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

130

3

take into account the expected monetary values of direct consequences of the accidents at the CTS ignoring losses inflicted by subsequent disturbances in the environment of the damaged system, but also indirect risks associated with secondary failures in the CTS environment. 2. Traditional risk assessment models According to the traditional risk assessment model, risk is considered to be a function of threat T , vulnerability V and consequences C : R=f ( T , V , C ). Here threat is defined as probability of some impact on the system (normal or abnormal loading regime) T = P ( L ), vulnerability is estimated as conditional probability of system’s failure given the impact occurs: V = P ( F | L ), and consequences are defined as losses that occur as a result of the impact and the subsequent system failure: C = E ( U | L , F ). Then the index of economic risk is determined by the Eq. (1):

(1)

( ) ( | ) ( | , ) R P L P F L E U L F   

Fig. 1. General risk assessment framework

Usually, technical systems are subjected to multiple loading regimes and multiple failure scenarios. Risk assessment for such systems implies assessment of a scenario tree (see Fig. 1). This is done by using graph models called scenario trees [3, 5, 10]. The system is designed to fulfill the so-called success scenario S 0 (i.e. a transition from its initial state IS to the designed end state ES 0 ). Since any failure scenario S i presents a deviation from the success scenario S 0 that corresponds to the successful functioning of the CTS, the scenario S i must have a disturbance point (initiating event) at which an extreme event, or loading regime L i occurs (Fig. 1). Each event L i gives rise to a branch of the scenario tree that has a corresponding set of scenarios S j that terminate with end states ( ES j ). In this case one can get a similar risk index using the matrix expression:

U U

    

    

[ P ES L P ES L P ES L 

[ [

| ] [ | ] [

| ] | ]

1 | ]

     

     

ES

1

(2)

m

1 1

2 1

1 2 P ES L P ES L 2 2

[ P ES L

2 | ]



R





ES

m

1 ( ); ( ); . . .; ( ) P L P L P L  n 2





 

2

. . .

. . .

{ } L

Threat

m     ES U

1   2 [ P ES L P ES L | ] [ | ] n [ P ES L | ] n m n

[ ] V

Vulnerability

{ } Consequences U