# Detection, Prognosis and Decision Support Tool for Offshore Wind Turbine Structures

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## Abstract

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## 1. Introduction

#### 1.1. Main Contributions

#### 1.2. Paper Organisation

## 2. Overview of the Developed System

## 3. Corrosion Detection and Prognosis

#### 3.1. Methodology

#### 3.2. Local Detection and Prognosis

#### 3.2.1. Corrosion Detection

#### 3.2.2. Corrosion Prognosis

#### 3.3. System-Level Prognosis

**k-out-of-n**or

**weighted k-out-of-n**. For the latter, each component has its own positive integer weight, such that the system is considered good if the total weight of good components is at least k [23]. Note that

**k-out-of-n**is a special case of the

**weighted k-out-of-n**(wherein the weight of each component is 1),

**1-out-of-n**is equivalent to a parallel connection, and

**n-out-of-n**represents a series connection. The algorithm for computing the system reliability $R\left(t\right)$ for a

**weighted k-out-of-n**system is described in [23]. Note that for the computation of the system $R\left(t\right)$, it is assumed that the components are independent.

**weighted k-out-of-n**structure. This is better expressed as a tree structure (see an illustration in Figure 3), where each parent node has a k value, and child nodes have an associated weight w. The leaves of such a tree correspond to the components, whose un-reliabilities $Q\left(t\right)$ are associated with the local RULs of the measurement locations. In addition to flexibility, the proposed structure allows for a systematic and easy calculation of the system reliability $R\left(t\right)$ departing from the algorithms described in [23].

## 4. Decision Support Tool

#### 4.1. Economical Optimization

#### 4.2. Definitions for Economical Optimization

- Capital costs (${C}_{CAPEX}\left(t\right)$)This cost involves the wind turbine investment ${C}_{WT}\left(t\right)$ (i.e., all costs related to the initial investment for bringing the wind turbine to an operable status), including the investment for implementing the monitoring and prognosis software and hardware ${C}_{MP}\left(t\right)$$${C}_{CAPEX}\left(t\right)={C}_{WT}\left(t\right)+{C}_{MP}\left(t\right)$$These costs may be considered as a single payment or spread in time following an amortization formula, taking into account loan interest rates. Note that ${C}_{CAPEX}\left(t\right)$ is a fixed cost that does not depend on ${t}_{D}$ or ${t}_{F}$, and so it does not contribute to the optimization of ${t}_{D}$. However, it does serve for the interpretation of the results.
- Operational costs (${C}_{OPEX}\left(t,{t}_{D},{t}_{F}\right)$)This cost term encompasses all ongoing expenses that are inherent to the operation of the wind turbine (such as operation, maintenance, inspection, insurance, leasing and taxes costs). With regard to the impact of the failure, we split this cost as$${C}_{OPEX}\left(t,{t}_{D},{t}_{F}\right)={C}_{OP}\left(t,{t}_{D},{t}_{F}\right)+{C}_{F}\left(t,{t}_{D},{t}_{F}\right)$$$${C}_{OP}\left(t,{t}_{D},{t}_{F}\right)=\left\{\begin{array}{cc}\begin{array}{c}{C}_{OP}\left(t,{t}_{F}\right)\\ 0\end{array}\hfill & \begin{array}{c}\mathrm{if}\text{}t\le {t}_{D}\\ \mathrm{otherwise}\end{array}\hfill \end{array}\right.$$$${C}_{OP}\left(t,{t}_{F}\right)=\left\{\begin{array}{cc}\begin{array}{c}{C}_{OP\phantom{\rule{0.166667em}{0ex}}H}\left(t,{t}_{F}\right)\\ {C}_{OP\phantom{\rule{0.166667em}{0ex}}F}\left(t,{t}_{F}\right)\end{array}\hfill & \begin{array}{c}\mathrm{if}\text{}t{t}_{F}\\ \mathrm{otherwise}\end{array}\hfill \end{array}\right.$$$${C}_{F}\left(t,{t}_{D},{t}_{F}\right)={C}_{F}\left(t,{t}_{D}\right)\delta \left(t-{t}_{F}\right)$$$${C}_{F}\left(t,{t}_{D}\right)=\left\{\begin{array}{cc}\begin{array}{c}{C}_{F}\left(t\right)\\ 0\end{array}\hfill & \begin{array}{c}\mathrm{if}\text{}t{t}_{D}\\ \mathrm{otherwise}\end{array}\hfill \end{array}\right.$$$$\delta \left(t-{t}_{F}\right)=\left\{\begin{array}{cc}\begin{array}{c}1\\ 0\end{array}\hfill & \begin{array}{c}\mathrm{if}\text{}x=0\\ \mathrm{otherwise}\end{array}\hfill \end{array}\right.$$Notably, the use of the delta Dirac function $\delta \left(t-{t}_{F}\right)$ reflects the fact that if the decommissioning takes place before the failure, there are no costs associated to it. The cost ${C}_{F}\left(t\right)$ includes both direct and indirect losses due to the failure occurrence. Direct losses ${C}_{F\phantom{\rule{4pt}{0ex}}D}\left(t\right)$ include, for instance, fines due to inoperability of the asset and inspections or corrective actions that need to take place because of the failure. Indirect losses ${C}_{F\phantom{\rule{4pt}{0ex}}I}\left(t\right)$ include environmental, human, and financial losses. Note that the production losses are included as part of $E\left(t,{t}_{D},{t}_{F}\right)$, which is defined below.
- Decommissioning costs (${C}_{DECEX}\left(t,{t}_{D},{t}_{F}\right)$)This one-time cost summarizes all costs related to the decommissioning of the wind turbine.$${C}_{DECEX}\left(t,{t}_{D},{t}_{F}\right)={C}_{DEC}\left(t,{t}_{F}\right)\delta \left(t-{t}_{D}\right)$$$${C}_{DEC}\left(t,{t}_{F}\right)=\left\{\begin{array}{cc}\begin{array}{c}{C}_{DEC\phantom{\rule{0.166667em}{0ex}}H}\left(t\right)\\ {C}_{DEC\phantom{\rule{0.166667em}{0ex}}F}\left(t\right)\end{array}\hfill & \begin{array}{c}\mathrm{if}\text{}t{t}_{F}\\ \mathrm{otherwise}\end{array}\hfill \end{array}\right.$$
- Produced energy ($E\left(t,{t}_{D},{t}_{F}\right)$)The produced energy is defined as:$$E\left(t,{t}_{D},{t}_{F}\right)={E}_{N}\left(t\right){c}_{L}\left(t,{t}_{D},{t}_{F}\right)$$$${c}_{L}\left(t,{t}_{D},{t}_{F}\right)=\left\{\begin{array}{cc}\begin{array}{c}1\\ 0\end{array}\hfill & \begin{array}{c}\mathrm{if}\text{}tmin\left({t}_{D},{t}_{F}\right)\\ \mathrm{otherwise}\end{array}\hfill \end{array}\right..$$
- Income for produced energy (${I}_{E}\left(t,{t}_{D},{t}_{F}\right)$)This income is defined as:$${I}_{E}\left(t,{t}_{D},{t}_{F}\right)={c}_{E}\left(t\right)E\left(t,{t}_{D},{t}_{F}\right)$$Note that the remaining value of the asset after decommissioning is not included explicitly as a separate income term, as it is not recurrent, it is highly uncertain and difficult to estimate years in advance. However, it can be included indirectly by the users of the methodology, by merging this remaining value as an income term (thus, a negative modifier) to the decommissioning term ${C}_{DEC}\left(t,{t}_{F}\right)$.

#### 4.3. Simulation

## 5. Graphical User Interface

## 6. Conclusions

**weighted k-out-of-n**: good structure. This flexible structure for encoding the system failure definition allows the user to choose from the default option ’series connection’, which leads to a strict definition of system failure, to more complex definitions that can be set based on the expert knowledge or know-how of the structural behaviours of the tower.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Economic Assumptions

**Figure A1.**Overview of the economic assumptions for the analysis, both the costs which are incurred only once (e.g., failure cost, investments, decommissioning) and monthly recurring costs (e.g., maintenance, incomes, environmental impact). All costs are normalized by turbine capacity MWp or by turbine production rate MWh. Incomes are presented as negative costs on this graph. Top pane shows monthly costs without interest impact, bottom pane shows cost discounted down to year X (here 2010), with monetary inflation and varied (linear) interest rates applied to energy price, wages, and capital cost.

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**Figure 1.**Overview of the corrosion detection and prognostic system coupled with the decision support tool.

**Figure 2.**Output of the corrosion prognosis algorithm based on the power-law corrosion model on (simulated) measurement data, along with the ground truth for reference.

**Figure 5.**Component-level

**Top pane**: Component system Unreliabilities $Q\left(t\right)$ (top pane, 5 components each depicted with a separate colour (including: blue, purple, orange, green, and red) and

**Bottom pane**: Resulting system-level unreliability $Q\left(t\right)$; with two timeseries: the series weighting of all component level unreliabilities (blue line) versus a weighting of the risk of failure of 3 out of 5 components (orange line), using the k-out-of-n: Good System Method. (blue line:) 5-out-of-5 (series connection) gives a 50th percentile at month ‘January 2040’; (orange line:) 3-out-of-5 gives a 50th percentile at month ‘August 2040’.

**Figure 7.**LCOE as function of the decommissioning time ${t}_{D}$, with system-level EOL distribution (${t}_{f}$) as presented in Figure 5 (for the series configuration). The blue points indicate the economical optima for different values of the risk aversion term ${c}_{RA}$: from bottom right being low ${c}_{RA}$ to top left being high ${c}_{RA}$ (inferring earlier decommissioning advice).

**Figure 8.**Browser window of the custom visualization software-tool. It consists of three areas: user input (red box), a 3D visualization area (green box), and a 2D time series visualization (blue box). All widgets are interactive and responsive. Reused from [9] with author permission.

**Figure 9.**Browser window of the custom visualization software-tool for decision support module. It consists of two areas: user input (software tool, top left), a visualization area (green rectangle, bottom), and a tabulated summary area (blue rectangle, top right).

TCO Metric | LCOE Metric | |||
---|---|---|---|---|

Risk Aversion Factor |
Optimal Decom. Date |
Est. TCO $[\mathrm{k}\u20ac/{\mathrm{MW}}_{\mathrm{peak}}]$ ^{1} |
Optimal Decom. Date |
Est. LCOE $[\u20ac/\mathrm{MWh}]$ |

${c}_{RA}=0$ | September 2039 | −5543.47 | July 2039 | 42.50 |

${c}_{RA}=0.7$ | November 2038 | −5284.50 | January 2039 | 43.31 |

^{1}a negative value is equivalent to gross profit.

Scenario | Planned Decom. | True TCO $[\mathbf{k}\u20ac/{\mathbf{MW}}_{\mathbf{peak}}]$ ^{1} | True LCOE $[\u20ac/\mathbf{MWh}]$ |
---|---|---|---|

A: No prognosis info. Early decom. | 2032-07-01 (early) | −4089.81 | 44.19 |

B: No prognosis info. Failure before decom. | 2040-01-01 (failure) | −5544.12 | 44.36 |

C1: With prognosis info, using TCO or LCOE metric with ${c}_{RA}=0$ | 2039-07-01 (maximizing expected mean) | −6031.34 | 41.15 |

C2: With prognosis info, using TCO or LCOE metric with ${c}_{RA}=0.7$ | 2039-01-01 (risk averse) | −5846.53 | 41.60 |

^{1}a negative value is equivalent to gross profit.

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**MDPI and ACS Style**

Vásquez, S.; Verhelst, J.; Brijder, R.; Ompusunggu, A.P.
Detection, Prognosis and Decision Support Tool for Offshore Wind Turbine Structures. *Wind* **2022**, *2*, 747-765.
https://doi.org/10.3390/wind2040039

**AMA Style**

Vásquez S, Verhelst J, Brijder R, Ompusunggu AP.
Detection, Prognosis and Decision Support Tool for Offshore Wind Turbine Structures. *Wind*. 2022; 2(4):747-765.
https://doi.org/10.3390/wind2040039

**Chicago/Turabian Style**

Vásquez, Sandra, Joachim Verhelst, Robert Brijder, and Agusmian Partogi Ompusunggu.
2022. "Detection, Prognosis and Decision Support Tool for Offshore Wind Turbine Structures" *Wind* 2, no. 4: 747-765.
https://doi.org/10.3390/wind2040039