PSI - Issue 22

Teresa Magoga et al. / Procedia Structural Integrity 22 (2019) 267–274 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

272

6

Fig. 3. Hourly D total at s3.1.2 versus N slam , v ave , over 522 hour subset

Based on the 522 hour subset, the rank correlation coefficients (  ) between N slam , v ave ,  1/3 , D wave and D total per hour at s2A.5.2 and s3.1.2 are given in Table 3. The corresponding p-values are shown in Table 4. A p-value is a measure of the strength of the evidence against the null hypothesis that no correlation exists between two variables. Most of the p-values in Table 4 are less than 0.05, indicating that the results are statistically significant with a 95% confidence level. However, with the exception of  1/3 at s3.1.2, the  values associated with v ave are not statistically significant. Table 3.  correlation coefficients between N slam , v ave ,  1/3 , D wave , and D total at s2A5.2 and s3.1.2 based on 522 hour subset N slam v ave [kn]  1/3 [MPa] @ s2A.5.2 D wave @ s2A.5.2 D total @ s2A.5.2  1/3 [MPa] s3.1.2 D wave @ s3.1.2 D total @ s3.1.2

N slam

1

v ave [kn]

0.076 0.232 0.251 0.252 0.220 0.262 0.262

1

 1/3 [MPa] @ s2A.5.2

-0.034 -0.057 -0.042 -0.092 -0.077 -0.087

1

D wave @ s2A.5.2 D total @ s2A.5.2  1/3 [MPa] s3.1.2

0.880 0.888 0.821 0.750 0.759

1

0.933 0.835 0.821 0.840

1

0.828 0.795 0.822

1

D wave @ s3.1.2 D total @ s3.1.2

0.813 0.830

1

0.939

1

Table 4. p-values for results in Table 3 N slam v ave [kn]

D total @ s3.1.2

 1/3 [MPa] @ s2A.5.2

D wave @ s2A.5.2

D total @ s2A.5.2

 1/3 [MPa] s3.1.2

D wave @ s3.1.2

N slam

1

v ave [kn]

0.519

1

 1/3 [MPa] @ s2A.5.2

<10

0.089 0.494 0.432 0.006 0.351 0.331

1

-3

D wave @ s2A.5.2 D total @ s2A.5.2  1/3 [MPa] s3.1.2

0.001

<10

1

-3

<10 <10

<10 -3 <10 -3

<10 -3 <10 -3 <10 -3 <10 -3

1

-3

<10 -3 <10 -3 <10 -3

1

-3

D wave @ s3.1.2 D total @ s3.1.2

0.007 0.006

<10 <10

<10 -3 <10 -3

1

-3

<10 -3

1

-3

The results shown in Table 3 indicate that, unsurprisingly, the values of  between D wave and D total at the two strain gauge locations are the largest (both equal to or greater than 0.933). D total as a function of D wave can be modelled by Equation 6:

1 total wave D c D c   

(6)

2

Using the non-linear least squares approach in MATLAB (MathWorks 2015) the coefficients c 1 and c 2 with confidence intervals, as well as the coefficient of determination R 2 , are found as per Table 5.