Issue 40

L. Zou et alii, Frattura ed Integrità Strutturale, 40 (2017) 137-148; DOI: 10.3221/IGF-ESIS.40.12 143 adjusted R-square= ( 1) 1 , ( ) SSE n SST    (21) where the residual degrees of freedom  is defined as the number of response values n minus the number of fitted coefficients m estimated from the response values. The adjusted R-square statistic can take on any value less than or equal to 1, with a value closer to 1 indicating a better fit. Negative values can occur when the model contains terms that do not help to predict the response. Root mean squared error ( RMSE ) is also known as the fit standard error and the standard error of the regression. It is an estimate of the standard deviation of the random component in the data, and is defined as SSE RMSE MSE    (22) Similar with SSE , an MSE value closer to 0 indicates a fit that is more useful for prediction. Figure 3 : Fitting results of the three relations. Basquin Langer Three parameters SSE 4.043e+04 4.853e+04 4.03e+04 R-square 0.7661 0.7192 0.7668 Adjusted R-square 0.7623 0.7147 0.7592 RMSE 25.54 27.98 25.7 Table 2 : Goodness-of-fit statistics. As could be seen from Fig. 3 and Tab. 2, the fitting effect of Langer is the worst thus it isn’t suitable for this group of fatigue data. Fitting results of Basquin and three parameters are close. From the perspective of higher application security, we choose the Basquin model as the fatigue stress-life relation for this group of fatigue data of aluminum alloy welded joints. Thus in this paper, Basquin model is used and the mean S-N curve is fitted by the least square method based on the nodal force based structural stress according to the collected fatigue data of aluminum alloy welded joints. Scatter of fatigue data based on nominal stress and the mean S-N curve based on equivalent structural stress in log-log coordinates are shown in Fig. 4 and Fig.5. The goodness-of-fit statistics including SSE, R-square, adjusted R-square and RMSE by using nodal force based structural stress are shown in Tab. 3.