PSI - Issue 64

1006 Amir Mofidi et al. / Procedia Structural Integrity 64 (2024) 999– 1008 Mofidi et al./ Structural Integrity Procedia 00 (2019) 000 – 000 A multi-metric comparative study was conducted where a variety of statistical measures including variation-based, error-based, and correlation-based metrics were considered including the mean of / ( Mean ), coefficient of variation ( CoV ) of / ratio, mean absolute error ( MAE ), normalized root mean squared error ( NRMSE ), root mean squared logarithmic error ( RMSLE ), the coefficient of determination R 2 , the coefficient of efficiency i.e. , R 2 with respect to 1:1 line, introduced as R 2 1:1 here, and the index of agreement ( d ), where R 2 1:1 and d were calculated using Eqs. 18 and 19, respectively. 8



(18)

2

exp V V V V − − exp ( f f

)

fcal

2 1:1

1.0 = −

R



2

(

)

exp

f

(19)

2 − + −  exp V V V V V V − exp ( ) f fcal f

1.0 = −

d



2

(

)

exp

f

exp

f

fcal

where , and ̅ are the experimental shear contribution of NSM FRP, the calculated shear contribution of NSM FRP using a certain model, and the average of experimental shear contributions of NSM FRP, respectively. Table 1 reveals the overall results of the comparative study presented in this article. In this regard, Rizzo and De Lorenzis (2009b) upper GIP and Parreti and Nanni (2004) models produced the most conservative results with Mean values of 2.04 and 1.90, respectively, followed by the model by Rizzo and De Lorenzis (2009b) Lower GIP with a Mean value of 1.76. Table 1. Statistical indicators to compare the accuracy of the design models.

modified Mofidi et al. (2016)

Rizzo and De Lorenzis (2009b) Lower GIP

Rizzo and De Lorenzis (2009b) Upper GIP

Dias and Barros (2013)

Perera et al. (2014)

Bianco et al. (2014)

Mofidi et al. (2023)

Parretti and Nanni (2004)

Model

1.90 0.76

1.76 0.69

2.04 0.74

0.95 0.46

0.74 0.44

1.55 0.55

1.22 0.94

1.12 0.55

Mean CoV MAE

29.94 0.68 0.39 0.10 -0.49 0.55

23.92

31.53 0.70 0.38 0.08 -0.59 0.54

21.07

27.48 0.66 0.29 0.34 -0.41 0.69

19.73

22.64

19.11

0.55 0.32 0.34 0.01 0.73

0.50 0.27 0.27 0.19 0.70

0.46 0.26 0.59 0.33 0.84

0.48 0.26 0.45 0.12 0.79

0.43 0.27 0.46 0.41 0.81

NRMSE RMSLE

R 2 R 2

1-1

d

Meanwhile, Mofidi et al. (2023) model produced a conservative and economical value for Mean equal to 1.12. The models that produced the most unsafe predictions were Perera et al. (2014) and Dias and Barros (2013) with Mean values of 0.74 and 0.95, respectively. The same models produced the best CoV with 0.44 and 0.46, correspondingly, followed by Mofidi et al. (2023) and Bianco et al. (2014) both producing a CoV of 0.55. The most accurate models when it comes to the produced MAE were Mofidi et al. model (2023), Bianco et al. (2014), and Dias and Barros (2013) with MAE s of 19.11, 19.73, and 21.07, respectively. The best models when it comes to the results of NRMSE are Mofidi et al. (2023), Bianco et al. (2014), and modified Mofidi et al. (2016) with NRMSE s of 0.43, 0.46, and 0.48. The best models in terms of the results of the RMSLE s are Mofidi et al. (2023) and Dias and Barros (2013) both with 0.27 RMSLE , followed by Bianco et al. (2014) and modified Mofidi et al. (2016) with RMSLE of 0.26. The most accurate models considering the coefficient of determination were Bianco et al. (2014), Mofidi et al. (2023), and modified Mofidi et al. (2016) with R 2 equal to 0.59, 0.46, and 0.45, respectively. When it comes to the