PSI - Issue 72

Emre Kara / Procedia Structural Integrity 72 (2025) 77–84

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Fig. 5. Determination matrices of the output parameters on each input for: (a) 50 Hz, (b) 70 Hz, (c) 90 Hz, (d) 110 Hz, (e) 130 Hz. In Figure 4, sensitivity analysis determines the extent to which varying input parameters affect an output parameter for each frequency value. Positive sensitivities indicate that increasing the input will raise the output, and negative sensitivities indicate that increasing the input will lower the output. For instance, the coefficient β 0 (P5) exhibits sensitivity to the variables h 0 (positive behavior), d c (negative behavior), h c (negative behavior) and h 0 (negative behavior) at the frequencies of 50, 70, 90, and 130 Hz, respectively. Notably, there is no sensitivity of β 0 to any modifications in input parameters at the frequency of 110 Hz. Another tool utilized for identifying the correlation between the input and output parameters is the determination histogram. In Figure 5, the coefficient of determination (R 2 ) indicates the portion of the data point variation that can be accounted for by a quadratic relationship. It shows the proximity of the data points to the quadratic regression curve. In other words, the coefficient of determination will be closer to 1, the closer the samples are to the curve. Based on the results, It is clear that d 0 (P1) exhibits the strongest correlation with the output parameter, Re (P7). This is not surprising, given that Eq. 9, which determines Re, incorporates d 0 .