PSI - Issue 44

Francesco Nigro et al. / Procedia Structural Integrity 44 (2023) 1704–1711 F. Nigro, R. Falcone, E. Martinelli/Structural Integrity Procedia 00 (2022) 000–000

1706

3

• the “local” part that states the number of FRP layers employed for the confinement of the column ends, ranging from 0 to 3; • the “global” part, which points out the steel profile eventually employed for the realization of a concentric bracing system at the bottom floor; the number (that variates from 0 to 7) represents the “section ID” ( ID sec ) of the profile, among a certain number of usable bracing profiles. 2.2. Definition of the first population Many choices can be made to generate the first population. On the one hand, the first population can be defined on the basis of some engineering criteria (Faella et al., 2008; Baros and Dristos, 2008). On the other hand, it is possible to generate a fully random population, with the aim to better cover the entire search space. In principle, as shown in Fig. 1, the first population can be ideally divided into three partitions, consisting in: N loc chromosomes characterized by the presence of only local interventions; N glob chromosomes characterized by the presence of only global interventions; N mix chromosomes characterized by the presence of both local and global interventions.

Fig. 1. Outline of the first population.

2.3. Objective function and penalty definition In the present work, the objective function f(x) is represented by the initial cost of intervention required for upgrading the seismic performance of the structure. Such cost is given by the sum of the costs needed for the realization of local interventions ( C loc ), of the global interventions ( C glob ), of the addition of micropiles for an eventual upgrading at the foundation level ( C found ). Moreover, to ensure that the “optimal” solution suggested by the algorithm is able to satisfy some engineering requirement, it is necessary to add the penalty cost ( Φ pen ) only to those solutions that do not present such requirements. The engineering requirement can be represented by one or more parameters related to the expected seismic performance; the presence of such “constraint” to the solution, enables to get a technically admissible “optimal” solution. In the present study, a constraint is imposed in order to achieve an optimal solution that belongs to a certain target seismic risk class, with respect to the Italian classification (DM 65 07/03/2017). The application of the aforementioned definitions are clarified by the following expressions.

( ) f x C x C x C x = + + ( ) ( ) ( )

( ) + Φ = pen

( ) x C x

( ) x

+ Φ

(1)

loc

glob

found

tot

pen

0

if

)

x x

;

(

1

r r

≤

( ) x  Φ  = pen

(2)

tot C (x); if

( 1 ) >

6 10 ⋅



   

  

  ≤

  

ISV

( )

PAM x

(3)

arg

t

et

1

;

 

 

( ) r x max =

( )

PAM

ISV x

arg

t

et

where: r(x) is the constraint concerning the target seismic risk class; PAM(x) is the actual value of the parameter PAM for the generic chromosome x ; PAM target is the maximum value of the admissible PAM for the desired (target) seismic risk class; ISV(x) is the actual value of the parameter ISV for the generic chromosome x ; ISV target denotes the minimum