Computational performance of risk-based inspection methodologies for offshore wind support structures

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Computational performance of

risk-based inspection methodologies

for offshore wind support structures

P.G. Morato, L. Marquez & P. Rigo

Department of ArGEnCO,

University of Liege (Belgium)

J.S. Nielsen

Department of Civil Engineering,

Aalborg University (Denmark)

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Introduction – Offshore wind substructures

Information available

Deterioration

Fatigue & corrosion

Source: https://www.researchgate.net/figure/Optical- strain-gauges-as-installed-at-a-Belwind-and-b-Northwind

….Inspections

Source:http://windpowernejikata.blogspot.com/2017/05/wind-power-gif.html

Monitoring…

Source: https://www.deltares.nl/en/projects/cutting- maintenance-costs-offshore-wind-farms-using-improved-forecasts

Sequential decision making under uncertainty

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OWT Risk-based inspection planning

Inspection

model

Maintenance

policy

Deterioration

model

Cost

model

Repair

model

Expected

maintenance

costs

Offshore wind structures deterioration: fatigue & corrosion

Reliability updating

Risk-based decision making

Decision

rules

+

1

2

3

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SN Curves / Miner’s Rule

1) Deterioration – Fatigue & corrosion

Bi-linear SN Curve

𝑔

_𝑆𝑁

(𝑡) =

Δ

− 𝑛

_𝑦

𝑡

𝑞

𝑚

₁

𝑎

₁

Γ 1 +

𝑚

₁

ℎ

;

𝑆

₁

𝑞

ℎ

+

𝑞

𝑚

₂

𝑎

₂

𝛾 1 +

𝑚

₂

ℎ

;

𝑆

₁

𝑞

ℎ

SN Curve for tubular joints

‘DNV-GL RP C203’

FDF = 2

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Calibration SN Curves – FM Model

1) Deterioration – 1D FM

1D Paris’ Law

𝑎

_𝑡+1

= 𝑎

_𝑡

2−𝑚

2 ₊

2 − 𝑚

2 𝐶 𝑌

𝑔

𝜋

0.5 _𝑆

𝑒

𝑚

𝑛

2 2−𝑚

; 𝑔𝑖𝑣𝑒𝑛

𝑎

₀

Calibration

𝑔

𝐹𝑀

𝑡 = 𝑎

𝑐

− 𝑎(𝑡)

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Calibration SN Curves – FM Model

1) Deterioration – 2D FM

2D Paris’ Law – Stress intensity factor

𝑑𝑎

𝑑𝑛

=

𝐶

Δ𝐾

𝑎

𝑚

𝑑𝑐

𝑑𝑛

=

𝐶

Δ𝐾

𝑐

𝑚

Δ𝐾

_𝑎

=

S

_e

𝜋𝑎 [𝑌

_𝑚𝑎

𝑎, 𝑐 𝑀

_𝑘𝑚𝑎

𝑎, 𝑐 1 − 𝐷𝑂𝐵 + 𝑌

_𝑏𝑎

𝑎, 𝑐 𝑀

_𝑘𝑏𝑎

𝑎, 𝑐 𝐷𝑂𝐵]

Δ𝐾

_𝑐

=

S

_e

𝜋𝑎 [𝑌

_𝑚𝑐

𝑎, 𝑐 𝑀

_𝑘𝑚𝑐

𝑎, 𝑐 1 − 𝐷𝑂𝐵 + 𝑌

_𝑏𝑐

𝑎, 𝑐 𝑀

_𝑘𝑏𝑐

𝑎, 𝑐 𝐷𝑂𝐵]

System of ordinary differential equations

𝑔

_𝐹𝑀

𝑡 = 𝑎

_𝑐

− 𝑎(𝑡)

𝑔𝑖𝑣𝑒𝑛

𝑎

₀

, 𝑎

₀

/𝑐

₀

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Fracture Mechanics models (Unconditional case)

1) Deterioration – FM / Reliability

2D Paris’ Law

Stress intensity factor

𝐶𝑃𝑈 𝑡𝑖𝑚𝑒 ≈ 3 𝑚𝑖𝑛

1D Paris’ Law

𝐶𝑃𝑈 𝑡𝑖𝑚𝑒 ≈ 1 𝑑𝑎𝑦

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2) Updating reliability (DBNs)

𝑎

₁

𝑆

_𝑒

𝐶

𝑌

_𝑔

𝐾

𝑍

₁

𝑎

_𝑡+1

= 𝑎

_𝑡

2−𝑚

2 ₊

2 − 𝑚

2 𝐶 𝑌

𝑔

𝜋

0.5 _𝑆

𝑒

𝑚

𝑛

2 2−𝑚

; 𝑔𝑖𝑣𝑒𝑛

𝑎

₀

𝑎

₀

𝐾

𝑎

₂

𝑍

₂

𝐾

𝑎

₃

𝑍

₃

𝐾

𝑎

_𝑛

𝑍

_𝑛

𝐾

…

(1) Monte Carlo simulations

(2) Dynamic Bayesian Networks (DBNs)

…

PoD Curves

𝒑(𝒁|𝒂)

Inspection quality

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(1) Monte Carlo simulations

(2) Dynamic Bayesian Networks (DBNs)

𝐶𝑃𝑈 𝑡𝑖𝑚𝑒 ≈ 3 𝑚𝑖𝑛

𝐶𝑃𝑈 𝑡𝑖𝑚𝑒 ≈

0.1 s

2) Updating reliability (DBNs)

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Fracture Mechanics models (including inspections)

2) Updating reliability – FM 1D or 2D?

Unconditional (No inspections)

Conditional (Inspections)

different!

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Fracture Mechanics models (including inspections)

2) Updating reliability – FM 1D or 2D?

Crack distribution

Failure

state

Years

Conditional (Inspections)

different!

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3) Maintenance decision problem

inspection no inspection detection no detection no repair repair no repair repair no repair fail surv. fail surv. fail surv. fail surv. fail surv. fail surv. inspection no inspection detection no detection no repair repair no repair surv. fail surv. fail surv. fail surv. fail repair repair

12

20

_{=3.8e21 branches}

1 second per branch = 1.24e14 years

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3) RBI / Heuristics: Direct search policies

Deterioration

model

Inspection

model

Cost

model

Repair

model

Decision

rules

3 years

_{8 years}

_{14 years}

‘Periodic inspections’

‘Reliability threshold’

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3) RBI / Heuristics: Direct search policies

Deterioration

model

Inspection

model

Cost

model

Repair

model

Decision

rules

‘Periodic inspections’

‘Reliability threshold’

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3) POMDPs - Methodology

Dynamic

Bayesian

Network

Deterioration

model

Inspection

_model

POMDP

model

POMDP

policy

Cost

model

Transition matrix

Repair

model

Emission matrix

Rewards

Expected

maintenance costs

POMDP

RBI

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3) POMDPs – Observations (emission)

Inspections

Monitoring

No inspection?

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3) POMDPs – CPU time

Application: ‘SARSOP Algorithm’: POMDP 200 states

𝐶𝑃𝑈 𝑡𝑖𝑚𝑒 ≈ 60 𝑠

…

• No detection

• Mild damage

• Severe damage

“POMDP based Maintenance Optimization of Offshore Wind Substructures including Monitoring

Morato, P.G., Nielsen, J.S., Mai, A.Q. and Rigo, P., ICASP13 (2019)”

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Discussion & Conclusions

1) Deterioration model

1D-FM

is faster than

2D-FM

but yields different results

2) Updating reliability

DBNs

are faster than MCS (similar result)

3) Risk-based inspection planning

POMPD

for complex decision problems

• Future:

▪ System-level maintenance policies

▪ Different deterioration models

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