Optimal Maintenance Schedule for a Wind Power Turbine with Aging Components
Round 1
Reviewer 1 Report
This manuscript presents a proposed maintenance schedule based on the renewal reward method. A multi-component setting with a virtual maintenance model is exploited to predict the life expectancy of a wind turbine’s four main components as well as calculate total savings according to Weibull distribution. The topic of the paper is interesting, and the structure is well-written and well-organized. There are some minor concerns to be addressed or answered:
1. Line 3: Are there any limitations to performing preventive maintenance by reference <No3>?
2. Section 7: Can the main errors in these specific components (especially the gearbox), as well as the possible failure frequency or life expectancy, be summarized? The abstract shows 30% lower costs, but it is not evident in the main text.
3. Over 4000 dollars are estimated to be the total savings of PM, as offshore wind farms are indeed hard to visit, and planning needs to be precise. What do the results in Table 3 ( needs annotation) represent? The cost reduction of the optimization model of fake components?
4. Is the Matlab file size and range important, requiring exclusive hardware to run, or is it defined as simple?
5. What is considered ideal for future work? A separate paragraph is required
Author Response
Dear Editors,
We wish to express our gratitude to two referees for the helpful comments and suggestions. Below, each comment is addressed by the respective changes made in the manuscript. We hope the edited version will be found suitable for publication in the journal “Algorithms”.
On behalf of the authors,
Serik Sagitov
Reviewer 1
Comment 1: Line 3: Are there any limitations to performing preventive maintenance by reference<No3>?
Answer: We have added:
“Compared to our setting, this paper considers one-component system and relies on a different survival function.”
Comment 2: Section 7: Can the main errors in these specific components (especially the gearbox), as well as the possible failure frequency or life expectancy, be summarized? The abstract shows30% lower costs, but it is not evident in the main text.
Answer: In section 7.4, the sentence
“On the other hand, according to Table 2 the PM planning may save around 4000 US dollars per month compared to the pure CM strategy.”
is replaced by
“On the other hand, according to Table 2 the PM planning may save around 4000 US dollars per month, that is around 30%, compared to the pure CM strategy. In all five scenarios presented in Table 2, the optimal maintenance plan includes a PM activity for the gearbox. In four of the case, a PM for the rotor is suggested. This is due to the higher replacement costs and failure frequency of the gearbox and the rotor. Notably, in one of the scenarios, the optimal maintenance plan suggests performing PM on all four components simultaneously.”
Comment 3: Over 4000 dollars are estimated to be the total savings of PM, as offshore wind farms are indeed hard to visit, and planning needs to be precise. What do the results in Table 3 (needs annotation) represent? The cost reduction of the optimization model of fake components?
Answer
- The sentence
“The following three tables juxtapose the results produced by the two methods:”
is replaced by
“The following table juxtaposes the results produced by the two methods. It turns out that the optimal maintenance plans obtained by these two algorithms are almost identical across different scenarios, demonstrating the accuracy of the new algorithm. Importantly, the new algorithm runs 25 times faster than the NextPM algorithm.”
- We have added the following annotation to Table 3:
“A comparison of the earlier NextPM algorithm and the algorithm of this paper.”
- We have removed the sentence:
“The optimal schedules are almost identical, demonstrating the accuracy of the new algorithm. Importantly, the new algorithm is much faster than the previous one.”
Comment 4: ls the Matlab file size and range important, requiring exclusive hardware to run, or is it defined as simple?
Answer: We agree with the referee that mentioning the programming language Matlab sounds misleading. What is important is the comparison of the performance of the two algorithms in terms of the running time. Therefore, we have removed from the table the reference to the Matlab and instead we mention the CPU time.
Comment 5: What is considered ideal for future work? A separate paragraph is required.
Answer: We have added a new section titled “Conclusions and future work”.
This paper introduces a new optimization algorithm relying on the renewal-reward theorem. In the multi-component setting, a new concept called the virtual replacement is introduced, allowing us to treat each replacement event as a renewal event, even when some components are not actually replaced with the new ones.
The new algorithm is illustrated by careful simulation studies in the framework of a four-component system of a wind turbine, searching for the optimal maintenance plans under various initial conditions.
In the sensitivity analysis 1, we conducted a detailed study on the replacement cost of a single component based on its age $a$ at a potential replacement moment $t$. Our findings indicate that the replacement cost of the component increases as the parameter $a$ increases. For the component with $a$ below a certain critical value, the component is deemed to be in a sufficiently good condition which does not require a replacement. However, when the age $a$ exceeds the critical value, the optimal solution is to plan for a PM activity at the time $t$.
The sensitivity analysis 2 examines the influence of the crucial parameter m representing the monthly value depreciation of a generic wind turbine component. Our results show that as m increases, the optimal PM time for the component also increases. When m is large enough, the optimal solution is to never perform the PM activity.
The sensitivity analysis 3 deals with the effect of the starting time s of the scheduling period $[s,T]$. For a single-component system, we have observed that as long as $s$ is not too close to $T$, the optimal solution is to perform a PM when the component in question reaches a certain critical age.
The case study 1 estimates that compared to the pure CM strategy, our optimization algorithm on average saves around 30% of the maintenance costs. In the case study 2, we compared our new algorithm with an earlier algorithm NextPM from [7]. The study demonstrates that the new algorithm yields precise outcomes while significantly reducing CPU processing time. Compared to the NextPM algorithm, our new algorithm has the advantage of being able to handle the age-dependent PM costs.
The algorithm of this paper can handle only to the replacement maintenance activities. In the future, it would be worthwhile to study how other maintenance activities such as inspection and minor/major repair, affect the optimal PM scheduling plan. Another interesting development would be to consider the case when the PM replacement cost is a non-linear function of the component’s age. Finding the optimal PM scheduling plan in this case is an interesting and challenging problem.
Reviewer 2 Report
The article deals with a very current topic related to the maintenance planning of wind turbines. It has great potential for publication, but the following details need to be added:
- line 73: please define variable E(L)
- Optimal maintenance algorithm for multi components is presented in chapter 6. Please indicate the appropriate optimization methods, suitable for solving the formulated task
- The article lacks a general summary of the achieved results and highlighting the scientific contribution in the addressed area. At the end of the article, I recommend adding a chapter "Conclusion"
Author Response
Dear Editors,
We wish to express our gratitude to two referees for the helpful comments and suggestions. Below, each comment is addressed by the respective changes made in the manuscript. We hope the edited version will be found suitable for publication in the journal “Algorithms”.
On behalf of the authors,
Serik Sagitov
Reviewer 2
Comment 1: line 73: please define variable E(L)
Answer: We have added “, where E(L) is the expected value of the random variable L.”
Comment 2: Optimal maintenance algorithm for multi components is presented in chapter 6. Please indicate the appropriate optimization methods, suitable for solving the formulated task.
Answer: We have added the following paragraph:
“This optimization problem is solved using the standard approach for the case when all variables are binary, and the objective function is a linear function of the variables $(y_{s+1},\ldots, y_T)$ and $z$. According to constraint (8b), only one of the variables $(y_{s+1},\ldots, y_T, z)$ can be equal to 1, so that by selecting the variable with the smallest coefficient, we can determine which one is equal to 1. As a result, we can determine the optimal values of the target variables $\boldsymbol x_s$ subject to the remaining constraints.”
Comment 3: The article lacks a general summary of the achieved results and highlighting the scientific contribution in the addressed area, At the end of the article. I recommend adding a chapter "Conclusion"
Answer: We have added a new section titled “Conclusions and future work”:
This paper introduces a new optimization algorithm relying on the renewal-reward theorem. In the multi-component setting, a new concept called the virtual replacement is introduced, allowing us to treat each replacement event as a renewal event, even when some components are not actually replaced with the new ones.
The new algorithm is illustrated by careful simulation studies in the framework of a four-component system of a wind turbine, searching for the optimal maintenance plans under various initial conditions.
In the sensitivity analysis 1, we conducted a detailed study on the replacement cost of a single component based on its age $a$ at a potential replacement moment $t$. Our findings indicate that the replacement cost of the component increases as the parameter $a$ increases. For the component with $a$ below a certain critical value, the component is deemed to be in a sufficiently good condition which does not require a replacement. However, when the age $a$ exceeds the critical value, the optimal solution is to plan for a PM activity at the time $t$.
The sensitivity analysis 2 examines the influence of the crucial parameter m representing the monthly value depreciation of a generic wind turbine component. Our results show that as m increases, the optimal PM time for the component also increases. When m is large enough, the optimal solution is to never perform the PM activity.
The sensitivity analysis 3 deals with the effect of the starting time s of the scheduling period $[s,T]$. For a single-component system, we have observed that as long as $s$ is not too close to $T$, the optimal solution is to perform a PM when the component in question reaches a certain critical age.
The case study 1 estimates that compared to the pure CM strategy, our optimization algorithm on average saves around 30% of the maintenance costs. In the case study 2, we compared our new algorithm with an earlier algorithm NextPM from [7]. The study demonstrates that the new algorithm yields precise outcomes while significantly reducing CPU processing time. Compared to the NextPM algorithm, our new algorithm has the advantage of being able to handle the age-dependent PM costs.
The algorithm of this paper can handle only to the replacement maintenance activities. In the future, it would be worthwhile to study how other maintenance activities such as inspection and minor/major repair, affect the optimal PM scheduling plan. Another interesting development would be to consider the case when the PM replacement cost is a non-linear function of the component’s age. Finding the optimal PM scheduling plan in this case is an interesting and challenging problem.
