PSI - Issue 30

Dmitry O. Reznikov et al. / Procedia Structural Integrity 30 (2020) 128–135 Dmitry O. Reznikov/ Structural Integrity Procedia 00 (2020) 000–000

134

7

where { ES (e) }={ P ( ES 0

( e ) ), P ( ES 1 ( s ) ) , …, P ( ES q

( e ) ), …, P ( ES p ( e ) )} is the vector of the end states of the system’s environment, ( s ) )} is the vector of the end states of the system, [V (e) ( i , j )]= P ( ES i ( e ) | ES j ( s ) ) is

{ ES ( s ) }={ P ( ES 0

( s ) ) , P ( ES 1

the matrix of environment vulnerability.

Fig. 3. Propagation of the accident in the system’s environment

Then one should estimate indirect losses that occur due to various end states of the environment { U ( e ) }={ U 0 ( e ) , U 1 ( e ) ,…, U p ( e ) } and get the assessment of the indirect risk to the system environment due to the potential accidents at the system. Then the index of indirect risk to the system’s environment can be estimated as:

s

s

)

)

    

      

( ) e P ES ES [ |

( ) e P ES ES [ |

(

(

]

]

    

( ) e

( U ES ind

)



p

0

0

0

0

(11)





R

s

s

)

)

(

(

( P ES

P ES

); . . .; (

)

. . .







ind

q

0

 

 

s

s

)

)

( ) e

( U ES ind

( ) e P ES ES [ |

( ) e P ES ES [ |

(

(

)

]

]



0

q

p

q

0

or in the short form:

ind R 

.

( ) ( ) { }[ ]{ } s e ind ES V U

Thus the total economic risk generated by the CTS can be represented as a sum of direct (10) and indirect risks (11):

( ) ][ ]{ } { }[ ]{ } s e dir ind R R R L V V V U ES V U     . ( ) { }[ ][ dir ind Mat Comp Str

(12)

4. Conclusions The proposed approach is based on examining a chronological series of the subsequent discrete failure events occurring at various scale levels of the CTS and its environment. It has substantial limitations as it does not include convergent nodes allowing one to describe the system response to combined action of two or multiple impacts and feedback loops describing interactions of initial and secondary failure processes. This approach however provides an opportunity to describe multilevel fracture in a probabilistic formulation and to obtain an express assessment of risks induced by the complex technical systems.