PSI - Issue 47

934 3 Typical density functions �� � are usually left shifted, right shifted or centered like the law. It is also cited by Naess and Moan � 2013 � that a signal spectrum analysis is well represented with various normalized functions. This necessitates to get the and parameters for an arbitrary shaped distribution. 1. Parametering on the Using the linearization form given by Monchy and Vernier � 2010 � in Eq. 2: � �� � 2 � such that: � � � ��� � ��� �� � 3 � � � � �� � 4 � ��� � � , � 5 � the parameters and have always been obtained by the graphical method using the . This method is tedious and the obtained data can generate a nonlinear curve in some cases which needs to be difficultly adjusted to get a linear curve established by Bellaouar and Beleulmi � 2013 � and Monchy and Vernier � 2010 � . 2. Optimized process Based on the square total error minimization where the optimization model is defined with the utility objective function: � � � � � � � � � 6 � With the decision variables: � � � ⌊ � , � , ⋯ , � ⌋ � Such that the errors are: � � � � � ∗ � � 7 � � are the statistical data values for � 1 Let be the linear regression function given by Moussaoui � 2022 � : � ∗ � � . � � � �� � . � � � � � 8 � Eq. 8 approximates the values � of the � � 1 � vector � and � are the searched unknown constants � 2 functions are selected for the linear regression case The presented example uses � 5 discrete values Mohammed Lamine Moussaoui / Procedia Structural Integrity 47 (2023) 932–937 Mohammed Lamine Moussaoui / Structural Integrity Procedia 00 (2023) 000–000

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