# Evaluation of uncertainty in quantitative analysis

2022-08-18
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Evaluation of uncertainty in quantitative analysis of longitudinal wave flaw detection

preface

measurement uncertainty (hereinafter referred to as uncertainty) is used to characterize the dispersion of reasonably assigned measurement values. It is an important parameter for evaluating measurement results [1, 2]. In order to standardize the correct evaluation and use of measurement results, seven organizations including international standardization jointly formulated the "guidelines for the expression of measurement uncertainty" in 1993 and have been widely used. In 1996, uncertainty was popularized in metrological verification in China, but it is not widely used in quantitative analysis of nondestructive testing. In order to be in line with international practice, this paper applies uncertainty to nondestructive testing and discusses it with you

the error of longitudinal wave flaw detection comes from the flaw detector, probe, test block, workpiece, couplant, etc. there is measurement uncertainty in the process of defect positioning measurement and quantitative analysis. The evaluation uncertainty can show the reliability of flaw detection analysis results, which has a good promotion value

1 defect positioning

adjust the longitudinal wave scanning speed according to 1:n, and the horizontal scale value opposite the front of the defect wave is f, then the distance between the defect and the probe is :

xf=n f (1)

1.1 instrument, workpiece

(1) epoch- Ⅱ ultrasonic flaw detector; (2) 2.25p0.75 probe; (3) Csk-i test block; (4) 100 mm thick workpiece

1.2 measurement of position

the instrument adjusts the scanning speed according to 1:1, the horizontal scale value is 69.64, the defect position:

xf=n f=69.64 mm

1.3 uncertainty evaluation

(1) the uncertainty caused by adjusting the scanning speed

the reading error limited by the minimum scale of the display screen will be generated when the scanning speed is adjusted. If the minimum horizontal scale of the instrument used is 0.1, the reading can reach the minimum scale of 1/10, that is, the reading error distribution range is (-1/10, +1/10) scale, which is uniformly distributed, and the standard uncertainty (expressed in relative uncertainty) :

; Its reliability is 50%, and the degree of freedom v1= (50%) -2=2

(2) horizontal influence

the horizontal linearity of the instrument affects the positioning accuracy of defects. After verification, the horizontal linearity of the instrument is 5.7, which obeys the normal distribution (k=3), and its standard uncertainty:

(class B): its value is reliable, and the degree of freedom v2=

horizontal scale error is affected by the resolution of the instrument (resolution 0.01), which obeys the uniform distribution, and its error is 1/2 resolution, Distribution range (-0.005, +0.005) [managed by haydale and an integrated team from the Faculty of engineering, Cardiff University, UK 5], and its standard uncertainty (expressed in relative uncertainty):

; (class B); The reading reliability is 50%, the degree of freedom v3= (50%) -2=2

the horizontal scale value is measured for 10 times respectively, and the mean value is 69.64, the standard deviation is s=0.21, and its standard uncertainty (expressed as relative uncertainty):

; (a): degree of freedom v4=n-1=9

horizontal scale synthetic standard uncertainty is the synthesis of the three standard uncertainties of the instrument's horizontal linearity, instrument resolution and horizontal scale value repeated observation, that is, the synthesis of the above three categories A and B:

(3) result evaluation

transfer function of each component:

defect positioning, its synthetic uncertainty:

effective degree of freedom:

take the confidence level of 95%, TP (0.95) =1.96

defect location: XF (1 tpuc (XF)) =69.64 (18.8)

its absolute uncertainty (synthetic standard) UC (XF) = (XF) =0.3127

2 defect quantitative analysis

defect equivalent size is calculated by the following formula:

(2)

from formula (2), it can be seen that the defect equivalent size is affected by defect location, workpiece thickness and attenuation

2.1 change of attenuation

the change of attenuation in detection is caused by vertical linearity, probe frequency, attenuator error, couplant, medium attenuation, etc

2.1.1 effect of vertical linearity

the relationship between vertical linearity and attenuation is obtained from the following formula:

(3)

where: H0 ideal wave height H1 measured wave height (below, H1 is replaced by H1 as the first measured wave height, H1 is replaced by H1 as the second measured wave height)

① effect of primary wave height

transfer function 0= 10.9

the linear error is 4.7, which obeys the normal distribution (k=3), and the standard uncertainty (expressed by relative uncertainty):

(class B); Its value is stable, and the degree of freedom v5=

the reading error is 1/2 of the resolution, obeying the uniform distribution range (-0.5, +0.5), and the standard uncertainty (expressed in relative uncertainty):

; (class B) its estimated reading reliability is 50%, and the degree of freedom v6= (50%) -2=2

the uncertainty of the primary wave height in the static strength demand stage (1906 ~ 1959) is the combination of the above two items a and B, namely:

② the influence of the secondary wave height

the transfer function

the linear error of the secondary wave height is 4.7, and its standard uncertainty:

reading error the same primary wave, u8=u6, v8=v6

the uncertainty caused by linear error is the synthesis of the standard uncertainty of the primary wave height and the secondary wave height, that is:

2.1.2 attenuation caused by frequency

influence of frequency on attenuation:

transfer function:

frequency error 10%, subject to normal distribution (k=3), standard uncertainty:

; Its value is stable, the degree of freedom v9=

the width of attenuation is about 60mm, the standard uncertainty:

2.1.2 the influence of coupling agent

change the thickness of coupling agent, measure its attenuation, and analyze it with statistical methods to obtain its uncertainty (the number of tests this time is 10), the average value of the test is 5.5 dB, the standard deviation s=0.566, the standard uncertainty:

expressed in relative uncertainty:; Degree of freedom v10==9

the error caused by reading is 1/2 of the resolution, which follows a uniform distribution, and its distribution range is (-0.05, +0.05). Standard uncertainty:

is expressed in relative uncertainty:; The reading reliability is 50%, and the degree of freedom v11= (50%) -2=2

the influence of attenuator accuracy (measured at 12dB):

attenuator error is 0.5dB, which obeys the normal distribution (k=3), and the standard uncertainty:

is expressed in relative uncertainty; Its value is stable, and the degree of freedom v12=

the uncertainty of attenuation caused by coupling agent is the synthesis of the above three categories A and B:

2.1.4 medium attenuation

the workpiece is checked repeatedly (10 times), and the medium attenuation is obtained, with an average of 5 Rotating Zigzag rods 3. Standard deviation s=0.2 dB, standard uncertainty:

expressed in relative uncertainty:; Degree of freedom v13==9

standard uncertainty caused by reading: u 14=u11=0.029 dB (class B)

expressed in relative uncertainty:; Degree of freedom v14=v11=2

effect of attenuator: u15=u12=0.167 dB (class B)

expressed in relative uncertainty:; Degrees of freedom v15=v12=

the uncertainty of medium attenuation is the combination of the above three categories A and B:

2.1.5 the change of repeated observation results of attenuation

the workpiece is measured for 10 times, and the average value is 6.2, the standard deviation is s=0.58, and its standard uncertainty:

is expressed in relative uncertainty:; Degree of freedom v16==9

standard uncertainty caused by reading error: u17=u11=0.029 dB (class B)

expressed in relative uncertainty:; Degree of freedom v17=v11=2

the influence of attenuator, its standard uncertainty: u18=u12=0.167 dB (class B)

expressed in relative uncertainty:; Its value is stable, and the degree of freedom v18=

synthetic standard uncertainty:

so far, the uncertainty of various factors affecting the attenuation is:

2.2 thickness influence

10 times of measurement, the mean value is 100, the standard deviation is s=0.15 mm, the standard uncertainty:

expressed in relative uncertainty: u 19=4.74 -4; Degree of freedom v19==9

the minimum reading of the caliper is 0.02, and its error follows a uniform distribution, with a distribution range (-0.01, +0.01). Its standard uncertainty:

is expressed in relative uncertainty: u 20=5.8; Degree of freedom v20= (50%) -2=2

the caliper uncertainty is 0.05 (k=3), which obeys the normal distribution. The standard uncertainty:

is expressed in relative uncertainty:; Its value is stable, and the degree of freedom v21=

the composite standard uncertainty of workpiece thickness is synthesized by the above three items, namely:

2.3 defect equivalent size

transfer function:

composite standard uncertainty:

expressed in relative uncertainty: u c() =3.08

effective degree of freedom:

the confidence level is taken as 95%, Then the coverage factor: TP (4) =2.78

u= (f) =2.78 0.0613=0.17

the final result of equivalent size is f = 1.99 0.17 mm (where 0.17 mm is the measurement uncertainty of the test result)

3 conclusion

through the calculation and evaluation of the measurement uncertainty of longitudinal wave flaw detection quantitative analysis, we can know the reliability of flaw detection quantitative analysis results, It can also determine the error source of the test process and result analysis and the influence degree of the test results. As an important part of test results, the evaluation of measurement uncertainty can be applied to various fields of quantitative analysis of nondestructive testing

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