PSI - Issue 38

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Kihm, Miu, Bonato / Structural Integrity Procedia 00 (2021) 000 – 000

Frédéric Kihm et al. / Procedia Structural Integrity 38 (2022) 12–29

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Table 4. OLS results.for the case with only TemperatureDamage input Dep. Variable: StrainDamage R-squared

0.834 0.833

No. Observations

182 180

Adj. R-squared Prob (F-statistic):

Df Residuals

3.99e-72

Df Model

1

coef

P value

[0.025 -0.000 0.010

0.975] 0.000 0.011

const

-0.0001 0.0107

0.318 0.000

TemperatureDamage

The p- value of the model’s F - statistic indicates the model parameters’ overall statistical significance. This means that the presence of the model parameters (just temperature, in this case) is far more justified than merely predicting the average in the training set. On top of this, the p-values of all the slopes (only temperature in this case) indicate statistical significance. This means that all parameters (again, only temperature in this case) are likely useful in explaining the variance in the output. The above statistical results indicate that we are in a position to explore what happens if we augmented the model’s complex ity by including additional parameters besides temperature. The next step was to consider how well both the temperature damage and pressure damage (the input second most correlated with the output) predicted the strain damage. The results of the Ordinary Least Squares function are presented in Table 5:

Table 5. OLS results.for the case with TemperatureDamage and PressureDamage inputs Dep. Variable: StrainDamage R-squared 0.830 No. Observations 138 Adj. R-squared 0.827 Df Residuals 135 Prob (F-statistic): 1.20e-52 Df Model 2

coef

P value

[0.025 -0.001 0.010 0.000

0.975] 0.000 0.011 0.002

const

-9.533e-05

0.668 0.000 0.006

TemperatureDamage

0.0104 0.0010

PressureDamage

This time the effect of the added pressure parameter is statistically significant. However, the pressure parameter’s slope expectation is an order of magnitude smaller than the temperature slope. Note that the data is scaled prior to least squares fitting, so the slopes are directly comparable. Despite this difference in the slope values, there are some differences in predictions between the temperature-only model and the temperature-plus-pressure model, as displayed in Fig. 6.

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