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Uncertainties and errors in Non-Destructive Characterisation of Discontinuities Alexandar Skordev Contact

INTRODUCTION

One of the up-to-date objectives of the non-destructive evaluation of discontinuities is to obtain a higher accuracy of their characteristics. In order to evaluate or manage the quality of NDT we need to formulate some specific parameters and a database for the accuracy of the non-destructive evaluation of discontinuities in materials and products. Operating machinery, constructions and elements according to modern philosophy "Damage Tolerance" raises the problem of the accuracy of non-destructive characterisation of discontinuities. Because it would not be efficient without data for the most probable characteristics of the NDT detected discontinuities and the evaluation of their accuracy.
   The terms of accuracy in non-destructive characterisation are not universal and regulated, and there is not enough comparable and reliable information about errors and uncertainties in evaluation of discontinuities' dimensions with the main NDT methods: ultrasonic reflectors, radiography, magnetic power and eddy-current with double-coil surface probes.
   The aim of this work is to clarify the use of terms "error" and "uncertainty" and to present some related data in the field of non-destructive characterisation of the two main characteristics of the discontinuities: location and size. We suggest a methodology for horizontal interspecies multiplication of the results from different methods for non-destructive characterisation of discontinuities based on main physical principles such as reflection, transmission etc., through grouping the primary information parameters.

DEFINITIONS AND FACTORS AFFECTING THE VALUE OF ERRORS AND UNCERTAINTIES OF THE RESULTS

"Error" and "uncertainty" are fundamental notions in metrology [1]. The common point in their use is that both of them characterise the accuracy of results obtained by measurement of physical quantities. And the difference - according to [2] - is that "error" is used when the value of the measured quantity is known. While "uncertainty" is used in any other case, especially when the value of the measured quantity is unknown. This value is defined by the dispersion or the standard deviation of the results from independent measurements. The uncertainty of the results of measurements is the sum of the uncertainties of the calibration and on-line measurement processes. There are some systematic and some random factors, affecting the uncertainty of the results of measurements. The errors of the measurements could be systematic and random and they reflect the effects of these factors on the value of uncertainty of the results.
   Various authors, presenting the main methods of non-destructive characterisation of discontinuities have used the term "error". [3,4,5,6,7,8,9]. Although not properly mentioned in the text, most of the publications compare the results of the corresponding characterisation of discontinuities with the real characteristics of artificial and real discontinuities. The factors affecting the systematic and the random errors in ultrasonic characterisation of discontinuities' location are systematized in [4,10,11]. The analysis of methodology of error evaluation in the above-mentioned characterisation (although based on repeated independent measurements) shows that the error, resulting from real discontinuities, can be precisely evaluated only in particular case (and does not allow a reproduction of the measurements), because we have to destroy the object in order to evaluate the error. The obtained errors could be used as basic data for similar characterisations or as error edge values for the methods, used for evaluation of these characteristics.
   There is no principle difference between the results of a physical quantity measurement in applied metrology, and on the other hand, the results of the non-destructive characterisation. The evaluation of indications' characteristics and the solution of the inverse problem: the reconstruction of the object using its image/o6pa3/picture, makes the problem more difficult to solve. Although the process of characterisation of discontinuities is not called "measurement", for many reasons, it is a measurement process by its character. That is why there is no obstacle to describe the accuracy of characterisation by the term "uncertainty". As the uncertainty parameter is a statistically determined value, obviously, it could be used in characterisation of every process for evaluation of characteristics of real discontinuities without destroying their object. In other words, the uncertainty refers to every real result of the non-destructive characterisation. The error, unlikely to the uncertainty could be reproduced repeatedly. Nowadays the term "uncertainty" is rarely used in the publications. Sometimes the standard deviation of the obtained and statistically processed results of the discontinuity's location and size are given.
   The problem that in metrology there is no such term as "continuity" and the calibration requires universal and regulated etalons for the corresponding physical quantity, could find its methodological solution by conventional calling the setting up - "calibration".
   The introduction of the term "uncertainty" in non-destructive characterisation requires special attention on its similarities and differences with the already common term "reliability". Both terms qualify the quality of NDT. But "uncertainty" is a measure for the dispersion of the results, while "reliability" is a measure for the coincidence of the non-destructive evaluation with the real condition of the controlled object. There is no obstacle for the use of the collocation "uncertainty of the reliability" of results obtained after repeated tests and their statistical proceeding.
   The application of procedures defining the uncertainty as a dispersion of the results or as a standard quadratic mean deviation near the most probable mean value, and by other methods, known as evaluation types A and B in [2], are applicable, without any visible obstacles, at the current stage of development of non-destructive characterisation.

REVIEW OF ERROR AND UNCERTAINTY VALUES IN NON-DESTRUCTIVE CHARACTERISATION OF DISCONTINUITIES

Location of discontinuities
The most exhaustive data we can refer to is from the ultrasonic characterisation with reflection methods with normal and angle probes. The error of reading of positions of echoes on the display for the A-scan is 1% (display with a 100-graduated scale) or 2 % (display with a 50-graduated scale) [4], non-linearity of the display - 3% [4], instability of the acoustic couplingusing angle probe - up to 5% [12], temperature margin of 50^o C and use of angle probes - +12.3% ¸ 12.7% [4], change of the angle of the angle probe - accordingly to Table1 [12]. The sum error in location evaluation with ultrasonic inspection of welded joints is presented in Table 2 [9]. In EN 1714 the change of the indications of the time base over 2% of the range requires some correction steps.

Change of the angle of the probe	± 30'	± 1o	± 2o
Location error in mm	± 3.1	± 6.2	+ 12.3 - 12.7
Table 1:

Reflector type	Thickness in mm	Errors for close to surface discontinuities on		Errors for fully embedded discontinuities
		scanning surface	back surface
				Depth,Smm	Errors, mm
Point, Line, volume	10-25	± 2	± 2	5-25	± 2
	25-75	± 2	± 3	25-75	± 3
	75-125	± 2	± 4	75-125	± 4
Edge of planar defect, multiple	10-25	± 2	± 3	5-25	± 3
	25-75	± 2	± 3	25-75	± 4
	75-125	± 2	± 5	75-125	± 6
Table 2:

The standard deviation of the three dimensions of discontinuities in welded joints, evaluated thanks to the results of the examinations in NORDTEST Certification Center [13] are in Table 3, where X - is the lengthwise coordinate, Y - is the widthwise coordinate, Z -is the depthwise coordinate.

Standard deviation in x, y, z-direction		Welded joint type
		Butt welds	Pipe welds	T-welds	Nozzle-welds
X	min	1.99	0	3.11	2.88
	mean	5.11	6.75	6.16	7.64
	max	11.82	11.75	10.32	11.99
Y	min	0.6	1.0	0.99	0.5
	mean	1.85	1.64	1.85	2.04
	max	3.47	2.59	2.41	2.81
Z	min	0.69	1.01	1.36	1.25
	mean	1.74	1.72	2.26	2.13
	max	3.28	2.62	3.70	2.71
Table 3: Accuracy of discontinuity location in X, Y and Z-directions (mm)

The velocity of ultrasonic waves with frequency 5 MHz measured in 15 calibration blocks type V1 using the impulse echo-method results in systematic errors for shear waves caused by coupling and diffraction up 12.5¸ 14.5 m/s and uncertainty ± 2.5 m/s due to coupling factors and ±4 m/s to diffraction reasons or a total of 0.11% compared to c_l = 5890 m/s and for shear waves: ±1 m/s or 0.03%. Uncertainty of measurement of the attenuation is ±0.02 dB/mm or 16%. Uncertainty of "calibration" of index points and angles of an angle probe 45^° are respectively ± 0.6 mm and ±0.3^°, and for 70^°: ± 1.2 mm and ±0.5^°[14].

Discontinuities sizing by radiography
Errors of densitometer evaluation of depth of recess radiated with X-rays in the direction of the recess wall in steel piece with 12mm thickness are in Table 4.

Depth of the recess tolerance ±0.05mm	3.10	2.60	1.2	1.00	0.50	0.25
Measured depth on indication, mm	3.15	2.55	1.22	1.18	0.69	0.60
Relative error, %	1.6	1.9	1.7	18	38	140
Table 4:

Discontinuity sizing with eddy-current method using encircling coil
Errors of evaluation of indications of a lengthwise recess in cylindrical non-ferromagnetic bar are up to 35% for the modulus and up to 5% for the phase [7].

Discontinuity sizing with ultrasonic reflector methods
Errors and uncertainties of characteristics, from the sizing of discontinuities, obtained from our research and already published, are systematized in Table 5.


Table 5:

Note: The value in () is basic or mean and in [] the value from the corresponding publication.

Although the conditions of characterisation are not perfectly comparable, the above-mentioned data from ultrasonic evaluation of the size of discontinuities could be summarized in following key-points:

1. Height of the echo from reference reflectors is defined with an error up to 9% and uncertainty ranging from 0.2 to 1.1.dB, which is quite low compared to the standard level -4 dB.
2. The uncertainty of echo's height evaluation from real discontinuities in welded joints is 4.8¸ 6 dB, and in thin sheets with Lamb waves is 0.2 1 dB.
3. The length of discontinuities in welded joints is defined with an error between ± 4 and ± 10 mm or up to 30% and with uncertainty between 7.3 and 8.2 mm.
4. The human factor in inspection of welded joints causes errors of 2.8 or 19% and uncertainty between 0.4 and 1.05.

Although the above-mentioned conclusions could be considered insufficient and fragmentary, they serve as a departure point for the establishment of database for the errors and uncertainties of non-destructive characterisation of discontinuities. The lag behind of the methods other than ultrasonic is obvious.

METHOD FOR INTERSPECIES MULTIPLICATION OF THE RESULTS FROM THE EVALUATION OF ERRORS AND UNCERTAINTIES OF NON-DESTRUCTIVE CHARACTERISATION

During the last years the bases of the general theory of non-destructive characterisation of discontinuities have been established [18]. The comparison between the information indications of the characteristics of discontinuities uncovered the similarity of, different by their nature, methods for non-destructive inspection. So the non-destructive inspection methods could be divided into two main groups: reflection methods - ultrasonic reflection, eddy-current, magnetic ferroprobes, etc.; and transmission methods: radiography, penetration, magnetic-powder method, etc. The main characteristics of the indications of discontinuities in both groups are very close and their unification is really feasible. It was proved that the method for evaluation of discontinuities' dimensions through the dynamic behavior of the echo height, also known as moving the probe method, could be applied in eddy-current and magnetic ferroprobes methods. The unsharpness of the image in radiography could be used for the indications of magnetic-powder and penetration methods. The similar nature of the information characteristics allows comparing the errors and uncertainties in non-destructive characterisation of discontinuities.
   The transfer of the result's errors and uncertainties in characterisation of discontinuities with the methods from the both groups could be called - method for interspecies multiplication.
   The application of this method in practice will accelerate the establishment of a database for the accuracy of non-destructive characterisation, and will satisfy the constantly increasing needs of NDT management and the up-to-date and pragmatic philosophy of "damage tolerance" in exploitation of machines and constructions.

CONCLUSION

In this report we tried to describe and back with arguments the perspectives of the use of the results' uncertainty in non-destructive characterisation of discontinuities. The presented results could be a basis for a database for non-destructive characterisation accuracy. We believe that the suggested method for interspecies multiplication of the results from evaluation of accuracy of non-destructive characterisation will help the fast establishment of a database for all spheres of use of the non-destructive characterisation of discontinuities.

BIBLIOGRAPHY

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