Issue 21

A. De Iorio et alii, Frattura ed Integrità Strutturale, 21 (2012) 21-29; DOI: 10.3221/IGF-ESIS.21.03 24 Figure 7 : Crack growth data with best-fit curves. Moreover, normality tests of the residuals have been carried out using the χ 2 test and the frequency distributions of the residuals computed for each specimen tested have been also diagrammed to verify that the mean was close to zero and the standard deviation was very small, in other words that the conditions to guarantee a small error in the estimation of the crack lengths by means of the model were satisfied [9]. In Fig. 8, as an example, three of the aforementioned distributions are reported, one for each set. Figure 8 : PDF of residuals of three selected best-fit, one for each set. From the examination of the normality test results, it has been noted that the majority of them verify the expected conditions (see. Tab. 1), whereas the others do not pass the test due to some large anomalies present in the frequency distribution diagrams. However, if the graphs of the raw data are observed in details in the fields corresponding to each anomaly, it can be seen that the data points move away from the trend of all other points in either an irregular or anomalous manner. Numbers of best-fit with normal distribution of residuals Numbers of best-fit with non normal distribution of residuals Set _ I 47 13 Set _ II 32 28 Set _ III 31 29 Table 1 : Results of normality tests. The outliers in the graphs of the mean and standard deviation are not only due to the random scatter in the raw data, but also to the fact that in some experimental curves there are data points sequences that do not follow the trend of the whole test. This anomaly affects the response of the optimization algorithm used in the non-linear least square method. The best-fitting model parameters obtained for these latter experimental curves define a solution with a residual distribution