Presentation: Risk based inspection and maintenance planning of miter gates

(1)

RISK BASED INSPECTION AND MAINTENANCE PLANNING OF

MITER GATES

Authors : Thuong Van DANG, Pablo G. MORATO, Quang Anh MAI, Philippe RIGO

(2)

TARGET

(3)

METHODOL

OGY

Cyclic loading Fatigue Failure Inspection and Repair E x p e ct e d c o st Failure cost Repair cost

Inspection cost Total cost Optimum

Maintenance efforts

Optimal strategy

Lock gates : miter gates, vertical lift gates, Movable weirs, tainter gate

(4)

MESSAGE

OBJECTIVE

Dynami c Bayesia n network Cost model Risk-based inspection Inspections performed at regular time intervals Inspections performed when failure probability threshold is reached

(5)

OUTLINE

Equivalent stress range

Fatigue crack growth model

Dynamic Bayesian Network (DBN)

Risk based decision analysis Conclusion

(6)

EQUIVALENT STRESS RANGE

m, C: material parameters

n : number of lockages (cycles) T : time of observations (years)

: total fatigue damage

(7)

a) Paris’s law:

b) The failure event is defined by the limit state function:

Failure of the element occurs if g c) The crack size at time t (m2) is:

FATIGUE CRACK

GROWTH MODEL

(8)

Variable Description Distribution Mean Std/Cov

[mm] Initial crack size Exponential 0.16

[mm] Critical crack size Deterministic 25

∆ [Mpa] Stress range Deterministic 57

Ln(C) Material parameter Normal -26.80 Std = _0.29

m Material parameter Deterministic 3

Load uncertainty Lognormal 1 Cov = _0.25

Y Geometry function Deterministic 1.12

n No. of cycles/year Deterministic 7048

Variable Description Distribution Mean Std/Cov

Initial crack size Exponential 0.16

Critical crack size Deterministic 25

∆ [Mpa] Stress range Deterministic 57

Ln(C) Material parameter Normal -26.80 Std = _0.29

m Material parameter Deterministic 3

Load uncertainty Lognormal 1 Cov = _0.25

Y Geometry function Deterministic 1.12

n No. of cycles/year Deterministic 7048

FATIGUE CRACK

GROWTH MODEL

(9)

BAYESIAN NETWORK

 _{ stress range (Mpa)}

 The damage crack size a₀ and

a₁(mm)

 Variable I₁ stands for a possible

inspection outcome of the condition a

Directed Acyclic Graph (DAG) • qualitative Local probability distributions • _quantitative Bayesia n netwo rk I₁= 0 No inspection I = 1 Inspection Inspection decisions

(10)

DYNAMIC BAYESIAN NETWORK

= �_{� − 1}1− �2 +q ¿2/ (2 − �) ��=¿

(11)

Probability of detection (POD) describes the probability of detecting the crack and is given by:

I_t

D is the event of detection, a (mm) is the detectable crack and α, γ are regression parameters.

DYNAMIC BAYESIAN NETWORK

Instantiating the inspection variable I_t

(12)

RISK BASED DECISION

ANALYSIS

The total expected cost during the lifetime :

is annual failure probability, is the probability that a repair is performed and is the cumulative failure.

Costs Value (money

unit)

Failure cost, 106

Inspection cost, 0.002

Repair cost, 0.04

Discounting _0.03

Costs Value (money

unit) 106

(13)

RISK BASED DECISION

ANALYSIS

Optimum _Optimum Optimal inspection inverval every 11 years = 1.0742 x10 Optimal inspection performed at = 3x10-4 = 0.96095 x104

(14)

• The different stress-ranges occurring during the year are represented by an equivalent stress-range value.

• A framework where Dynamic Bayesian network is used for risk-based inspection planning of a miter gate welded joint considering inspection data.

• Further work can be used to consider the multiple structural components of a gate.