A method for determining the layout of a yaw system based on the Delphi method and the analytic hierarchy process

Abstract

Wind power technology has been widely used due to its characteristics of environmental protection, sustainability and low cost. The yaw system plays a vital role in improving the energy capture efficiency of a wind turbine. However, the method of layout determination is lacking in the yaw system. To solve this problem, a method that combines the Delphi method and the analytic hierarchy process was proposed in this study. Twelve evaluation indexes, including transmission efficiency, ratio range, operating temperature range and others, were identified by screening 18 technical indicators using the Delphi method. Subsequently, the evaluation system of the yaw system was established. Then, six configuration schemes were selected. Experts’ scores of schemes were collected according to the evaluation system and the score matrix of evaluation indexes was obtained. The hierarchical model of the evaluation indexes of the yaw system was established and the comprehensive weight was obtained by using the analytic hierarchy process. After calculating the comprehensive evaluation score, the comprehensive evaluation result was obtained. The 2Z-X(A) negative mechanism, which achieved the highest score of 0.9227, is the optimal scheme. A new method and specific process are provided for designers. The research gap in the scheme selection method for yaw systems is filled.

Graphical Abstract

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renewable energy generation, wind power, yaw system, Delphi method, analytic hierarchy process

Introduction

Wind power technology, as a widely recognized renewable-energy tool, is a critical means to reduce carbon emissions and achieve carbon neutrality [1]. With the inevitable consumption of energy resources, global attention on renewable energy is increasing. Because of its advantages of environmental protection and low cost, wind power technology has been widely used [2]. According to the latest Renewable Energy Generation Costs 2022 report from IRENA (International Renewable Energy Agency), the global average cost of onshore wind power projects is $0.033/kWh, which is slightly less than half of the cost of the cheapest fossil fuel power projects [3], showing an unrivalled price advantage. The yaw system plays a key role in increasing the energy capture of the wind turbine (WT). It rotates the nacelle around the tower axis and continuously aligns the rotor-swept area with the direction of the incoming wind [4]. A failure survey [5] showed that, although the yaw system accounted for only 1.4% of the total WT cost, its downtime distribution probability reached 13.3%, ranking third; the average downtime per failure was 259.4 hours, ranking second. Recently, the apparent influence of the yaw system on WT energy capture, WT wake [6, 7] and dynamic behaviour [8] has been found by scholars. Some scholars have conducted research on the yaw system in recent years, including control strategy [9, 10], load sharing and distribution [11], mechanical properties analysis [12], cost reduction [13] and fault analysis [14, 15].

However, research on the design of yaw systems is still insufficient. According to a survey by Kim and Dalhoff [16], patents related to the entire yaw system account for only 0.53% of total WTs. Traditional yaw system design is typically based on trial and error, design experience and design intuition. The design process is ambiguous and non-quantifiable, often heavily reliant on individual designer experience. This reliance may lead to low design efficiency, inability to consider expert opinions and potential oversight of superior designs. This phenomenon is especially reflected in determining the configuration of the gearbox of the yaw system, which is one of the most basic steps of yaw system design. The multistage planetary gear train is used by Wan et al. [17] for the yaw gearbox, but the reasons for its use are not stated. The combined oscillatory pin mechanism is used in the yaw system by E et al. [18], after comparing it briefly with the traditional scheme in volume, gear ratios, etc., but the comparison process is not quantitative and the perspective of discussion is limited. Regarding tidal current energy converters that are similar to WTs, Li and Zhu [19] pointed out that gearbox selection was a fundamental problem to be solved in power train configuration selection. The different layouts of tidal current energy converters are summarized and compared by them. However, their approach needs to be refined, as there is no clear operational process. Abundo et al. [20] proposed a gear combination optimization method to be applied to tidal current energy converters. The application process of the method is clear, but it only considers three criteria: maximum energy output, cost and weight. The perspective considered is relatively limited. This issue is also of interest in other related fields. Hayat and Mankar [21] proposed a search algorithm for gearbox selection and design in robotic arms. The proposed method is highly practical and performs well in the field of robotic arms. However, its applicability is limited, primarily targeting robotic arms equipped with multi-degree-of-freedom motors. It is challenging to directly apply it to yaw systems. In general, a reliable basis for the selection of gearbox schemes for yaw systems is missing and a determination method is lacking but can be obtained through the present research. In the yaw system, the gearbox has the function of reducing speed and increasing torque [22]. The bearing capacity, mechanical properties and reliability of the yaw gearbox reflect the performance of the yaw system, which are the key factors affecting the safe, stable and efficient operation of the whole WT [23]. It can be said that to explore the layout of the yaw system is to explore the configuration scheme of the yaw gearbox. Overall, the selection of a yaw system layout lacks reliable grounds and cannot be directly obtained through existing research. Among existing studies, there is no method that can comprehensively consider multiple expert opinions from various perspectives. This may pose the risk of design falling into conventional thinking patterns.

Suppose there is a method at the initial stage of design. In that case, the designer can compare many gearbox configuration schemes used in other fields according to the characteristics and select the most suitable schemes for the yaw system. The method will make the subsequent design stand on a superior basis. On this basis, the load sharing or mechanical properties analysis research can produce more meaningful results.

Such a method is proposed on the premise that the evaluation criteria are determined. The characteristics of schemes cannot be explicitly quantified without rational evaluation criteria. As long as the evaluation criteria are determined, the problem can be regarded as a multicriteria decision-making (MCDM) problem, which can be solved by using the existing methods [24]. In this study, a combination of the Delphi method (DM) and the analytic hierarchy process (AHP) is used to determine the matching degree of schemes and the yaw system. The DM proposed by Dalkey and Helmer has been extensively used to obtain consistent answers through questionnaire results [25]. Anonymous reply, multiple iterations and statistical group reply are its three characteristics [26, 27]. Venkatesh et al. [28] used the DM to identify barriers to the development of coastal shipping in India. Soleymani et al. [29] used the DM to explore the impact of sustainable entrepreneurship indicators on rural economic development in Iran. Wrålsen et al. [30] used the DM to explore a circular business model for batteries. The AHP was proposed by Saaty to solve complex decision-making problems involving multicriteria, quantitative and qualitative data [31, 32]. Sivaprakasam and Angamuthu [33] created a multiple attributes group decision-making (MAGDM) algorithm based on the AHP method to recruit the best candidate for an assistant professor job in an institute. Jagtap and Karande [34] utilized a combination of the AHP and other methods for the selection of non-traditional machining processes. Contreras et al. [35] used the AHP as a decision-making algorithm to plan microgrids.

To determine a yaw system layout scheme, this study will focus on the following work: (i) establishment of an evaluation system of the yaw gearbox based on expert opinions on evaluation indexes, which are processed using the DM; (ii) establishment of the score matrix of evaluation indexes via a quantitative representation of experts’ opinions on the characteristics of the schemes being offered; (iii) obtaining the comprehensive weight and the comprehensive evaluation result obtained by using the AHP based on the hierarchical model of evaluation indexes of the yaw system.

1 Methodology

The proposed research methodology is divided into three stages. First, the DM is used to identify related technical indicators according to the input of the expert group. According to the results of the DM, an evaluation system of the yaw system is established. Second, the DM is used again to obtain the evaluation indexes score for the proposed schemes. Finally, the AHP is used to determine the comprehensive weight and obtain the comprehensive evaluation result. These three stages are described in detail.

1.1 Establishment of an evaluation system of the yaw system

1.1.1 Preparation process of the DM questionnaire

By considering the characteristics of the gearbox in the yaw system, we design a questionnaire including several relevant technical indicators. Several experts in related fields are invited to participate in the questionnaire survey to identify the indicators.

1.1.2 Survey process

In this stage, two rounds of conventional expert surveys are implemented. In the first round, the experts are asked to select the most important evaluation indexes for the yaw system design from the questionnaire. After this round, a facilitator participates in an anonymous summary of expert opinions and a preliminary list of evaluation indexes is obtained. In the second round, experts are encouraged to revise their opinions based on the preliminary list. Then, the final collation is made to form the final list. The evaluation system of the yaw system is established according to the final list.

1.2 Establishment of the score matrix of evaluation indexes

1.2.1 Preparation process of the DM questionnaire

The preparation of the questionnaire is based on the evaluation system and the object of solicitation is still the experts invited in the previous stage. There are multiple sets of questions in the questionnaire, corresponding to multiple different schemes provided by the facilitator. Experts are asked to rate these schemes. The questionnaire is available in the Supplementary data.

1.2.2 Survey process

In this stage, two rounds of expert surveys are still implemented. In the first round, the experts rate multiple sets of scores and return questionnaires. Afterwards, the facilitator anonymously summarizes the expert opinions and obtains the preliminary score list. In the second round, the experts are encouraged to modify their scores according to the preliminary score list. A final collection of revised ratings is conducted for the establishment of the score matrix of evaluation indexes.

The score matrix of evaluation indexes is shown as follows:

\begin{array}{l} U = (\begin{array}{c} u_{j}^{i} & u_{j}^{i + 1} & u_{j}^{i + 2} & \dots & u_{j}^{i + n} u_{(j + 1)}^{i} & u_{(j + 1)}^{i + 1} & ⋮ u_{(j + 2)}^{i} & ⋱ & ⋮ ⋮ & ⋱ & ⋮ u_{(j + m)}^{i} & \dots & \dots & \dots & u_{(j + m)}^{i + n} \end{array}) \end{array}

(1)

where i, i + 1, i + 2 ..., i + n are the number of configuration schemes, and there are i + n configuration schemes; j, j + 1, j + 2, ..., j + m are the index number, and there are j + m indexes (i, j ∈ N^*).

1.3 Obtaining the weight and the comprehensive evaluation result

1.3.1 Establishment of a hierarchical model

The hierarchical model consists of four hierarchies: goal hierarchy, criteria hierarchy, index factor hierarchy and alternative hierarchy. The problem to be solved is considered to be the goal hierarchy. The criteria hierarchy and the index factor hierarchy are composed of the evaluation indexes and sub-evaluation indexes in the evaluation system, respectively. The alternative hierarchy consists of various given schemes.

1.3.2 Determination and consistency check of the judgment matrix

The r_vw (1 ≤ v ≤ t, 1 ≤ w ≤ t) is the judgment value of a hierarchy, which indicates the importance degree between element v and element w. The judgment value r_vw can be determined by using the 1–9 comparison scale method, as shown in Table 1.

Table 1.

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The judgment value r_vw

$r_{v w}$	Description
1	Element v is of equal importance compared to element w
3	Element v is slightly more important than element w
5	Element v is significantly important compared to element w
7	Element v is strongly important compared to element w
9	Element v is extremely important compared to element w
2, 4, 6, 8	Indicates the intermediate value of the above judgment

$r_{v w}$	Description
1	Element v is of equal importance compared to element w
3	Element v is slightly more important than element w
5	Element v is significantly important compared to element w
7	Element v is strongly important compared to element w
9	Element v is extremely important compared to element w
2, 4, 6, 8	Indicates the intermediate value of the above judgment

Table 1.

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The judgment value r_vw

$r_{v w}$	Description
1	Element v is of equal importance compared to element w
3	Element v is slightly more important than element w
5	Element v is significantly important compared to element w
7	Element v is strongly important compared to element w
9	Element v is extremely important compared to element w
2, 4, 6, 8	Indicates the intermediate value of the above judgment

$r_{v w}$	Description
1	Element v is of equal importance compared to element w
3	Element v is slightly more important than element w
5	Element v is significantly important compared to element w
7	Element v is strongly important compared to element w
9	Element v is extremely important compared to element w
2, 4, 6, 8	Indicates the intermediate value of the above judgment

Based on comparing the elements of the same hierarchy pairwise, the relative importance of each element is derived to form the judgment matrix R_t×t. The judgment matrix R_t×t can be obtained as follows:

\begin{array}{l} R_{t \times t} = (\begin{array}{c} 1 & r_{12} & r_{13} & \dots & r_{1 t} \frac{1}{r_{12}} & 1 & r_{23} & \dots & r_{2 t} \frac{1}{r_{13}} & \frac{1}{r_{23}} & 1 & \dots & r_{3 t} ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \frac{1}{r_{1 t}} & \frac{1}{r_{2 t}} & \frac{1}{r_{3 t}} & \dots & 1 \end{array}) \end{array}

(2)

Then, the consistency test is carried out on all the judgment matrixes to check whether they are qualified. The process of consistency check refers to the research of Cheng et al. [36]. Consistency check tests the consistency of the matrix by determining the consistency ratio (CR), which is solved by using Equation (3). It is equal to the ratio of the consistency index (CI) to the average random consistency index (RI). CI is solved by using Equation (4). $λ_{m a x}$ is the maximum eigenvalue of the judgment matrix R_t×t. According to Table 2, RI can be obtained.

Table 2.

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The value of RI

t	1	2	3	4	5	6
RI	0	0	0.58	0.9	1.12	1.24

Table 2.

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The value of RI

t	1	2	3	4	5	6
RI	0	0	0.58	0.9	1.12	1.24

When CR < 0.1, it is considered that the degree of inconsistency of the judgment matrix is acceptable; when CR ≥ 0.1, it is unacceptable and should be adjusted.

\begin{array}{l} C R = \frac{C I}{R I} \end{array}

(3)

\begin{array}{l} C I = \frac{λ_{m a x} - t}{t - 1} \end{array}

(4)

1.3.3 Determination of the weight

For the judgment matrix that passes the consistency check, weight W_v can be determined through Equation (5) according to the research of Dong et al. [37]. The weight vector (WV) is shown by Equation (6):

\begin{array}{l} W_{v} = \frac{\sqrt[t]{\prod_{w = 1}^{t} r_{v w}}}{\sum_{w = 1}^{t} \sqrt[t]{\prod_{w = 1}^{t} r_{v w}}}, v = 1, 2, 3, \dots, t \end{array}

(5)

\begin{array}{l} W V = (W_{1}, W_{2}, W_{3}, \dots, W_{t}) . \end{array}

(6)

It is feasible to multiply the index factor hierarchy and the corresponding weights of the criteria hierarchy to obtain the comprehensive weight (CW).

1.3.4 Determination of the comprehensive evaluation result

The comprehensive evaluation result is obtained by comparing the comprehensive evaluation score V. V is shown by Equation (7):

\begin{array}{l} V = C W * U \end{array}

(7)

2 Application and result

The detailed application process and results are shown in the following paragraphs.

2.1 The evaluation system of the yaw system

2.1.1 Preparation process of the DM questionnaire

A questionnaire is set up including 18 technical indicators. These technical indicators are proposed based on the functional requirements of the yaw system. To ensure the operational objectives of the yaw system, the transmission efficiency, rated transmission torque, gear ratio range, operating temperature range and load capacity are proposed. To facilitate system installation, the dimensions and weights, maintenance ease and maintenance costs are proposed. To ensure reliable and energy-efficient system operation, the energy loss, operating life, reliability, environmental adaptability, operating costs and return on investment are proposed. To ensure system harmony with people and the environment, the noise generation, end-of-life costs, environmental benefits and social benefits are proposed. Ten experts and scholars are invited into this stage, including three researchers in the field of wind power, all of whom have >5 years of research experience; three mechanical engineers, all of whom have been involved in the whole process of designing and manufacturing at least three types of gearboxes; two WT maintenance engineers; and two researchers in the field of the environment, who are well aware of environmental policies and have >2 years of research experience in the field of sustainable development. They are asked to select the most important evaluation indexes that meet the yaw system design and could supplement the unmentioned technical indicators.

2.1.2 Survey process

The preliminary list is collated by the facilitator and then sent to the experts, after the first round of expert surveys. The selected times of each evaluation index can be understood by experts. The final list is sorted out after the second round. Each evaluation index in it is selected by >80% of the experts. The 12 most representative evaluation indexes are obtained through the DM. They are divided into three categories: Evaluation Indexes X = {X_a, X_b, X_c} = {Main Technical Parameters, Overall Characteristics, Costs and Benefits}. The indexes in the Main Technical Parameters are inherent properties of the schemes and can be quantified by calculation. X_a = {X_a1, X_a2, X_a3, X_a4} = {Transmission Efficiency, Ratio Range, Operating Temperature Range, Dimensions and Weights}. The indexes in Overall Characteristics and Costs and Benefits need to be scored by experts according to experience. X_b = {X_b1, X_b2, X_b3, X_b4} = {Operating Life and Reliability, Environmental Adaptability, Installation and Maintenance Ease, Noise Generated}. X_c = {X_c1, X_c2, X_c3, X_c4} = {Operating Costs, Maintenance Costs, End-of-life Costs, Public Benefits}. Classification of evaluation indexes is helpful to simplify the determination of the weight and the comprehensive evaluation result.

According to the expert opinions, the evaluation system of the yaw system is established, including the evaluation indexes tree (as shown in Fig. 1) and the score calculation rule tables (as shown in Tables 3–11).

Table 3.

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Rules for calculating the Main Technical Parameters scores

Subcriteria	Score	Description
Transmission efficiency	$S_{a 1} = {\begin{array}{c} 0.2, & η < 0.5 1.74 (η - 0.5) + 0.2, & 0.5 \leq η < 0.96 1, & 0.96 \leq η \end{array}$	η is the theoretical transmission efficiency of the scheme at a transmission ratio of 1200 ± 200
Ratio range	$S_{a 2} = {\begin{array}{c} 0.2, & (i_{m a x}, i_{m i n}) . \notin (- 2000, 800) \frac{min (i_{m a x}, 2000) - m a x (i_{m i n}, 800)}{1200}, & i_{m a x} 〈 2000 o r i_{m i n} 〉 800 1, & (i_{m a x}, i_{m i n}) . \in (- 2000, 800) \end{array}$
Operating temperature range	$S_{a 3} = {\begin{array}{c} 0.2, & t_{m a x} \notin [20, 100] 0.6, & 60 < i_{m a x} \leq 100 1, & 20 \leq i_{m a x} \leq 60 \end{array}$	$t_{m a x}$ is the maximum operating temperature in a room-temperature environment

Dimensions and weights	$S_{a 4} = {\begin{array}{c} 0.2, & R K = γ 1 - \frac{0.8 \times (R K - 1)}{γ}, & 1 < R K < γ 1, & R K = 1 \end{array}$	RK is the ranking of the score of the gearbox in terms of volume and weight, and $γ$ is the number of schemes

Subcriteria	Score	Description
Transmission efficiency	$S_{a 1} = {\begin{array}{c} 0.2, & η < 0.5 1.74 (η - 0.5) + 0.2, & 0.5 \leq η < 0.96 1, & 0.96 \leq η \end{array}$	η is the theoretical transmission efficiency of the scheme at a transmission ratio of 1200 ± 200
Ratio range	$S_{a 2} = {\begin{array}{c} 0.2, & (i_{m a x}, i_{m i n}) . \notin (- 2000, 800) \frac{min (i_{m a x}, 2000) - m a x (i_{m i n}, 800)}{1200}, & i_{m a x} 〈 2000 o r i_{m i n} 〉 800 1, & (i_{m a x}, i_{m i n}) . \in (- 2000, 800) \end{array}$
Operating temperature range	$S_{a 3} = {\begin{array}{c} 0.2, & t_{m a x} \notin [20, 100] 0.6, & 60 < i_{m a x} \leq 100 1, & 20 \leq i_{m a x} \leq 60 \end{array}$	$t_{m a x}$ is the maximum operating temperature in a room-temperature environment

Dimensions and weights	$S_{a 4} = {\begin{array}{c} 0.2, & R K = γ 1 - \frac{0.8 \times (R K - 1)}{γ}, & 1 < R K < γ 1, & R K = 1 \end{array}$	RK is the ranking of the score of the gearbox in terms of volume and weight, and $γ$ is the number of schemes

Table 3.

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Rules for calculating the Main Technical Parameters scores

Subcriteria	Score	Description
Transmission efficiency	$S_{a 1} = {\begin{array}{c} 0.2, & η < 0.5 1.74 (η - 0.5) + 0.2, & 0.5 \leq η < 0.96 1, & 0.96 \leq η \end{array}$	η is the theoretical transmission efficiency of the scheme at a transmission ratio of 1200 ± 200
Ratio range	$S_{a 2} = {\begin{array}{c} 0.2, & (i_{m a x}, i_{m i n}) . \notin (- 2000, 800) \frac{min (i_{m a x}, 2000) - m a x (i_{m i n}, 800)}{1200}, & i_{m a x} 〈 2000 o r i_{m i n} 〉 800 1, & (i_{m a x}, i_{m i n}) . \in (- 2000, 800) \end{array}$
Operating temperature range	$S_{a 3} = {\begin{array}{c} 0.2, & t_{m a x} \notin [20, 100] 0.6, & 60 < i_{m a x} \leq 100 1, & 20 \leq i_{m a x} \leq 60 \end{array}$	$t_{m a x}$ is the maximum operating temperature in a room-temperature environment

Dimensions and weights	$S_{a 4} = {\begin{array}{c} 0.2, & R K = γ 1 - \frac{0.8 \times (R K - 1)}{γ}, & 1 < R K < γ 1, & R K = 1 \end{array}$	RK is the ranking of the score of the gearbox in terms of volume and weight, and $γ$ is the number of schemes

Subcriteria	Score	Description
Transmission efficiency	$S_{a 1} = {\begin{array}{c} 0.2, & η < 0.5 1.74 (η - 0.5) + 0.2, & 0.5 \leq η < 0.96 1, & 0.96 \leq η \end{array}$	η is the theoretical transmission efficiency of the scheme at a transmission ratio of 1200 ± 200
Ratio range	$S_{a 2} = {\begin{array}{c} 0.2, & (i_{m a x}, i_{m i n}) . \notin (- 2000, 800) \frac{min (i_{m a x}, 2000) - m a x (i_{m i n}, 800)}{1200}, & i_{m a x} 〈 2000 o r i_{m i n} 〉 800 1, & (i_{m a x}, i_{m i n}) . \in (- 2000, 800) \end{array}$
Operating temperature range	$S_{a 3} = {\begin{array}{c} 0.2, & t_{m a x} \notin [20, 100] 0.6, & 60 < i_{m a x} \leq 100 1, & 20 \leq i_{m a x} \leq 60 \end{array}$	$t_{m a x}$ is the maximum operating temperature in a room-temperature environment

Dimensions and weights	$S_{a 4} = {\begin{array}{c} 0.2, & R K = γ 1 - \frac{0.8 \times (R K - 1)}{γ}, & 1 < R K < γ 1, & R K = 1 \end{array}$	RK is the ranking of the score of the gearbox in terms of volume and weight, and $γ$ is the number of schemes

Table 4.

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Rules for calculating the Operating Life and Reliability scores

Level	Explicit description	$S_{b 1}$
Level 5	Very short lifespan and uneven loading. Frequent failures that may lead to damage or safety hazards. Frequent repair is required	0.2
Level 4	Shorter lifespans and uneven loads. Erratic performance or failure under certain conditions is caused. Regular maintenance and monitoring are required	0.4
Level 3	Medium-life, balanced load. The ability to operate under normal conditions is present. Regular maintenance is required	0.6
Level 2	Relatively long life, balanced loads, stable performance. Regular routine maintenance is required	0.8
Level 1	Long life, balanced load, stable operation. Regular routine maintenance is required	1

Level	Explicit description	$S_{b 1}$
Level 5	Very short lifespan and uneven loading. Frequent failures that may lead to damage or safety hazards. Frequent repair is required	0.2
Level 4	Shorter lifespans and uneven loads. Erratic performance or failure under certain conditions is caused. Regular maintenance and monitoring are required	0.4
Level 3	Medium-life, balanced load. The ability to operate under normal conditions is present. Regular maintenance is required	0.6
Level 2	Relatively long life, balanced loads, stable performance. Regular routine maintenance is required	0.8
Level 1	Long life, balanced load, stable operation. Regular routine maintenance is required	1

Table 4.

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Rules for calculating the Operating Life and Reliability scores

Level	Explicit description	$S_{b 1}$
Level 5	Very short lifespan and uneven loading. Frequent failures that may lead to damage or safety hazards. Frequent repair is required	0.2
Level 4	Shorter lifespans and uneven loads. Erratic performance or failure under certain conditions is caused. Regular maintenance and monitoring are required	0.4
Level 3	Medium-life, balanced load. The ability to operate under normal conditions is present. Regular maintenance is required	0.6
Level 2	Relatively long life, balanced loads, stable performance. Regular routine maintenance is required	0.8
Level 1	Long life, balanced load, stable operation. Regular routine maintenance is required	1

Level	Explicit description	$S_{b 1}$
Level 5	Very short lifespan and uneven loading. Frequent failures that may lead to damage or safety hazards. Frequent repair is required	0.2
Level 4	Shorter lifespans and uneven loads. Erratic performance or failure under certain conditions is caused. Regular maintenance and monitoring are required	0.4
Level 3	Medium-life, balanced load. The ability to operate under normal conditions is present. Regular maintenance is required	0.6
Level 2	Relatively long life, balanced loads, stable performance. Regular routine maintenance is required	0.8
Level 1	Long life, balanced load, stable operation. Regular routine maintenance is required	1

Table 5.

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Rules for calculating the Environmental Adaptability scores

Level	Explicit description	$S_{b 2}$
Level 5	It can only be adapted to a narrow temperature range. High and low temperature can easily lead to its transmission failure. It is unsuitable for environments with high humidity. It is easily affected by moisture	0.2
Level 4	Adaptation to high and low temperature is limited. Additional maintenance and monitoring are required. It is more reliable under dry conditions but with limited corrosion resistance	0.4
Level 3	Thermal expansion and contraction at high and low temperatures are somewhat adapted to. But transmission failure is a risk under extreme conditions. It works better under normal humidity conditions. It has moderate corrosion resistance	0.6
Level 2	It has good adaptability to high and low temperature adaptability. It can operate reliably under moderately high and low temperature conditions. It has good performance under high humidity conditions and high corrosion resistance	0.8
Level 1	It has excellent adaptability to high and low temperature adaptability. It can adapt to a wide range of temperatures. It has reliable operation even under high humidity conditions	1

Level	Explicit description	$S_{b 2}$
Level 5	It can only be adapted to a narrow temperature range. High and low temperature can easily lead to its transmission failure. It is unsuitable for environments with high humidity. It is easily affected by moisture	0.2
Level 4	Adaptation to high and low temperature is limited. Additional maintenance and monitoring are required. It is more reliable under dry conditions but with limited corrosion resistance	0.4
Level 3	Thermal expansion and contraction at high and low temperatures are somewhat adapted to. But transmission failure is a risk under extreme conditions. It works better under normal humidity conditions. It has moderate corrosion resistance	0.6
Level 2	It has good adaptability to high and low temperature adaptability. It can operate reliably under moderately high and low temperature conditions. It has good performance under high humidity conditions and high corrosion resistance	0.8
Level 1	It has excellent adaptability to high and low temperature adaptability. It can adapt to a wide range of temperatures. It has reliable operation even under high humidity conditions	1

Table 5.

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Rules for calculating the Environmental Adaptability scores

Level	Explicit description	$S_{b 2}$
Level 5	It can only be adapted to a narrow temperature range. High and low temperature can easily lead to its transmission failure. It is unsuitable for environments with high humidity. It is easily affected by moisture	0.2
Level 4	Adaptation to high and low temperature is limited. Additional maintenance and monitoring are required. It is more reliable under dry conditions but with limited corrosion resistance	0.4
Level 3	Thermal expansion and contraction at high and low temperatures are somewhat adapted to. But transmission failure is a risk under extreme conditions. It works better under normal humidity conditions. It has moderate corrosion resistance	0.6
Level 2	It has good adaptability to high and low temperature adaptability. It can operate reliably under moderately high and low temperature conditions. It has good performance under high humidity conditions and high corrosion resistance	0.8
Level 1	It has excellent adaptability to high and low temperature adaptability. It can adapt to a wide range of temperatures. It has reliable operation even under high humidity conditions	1

Level	Explicit description	$S_{b 2}$
Level 5	It can only be adapted to a narrow temperature range. High and low temperature can easily lead to its transmission failure. It is unsuitable for environments with high humidity. It is easily affected by moisture	0.2
Level 4	Adaptation to high and low temperature is limited. Additional maintenance and monitoring are required. It is more reliable under dry conditions but with limited corrosion resistance	0.4
Level 3	Thermal expansion and contraction at high and low temperatures are somewhat adapted to. But transmission failure is a risk under extreme conditions. It works better under normal humidity conditions. It has moderate corrosion resistance	0.6
Level 2	It has good adaptability to high and low temperature adaptability. It can operate reliably under moderately high and low temperature conditions. It has good performance under high humidity conditions and high corrosion resistance	0.8
Level 1	It has excellent adaptability to high and low temperature adaptability. It can adapt to a wide range of temperatures. It has reliable operation even under high humidity conditions	1

Table 6.

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Rules for calculating the Installation and Maintenance Ease scores

Levels	Explicit description	$S_{b 3}$
Level 5	The installation and maintenance process is extremely cumbersome. Specialized personnel and a great deal of time and resources are required. It demands high installation accuracy	0.2
Level 4	The installation and maintenance process is relatively complex. Additional operating procedures and equipment are required. It is less easy to implement	0.4
Level 3	The installation and maintenance process is relatively easy. Some specialized knowledge and operating skills are required. Its installation is overall easy to achieve	0.6
Level 2	The installation and maintenance process is quite easy. It can reduce the need for specialized skills and time to some extent. It can be installed quickly	0.8
Level 1	It is extremely easy to install and maintain. It is without much specialized knowledge and complex steps. It has a high fault tolerance	1

Levels	Explicit description	$S_{b 3}$
Level 5	The installation and maintenance process is extremely cumbersome. Specialized personnel and a great deal of time and resources are required. It demands high installation accuracy	0.2
Level 4	The installation and maintenance process is relatively complex. Additional operating procedures and equipment are required. It is less easy to implement	0.4
Level 3	The installation and maintenance process is relatively easy. Some specialized knowledge and operating skills are required. Its installation is overall easy to achieve	0.6
Level 2	The installation and maintenance process is quite easy. It can reduce the need for specialized skills and time to some extent. It can be installed quickly	0.8
Level 1	It is extremely easy to install and maintain. It is without much specialized knowledge and complex steps. It has a high fault tolerance	1

Table 6.

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Rules for calculating the Installation and Maintenance Ease scores

Levels	Explicit description	$S_{b 3}$
Level 5	The installation and maintenance process is extremely cumbersome. Specialized personnel and a great deal of time and resources are required. It demands high installation accuracy	0.2
Level 4	The installation and maintenance process is relatively complex. Additional operating procedures and equipment are required. It is less easy to implement	0.4
Level 3	The installation and maintenance process is relatively easy. Some specialized knowledge and operating skills are required. Its installation is overall easy to achieve	0.6
Level 2	The installation and maintenance process is quite easy. It can reduce the need for specialized skills and time to some extent. It can be installed quickly	0.8
Level 1	It is extremely easy to install and maintain. It is without much specialized knowledge and complex steps. It has a high fault tolerance	1

Levels	Explicit description	$S_{b 3}$
Level 5	The installation and maintenance process is extremely cumbersome. Specialized personnel and a great deal of time and resources are required. It demands high installation accuracy	0.2
Level 4	The installation and maintenance process is relatively complex. Additional operating procedures and equipment are required. It is less easy to implement	0.4
Level 3	The installation and maintenance process is relatively easy. Some specialized knowledge and operating skills are required. Its installation is overall easy to achieve	0.6
Level 2	The installation and maintenance process is quite easy. It can reduce the need for specialized skills and time to some extent. It can be installed quickly	0.8
Level 1	It is extremely easy to install and maintain. It is without much specialized knowledge and complex steps. It has a high fault tolerance	1

Table 7.

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Rules for calculating the Noise Generated scores

Level	Explicit description	$S_{b 4}$
Level 5	It is naturally prone to generating extremely significant noise that exceeds safety and environmental standards. Its noise may seriously impact the health of people and the environment	0.2
Level 4	It is naturally prone to relatively high noise levels. It may require additional acoustic measures to meet safety and environmental requirements	0.4
Level 3	It may cause noise. The noise level is acceptable in the general working environment. Its noise does not cause significant discomfort or health problems	0.6
Level 2	It is less likely to cause noise. It has less impact on the environment and people. Additional soundproofing measures are not required	0.8
Level 1	It has the unique feature of not causing noise. Its working noise does not significantly impact the working environment and personnel	1

Level	Explicit description	$S_{b 4}$
Level 5	It is naturally prone to generating extremely significant noise that exceeds safety and environmental standards. Its noise may seriously impact the health of people and the environment	0.2
Level 4	It is naturally prone to relatively high noise levels. It may require additional acoustic measures to meet safety and environmental requirements	0.4
Level 3	It may cause noise. The noise level is acceptable in the general working environment. Its noise does not cause significant discomfort or health problems	0.6
Level 2	It is less likely to cause noise. It has less impact on the environment and people. Additional soundproofing measures are not required	0.8
Level 1	It has the unique feature of not causing noise. Its working noise does not significantly impact the working environment and personnel	1

Table 7.

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Rules for calculating the Noise Generated scores

Level	Explicit description	$S_{b 4}$
Level 5	It is naturally prone to generating extremely significant noise that exceeds safety and environmental standards. Its noise may seriously impact the health of people and the environment	0.2
Level 4	It is naturally prone to relatively high noise levels. It may require additional acoustic measures to meet safety and environmental requirements	0.4
Level 3	It may cause noise. The noise level is acceptable in the general working environment. Its noise does not cause significant discomfort or health problems	0.6
Level 2	It is less likely to cause noise. It has less impact on the environment and people. Additional soundproofing measures are not required	0.8
Level 1	It has the unique feature of not causing noise. Its working noise does not significantly impact the working environment and personnel	1

Level	Explicit description	$S_{b 4}$
Level 5	It is naturally prone to generating extremely significant noise that exceeds safety and environmental standards. Its noise may seriously impact the health of people and the environment	0.2
Level 4	It is naturally prone to relatively high noise levels. It may require additional acoustic measures to meet safety and environmental requirements	0.4
Level 3	It may cause noise. The noise level is acceptable in the general working environment. Its noise does not cause significant discomfort or health problems	0.6
Level 2	It is less likely to cause noise. It has less impact on the environment and people. Additional soundproofing measures are not required	0.8
Level 1	It has the unique feature of not causing noise. Its working noise does not significantly impact the working environment and personnel	1

Table 8.

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Rules for calculating the Operating Costs scores

Level	Explicit description	$S_{c 1}$
Level 5	Its operating costs are high. It has significant costs for cooling, lubrication, etc.	0.2
Level 4	It has relatively high operating costs. Relatively large resources for cooling and lubrication are required	0.4
Level 3	It has operating costs in the general range. It requires some maintenance costs	0.6
Level 2	It has relatively low operating costs. It has an efficient operation with low energy and production costs	0.8
Level 1	Its operating costs are low. Resources are efficiently used to maintain quality operations with minimal energy and operating expenses	1

Level	Explicit description	$S_{c 1}$
Level 5	Its operating costs are high. It has significant costs for cooling, lubrication, etc.	0.2
Level 4	It has relatively high operating costs. Relatively large resources for cooling and lubrication are required	0.4
Level 3	It has operating costs in the general range. It requires some maintenance costs	0.6
Level 2	It has relatively low operating costs. It has an efficient operation with low energy and production costs	0.8
Level 1	Its operating costs are low. Resources are efficiently used to maintain quality operations with minimal energy and operating expenses	1

Table 8.

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Rules for calculating the Operating Costs scores

Level	Explicit description	$S_{c 1}$
Level 5	Its operating costs are high. It has significant costs for cooling, lubrication, etc.	0.2
Level 4	It has relatively high operating costs. Relatively large resources for cooling and lubrication are required	0.4
Level 3	It has operating costs in the general range. It requires some maintenance costs	0.6
Level 2	It has relatively low operating costs. It has an efficient operation with low energy and production costs	0.8
Level 1	Its operating costs are low. Resources are efficiently used to maintain quality operations with minimal energy and operating expenses	1

Level	Explicit description	$S_{c 1}$
Level 5	Its operating costs are high. It has significant costs for cooling, lubrication, etc.	0.2
Level 4	It has relatively high operating costs. Relatively large resources for cooling and lubrication are required	0.4
Level 3	It has operating costs in the general range. It requires some maintenance costs	0.6
Level 2	It has relatively low operating costs. It has an efficient operation with low energy and production costs	0.8
Level 1	Its operating costs are low. Resources are efficiently used to maintain quality operations with minimal energy and operating expenses	1

Table 9.

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Rules for calculating the Maintenance Costs scores

Levels	Explicit description	$S_{c 2}$
Level 5	Its maintenance costs are high. The frequency of maintenance is very high. A lot of money and resources are required for regular overhauls, replacement of parts and maintenance work	0.2
Level 4	Maintenance costs are relatively high. A high frequency of maintenance is required. Relatively large amounts of money and resources are required for maintenance and upkeep	0.4
Level 3	Maintenance costs and frequency are within the general range. It can be stably maintained with acceptable economic benefits	0.6
Level 2	It has relatively low maintenance costs and frequency. It spends low capital and resources on maintenance and upkeep	0.8
Level 1	Its maintenance costs and frequency are low. It utilizes resources very efficiently. The cost of consumables and personnel for its maintenance and upkeep work is almost negligible	1

Levels	Explicit description	$S_{c 2}$
Level 5	Its maintenance costs are high. The frequency of maintenance is very high. A lot of money and resources are required for regular overhauls, replacement of parts and maintenance work	0.2
Level 4	Maintenance costs are relatively high. A high frequency of maintenance is required. Relatively large amounts of money and resources are required for maintenance and upkeep	0.4
Level 3	Maintenance costs and frequency are within the general range. It can be stably maintained with acceptable economic benefits	0.6
Level 2	It has relatively low maintenance costs and frequency. It spends low capital and resources on maintenance and upkeep	0.8
Level 1	Its maintenance costs and frequency are low. It utilizes resources very efficiently. The cost of consumables and personnel for its maintenance and upkeep work is almost negligible	1

Table 9.

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Rules for calculating the Maintenance Costs scores

Levels	Explicit description	$S_{c 2}$
Level 5	Its maintenance costs are high. The frequency of maintenance is very high. A lot of money and resources are required for regular overhauls, replacement of parts and maintenance work	0.2
Level 4	Maintenance costs are relatively high. A high frequency of maintenance is required. Relatively large amounts of money and resources are required for maintenance and upkeep	0.4
Level 3	Maintenance costs and frequency are within the general range. It can be stably maintained with acceptable economic benefits	0.6
Level 2	It has relatively low maintenance costs and frequency. It spends low capital and resources on maintenance and upkeep	0.8
Level 1	Its maintenance costs and frequency are low. It utilizes resources very efficiently. The cost of consumables and personnel for its maintenance and upkeep work is almost negligible	1

Levels	Explicit description	$S_{c 2}$
Level 5	Its maintenance costs are high. The frequency of maintenance is very high. A lot of money and resources are required for regular overhauls, replacement of parts and maintenance work	0.2
Level 4	Maintenance costs are relatively high. A high frequency of maintenance is required. Relatively large amounts of money and resources are required for maintenance and upkeep	0.4
Level 3	Maintenance costs and frequency are within the general range. It can be stably maintained with acceptable economic benefits	0.6
Level 2	It has relatively low maintenance costs and frequency. It spends low capital and resources on maintenance and upkeep	0.8
Level 1	Its maintenance costs and frequency are low. It utilizes resources very efficiently. The cost of consumables and personnel for its maintenance and upkeep work is almost negligible	1

Fig. 1.

The evaluation indexes tree

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2.2 The score matrix of evaluation indexes

2.2.1 Preparation process of the DM questionnaire

Multiple schemes are provided by the facilitator, including the 2Z-X(A) negative mechanism [38] (Fig. 2), 3Z(I) mechanism [39] (Fig. 3), enclosed planetary drive mechanism [40] (Fig. 4), oscillatory pin mechanism [12] (Fig. 5), cycloidal mechanism [41] (Fig. 6) and abnormal cycloidal mechanism [42] (Fig. 7). They are numbered in turn. A detailed description of them can be found in the original texts of the references, which are also distributed to the experts.

Fig. 2.

Multistage 2Z-X(A) negative mechanism

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Fig. 3.

Combined 3Z(I) mechanism. (a) Rotating central wheel, (b) fixed inner gear ring, (c) planetary wheels, (d) planetary wheels, (e) rotating central wheel.

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Enclosed planetary drive mechanism. (a1, a2, a3) Rotating central wheel, (b1, b2, b3) inner gear ring, (c1, c2, c3) planet carrier.

Fig. 4.

Enclosed planetary drive mechanism. (a₁, a₂, a₃) Rotating central wheel, (b₁, b₂, b₃) inner gear ring, (c₁, c₂, c₃) planet carrier.

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Fig. 5.

Combined oscillatory pin mechanism. (a) Housings for oscillatory pin, (b) eccentric bushings, (c) biasing wheel, (d) input shaft, (e) oscillatory pin wheel, (f) oscillatory pin, (g) needle bearing, (h) needle.

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Fig. 6.

Cycloidal mechanism

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Fig. 7.

Abnormal cycloidal mechanism. (a) Angular contact ball bearings, (b) swivel arm bearings, (c) cylindrical roller bearings, (d) input shaft, (e) input flange hub, (f) intermediate hub, (g) gear, (h) housing, (i) gear, (j) internal gear ring, (k) eccentric cam, (l) key, (m) cylinder pin, (n) end ring.

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The questionnaire is made to solicit the score ${(S_{j}^{i})}^{σ}$ ⁠, which is sorted according to Equation (8) (σ is the serial number of the experts):

\begin{array}{l} u_{j}^{i} = \frac{\sum_{σ = 1}^{10} {(S_{j}^{i})}^{σ}}{10} \end{array}

(8)

2.2.2 Survey process

After two rounds of survey, the score matrix of evaluation indexes is obtained according to Equation (1), as follows:

\begin{array}{l} U = (\begin{array}{c} 0.859 & 0.768 & 0.632 & 0.837 & 0.95 & 0.98 1 & 1 & 1 & 1 & 0.416 & 0.833 0.92 & 0.92 & 0.72 & 0.88 & 0.84 & 0.84 0.568 & 0.328 & 0.888 & 0.632 & 0.952 & 0.232 0.82 & 0.82 & 0.6 & 0.48 & 0.62 & 0.78 0.96 & 0.96 & 0.96 & 0.64 & 0.64 & 0.8 0.94 & 0.92 & 0.92 & 0.62 & 0.62 & 0.78 0.78 & 0.78 & 0.78 & 0.6 & 0.6 & 0.64 0.92 & 0.92 & 0.76 & 0.94 & 0.92 & 0.9 0.84 & 0.84 & 0.840 & 0.52 & 0.52 & 0.66 0.68 & 0.68 & 0.66 & 0.84 & 0.86 & 0.84 0.94 & 0.66 & 0.64 & 0.92 & 0.7 & 0.66 \end{array}) \end{array}

(9)

2.3 The weight and the comprehensive evaluation result

2.3.1 Establishment of a hierarchical model

As shown in Fig. 8, the hierarchical model of evaluation indexes of the yaw system is built.

Fig. 8.

The hierarchical model of evaluation indexes of the yaw gearbox

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2.3.2 Determination and consistency check of the judgment matrix

According to Section 1.3.2, the judgment matrixes of the criteria hierarchy R_c and the judgment matrixes of index factor hierarchy R_if1, R_if2, and R_if3 and their consistency check are shown in Equations (10–13). Obviously, all judgment matrixes are qualified by CR < 0.10:

\begin{array}{l} R_{c} = (\begin{array}{c} 1 & 7 & 9 1 / 7 & 1 & 3 1 / 9 & 1 / 3 & 1 \end{array}), C R = 0.0692 < 0.1. \end{array}

(10)

\begin{array}{l} R_{i f 1} = (\begin{array}{c} 1 & 1 / 3 & 5 & 7 3 & 1 & 7 & 9 1 / 5 & 1 / 7 & 1 & 3 1 / 7 & 1 / 9 & 1 / 3 & 1 \end{array}), C R = 0.0610 < 0.1. \end{array}

(11)

\begin{array}{l} R_{i f 2} = (\begin{array}{c} 1 & 3 & 5 & 7 1 / 3 & 1 & 3 & 5 1 / 5 & 1 / 3 & 1 & 3 1 / 7 & 1 / 5 & 1 / 3 & 1 \end{array}), C R = 0.0433 < 0.1. \end{array}

(12)

\begin{array}{l} R_{i f 3} = (\begin{array}{c} 1 & 3 & 5 & 1 / 3 1 / 3 & 1 & 3 & 5 1 / 5 & 1 / 3 & 1 & 1 / 7 3 & 5 & 7 & 1 \end{array}), C R = 0.0433 < 0.1. \end{array}

(13)

2.3.3 Determination of the weight

According to Equations (5) and (6), the weights of the criteria hierarchy and the index factor hierarchy are obtained, and their weight vectors WV_c, WV_if1, WV_if2 and WV_if3 is shown in Equations (14–17):

\begin{array}{l} W V_{c} = (W_{c 1}, W_{c 2}, W_{c 3}) = (0.7854, 0.1488, 0.0658) \end{array}

(14)

\begin{array}{l} W V_{i f 1} = (0.2903, 0.5824, 0.0850, 0.0424) \end{array}

(15)

\begin{array}{l} W V_{i f 2} = (0.5638, 0.2634, 0.1178, 0.0550) \end{array}

(16)

\begin{array}{l} W V_{i f 3} = (0.2634, 0.1178, 0.0550, 0.5638) \end{array}

(17)

Then, according to the description in Section 1.3.3, $C W = (W_{c 1} \cdot W V_{i f 1}, W_{c 1} \cdot W V_{i f 1}, W_{c 1} \cdot W V_{i f 1})$ the CW is shown in Equation (18):

\begin{array}{l} C W = & (0.2280, 0.4574, 0.0668, 0.0333, 0.0839, 0.0392, 0.0175, & 0.0082, 0.0173, 0.0078, 0.0036, 0.0371) \end{array}

(18)

2.3.4 Determination of the comprehensive evaluation result

According to Equation (7), the comprehensive evaluation score V is shown in Equation (19). The best is the 2Z-X(A) negative mechanism and the rest are the 3Z(I) mechanism, oscillatory pin mechanism, enclosed planetary drive mechanism, abnormal cycloidal mechanism and cycloidal mechanism in order.

\begin{array}{l} V = (0.9227, 0.8832, 0.8355, 0.8667, 0.6366, 0.8322) \end{array}

(19)

3 Discussion

3.1 The comprehensive evaluation result and the weight

A method combining the DM and the AHP is proposed to select the most suitable layout schemes for the yaw system of WTs. According to the result, it can be found that the 2Z-X(A) negative mechanism is the most suitable scheme among the six schemes provided by the facilitator. Although this scheme has been used in the yaw system, evidence that contains contrasting processes is usually not given when it is selected. This research provides a sufficient basis for the application of this scheme in practical engineering problems.

The 2Z-X(A) negative mechanism has better performance than the other schemes. It can be argued that the reason for this is higher scores in indexes with high weights, such as transmission efficiency and ratio range. Specifically, transmission efficiency is considered more fully in this scheme. Moreover, by connecting this scheme in series, the range of transmission ratios required by the yaw system can be satisfied. In addition, it can also achieve the top ranking in less weighted but still indispensable indexes, such as operating life and reliability and environmental adaptability. This scheme is a superior layout suitable for yaw systems.

The 3Z(I) mechanism occupies second place in the results, which is well deserved. It can be widely used in high-torque gearboxes precisely because of its relatively good performance in all aspects. Its comprehensive evaluation score is only 0.0395 lower than the first-place score. Therefore, the 3Z(I) mechanism can be considered to have enough potential to be applied to yaw systems. It is also mentioned in [39] that the 3Z(I) mechanism is often used in combination with other configuration schemes. Its advantages should be emphasized when combined due to its excellent performance in the ratio range, environmental adaptability and operating costs.

The enclosed planetary drive mechanism is widely used in the transmission systems of WTs. Although it is highly anticipated by us, it only occupies fourth place. The reason could be that it has a low score in transmission efficiency with a considerable weight. It is used in the transmission system of WTs with a relatively small ratio range. However, the ratio range of the yaw system is strongly required. Too much closed power will be produced in this scheme when the ratio is large, which will result in low transmission efficiency.

Unfortunately, the cycloidal mechanism achieved the worst results among the six schemes. One of the main reasons may be that it lost too many points in the ratio range. There are other indexes that get low scores as well, such as Operating Life and Reliability, Installation and Maintenance Ease and Noise Generated. This may be caused by the fact that it consists of many parts. Its structure leads to its inappropriateness for the yaw system.

In addition, the weight should also be noted. As shown in Fig. 9, >75% of the weight of the criteria hierarchy is occupied by the Main Technical Parameters. For the design of a yaw system and even the design of an entire WT, meeting the technical requirements is undoubtedly the priority. As shown in Fig. 10, the most significant CW is the ratio range. It is taken as the most important indicator because of the working characteristics of the yaw system. Operating life and reliability, environmental adaptability and public benefits are relatively key issues. They are worthy of further attention from designers in subsequent research. End-of-life Costs, Maintenance Costs and Noise Generated are the bottom three in the index factor hierarchy, but this does not mean that they can be ignored entirely. Being selected as the most important indicators using the DM means that they are valued more than those that are not selected. End-of-life costs and maintenance costs are essential research directions in the yaw system for sustainable development, the whole life cycle and green manufacturing. The noise generated has an essential impact on the relationship between products and humans behind industrial production.

Fig. 9.

The weight of the criteria hierarchy

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Fig. 10.

The comprehensive weight of index factor hierarchy

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3.2 Appropriateness of the AHP

The AHP is applied for determination of the weight and the comprehensive evaluation result in this study. It can effectively reduce the complexity of this part of the research. Although the scores of the schemes in the 12 evaluation indexes are obtained, the cumulative results of these scores could not be used as the comprehensive evaluation results because the relative importance of the 12 evaluation indexes is different according to the focus of the problem. It is more scientific to use the AHP to process these scores. In addition, the weights of the evaluation indexes can be flexibly modified according to the change in the focus of the issue of concern. Then, more reasonable evaluation results can be produced.

However, in cases involving a large number of factors requiring comparison, the AHP necessitates a significant number of pairwise comparisons. Furthermore, the traditional AHP process for identifying relationships among distant criteria is often perceived as intricate and challenging. Certain modifications from traditional AHP methods are implemented in this research. The criteria hierarchy is divided into three parts, and pairwise comparisons are conducted among index factors within the same part. This approach avoids the need to define relationships between distant criteria and reduces the number of comparisons required.

In recent years, other methods have been applied to solve MCDM problems, such as BWM (best worst method) [43], DIBR (defining interrelationships between ranked criteria) [44], FUCOM (full consistency method) [45] and LBWA (level based weight assessment) [46]. BWM exclusively prioritizes the primary advantage of the criteria, deeming the contrast between secondary advantages as unnecessary [47]. However, in this application, the secondary advantages of the criteria may still influence the final results. DIBR also addresses the challenge of defining relationships between remote criteria, yet calculating these relationships is more intricate [44]. The number of comparisons made using LBWA and FUCOM is lower compared to those using other methods, demonstrating their advantages particularly well in problems with numerous criteria [45, 46]. Due to the limited number of criteria used in this study, the variation in the number of comparisons produced by different methods is minimal. However, LBWA is ineffective at dealing with the subjectivity of expert judgments [46] and FUCOM integrates certain characteristics of the AHP and BWM, resulting in increased mathematical complexity. Based on the aforementioned comparison, selecting the AHP as the method for weight generation in this study is deemed appropriate given its four key advantages: (i) simplicity in calculation, (ii) comprehensive consideration, (iii) reduction in the number of pairwise comparisons following improvements and (iv) elimination of comparisons with remote criteria subsequent to improvements.

3.3 Robustness

The potentially biased opinions of a few experts are attenuated when applying the DM, while the opinions endorsed by the majority of experts are reiterated. Additionally, the weighted indicators are assigned greater importance. These factors contribute to generating reasonable outcomes. However, to ensure the robustness of the results, special attention needs to be given to the selection of experts. In this application, to ensure impartial questionnaire results, it is advisable to first avoid selecting experts associated with the provided schemes. Furthermore, in order to ensure that experts can provide reasonable opinions on the main technical parameters, it is recommended that the number of experts who have conducted structural research on yaw systems and are familiar with the requirements of yaw systems for main technical parameters be controlled at >70%. Additionally, to obtain ratings on overall characteristics, experts’ understanding of reliability, adaptability, maintenance and noise will also be considered in the invitation process. Their experience and past research will be carefully reviewed. Given that there are relatively few individuals with in-depth research knowledge of costs and benefits, selected experts are encouraged to obtain relevant research reports.

3.4 Advantages and limitations of the methodology

This is the first time that the selection of a yaw system layout has been considered as an MCDM problem for resolution. The proposed method possesses desirable characteristics, as follows. First, it demonstrates a wide range of applicability. The evaluation system generated by this method can be applicable to yaw systems of various specifications. Second, this method exhibits portability. It has the potential to be applied to layout selection issues of other systems on WTs, such as the pitch systems and the transmission systems, due to their similar requirements. Third, it demonstrates a comprehensive consideration. Considering more indicators than other studies in the similar fields allows the results to be examined from multiple perspectives. Fourth, it features simple calculation. It combines the advantages of two classic methods: DM and AHP. With minimal calculative resources utilized, evaluation results can be obtained.

However, even though it has been emphasized that this method is effective, some things could be improved. First, the DM includes a section for experts to respond to the questionnaire, which means that there is a possibility that expert subjectivity could influence the results. Although many experts in different fields are selected to participate in the DM as much as possible, the influence of subjectivity cannot be excluded. In future studies, more comprehensive principles for expert invitation should be established. For example, the number of invited experts should be as large as possible and the experts should have as much work experience as possible. This approach will make the research more demanding. Balancing the difficulty of research while mitigating subjective influences poses a significant challenge. Second, in this approach, the generation of weights depends on the facilitator’s discretion. Weights have a significant impact on decision results. Therefore, determining weights must consider the current specific requirements and main focuses of the issues at hand. Thus, the facilitator should possess ample relevant knowledge and excellent analytical skills. Inviting such a facilitator is challenging. In future work, to address this challenge, exploring the possibility of forming a facilitating team comprising multiple individuals with diverse strengths could be considered. This approach may reduce the individual demands on the facilitator to a certain extent, thereby lowering the complexity of the study.

4 Conclusion

A method combining the DM and the AHP is proposed in this study to analyse the schemes provided. The 12 most important evaluation indexes are selected from 18 technology indicators using the DM. The evaluation system is established based on the 12 evaluation indexes, which are divided into three categories, as shown in Fig. 1 and Tables 3–11. The scores of experts on six schemes are collected according to the evaluation system using the DM. Then, the score matrix of evaluation indexes is established, as shown in Equation (9). After the hierarchical model of evaluation indexes is established, as shown in Fig. 8, the CW is obtained using the AHP, as shown in Equation (18). The comprehensive evaluation score V is calculated as shown in Equation (19) and the comprehensive evaluation result is determined. The 2Z-X(A) negative mechanism is the best scheme among the six schemes. It is followed by the 3Z(I) mechanism, oscillatory pin mechanism, enclosed planetary drive mechanism, abnormal cycloidal mechanism and cycloidal mechanism.

Table 10.

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Rules for calculating the End-of-life Costs scores

Level	Explicit description	$S_{c 3}$
Level 5	End-of-life costs are very high due to several factors, including significant dismantling costs and possible regulatory compliance costs. The disposal of discarded parts of it has a serious impact on the environment	0.2
Level 4	End-of-life costs are high due to several factors, which may require great dismantling costs or the need to meet regulatory and safety standards. The disposal of discarded parts may have a significant environmental impact	0.4
Level 3	End-of-life costs are in the general range. Some dismantling costs may be required. The disposal of discarded parts has a moderate environmental impact	0.6
Level 2	End-of-life costs are relatively low due to several factors. The disposal of discarded parts has a low environmental impact	0.8
Level 1	End-of-life costs are low. The dismantled parts can be maximized for reuse. The disposal of discarded parts has a shallow impact on the environment	1

Level	Explicit description	$S_{c 3}$
Level 5	End-of-life costs are very high due to several factors, including significant dismantling costs and possible regulatory compliance costs. The disposal of discarded parts of it has a serious impact on the environment	0.2
Level 4	End-of-life costs are high due to several factors, which may require great dismantling costs or the need to meet regulatory and safety standards. The disposal of discarded parts may have a significant environmental impact	0.4
Level 3	End-of-life costs are in the general range. Some dismantling costs may be required. The disposal of discarded parts has a moderate environmental impact	0.6
Level 2	End-of-life costs are relatively low due to several factors. The disposal of discarded parts has a low environmental impact	0.8
Level 1	End-of-life costs are low. The dismantled parts can be maximized for reuse. The disposal of discarded parts has a shallow impact on the environment	1

Table 10.

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Rules for calculating the End-of-life Costs scores

Level	Explicit description	$S_{c 3}$
Level 5	End-of-life costs are very high due to several factors, including significant dismantling costs and possible regulatory compliance costs. The disposal of discarded parts of it has a serious impact on the environment	0.2
Level 4	End-of-life costs are high due to several factors, which may require great dismantling costs or the need to meet regulatory and safety standards. The disposal of discarded parts may have a significant environmental impact	0.4
Level 3	End-of-life costs are in the general range. Some dismantling costs may be required. The disposal of discarded parts has a moderate environmental impact	0.6
Level 2	End-of-life costs are relatively low due to several factors. The disposal of discarded parts has a low environmental impact	0.8
Level 1	End-of-life costs are low. The dismantled parts can be maximized for reuse. The disposal of discarded parts has a shallow impact on the environment	1

Level	Explicit description	$S_{c 3}$
Level 5	End-of-life costs are very high due to several factors, including significant dismantling costs and possible regulatory compliance costs. The disposal of discarded parts of it has a serious impact on the environment	0.2
Level 4	End-of-life costs are high due to several factors, which may require great dismantling costs or the need to meet regulatory and safety standards. The disposal of discarded parts may have a significant environmental impact	0.4
Level 3	End-of-life costs are in the general range. Some dismantling costs may be required. The disposal of discarded parts has a moderate environmental impact	0.6
Level 2	End-of-life costs are relatively low due to several factors. The disposal of discarded parts has a low environmental impact	0.8
Level 1	End-of-life costs are low. The dismantled parts can be maximized for reuse. The disposal of discarded parts has a shallow impact on the environment	1

Table 11.

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Rules for calculating the Public Benefits scores

Level	Explicit description	$S_{c 4}$
Level 3	Negative impacts on society and the environment are possibly caused. Consideration of long-term impacts in scheme selection is lacking	0.2
Level 2	It balances the relationship between performance and cost, and between the economy and the environment at an acceptable level. It is in line with the sustainability objectives of the new-energy facility	0.6
Level 1	It can actively promote social and environmental sustainability. A positive impact on the environment is caused. A specific contribution is made to socio-economic development	1

Level	Explicit description	$S_{c 4}$
Level 3	Negative impacts on society and the environment are possibly caused. Consideration of long-term impacts in scheme selection is lacking	0.2
Level 2	It balances the relationship between performance and cost, and between the economy and the environment at an acceptable level. It is in line with the sustainability objectives of the new-energy facility	0.6
Level 1	It can actively promote social and environmental sustainability. A positive impact on the environment is caused. A specific contribution is made to socio-economic development	1

Table 11.

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Rules for calculating the Public Benefits scores

Level	Explicit description	$S_{c 4}$
Level 3	Negative impacts on society and the environment are possibly caused. Consideration of long-term impacts in scheme selection is lacking	0.2
Level 2	It balances the relationship between performance and cost, and between the economy and the environment at an acceptable level. It is in line with the sustainability objectives of the new-energy facility	0.6
Level 1	It can actively promote social and environmental sustainability. A positive impact on the environment is caused. A specific contribution is made to socio-economic development	1

Level	Explicit description	$S_{c 4}$
Level 3	Negative impacts on society and the environment are possibly caused. Consideration of long-term impacts in scheme selection is lacking	0.2
Level 2	It balances the relationship between performance and cost, and between the economy and the environment at an acceptable level. It is in line with the sustainability objectives of the new-energy facility	0.6
Level 1	It can actively promote social and environmental sustainability. A positive impact on the environment is caused. A specific contribution is made to socio-economic development	1

This study provides a new method and specific process for designers to carry out the early design work of a yaw system. Despite alternatives such as BWM, DIBR, FUCOM and LBWA, the appropriateness of the improved AHP in this study is underscored by its simplicity, comprehensive approach, reduced comparisons and refined handling of remote criteria. To ensure robustness, detailed requirements for expert selection are established. These requirements include avoiding scheme-associated experts, ensuring structural research experience and considering expertise in key parameters and overall characteristics.

The proposed method offers broad applicability, portability to other systems of WTs, comprehensive consideration of multiple indicators and simplicity in calculation. The research gap of a layout determination method with a contrast process on the yaw system is filled. However, challenges remain in mitigating expert subjectivity and ensuring suitable weight determination. Future improvements may involve establishing comprehensive principles for expert selection and exploring team-based facilitation to reduce individual demands and complexity.

Author contributions

ShuTing Lin

Investigation-Lead, Methodology-Lead, Writing – original draft-Lead, Writing – review & editing-Lead

Lanxing Lu

Writing – original draft-Supporting, Writing – review & editing-Supporting

Peng Zhang

Investigation-Supporting, Methodology-Supporting

Hua Li

Funding acquisition-Lead, Supervision-Lead

Conflict of interest statement

The authors report there are no competing interests to declare.

Funding

This work was supported by the Sichuan University—Dazhou Municipal People’s Government Strategic Cooperation Special Funds Project of China (2022CDDZ-08).

Data availability

The data underlying this article will be shared on reasonable request to the corresponding author.

References

[1]

Qiao

Wen

et al. .

Research on wind power project investment risk evaluation based on fuzzy-gray clustering trigonometric function

Energy Rep

2022

1191

–

1199

Article Contents

A method for determining the layout of a yaw system based on the Delphi method and the analytic hierarchy process

Abstract

Introduction

1 Methodology

1.1 Establishment of an evaluation system of the yaw system

1.1.1 Preparation process of the DM questionnaire

1.1.2 Survey process

1.2 Establishment of the score matrix of evaluation indexes

1.2.1 Preparation process of the DM questionnaire

1.2.2 Survey process

1.3 Obtaining the weight and the comprehensive evaluation result

1.3.1 Establishment of a hierarchical model

1.3.2 Determination and consistency check of the judgment matrix

1.3.3 Determination of the weight

1.3.4 Determination of the comprehensive evaluation result

2 Application and result

2.1 The evaluation system of the yaw system

2.1.1 Preparation process of the DM questionnaire

2.1.2 Survey process

2.2 The score matrix of evaluation indexes

2.2.1 Preparation process of the DM questionnaire

2.2.2 Survey process

2.3 The weight and the comprehensive evaluation result

2.3.1 Establishment of a hierarchical model

2.3.2 Determination and consistency check of the judgment matrix

2.3.3 Determination of the weight

2.3.4 Determination of the comprehensive evaluation result

3 Discussion

3.1 The comprehensive evaluation result and the weight

3.2 Appropriateness of the AHP

3.3 Robustness

3.4 Advantages and limitations of the methodology

4 Conclusion

Author contributions

Conflict of interest statement

Funding

Data availability

References

Supplementary data

Citations

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