PSI - Issue 42

Robert Basan et al. / Procedia Structural Integrity 42 (2022) 655–662 R. Basan et al. / Structural Integrity Procedia 00 (2019) 000–000

657

3

2. Evaluation methodologies and criteria In order to enable evaluation of accuracy of individual estimation methods and comparison of different ones, evaluation methodology and criteria are needed. Manson (1965) evaluates and compares proposed estimation methods by checking correspondence of experimental and estimated data i.e. experimental fatigue lives 2 N f,exp vs. estimated fatigue lives 2 N f,est and experimental strain amplitude Δ ε exp /2 vs. estimated strain amplitude Δ ε est /2. Main evaluation criterion determined from this data was conventional error criterion i.e percentage of data points falling within scatter band of predefined width. This methodology and criterion was mostly used, for example in Ong (1993), until Park and Song (1995) after recognizing certain shortcomings of error criterion proposed more detailed evaluation methodology and criteria as follows: • Error criterion i.e. fraction of data points within a scatter band with factor of s , E f ( s ):

N

2 1 2 range within the falling points of data Number f,exp f,est N s ≤

s

≤

( )

(1)

E s

=

f

points of data number Total

• Goodness of fit between the predicted and experimental values for individual datasets, ( E a ) Dset :

(

) (

) (

) ( β α

)

    − + − − + − − − + − − 4 1 1 1 1 1 1 1 i i i i β α

   

R

1 N

( ) E

 = Dset 1 i

i

(2)

=

Dset a

N

Dset

where N Dset is the number of individual datasets, α i and β i are regression coefficients for the i -th individual dataset according to the regression equation ( ) ( ) f,exp f,est log 2 log 2 N N β α = + and R i is the coefficient of correlation

• Goodness of fit between the predicted and experimental values for all data points, ( E a ) total :

(

) (

) (

) (

)

1

1 1 + − − + − − − + − − 1 1 1 1

R

−

α

β

α

β

( ) E

total

total

total

total

total

(3)

=

total a

4

where α total , β total and R total are the same coefficients as above obtained for all data points. • Average value of the above three parameters, Ē : ( ) ( ) 3 ( 3) Dset a total a f E E E s E + = + =

(4)

Additional evaluation criteria have been proposed in the literature since - Meggiolarro and Castro (2004) propose and use probability density function for evaluations in their paper and recently, Wächter and Esderts (2018) propose their methodology and use it for extensive evaluation of quality of existing estimation methods. However, for evaluation and comparison of performance of estimation methods, the error criterion (fraction of data points within a certain scatter band) is most frequently used in various papers published subsequently along with additional criteria as proposed by Park and Song (1995). In order to be comparable to other analyses and evaluations results available in literature such as Jeon and Song (2002) and Lee and Song (2006), evaluation criteria (1)-(4) are used in this research as well. In known references, evaluations of estimation methods and comparisons of estimated and experimental fatigue lives are mostly performed for complete range of fatigue lives and materials with wide range of monotonic properties, resulting in significant averaging of results of evaluations and possibly erroneous conclusions on