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18EDDY CURRENT AUTOMATED FLAW DETECTION SYSTEM SIGNAL POCESSING METHOD
Redka M., Kuts Y.
National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute "
Kyiv
ABSTRACT
A method for processing eddy current flaw detection signals based on determining the number of zeros of the analyzed signal in sliding mode is proposed. This method is characterized by low resource consumption, has a simple circuit implementation and can be used in automated eddy current non-destructive testing systems. Keywords: eddy current flaw detection, automated eddy current monitoring, signal detection.
Introduction. Eddy current flaw detection (ECFD) is based on the interaction of an alternating electromagnetic field with an electrically conductive control object (CO) [1, 2]. An essential feature of ECFD is that it is implemented in the absence of mechanical contact between the eddy current transducer (EDT) and the CO. This makes it possible to carry out ECFD in conditions of EDT movement relative to CO at a significant speed. This significantly increases the productivity of control and expands the possibilities of its automation. There are many factors creating the need to develop new and improve existing methods and tools of ECFD. These factors include the variety of technological processes for manufacturing products, their operating conditions, appearance of new materials and need to identify flaws in a wide range of their sizes and depths of occurrence
Usually, ECFD signals are generated by differential ECFD [3] provided that the components that are insignificant for ECFD are fully (or partially) compensated. These components include open-circuit voltage and driving voltage. Such signals are observed against the background of noise at different signal-to-noise ratios (s/n).
Various known methods can be used to distinguish signals from flaws in an additive mixture with noise. These methods include the method of optimal signal filtering [4], coordinated signal filtering [5], use of signals with various types of modulation and manipulation [6, 7], correlation signal reception [4, 5], split method [8], wavelet analysis method [9], etc. Implementating the potential of most of these methods requires knowing a copy of the desired signal. These methods are also characterized by a significant resource consumption of calculations. The resource consumption of calculations is understood as hardware and time costs for their implementation.
For a number of ECFD applications, there is another way of distinguishing signals from flaws. The EDT signals, as implementations of physical random processes, are time-varying function. Such functions have a finite number of maxima and minima at a finite observation time. Accordingly, these functions also have a finite number of intersections (the number of zeros) with an alternating-sign zero-level signal [10]. The dependence of the statistical characteristics of the number of zeros of the EDT signal on the signal-to-noise
ratio is the basis for the idea of a rapid method for detecting signal flaws in ECFD. This method was proposed in [11].
The research objective is to develop a method for distinguishing signals from flaws based on determining the number of zeros of the analyzed signal in sliding mode. It is also necessary to compare the efficiency and resource consumption of the proposed method with the basic one. The development of a low resource-consuming method for processing ECFD signals shall enable them to be used in automated ECFD systems with a significant scanning speed of CO. Statement of the problem. The common pattern of ECFD signal generation in the case of using transformer differential EDT is shown in Fig.1. Usually, such transducers are excited by a sinusoidal alternating electric current with a frequency of f. In the event of balanced secondary windings, a flawed radio pulse signal of the following type is generated during EDT scanning in the CO area
Ud(t,p) = U(t,p)cos[2nft — <p(t,p)] (1) where U(t,p),<p(t,p) is an envelope (amplitudetime characteristics of the signal, ATC) and an initial phase, respectively, 2nft — <p(t,p) is the phase-time or phase characteristic of the signal, FTC, p is a vector of the flaw parameters (for example, the depth and opening of crack, its length, etc.) and "EDT - CO" system parameters (the distance between the EDT and OK, the orientation of the EDT relative to the flaw, scanning mode, etc.).
f E"dt]_
Fig. 1. Signal generation in an eddy current flaw detector with a differential-type transformer EDT (SPU - signal processing unit)
A typical signal from a flaw in the case of EDT operating in dynamic mode and subject to the compensation of the open-circuit voltage and driving voltage is shown in Fig. 2.a. The characteristics of such a signal contain information about the flaws of a researchable object and require further measurement and analysis. Usually, such signals are observed against the background of noise (Fig. 2. b). As the flaw size decreases and the depth of their occurrence increases, the amplitude of the signal information component also decreases. This leads to a decrease in the s/n ratio and the
probability of distinguishing signals from flaws. In the absence of full open-circuit and driving voltage compensation, the signal also contains a harmonic component that is present during the entire analysis time (Fig. 2. c.). In most ECFD systems, signals are converted to digital codes by analog-to-digital converters (ADCs).
Fig. 2. Plots of the ECFD signal with full EDT compensation and no noise (a), ECFD signal with full EDT compensation and with noise (b) and signal plot
with incomplete EDT compensation with noise
The method proposed in [12] is used as the basic method for detecting radio pulse signals. This method involves analysing the circular statistics - the resultant vector length (or abbreviated r-statistics [13]). The value of r-statistics is determined by the difference in the phase characteristics of EDT signals. The values of r-statistics are obtained as a result of sliding window processing of the difference A$(t) = $(t) — 2nft. In this case, $(t) is the FTC of the mixture of the EDT signal and noise, and 2 nft is the FTC of the carrier signal. The current FTC values are calculated using the discrete Hilbert transform (DHT) of the signal. In the basic method, the window function has a fixed aperture of M. The presence of a flawed signal can be inferred from exceeding the threshold level by r-statistics. The computational complexity of this method is due to several factors. These factors include the implementation of DHT algorithms, calculation of FTC and trigonometric moments from A$(t). In addition, if the insignificant components of the EDT signal are not fully compensated, incorrect results may be obtained.
According to the method proposed, ECFD signals are detected by the number of zeros in the process. This does not take into account the sign of zeros which is a derivative sign at the moment when the signal crosses the zero level. In this case, the process zero is the intersection of the abscissa axis by an alternating-sign function with a zero constant component. The number of zeros in the noise process has certain statistical characteristics. When analyzing an additive mixture of the useful component of signal (amplitude-modulated harmonic signal) and noise, these characteristics vary. This feature is the basis of the method for detecting ECNDT signals against the background of noise. A common algorithm for implementing the method for detecting EDT signals against the background of noise disturbances is shown in Fig. 3.
Fig. 3. An algorithm for implementing the method for detecting ECFD signals against the background of noise by the number of zeros of the process
An algorithm for obtaining the resultant process zero vector Zj] for a signal-noise mixture consists of a sequence of actions. At the beginning of this algorithm, an external cycle is started, which implements signal scanning by the window function. At each iteration of the external cycle, an internal cycle starts. The internal cycle implements the process of counting the number of zeros of the process inside the window function. At each iteration of the internal cycle, the values of the current and following signal sample are multiplied. If the product sign is negative, there is a zero of process between these samples. In the event of detecting the following zero of process, the value Z [j, m] (m = 1... Mis the number of the signal sample in the window) is increased by one. After the internal cycle is completed, a result of Z[j,M obtained is divided by an aperture value of the window function in order to normalize the resultant vector: Zj]= Z[j,M] / M.
An important part of the research is to prove the possibility of using the proposed method for detecting ECFD signals and its advantage over the basic one in terms of resource consumption.
Simulation procedure. Simulation of the process of detecting radio-pulse ECFD signals against the background of noise was carried out in the MATLAB software environment. The simulation experiment consisted of the following steps:
1. Generating the sequences of radio pulses with a harmonic carrier signal shown in Fig.1. For further processing, a model of a signal-noise mixture of an uncompensated EDT was selected.
2. Conducting the window processing of this signal-noise mixture with determination of the number of process zeros in the analysis window in sliding mode.
3. Plotting and analyzing the process zero vector
Zj].
4. Implementing the DHT signal of uncompensated EDT and signal-noise mixture of uncompensated EDT.
5. Obtaining the FTC signal and signal-noise mixture and calculating their difference.
6. Performing the sliding window processing of the FTC difference with the calculation of the r-statistics vector value.
7. Plotting the vectors of r-statistics and zeros of the process Zj].
8. Calculating the efficiency of methods for detecting ECFD signals against the background of noise.
9. Evaluating the resource consumption of methods for detecting ECFD signals against the background of noise.
Simulation parameters. For the simulation experiment, the following parameters were selected: frequency of the harmonic carrier signal f = 1 MHz; s/n ratio = (1,2,5,10) to test the effectiveness of these methods at various s/n ratios; sampling rate Fs= 12.8 MHz; sample size Ж=25600; window function aperture M=256, radio pulse shape - Gaussian, number of pulses - 2.
Analysis of simulation observations. Verification of the efficiency of methods for detecting ECNDT signals against the background of noise was carried out by calculating the efficiency coefficient of the Kef. This coefficient for the basic method is calculated as Kef =
Ta/y , where TA is an average amplitude value of the r-
rn is an average value of the noise r-statistics. For the method proposed, Kef=Z„/Zs, where Zs is an average value of the process zero vector in areas with a useful signal component, and Z„ is an average value of the process zero vector in areas with noise only. A graphical representation of the r-statistics vectors and zeros of the process obtained during simulation for the ratio s/n=2 is shown in Fig. 5.
Fig. 5. r-statistics vector (a) and process zero vector
Z[j] (b)
The values of the calculated efficiency coefficients of methods for various s/n ratios are shown in Table 1.
statistics in areas with a useful signal component, and
Values of Kef and resource consumption of ECNDT signal detection methods
Table 1.
s/n Kef Resource consumption, ms
r-statistics method Process zero method r-statistics method Process zero method
1 6 4.5 650 58
2 6 6 600 70
5 1.1 6 564 48
10 1 8 649 54
The results of the simulation experiment showed that in the case of lower s/n ratios, the method of detecting signals by determining the vector of r-statistics proved to be more efficient. However, in some cases, the use of this signal detection method is ineffective. Such cases include the absence of full compensation of the open-circuit and driving voltage in the EDT with an increase in the s/n ratio. In turn, the method of detecting signals based on the number of zeros of the process is more efficient at higher values of the s/n ratio.
Also, during the simulation experiment, the level of resource consumption of these methods was estimated. The main indicator of resource consumption was the time spent calculating the resultant vectors of r-statistics and Zj].
The simulation experiment was carried out on a personal computer with the following specifications:
• Processor clock speed - 3.9 GHz;
• Number of processor cores/threads - 6/12;
• RAM capacity - 16 GB;
• RAM frequency - 3.2 GHz;
The time required to perform signal detection algorithms for each of the methods was calculated using the tic toc functions of the embedded MATLAB start stopwatch timer. Time taken by the algorithm of the basic and proposed methods is shown in Table. 1. The
large difference in the algorithm execution time for the basic and proposed signal detection methods is due to the lack of necessity to use additional libraries in the proposed method. In turn, the basic method requires DHT and scan of the signal phase responses, and so on.
Developing a low resource-consuming method for processing ECFD signals shall enable detecting flaws at a significant rate of data input. At the same time, there shall be no significant decrease in the reliability of control results, and this method shall simplify their circuit implementation.
Conclusion. The possibility of detecting ECFD signals observed against the background of noise, provided that EDT compensation is incomplete, has been studied. The method is based on calculating the process zero vector during window processing in sliding mode. The efficiency of the proposed and basic method has been compared. The basic method involves analyzing the vectors of r-statistics determined by the signal phase characteristic. The proposed method is free from a number of shortcomings of the basic one, the main one being the high resource consumption for its implementation. It is shown that the efficiency coefficient of the proposed method makes it possible to detect ECFD signals against the background of noise at low s/n values.
References
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РОЗРОБКА КРИТЕР1Я ЕФЕКТИВНОСТ1 КОРЕЛЯЦШНО-ШТЕРФЕРОМЕТРИЧНИХ
РАДЮПЕЛЕНГАТОР1В
Ципоренко В.В.,
кандидат технгчних наук, доцент Ципоренко В.Г.
кандидат технгчних наук, доцент Державний утверситет «Житомирська полтехнгка»
Житомир, Украша
DEVELOPMENT OF CRITERIA OF EFFICIENCY OF CORRELATION-INTERFEROMETRIC
DIRECTION FINDERS
Tsyporenko V.,
Ph.D., associate professor Tsyporenko V.
Ph.D., associate professor Zhytomyr Polytechnic State University Zhytomyr, Ukraine
АННОТАЦ1Я
Отримаш piBHAHHA ефективносп пеленгування за вщношенням точнють/(швидкодш, апаратурш витрати), а також у сшввщношенш шлькосл операцш i каналiв на один бгг шформацп. При цифровш реалiзацii алгоршшв кореляцшного пеленгування гх вщповщш часовi витрати оцшено бшьш ушфжованим i узагальненим показником, таким як кшьшсть операцш кореляцшного оброблення. Виконано аналiз запропонованих рiвнянь критерш ефективносп алгоритмш пеленгування. Запропоноваш оцшки ефективносп за вiдношенням (точнiсть/швидкодiя), що не залежать вiд апрiорi невизначених i рiзних абсолютних значень параметрiв точносп, швидкодй' i апаратурних витрат. Це дозволяе оцiнити ефективнiсть рiзних варiантiв алгоритму пеленгування, яш вiдповiдають рiзним умовам застосування i
