higher reflection coefficient than
water, the sum of the peak voltages of air should be comparatively higher than water. This fact was again demonstrated by this research, sum of the peaks attenuation of each split signal is indeed higher in air than water.
Both metal and concrete samples were tested. Before proceeding to concrete, metal sample was used in order to prove that SSP is able to detect the existence of air pockets. In the following section, results of metal will be examined first, then followed by concrete.
Metal:
Figure 4. Ultrasonic measurement setup for metal sample |
The ultrasonic measurement setup for metal sample is shown in Figure 4. In this measurement, a 5 cm thick aluminum was used. Pulse-echo mode was employed to receive echo signals, while
signals were recorded and turned into digital data by UMS. The recorded metal-to-air and metal-to-water data were then imported to Matlab and plotted as 
Figure 5 and 6. At this point, the existence of air pockets behind the metal sample can be determined by comparing the peak voltages of air and water - the one with the higher attenuation found the existence of air pockets inside since air has a higher reflection coefficient than water. The reflection coefficient is calculated as follows:
R = r2 - r1 / r2 + r1
Equ. 6
where R is the reflection coefficient going from medium 1 to medium 2 and r1 and r2 are the characteristic impedance of the medium. The characteristic impedance for the medium are as follows:
Aluminum : 17 x
106
water : 1.48 x
106
air : 415
and the reflection coefficients were calculated by Equ.
6:
metal-to-air : 99.99%
metal-to-water : 83.98%
and the percentage change is calculated by:
%change = Rmetal-air - Rmetal-water / Rmeta1 -water
Equ. 7
By Equ. 7, the theoretical percentage change between air and water is 16%. In comparison, the experimental percentage change can be calculated by observing the peak values of figure 5 and figure 6.
The peaks are:
metal-to-air : 2.2013 volts
metal-to-water : 1.8975 volts
which yields a percentage change of 16%. Since the two percentage changes are comparatively close, the existence of air pockets can be determined.
Although the existence of air pockets in metal sample can
be detected as mentioned above, the obtained data will process further calculation in order to be consistent with the SSP procedure in concrete. The procedure is summarized as the following:
- the difference by subtracting the signal of metal-to-air from metal-to-water and proceeded to SSP. ( Figure 7)
- the difference of two sets of metal-to-water data ( Figure 8 & 9) and proceeded to SSP. ( Figure 10)
- the ratio by dividing the output from Step 1 by Step 2.
This ratio will be used to determine the existence of air pockets.
The theoretical location of echo is calculated by the following formula:
dt= d / v
Equ. 8
where d is the distance which is twice of the thickness, and v is the velocity of the signal travel in aluminum (6300 m/s). The expected echo is at t = 15.9 us. Figure 5 and 6 show the echo in this measurement is at t = 17us. After FFT, the frequency response of output 1 and output 2 are shown in Figure 11 and 12.
By SSP, the bandwidth was found equal to 200,000 Hz and 3 filters were used. The bandpass filter responses are shown in Figure 13-18. Time Signals with individual frequency band are calculated by IFFT as shown in Figure 19-24.
After processing SSP, the sum of the peak voltages are
found:
metal-to-air - metal-to-water : 1.74 x 10-4
metal-to-water - metal-to-water : 1.189 x 10-4
and the percentage change is 46%. With such a significant percentage change, the existence of air pockets can be determined.
Concrete:
Figure 25. Ultrasonic measurement setup for concrete sample |
Figure 25 shows the measurement setup for concrete.
In this study, a thickness of 0.6 cm concrete sample, with a velocity of 4400 m/s, was used. A block of plexiglass (1") was placed in between the ultrasonic transducer and the concrete sample because it can delay the location of the back wall echo (echo from concrete-to-water or concrete-to-air) so that it would not appear in the initial excitation of the ultrasonic pulse.
The existence of air pockets is-difficult to determine through concrete by comparing the two peak voltages with the
reflection coefficients. However, comparison are being made. The characteristic impedance of concrete is 8.0 x 106. Thus, the reflection coefficients between air and water can be found by Equ. 7:
concrete-to-air : 99.99%
concrete-to-water : 68.78%
The theoretical percentage change of the coefficient between water to air was 45.4%. By observing the attenuation in figure 26 and 27, the peak voltages are:
concrete-to-air : 0.5778 volts
concrete-to-water : 0.5340 volts
which yields a percentage change of 8.2%. With such differences in the two percentage changes, the detection of air pockets is unreliable stated, therefore, SSP was performed.
From Equ. 8, the back wall echo was calculated and found at t = 25us. While the plexiglass echo, which was calculated from the surface of plexiglass and concrete, was found at t = 23us and lasted for lOus. So, the back wall echo was resided within the plexiglass echo. The signals are shown in figure 26 and 27. In order to observe the significance of the back wall echo, the difference of the data in concrete-to-water and concrete-to-air (as shown in Figure 28) was taken and sent to SSP. Since the input to SSP has to be the difference of two sets of data, the difference
( Figure 31) of two sets of concrete-to-water data ( Figure 29 and 30) was obtained and proceeded to SSP. So by comparing the two outputs, the existence of air pockets can be easily determined.
The spectrum of the two signals are shown in figure 32 and 33. By SSP the bandwidths of 110,000 Hz (for the difference of air and water) and 250,000 Hz (for the difference of water and water) were found. Both spectrum used three Gaussian overlapping filters. The magnitude of filter responses are shown in Figure 34 - 39. Figure 40 - 45 show the time domain of the split spectrum.
After SSP, the sum of the peak voltages were:
concrete_to air - concrete-to-water = 5.244 x 10-5
concrete_to_water - concrete-to-water = 2.3673 x 10-5
which yielded a ratio of 2.215 and a percentage change of 121%. With this significant percentage change, the existence of air pockets can be concluded.