REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION
An essential component of ultrasonic nondestructive testing is determining the delay time between the transmitted and received signals. Therefore, the accuracy of determining the onset of both the transmitted and received pulse affects the accuracy of all subsequent calculations. The main measuring...
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General Energy Institute of the National Academy of Sciences of Ukraine
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System Research in Energy| _version_ | 1871104400710172672 |
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| author | Bohachev, Ihor Kozyr, Oleh Sozonov, Stanislav |
| author_facet | Bohachev, Ihor Kozyr, Oleh Sozonov, Stanislav |
| author_institution_txt_mv | [
{
"author": "Ihor Bohachev",
"institution": null
},
{
"author": "Oleh Kozyr",
"institution": null
},
{
"author": "Stanislav Sozonov",
"institution": null
}
] |
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| datestamp_date | 2026-07-18T12:57:49Z |
| description | An essential component of ultrasonic nondestructive testing is determining the delay time between the transmitted and received signals. Therefore, the accuracy of determining the onset of both the transmitted and received pulse affects the accuracy of all subsequent calculations. The main measuring transducers are usually piezoelectric. A relatively new approach involves using small-aperture magnetostrictive transducers as a generator and receiver of the ultrasonic signal. Such magnetostrictive sensors have low-current excitation coils, resulting in low amplitudes of received signals. Therefore, it is an urgent task to develop algorithms for determining the onset of a pulse that could reduce the noise present in the signal or not be sensitive to it. In this paper, a method for determining the onset of an ultrasonic pulse is proposed based on utilizing a standard function from the LabVIEW library to determine the position of the peak value of a periodic pulse. The mathematical expressions for modeling transmitted and received pulses were obtained. Based on these mathematical expressions, a modeling experiment was conducted to verify the accuracy of determining the beginning of the probing pulse by the proposed method. The simulation experiment was performed with noise following a Gaussian distribution for the range of standard deviation (SD) values from 0 to 10. According to the modeling results, it was found that the proposed method allows determining the beginning of the probing pulse with a relative error not exceeding 3.5 % for the values of the SWR less than 2. |
| doi_str_mv | 10.15407/srenergy2025.01.085 |
| first_indexed | 2026-03-24T02:03:30Z |
| format | Article |
| fulltext |
Системні дослідження в енергетиці. 2025. 1 (81) 85
ISSN 2786-7102 (Online), ISSN 2786-7633 (Print)
https://doi.org/10.15407/srenergy2025.01.085
UDC 620:9
Ihor Bohachev1*, PhD (Engin.), Senior Researcher, https://orcid.org/0000-0001-7781-5767
Oleh Kozyr2, PhD (Engin.), Associate Professor, https://orcid.org/0000-0002-9285-5940
Stanislav Sozonov1, https://orcid.org/0000-0002-7584-4529
1General Energy Institute of NAS of Ukraine, 172, Antonovycha St., Kyiv, 03150, Ukraine;
2National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 37,
Beresteiskyi Prosp., Kyiv, 03056, Ukraine
*Corresponding author: biv_vdoe@ukr.net
_______________________________________________________________________________________
REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF
ULTRASONIC PULSE ONSET DETECTION
Abstract. An essential component of ultrasonic nondestructive testing is determining the delay time between
the transmitted and received signals. Therefore, the accuracy of determining the onset of both the transmitted
and received pulse affects the accuracy of all subsequent calculations. The main measuring transducers are
usually piezoelectric. A relatively new approach involves using small-aperture magnetostrictive transducers as
a generator and receiver of the ultrasonic signal. Such magnetostrictive sensors have low-current excitation
coils, resulting in low amplitudes of received signals. Therefore, it is an urgent task to develop algorithms for
determining the onset of a pulse that could reduce the noise present in the signal or not be sensitive to it. In this
paper, a method for determining the onset of an ultrasonic pulse is proposed based on utilizing a standard
function from the LabVIEW library to determine the position of the peak value of a periodic pulse. The
mathematical expressions for modeling transmitted and received pulses were obtained. Based on these
mathematical expressions, a modeling experiment was conducted to verify the accuracy of determining the
beginning of the probing pulse by the proposed method. The simulation experiment was performed with noise
following a Gaussian distribution for the range of standard deviation (SD) values from 0 to 10. According to
the modeling results, it was found that the proposed method allows determining the beginning of the probing
pulse with a relative error not exceeding 3.5 % for the values of the SWR less than 2.
Keywords: ultrasonic signal, magnetostrictive sensor, signal-to-noise ratio.
1. Introduction
One of the most common methods of controlling the properties of products in production is non-destructive
testing [1]. Ultrasonic non-destructive testing is especially widely used. This method uses an acoustic signal to
probe the sample under test. In this case, both the pulse sent and the reflected from the interference are measured.
Any measurements are sensitive to interference, noise, etc. This is especially true for non-destructive
ultrasonic testing, since the sensing signal must pass through the test sample to be reflected and be perceived by
the receiving sensor. Accordingly, the received signal will have low amplitude values and therefore must be
amplified by hardware or software, which in turn leads to amplification of noise and interference in addition to the
signal [2]. The use of low-pass filters leads to a phase shift of the probing pulse, thereby increasing the error in
determining the beginning of the pulse. In addition, hardware filters have nonlinearities, which also distorts the
measuring signal at ultrasonic frequencies.
Let's consider the main examples of denoising ultrasonic signals that are used in practice. Thus, in
biomedical applications of ultrasound signals to create ultrasound images for diagnostic purposes, these images
contain speckle noise [3]. The presence of these noises leads to uncertainty in diagnosis, as they distort image
details such as limits and edges. Existing denoising algorithms remove these noises without maintaining the actual
limits and edges. Therefore, the paper [3] analyzes 27 algorithms that perform smoothing or elimination of speckle
Системні дослідження в енергетиці. 2025. 1 (81) 86
noise and are used in medical ultrasound image processing. In addition, in images used for biomedical purposes,
digital image processing methods are widely used to de-noise them [4]. In the paper [5], the Wavelet transform
algorithm for noise filtering was proposed and its efficiency was evaluated on 292 images. The results obtained in
[5] indicated that the effectiveness of the application of Wavelet transform algorithms depends on the selected
filter parameters and their values, the ultrasonic signals themselves and the types of noise. And the algorithm
proposed in the paper [6] based on the orthonormal wavelet family was tested on 110 images and showed its
effectiveness.
A feature of the medical use of ultrasound signals is that the probing pulse is actively absorbed by the tissue,
and the increase in the intensity of the pulse is limited by medical indicators [7]. Therefore, the reflected signal
has a small amplitude value and signal-to-noise ratio. In the paper [7], the use of neural network methods of signal
processing to reduce noise and improve the signal-to-noise ratio is proposed.
Recently, the use of blind source separation techniques for filtering ultrasound images has become quite
popular [8]. At the heart of these algorithms is an approach that attempts to decompose the received signal into the
components of which it might have been composed. At the same time, a feature of this algorithm is that it tries to
separate a useful signal or a combination of signals and noises with minimal initial information about them.
Accordingly, the work [8] analyzed the effectiveness of using such methods.
One type of noise that distorts an ultrasonic image is diffuse reverberation, which occurs due to the presence
of multiple reflections of the probing pulse before reaching the receiving sensor. The presence of this noise distorts
the image and increases the error in determining the onset of the probing pulse [9]. In the paper [9], a denoising
algorithm based on a 3D fully convolutional neural network was proposed. The disadvantage of this method is
that it suppresses uncorrelated and low-amplitude signals. Therefore, it cannot be used to analyze the signal of
magnetostrictive sensors.
As for ultrasonic non-destructive testing itself, one of the newest methods used for testing is phased array
ultrasonic testing. It is used to assess the integrity of materials or structures. The use of this approach to test
composite materials, with significant acoustic absorption, is accompanied by exposure to significant electrical
noise [10]. In general, there is a significant demand for the use of composite materials in heavy-loaded structures
in the aerospace industry, wind turbines, in the transport industry, medical equipment, etc. [11]. For such materials,
it was proposed in [10] to use a time-varying filter empirical mode decomposition joint wavelet thresholding
method to de-noise the sensing signal.
Noise reduction of ultrasonic echo-pulse signals is an important task in non-destructive testing in industry.
The presence of significant noise and low signal-to-noise ratio are the main obstacle to obtaining accurate values
of the start of the probing pulse [12]. The paper [12] proposes an algorithm for noise suppression when using non-
destructive testing in production, which is based on a combination of several statistical methods of signal
processing. In addition, to reduce the impact of noise on the received ultrasonic echo signal, signal processing
methods based on wavelet functions are used, which allows to increase the signal-to-noise ratio [13]. In addition,
a phase method for determining the probing impulse of magnetostrictive sensors against the background noise was
developed [14]. This method [14] is based on the use of the discrete Hilbert transformation, which allows to
determine the envelope and phase of signals.
Determining the beginning of the sent and received pulses determines the accuracy of the signal delay
calculation and the determination of non-destructive testing parameters. Noise and interference prevent accurate
pulse onset detection. There are two approaches to finding the onset of the pulse for a noisy signal. The first is to
de-noise the signals, usually using statistical methods, and then the filtered signal is used to find the beginning of
the pulse. This approach was applied in the works discussed above.
The second approach is to use algorithms to determine the onset of the pulse in the presence of noise in the
signal. Since any signal filtering or denoising introduces certain distortions into the signal, and then the algorithm
for determining the onset of the pulse introduces its own errors. The task is to try to find the beginning of the
Системні дослідження в енергетиці. 2025. 1 (81) 87
impulse by its certain characteristic features without getting rid of the noise. Thus, in the paper [14], a method for
determining the beginning of an ultrasonic signal for testing the integrity of structures is considered. In this work,
the method of signal analysis using continuous wavelet transform preprocessing and machine learning algorithms
was applied. The paper [15] examines the approximation of an ultrasound signal using the particle swarm
optimization algorithm to determine the onset of the pulse. In the paper [16], a simpler approach to signal
approximation based on the Levenberg-Marquardt optimizing algorithm was proposed.
This work is devoted to the second approach to determining the beginning of the probing pulse.
2. Probing pulse simulation
The process of ultrasonic non-destructive testing using low-aperture magnetostrictive sensors involves
parallel measurement of the sent and reflected pulses [17]. The measurement process is performed over a specified
time with a constant sampling rate. These measurements are performed using continuous signal sampling hardware
from magnetostrictive sensors [18]. The resulting voltage values are stored in the form of arrays of real numbers.
These are so-called time samples of the current voltage values at the output of magnetostrictive sensors.
The sampling simulation should reflect the basic parameters of the ultrasound signals. Usually, the duration
of the measurement is much longer than the duration of both the sent and reflected signals combined. In addition,
the measurement itself begins long before the probe pulse is sent, which makes it possible to determine the
beginning of the pulse. Therefore, both samples contain both the probing pulse itself and regions with a complete
absence of an informative signal. In the following, we will consider the sampling of the sent signal, but all of the
above can be used for sampling with a reflected pulse.
The sample can be divided into three regions and described by the following expression [19]:
𝑓(𝑡) = {
𝑓0(𝑡), 0 ≤ 𝑡 < 𝑡0
𝑓𝑇(𝑡), 𝑡0 ≤ 𝑡 < 𝑛𝑝 ∙ 𝑇
𝑓0(𝑡), 𝑡0 + 𝑛𝑝 ∙ 𝑇 ≤ 𝑡 < 𝑡𝑑
. (1)
Descriptions of the values specified in (1), as well as those that will be found in the text below, are given in
Table. 1. In addition, it provides their values that were used in the sample modeling.
Table 1. Variable values and descriptions
Parameter Value Description
𝑡0, 𝜇𝑠 3 The target value of all measurements in non-destructive
testing. Time of the onset of the probing pulse
𝑇, 𝜇𝑠 2 Pulse period
𝑡𝑠, 𝑛𝑠 20 Sampling period
𝑡𝑑 , 𝜇𝑠 15 Measurement duration
𝑛𝑝 2 Number of periods
𝐴, 𝑉 6 Pulse amplitude
phase, rad𝜃 0 Initial pulse phase
The three regions in expression (1) are described by three functions. In addition, these three areas differ in
time ranges. The first region (1) does not carry an informative signal and is modeled by a function that returns
zero values in the specified time range:
𝑓0(𝑡) = 0. (2)
Системні дослідження в енергетиці. 2025. 1 (81) 88
The expression (2), regardless of the current value of the timestamp, returns a zero value. This expression
will be used to create subarrays of the sample that simulate the absence of a probing pulse. According to (1), there
are two such subarrays – at the beginning and at the end of the sample. That is, two of the three regions represent
the absence of the pulse.
The third region contains the pulse itself. The probing pulse was modeled by a harmonic signal, which can
be described by the expression:
𝑓𝑇(𝑡) = 𝐴𝑠𝑖𝑛 (2𝜋
1
𝑇
𝑡 + 𝜃). (3)
The expressions (2) and (3) are represented for a continuous independent variable, i.e. time. In the
calculations, discrete expressions are used to obtain samples. In this case, the time variable is a discrete quantity
and is a uniform sequence with a constant step. This step is the time sampling period 𝑡𝑠 of the signal (Table 1).
Thus, the nth element of the array of zeros, based on the expression (2), will look like:
𝑦0[𝑛] = 𝑓0(𝑡[𝑛]) = 0. (4)
Similarly, we get the value of the nth element of the array containing the probing pulse, based on (3):
𝑦𝑇[𝑛] = 𝑓𝑇(𝑡[𝑛]) = 𝐴𝑠𝑖𝑛 (2𝜋
1
𝑇
𝑡[𝑛] + 𝜃). (5)
The expression (5) was used to derive one period of the pulse. Since the number of periods was chosen to
be 𝑛𝑝 = 2 (Table 1), the second period was obtained by copying the first.
Since the sample is discrete, it has a limited number of values. In addition, it is necessary to determine the
size of the sample subarrays that correspond to the corresponding areas (1).
The first region (1) corresponds to the time period [0, 𝑡0). Accordingly, we determine the size of the subarray
using the sampling period 𝑡𝑠:
𝑁𝑏 =
𝑡0
𝑡𝑠
. (5a)
Based on (5a), we determine the value of the nth element of the time array of the first region:
𝑡[𝑛𝑏] = 𝑛𝑏 ∙ 𝑡𝑠; 𝑛𝑏 ∈ {0,1,… ,𝑁𝑏 − 1}. (6)
Using (4) and (6), we obtain the expression of the current value of the array of the first area of the voltage
sample:
𝑦𝑏0[𝑛𝑏] = 𝑓0(𝑡[𝑛𝑏]) = 0. (7)
The array of the second area contains the values of the probing pulse. The size of the array of one pulse
period on the time interval [0, T) is:
𝑁𝑇 =
𝑇
𝑡𝑠
. (8)
Системні дослідження в енергетиці. 2025. 1 (81) 89
The corresponding time array of one pulse period based on (8) is determined from the expression:
𝑡[𝑛𝑇] = 𝑛𝑇 ∙ 𝑡𝑠; 𝑛𝑇 ∈ {0,1,… ,𝑁𝑇 − 1}. (9)
The array of voltages of one period is calculated using (9):
𝑦𝑇[𝑛𝑇] = 𝑓𝑇(𝑡[𝑛𝑇]) = 𝐴𝑠𝑖𝑛 (2𝜋
1
𝑇
𝑡[𝑛𝑇] + 𝜃). (10)
As already noted, the array of values of the probing pulse voltages is formed by concatenation of the array
of one pulse period with itself.
The last third region is the array of zeros, which, like the first region, is calculated based on equation (4).
To calculate the length of the array, it is necessary to take into account the time intervals of the previous two
regions:
𝑁𝑎 =
𝑡𝑑−(𝑛𝑝∙𝑇+𝑡0)
𝑡𝑠
. (11)
The time array of the third region based on (11) will be:
𝑡[𝑛𝑎] = 𝑛𝑎 ∙ 𝑡𝑠; 𝑛𝑎 ∈ {0,1,… ,𝑁𝑎 − 1}. (12)
The corresponding array of voltages of the third region on the voltage of the time array (12) is determined:
𝑦𝑎0[𝑛𝑎] = 𝑓0(𝑡[𝑛𝑎]) = 0. (13)
The final array of voltage values of the probing pulse is formed on the basis of the concatenation of the
arrays of the three regions (7), (10), and (13), which can be described by the expression:
𝑦[𝑛] = 𝑦𝑏0[𝑛𝑏] + 𝑦𝑇[𝑛𝑇] + 𝑦𝑇[𝑛𝑇] + 𝑦𝑎0[𝑛𝑎]. (14)
The time array corresponding to (14) is calculated based on the sizes of the respective component arrays
(5a), (8), and (11) and is calculated accordingly:
𝑡[𝑛] = 𝑛 ∙ 𝑡𝑠; 𝑛 ∈ {0,1,… , (𝑁𝑏 +𝑁𝑇 +𝑁𝑇 +𝑁𝑎) − 1}. (15)
Expressions (14) and (15) allow to simulate the measurement of the probing pulse and obtain a sample for
testing the algorithms for finding the beginning of the pulse.
3. Implementation of the probing pulse modeling algorithm
3.1. Modeling the ideal sample
Using the graphical programming environment LabVIEW, virtual instruments (VIs) were developed to
simulate the measurement of the probing pulse.
Системні дослідження в енергетиці. 2025. 1 (81) 90
First of all, a VI was implemented that allows to sample an ideal probing pulse without noise. This sample
was used to test the algorithm for determining the onset of the pulse. The front panel (FP) of the developed VI is
shown in Fig. 1. The FP contains widgets for controlling the pulse and sample parameters (Table 1), and a
waveform graph for displaying the resulting sample with an indication of the beginning of the simulated pulse
(Fig. 1).
Figure 1. FP of the VI that models the probing pulse
The graphical code for the implementation of the algorithm for modeling an ideal sample of probing signal
voltage values in the form of a block diagram (BD) is shown in Fig. 2.
Figure 2. BD of the VI that models the probing pulse
This VI (Fig. 2) contains subVIs for implementing arrays of the corresponding three regions (1). The first
and third regions of null values are created by subVI zero_signal.vi, which implements the generic expression (4)
and expressions for the corresponding regions (7) and (13).
The probing pulse region based on expression (5) implements a impulse.vi that creates 𝑛𝑝 pulse periods,
according to expression (10).
The sizes of the corresponding time and voltage arrays according to (5a) and (8) are implemented in the
corresponding subVIs. The size of the array of the third region (11) is implemented in the main VI (Fig. 2). In
addition, the time arrays were not implemented separately, because the generated sample is stored using the
waveform data type implemented by LabVIEW. This data type stores the array of signal values, the sample
Системні дослідження в енергетиці. 2025. 1 (81) 91
period 𝑡𝑠 and the measurement start time This data type is convenient because it does not consume the space of
the computer's main memory to store an array of timestamp values. If you need such an array, for example, to
display a signal on a graph, then a time array will be implemented.
The concatenation of the arrays in (14) is implemented in the main VI (Fig. 2). This VI will be used as
subVI in other VIs elsewhere.
3.2. Modeling a sample with a noise
The following VI implements simulation of the measurement process (Fig. 3, Fig. 4). The FP of this VI
contains an additional control − the values of the standard deviation, S, V (Fig. 3). Real measurements are simulated
by adding a random variable − measurement error, interference, etc. − to the ideal sample produced by VI in Fig. 2.
Figure 3. FP of the VI that models measured sample
For this work, a random variable is chosen with a normal law of distribution of possible values − centered
with a variable standard deviation, which is specified by the corresponding control (Fig. 3).
The VI (Fig. 4) forms an ideal sample based on subVI impulse_simulation.vi, which was considered earlier
(Fig. 2).
Figure 4. BD of the VI that models measured sample
Системні дослідження в енергетиці. 2025. 1 (81) 92
The VI (Fig. 4) is the main one in the simulation of the measurement sample, which was used to determine
the onset of the probing pulse.
3.3. Algorithm for determining the beginning of the probing pulse
To determine the beginning of the probing pulse, we will use the built-in Pulse Measurements VI [20],
which belongs to the Waveform Measurements VIs palette. This VI is designed to analyze periodic signals and
establish their characteristics: period, pulse width, duty cycle and pulse center of a selected pulse. FP of the VI
(Fig. 5) contains two additional display elements: the defined value of the pulse start time t0_fit and the value of
the relative error of its determination dt0, %.
Figure 5. FP of the VI that determines the start time of the pulse
To determine the beginning of the pulse, the pulse center parameter was taken as a basis. This parameter
sets the time that corresponds to the peak of the pulse. Since this VI (Fig. 6) is designed for the analysis of periodic
signals, it accordingly needs at least one period for analysis (the algorithm looks for the intersection of the midline
line with a signal, and at the beginning of the pulse this intersection is absent), so the first positive half-period of
the sine wave is skipped. In the case of a probing signal, we have only two periods, which will allow us to find the
peak only in the second period.
Figure 6. BD of the VI that determines the start time of the pulse
Системні дослідження в енергетиці. 2025. 1 (81) 93
In addition, the algorithm for determining the pulse center requires specifying the polarity of the pulse, that
is, it will be a pulse containing rising and descending edges (high pulse) in relation to the midline or vice versa
(low pulse). In Fig. 5, a high pulse (marked t_center) was found. Accordingly, an example of low pulse is shown
in Fig. 7. The pulse center of the high pulse is calculated using the formula:
𝑡с =
𝑡𝑓−𝑡𝑟
2
,
where 𝑡𝑟 is the time of crossing the midline with a rising front; 𝑡𝑓 – the time of crossing the middle line with a
falling front.
Finding the pulse center of the positive half-period of the second pulse period, it is possible to find the
beginning of the pulse from the expression:
𝑡0 = 𝑡с − 𝑇 ∙ 1.25. (16)
As can be seen from Fig. 5. This value is calculated without error for a perfect sample, without noise.
For the polarity of the low pulse, which is placed at 0.75 period relative to the beginning of the probing
pulse, the expression (16) for calculating the beginning of the probing pulse will be as follows:
𝑡0 = 𝑡с − 𝑇 ∙ 0.75. (17)
The result of using the expression (17) can be seen in Fig. 7.
Figure 7. Determination of the onset of pulse in the case of low pulse polarity
As in the case of high pulse for low pulse the algorithm determines the beginning of the pulse without error.
Next, the proposed pulse onset detection algorithm was tested for samples that simulate real measurements.
The pulse onset detection algorithm used the high pulse polarity of Fig. 5 based on expression (16).
Thus, in the case when the standard deviation of Gaussian noise was 1/6 of the pulse amplitude, the
measurement error was only <1 % (Fig. 8).
Системні дослідження в енергетиці. 2025. 1 (81) 94
Figure 8. Determination of the onset of the pulse for a standard deviation equal to 1/6 of the pulse amplitude
For the case when the standard deviation of Gaussian noise was 2/3 of the amplitude of the pulse, the
measurement error was almost 12 % (Fig. 9).
Figure 9. Determination of the origin of the pulse for a standard deviation equal to 2/3 of the pulse amplitude
4. Simulation experiment
To obtain a complete picture of the dependence of the error in determining the beginning of the probing
pulse on the value of the noise standard deviation, VI was developed, which allowed iteratively obtaining an array
of relative error values for an array of standard deviation in the range from 0 to 10 with a step of 0.5 (Fig. 10).
Системні дослідження в енергетиці. 2025. 1 (81) 95
Figure 10. BD of the VI which iteratively determines the relative error in determining the origin of the pulse for
different values of the standard deviation
The graph of the possible dependence of the error in determining the beginning of the sensing pulse by the
proposed algorithm on the value of the noise standard deviation is shown in Fig. 11. As can be seen from the graph,
small error values occur up to a PSF value of less than 2. Further, with increasing standard deviation, the error
becomes significant, more than 100 %, and can change sign randomly.
Figure 11. Graph of relative error values for determining the beginning of the sounding pulse by the proposed
methods for the values of standard deviation
To verify the algorithm for determining the onset of a pulse based on the low pulse polarity, the VI shown
in Fig. 10 was modified. A data stream was added to the loop with the algorithm for determining the beginning of
the pulse based on the low pulse polarity (Fig. 7) based on expression (17). As a result, this VI (Fig. 12) returned
pairs of error and standard deviation arrays.
Системні дослідження в енергетиці. 2025. 1 (81) 96
Figure 12. BD of the VI from Fig. 10 which further specifies the error in determining the onset of the pulse for low
pulse polarity
The resulting graph of the values of the pulse onset detection error and the values of the noise standard
deviation for both polarities is shown in Fig. 13.
Figure 13. Graph of relative error values for determining the onset of the pulse by the proposed method for two
polarities and standard deviation
As can be seen in Fig. 13, at the values of the standard deviation greater than 2, the relative error in
determining the pulse onset increases enormously to ±175 %, in addition to changing its sign randomly. In other
words, at an FSR greater than 2, no dependence between the error and the standard deviation can be traced, since
in the FSR range from 3 to 4, the error value drops sharply to less than 20 %.
Limiting the value of the standard deviation to the range from 0 to 2, we get a graph that allows us to estimate
the dependence of the relative error in determining the onset of the pulse by the proposed method, for two
polarities, on the values of the standard deviation (Fig. 14).
As can be seen in Fig. 14, the maximum value of the relative error does not exceed 3.5 %, for the maximum
value of standard deviation 2.
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Figure 14. Graph of the dependence of the relative error of determining the onset of the pulse by the proposed
method for two polarities on the standard deviation
As can be seen in Fig. 14, the use of the proposed method for determining the onset of the pulse has a lower
relative error in the case of choosing the polarity of low pulse. However, the difference in relative errors in the
two polarities is not significant, since it does not exceed 0.3 % in the range of standard deviation values from 0 to
2.
5. Conclusions
The paper proposes a method for determining the onset of the pulse of a probing ultrasonic signal, which is
based on the use of a basic algorithm for determining the coordinate of the maximum of a certain periodic pulse,
which is included in the library of the LabVIEW software development environment.
In the work, numerical simulations were performed using the proposed algorithm to determine the beginning
of the probing pulse. The independent variable was the value of the noise standard deviation, which was selected
in the range from 0 to 10. According to the results of the simulation, it was found that this algorithm allows to
determine the beginning of the pulse with a relative error that does not exceed 3.5 %.
Mathematical expressions for modeling the probing pulse were also obtained in the work. The resulting
mathematical apparatus will make it possible to simulate a probing pulse of any shape.
Author Contributions. Refinement of the methodology and study ideology, acquisition and analysis of
research data – I. Bohachev; signal modeling and development of data processing algorithms – O. Kozyr; drafting
of the preliminary manuscript and collection of research data – S. Sozonov.
Funding. The article was developed as part of the research project titled “Development of Methods and
Tools for Environmental Monitoring of Energy Facilities Utilizing Wireless Sensor Networks”.
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ЗМЕНШЕННЯ ВПЛИВУ ШУМІВ НА ТОЧНІСТЬ ВИЗНАЧЕННЯ
ПОЧАТКУ УЛЬТРАЗВУКОВОГО ІМПУЛЬСУ
Ігор Богачев1*, канд. техн. наук, ст. досл., https://orcid.org/0000-0001-7781-5767
Олег Козир2, канд. техн. наук, доцент, https://orcid.org/0000-0002-9285-5940
Станіслав Созонов1, https://orcid.org/0000-0002-7584-4529
1Інститут загальної енергетики НАН України, вул. Антоновича, 172, Київ, 03150, Україна;
2Національний технічний університет України «Київський політехнічний інститут імені Ігоря
Сікорського», Берестейський проспект, 37, Київ, 03056, Україна
*Автор-кореспондент: biv_vdoe@ukr.net
Системні дослідження в енергетиці. 2025. 1 (81) 99
Анотація. Важливою складовою ультразвукового неруйнівного контролю є визначення часу затримки між
відправленим та отриманим сигналами. Тому точність визначення початку як відправленого, так і отриманого
імпульсу випливає на точність усіх подальших розрахунків. Основними вимірювальними перетворювачами
зазвичай є п’єзоелектричні перетворювачі. Порівняно новим підходом є використання малоапертурних
магнітострикційних перетворювачів у якості генератора та приймача ультразвукового сигналу. Такі
магнітострикційні сенсори мають маловиткові котушки збудження і, внаслідок цього, малі амплітуди
прийнятих сигналів. Тому актуальним завданням є розробка алгоритмів визначення початку імпульсу, які б
могли зменшувати наявні у сигналі шуми або не бути чутливими до них. У даній роботі запропоновано метод
визначення початку ультразвукового імпульсу, який базується на використанні стандартної функції із
бібліотеки LabVIEW, для визначення положення пікового значення періодичного імпульсу. Отримано
математичні вирази для моделювання відправленого та отриманого імпульсів. На основі цих математичних
виразів було проведено моделюючий експеримент для перевірки точності визначення початку зондуючого
імпульсу запропонованим методом. Моделюючий експеримент виконувався для шуму, який мав гаусівський
розподіл для діапазону значень середньоквадратичного відхилення (СКВ) від 0 до 10. За результатами
моделювання було встановлено, що запропонований метод дозволяє визначати початок зондуючого імпульсу з
відносною похибкою, яка не перевищує 3,5 % для значень СКВ менше 2.
Ключові слова: ультразвуковий сигнал, магнітострикційні сенсори, співвідношення сигнал / шум.
Надійшла до редколегії: 30.12.2024
|
| id | systemreorg-article-888 |
| institution | System Research in Energy |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:23:30Z |
| publishDate | 2025 |
| publisher | General Energy Institute of the National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | systemreorg/76/258d6e07cce9d9856b61a0c5e2f54e76.pdf |
| spelling | systemreorg-article-8882026-07-18T12:57:49Z REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION Зменшення впливу шумів на точність визначення початку ультразвукового імпульсу Bohachev, Ihor Kozyr, Oleh Sozonov, Stanislav ultrasonic signal, magnetostrictive sensor, signal-to-noise ratio. ультразвуковий сигнал, магнітострикційні сенсори, співвідношення сигнал / шум. An essential component of ultrasonic nondestructive testing is determining the delay time between the transmitted and received signals. Therefore, the accuracy of determining the onset of both the transmitted and received pulse affects the accuracy of all subsequent calculations. The main measuring transducers are usually piezoelectric. A relatively new approach involves using small-aperture magnetostrictive transducers as a generator and receiver of the ultrasonic signal. Such magnetostrictive sensors have low-current excitation coils, resulting in low amplitudes of received signals. Therefore, it is an urgent task to develop algorithms for determining the onset of a pulse that could reduce the noise present in the signal or not be sensitive to it. In this paper, a method for determining the onset of an ultrasonic pulse is proposed based on utilizing a standard function from the LabVIEW library to determine the position of the peak value of a periodic pulse. The mathematical expressions for modeling transmitted and received pulses were obtained. Based on these mathematical expressions, a modeling experiment was conducted to verify the accuracy of determining the beginning of the probing pulse by the proposed method. The simulation experiment was performed with noise following a Gaussian distribution for the range of standard deviation (SD) values from 0 to 10. According to the modeling results, it was found that the proposed method allows determining the beginning of the probing pulse with a relative error not exceeding 3.5 % for the values of the SWR less than 2. Важливою складовою ультразвукового неруйнівного контролю є визначення часу затримки між відправленим та отриманим сигналами. Тому точність визначення початку як відправленого, так і отриманого імпульсу випливає на точність усіх подальших розрахунків. Основними вимірювальними перетворювачами зазвичай є п’єзоелектричні перетворювачі. Порівняно новим підходом є використання малоапертурних магнітострикційних перетворювачів у якості генератора та приймача ультразвукового сигналу. Такі магнітострикційні сенсори мають маловиткові котушки збудження і, внаслідок цього, малі амплітуди прийнятих сигналів. Тому актуальним завданням є розробка алгоритмів визначення початку імпульсу, які б могли зменшувати наявні у сигналі шуми або не бути чутливими до них. У даній роботі запропоновано метод визначення початку ультразвукового імпульсу, який базується на використанні стандартної функції із бібліотеки LabVIEW, для визначення положення пікового значення періодичного імпульсу. Отримано математичні вирази для моделювання відправленого та отриманого імпульсів. На основі цих математичних виразів було проведено моделюючий експеримент для перевірки точності визначення початку зондуючого імпульсу запропонованим методом. Моделюючий експеримент виконувався для шуму, який мав гаусівський розподіл для діапазону значень середньоквадратичного відхилення (СКВ) від 0 до 10. За результатами моделювання було встановлено, що запропонований метод дозволяє визначати початок зондуючого імпульсу з відносною похибкою, яка не перевищує 3,5 % для значень СКВ менше 2. General Energy Institute of the National Academy of Sciences of Ukraine 2025-02-27 Article Article application/pdf https://systemre.org/index.php/journal/article/view/888 10.15407/srenergy2025.01.085 System Research in Energy; No. 1 (81) (2025): System Research in Energy; 85-99 Системні дослідження в енергетиці; № 1 (81) (2025): Системні дослідження в енергетиці; 85-99 2786-7102 2786-7633 en https://systemre.org/index.php/journal/article/view/888/796 Copyright (c) 2025 Ihor Bohachev, Oleh Kozyr, Stanislav Sozonov https://creativecommons.org/publicdomain/zero/1.0 |
| spellingShingle | ultrasonic signal magnetostrictive sensor signal-to-noise ratio. Bohachev, Ihor Kozyr, Oleh Sozonov, Stanislav REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION |
| title | REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION |
| title_alt | Зменшення впливу шумів на точність визначення початку ультразвукового імпульсу |
| title_full | REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION |
| title_fullStr | REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION |
| title_full_unstemmed | REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION |
| title_short | REDUCING THE INFLUENCE OF NOISE ON THE ACCURACY OF ULTRASONIC PULSE ONSET DETECTION |
| title_sort | reducing the influence of noise on the accuracy of ultrasonic pulse onset detection |
| topic | ultrasonic signal magnetostrictive sensor signal-to-noise ratio. |
| topic_facet | ultrasonic signal magnetostrictive sensor signal-to-noise ratio. ультразвуковий сигнал магнітострикційні сенсори співвідношення сигнал / шум. |
| url | https://systemre.org/index.php/journal/article/view/888 |
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