Evaluation of uncertainty in quantitative analysis

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 [3]:

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) [4]:

; 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: