Numeric optimal sensor configuration solutions for wind turbine gearbox based on structure analysis
2017; Institution of Engineering and Technology; Volume: 11; Issue: 12 Linguagem: Inglês
10.1049/iet-rpg.2016.0157
ISSN1752-1424
AutoresGuilan Wang, Hongshan Zhao, ShuangWei Guo, Zengqiang Mi,
Tópico(s)Machine Fault Diagnosis Techniques
ResumoIET Renewable Power GenerationVolume 11, Issue 12 p. 1597-1602 Research ArticleFree Access Numeric optimal sensor configuration solutions for wind turbine gearbox based on structure analysis Wang GuiLan, Corresponding Author Wang GuiLan wang.guilan@163.com Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this authorZhao HongShan, Zhao HongShan Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this authorGuo ShuangWei, Guo ShuangWei Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this authorMi ZengQiang, Mi ZengQiang Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this author Wang GuiLan, Corresponding Author Wang GuiLan wang.guilan@163.com Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this authorZhao HongShan, Zhao HongShan Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this authorGuo ShuangWei, Guo ShuangWei Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this authorMi ZengQiang, Mi ZengQiang Electrical and Electronic Engineering, North China Electric Power University, Baoding, Hebei, People's Republic of ChinaSearch for more papers by this author First published: 01 September 2017 https://doi.org/10.1049/iet-rpg.2016.0157Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The wind turbine gearbox, an important component of wind turbines, has a high failure rate and maintenance cost; therefore, several vibration sensors are installed to execute effective condition monitoring, fault diagnosis, and prediction, for reducing the downtime caused by faults. The sensor positions should directly and accurately reflect the gearbox operating status and provide several signals to the condition monitoring system. This article studies a gearbox model and the gear tooth faults, and builds a gearbox gear vibration model involving these faults. Using structure analysis, sensor configuration solutions rendering all the tooth faults detectable and all the faults isolable are, respectively, obtained, based on the gear vibration model. The sensor configuration solutions of the wind turbine gearbox can guide wind turbine gearbox sensor installation in practice and support common wind turbine gearbox sensor configuration solutions in theory. 1 Introduction The wind turbine gearbox, an important component of a wind power generation system, has very high failure rates. To reduce system maintenance cost and improve reliable runtime, general solution is to install a real-time status monitoring, fault diagnosis, and fault forecast system, based on the vibration signals in a wind power plant. Various vibration signals can be obtained from the vibration sensors mounted on the gearbox. The sensor configuration and the determination of the position and number of sensor are to be studied in wind turbine system. The sensor position determines whether it can directly reflect the operational status of the gearbox and provide precise and accurate vibration signal, without missing vital information collection; however, considering the costs involved, the sensor numbers should be optimal and sufficient, so that vital information collection is not missed. Hence, the main task of the sensor configuration is to determine the optimal sensor position and number for best performance with limited cost. As per the ISO2373 standard recommendation, the determination of the sensor position should follow a principle that the measurement point has a maximum rigidity and the shortest transmission path, and the sensor mount should fully reflect the main operating states of the machine. A few typical sensor configuration solutions of the wind turbine gearbox are given in [1-3]; however, intensive research in the related fields is less. Sensor configuration based on the structural analysis method analyses the relationships between the structural model of the system and the parameters [4-8], and derives the optimal sensor configuration solution which can identify and isolate the maximum numbers of faults with a minimum number of sensors; several applications, exhibiting good performances, have been accomplished in various fields [9-12]. This paper is committed to obtain sensor configuration in wind turbine gearbox using structure analysis method, which provides effective signal in gear fault detection and isolation. In order to achieve the goal, first, we should obtain wind turbine gearbox fault model involving gear fault, and determine the parameter in model reflecting gear fault. As the internal structure of a wind turbine gearbox is highly complex, the establishment of a precise vibration model to simulate its dynamic behaviour is a considerable challenge in mechanics research. Wind turbine gearbox component models were built with different degrees of freedom; a planetary gear model involving tooth wedging and bearing clearance non-linearity was built in [13], but there were nine degrees of freedom, which is not easy to achieve in practice. The planetary model in [14] has three degrees of freedom, and has the acceleration variables in the horizontal and vertical direction, which are important vibration signal sources. They are always measured in practice, but rarely seen in the other models. Entire wind turbine and a transmission system models were established in [15, 16], respectively; however, there are no measuring parameters and they were not detailed enough for the gearbox. Therefore, the planetary model in [14] and the two-stage parallel gear model in [17] are adopted in this paper, and we combine them together, so a gearbox model containing one-stage planetary gear and two-stage parallel gear is accomplished. The gear is the component that is most likely to fail in a gearbox and >60% of gearbox failure is caused by the gear. The types of gear failure include tooth wear, pitting, broken teeth etc. and the reasons for gear failure are generally manufacturing errors, poor assembly, bad lubrication, overload, and operational errors. However, and all this cannot be observed in a vibration model. Some researchers mention that mesh stiffness, which always appears in a vibration model, can reflect gear failure [18-21]. The reduction in the mesh stiffness results in gear failures of different degrees; with the decrease in the mesh stiffness, the gear fault becomes more serious. Furthermore, the mesh stiffness is included in the model we build, so we can successfully fulfil the structural analysis for the wind turbine gearbox. Finally, we discuss about the sensor configuration solution obtained in this paper, and give an example of gear fault diagnosis application of wind turbine gearbox, which verifies our sensor configuration solution effectiveness. In summary, this paper studies a wind turbine gearbox vibration model, analyses the failure mechanism, and builds a wind turbine gearbox vibration model involving a tooth fault. Based on the vibration model, structure analysis is carried out and optimised sensor configuration solutions that can identify and isolate the maximum number of faults, with a minimum number of sensors, are achieved. The theoretical analysis for proving the result is also presented. The optimal sensor configuration solution obtained in this paper supports practical solutions in theory and provides considerably better solutions for engineers. 2 Wind turbine gearbox modelling involving gear tooth faults 2.1 Wind turbine gearbox internal structure A 1.5 MW wind turbine model is used in this paper, with a one-stage planetary gear and two-stage parallel gear gearbox as shown in Fig. 1. The main components of the gearbox are the planetary ring (r), planet carrier (c), three planetary gears (gp1, gp2, gp3), sun gear (gs), low-speed shaft (sh1), low-speed shaft gear (g1), medium-speed shaft (shm), medium-speed gear (g2, g3), high-speed shaft (shh), and the high-speed shaft gear (g4). Fig. 1Open in figure viewerPowerPoint Internal structure of the wind turbine gearbox A vibration model of the wind turbine gearbox including a one-stage planetary gear and two-stage parallel gears is built. At present, the existing model is not suitable for structure analysis. Some models have been built with an overall perspective [15, 16], but they have insufficient or no parameters that can be used for vibration analysis. Some models contain only planetary gear [13] and are too complex with too many parameters not fit to practical application. We have selected the planetary gear model in [14] because it has sufficient parameters and four degrees of freedom (not too big, nor not too small, but the right size), and also has two important parameters for vibration analysis (planetary gear ring vibration accelerations in the horizontal and vertical directions), which always measured in a project, and they are not present in other models. For the two-stage parallel gear model, we have selected model in [17], for it has the same degrees of freedom with [14], so can be easily combined with the planetary gear model in [14]. According to the d'Alembert principle, a wind turbine gearbox vibration model including one-stage planetary gear and two-stage parallel gears is established. The model includes 20 planetary gear equations from [14] with 20 variables, 3 of which are the measurement points: the carrier rotating acceleration, the ring horizontal vibration acceleration, and the vertical vibration acceleration. In addition, there are 24 equations for the two-stage parallel gears derived from [17], containing 24 variables, 9 of which are the measurement points: the radial vibration acceleration, the longitudinal vibration accelerations, and the axial vibration accelerations of gears g1, g2, and g4. All these12 measurement points are mostly popular positions for sensors installed on the gearbox. The planetary gear portion has four degrees of freedom: the X-gear radial, Y-gear longitudinal, Z-axial gear, and the gear axial rotation; in addition to the same four degrees of freedom as that of the planetary gear, another two degrees of freedom are also contained in the parallel gear portion, the gear radial rotation acceleration, and the gear longitudinal rotation acceleration. 2.2 Wind turbine gearbox vibration model involving tooth faults Wind turbine gearbox failure mainly occurs in the gears and shafts, only gear fault is considered in this model. Related research demonstrate that when tooth faults such as tooth cracking, tooth flaking, or tooth broken occur, the tooth mesh stiffness decreases significantly [18-21]. More severely the fault is, more sharp the mesh stiffness will decrease. Therefore, the tooth mesh stiffness can be used as a tooth fault indicator. From [18], the tooth mesh stiffness can be computed by the following formula: (1) From (1), we observe that a decrease in the tooth mesh stiffness ks may be caused by a reduction in the tooth rigidity of k1 or k2, or both; hence, a reduction in the rigidity can indicate a fault. From Fig. 1, the mesh stiffness of the gear pairs krp, ksp, k12, and k34 (p = 1, 2, 3) can be obtained, in which nine rigidities are involved; the corresponding kr, ks, kp1, kp2, kp3, k1, k2, k3, k4 gear faults are shown in Table 1. Table 1. Fault definition Fault names Fault types Indicating parameter fr ring gear tooth fault kr fs sun gear tooth fault ks fp1 planet gear, gp1, tooth fault kp1 fp2 planet gear, gp2, tooth fault kp2 fp3 planet gear, gp3, tooth fault kp3 f1 gear, g1, tooth fault k1 f2 gear, g2, tooth fault k2 f3 gear, g3, tooth fault k3 f4 gear, g4, tooth fault k4 Changing km(kr, ks, kp1, kp2, kp3, k1, k2, k3, k4) in the vibration model to (1−fm)km implies that if no faults occur, then, the value of fm is zero; else, it is non-zero. fm is then the fault parameter representing a fault. Replacing all the mesh stiffness, krp, ksp, k12, and k34 (p = 1, 2, 3), and the nine rigidity, the following 44 gearbox gear vibration equations involving tooth faults are obtained (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) In addition, the values of in the equations are depicted in (55)–(61) in the Appendix. 2.3 Simplified fault-involved wind turbine gearbox vibration model In the fault-involved wind turbine gearbox vibration model, a fault may appear repeatedly in several equations. To simplify the later analysis, a fault should only appear once in one equation. This can be accomplished through the following steps: Regard every fault, such as fm, as a variable and denoted as variable xfm; Conjunct the fault and the variable through an equation, as shown in (46)–(54). Thus, every fault appears only once in one equation; the equation is then called a fault-influenced equation, denoted by efm, for example, efr = e45. (46) (47) (48) (49) (50) (51) (52) (53) (54) Replacing the fm in (2)–(45) by xfm, the fault-involved wind turbine gearbox vibration model is achieved, including the equation set E = {e1,e2,…,e53}, the variable set X = {x1,x2,…,x44,xfr,xfs,…,xf4}, and the fault set F = {fr,fs,…,f4}. 2.4 Wind turbine gearbox structural model Finally, we construct the structural model (denoted by M) of the fault involved wind turbine gearbox vibration model, in which the row vectors correspond to the equations in E and the column vectors correspond to the variables in X. If an equation x include a variable y, then the value of the cell (x, y) is 1, otherwise it is 0, as shown in Fig. 2. The faults included in the equations are also displayed in the F region of Fig. 2. Fig. 2Open in figure viewerPowerPoint Structural model, M, of the wind gearbox vibration model involving faults 3 Wind turbine gearbox sensor configuration rendering all the faults detectable 3.1 Dulmage–Mendelsohn decomposition and Hasse diagram of the partially ordered blocks Note the (E, X) of M as M0, and D–M decomposition is performed on M0. Through transformation M0 becomes into a just-determined model, including 14 strongly connected components, b1, b2, …, and b14, as depicted in Fig. 3. The partial order Hasse diagram is shown in Fig. 4 and relationships between the faults and blocks are also displayed. Fig. 3Open in figure viewerPowerPoint D–M decomposition structure model matrix Fig. 4Open in figure viewerPowerPoint Hasse diagram of the partially ordered blocks 3.2 Equivalent fault class When the faults in higher-order blocks are detectable with additional sensors, the faults in the lower-order blocks can also be detected [22]. For example, from Fig. 4, fr belongs to block b6, and b6 < b3, b3 < b1, b3 < b2; hence, when variable x3 in b3, variable x19 in b1 or variable x20 in b2 is measured, fr would all become detectable. Similarly, for the blocks including faults fs, fp1, fp2, and fp3, their order is lower than b3, b2 and b1, so if x3, x19, or x20 is measured, they would all be detectable. Hence, when any variable in {x3, x19, x20} is measured, the faults in {fr,fs,fp1,fp2,fp3} would all be detectable. This fault set is called an equivalence class denoted by[fr],[fs],[fp1],[fp2], or [fp3], and the variable set can be denoted by D([fr]), D([fs]), D([fp1]), D([fp2]) or D([fp3]). From Fig. 4, we can also see that there are totally three equivalence classes in the gearbox model, [fr], [f1], and [f3], and the corresponding variable sets are: (i) D([fr]) = D([fs]) = D([fp1]) = D([fp2]) = D([fp3]) = {x3,x19,x20} (ii) D([f1]) = D([f2]) = {x21,x22,x23,x27,x28,x29} (iii) D([f3]) = D([f4]) = {x39,x40,x41}. Moreover, the three equivalence classes, [fr], [f1], and [f3], are at the same level; hence, the maximal fault class of the model is {[fr],[f1],[f3]}. So, to render all the faults detectable, only a minimum sensor hitting set of D([fr]), D([f1]), and D([f3]) is needed to be installed in the gearbox and the number of sensors is the least. The sensor configuration procedure for detecting all the faults can be achieved through the following function, Ɗ: Detectability Function Ɗ = Detectability(M,F,P); Mis the structure model, F the fault set expected to be detectable, and P the measure point variable. Compute the block and fault class orders using M; Fm = set of maximal fault classes among [f] s.t. D([f]) ≠ Ø; Ɗ = {D([f])ǀ[f]∈Fm}; 3.3 Numeric optimal sensor configuration solution rendering all the faults detectable From Section 3.2, we know that if the minimum sensor hitting set D([fr]), D([f1]), and D([f3]), installed on the gearbox, all the tooth faults will be detectable. By computation with the function Detectability, the minimal fitting sets are Sd = {{λ1,λ2,λ3}|λ1∈{x3,x19,x20}, λ2∈{x21,x22,x23,x27,x28,x29}, λ3∈{x39,x40,x41}}, implying that at least three sensors are needed to render all tooth faults detectable, and a total of 54 selectable solutions are available for their positioning. With adequate sensors, all the faults can be detected; however, if only a part of the fault set F is expected to be detectable, we can just modify the parameter F in the function Ɗ. For example, if only fault fr is concerned, we can only alter F to {fr}, and the result is {{λ1}|λ1∈{x3,x19,x20}}, implying that only one sensor is needed to render fr detectable. 4 Numeric optimal wind turbine gearbox sensor configuration rendering all the faults isolable 4.1 Sensor configuration for isolating all the faults using a minimum number of sensors The problem of achieving maximum fault isolation for the set of single faults F can be divided into |F| subproblems, one for each fault as follows. For each fault fj∈F, find all the measurements that render the maximum possible number of faults fi∈F\{fj} isolable from fj. Then, combining the results of all the subproblems, the solution can solve the isolation problem. Each subproblem can be formulated into a detectable problem, as demonstrated in the following. Assume that M is a model, including sensors rendering all the faults are detectable, and MS represents a set of equations describing an additional sensor set. Given the sensor set S, a fault fi is isolable from fj in the model M∪MS, if . Thus, faults in the exactly determined part of M∪MS are structurally detectable; hence, they are isolable with fj. The procedure can be completed by the following function IsolabilitySubProblem. Ɗ = IsolabilitySubProblem(M,F,P,f); M, F, and P see function Detectability, f is the fault to isolate {M0 = just-determined part of M\{ef}; F0 = the set of faults, F, included in M0; Ɗ = Detectability(M0,F0,P);} All the fault isolations are handled by the function Isolability as follows: function Ɗ = Isolability(M,F,P) {Ɗ = Ø; for fi∈F {F′ = F\{fi}; Ɗ = Ɗ∪IsolabilitySubProblem(M,F′,P,fi);}} Finally, a minimal sensor set that maximises the isolability can be determined by applying a minimal hitting set to the sets on the output Ɗ. 4.2 Numeric optimal sensor configuration solutions for a wind turbine gearbox As mentioned in Section 3.3, if any measurement set in Sd = {{λ1,λ2,λ3}|λ1∈{x3,x19,x20}, λ2∈{x21,x22, x23,x27,x28,x29}, λ3∈{x39,x40,x41}} is added to the gearbox, all the tooth faults will be detectable. Assume that the sensor set S = {S3, S21, S39} is added to the measurement variables {x3, x21, x39}, rendering all the tooth faults are detectable. Accordingly, equation set MS: x3 = S3, x21 = S21, x39 = S39, should be merged into M. Then, consider a subproblem associated with the fault fr. The model M′ = M∪MS\efr is in the just-determined part, and by adding a minimal sensor set {x19, x20}, F\fr will all be detectable, i.e. F\fr of fr is isolable. Then, the other faults, fs, fp1, …,f4, respectively, are rendered isolable by the minimal sensor set, for fs is {x19,x20}, fp1 is {x19,x20}, fp2 is {x19,x20}, fp3 is {x19,x20}, f1 is {x22,x23,x27,x28,x29}, f2 is {x22,x23,x27,x28,x29}, f3 is {x40,x41}, and f4 is {x40,x41}. Hence, we know that, when {x3,x21,x39} is measured to guarantee all the faults are detectable, the minimal hitting set of all the isolable faults is {{λ1,λ2,λ3}|λ1∈{x19,x20},λ2∈{x22,x23,x27,x28,x29},λ3∈{x40,x41}}. Similarly, every other sensor set in Sd is analysed and the minimal hitting sets of the results of the function Isolability are obtained; Si = {{λ1,λ2,λ3,λ4,λ5,λ6}|{λ1,λ2}∈{x3,x19,x20},{λ3,λ4}∈{x21,x22,x23,x27,x28, x29}, {λ5,λ6∈{x39,x40,x41}}, a total of 135 solutions, which are the final sensor configuration solutions with a minimal number of six sensors, rendering all the faults isolable. 5 Analysis 5.1 Discussion about the wind turbine gearbox sensor configuration solutions Through structure analysis on the gearbox model involving faults, the minimal-number sensor configuration solutions rendering all the faults detectable are obtained: Sd = {{λ1,λ2,λ3}|λ1∈{x3,x19,x20},λ2∈{x21,x22,x23,x27,x28,x29},λ3∈{x39,x40,x41}}, and sensor configuration rendering all faults isolable are Si = {{λ1,λ2,λ3,λ4,λ5,λ6}|{λ1,λ2}∈{x3,x19,x20},{λ3,λ4}∈{x21,x22,x23,x27,x28,x29}, {λ5,λ6∈{x39,x40,x41}}. From the results, we can see that all the 12 measurements are divided into three parts: x3, x19, and x20, situated in planetary gear; x21, x22, x23, x27, x28, and x29, situated in meshing gears g1 (connected to the low-speed shaft) and g2 (connected to the middle-speed shaft); x39, x40, and x41, situated in gear g4 (connected to the high-speed shaft). To make all the faults detectable, three sensors, each on one part, are needed; whereas, to be detectable and isolable, six sensors, two on every part, are needed; this is consistent with the solutions used in practice. Hence, this paper provides the theoretical evidence and can guide direct application. At the same time, the results are all determined by the structure model, which reflects the internal relationship between the variables (the measuring points, in particular) and the equations. From Figs. 3 and 4, we can seen that, the just-determined part includes 14 blocks: the 12 measurement variables are scattered in five blocks: x19 lies in b1, denoted as x19→b1; similarly, x20 lies in b2 similarly, denoted as x20→b2; and we can also obtain that: x3→b3, {x21,x22,x23,x27,x28,x29}→b4, {x39,x40,x41}→b5. Also, only three parts b1, b2, and b3 are strongly connected blocks, that is, they have no intersection with other blocks and are independent parts. Similarly, blocks b4 and b5 are also independent, and have no intersection with other blocks. Then there are three independent parts altogether. So, if any variable is measured by adding a sensor, the corresponding blocks will become into the over-determined part, and their faults become detectable; hence, the measurement variables in every independent part fulfilling the same role in the fault determination, they can be alternatives for each other. This is the reason why the measurement variables are divided into three parts, and it provides a theoretical explanation for common sensor configuration solutions. In this paper, all the faults are detectable and isolable because each block is only related to one fault (as seen in Fig. 4). If one block is related to two or more faults, then these faults can be detectable, but may not be isolable. Sometimes, only part of the faults is expected to be detectable or isolable, this can be accomplished by altering F in the function, which only including the faults interesting. As the sensor configuration is determined by the structure model, the most important and difficult step in the structure analysis procedure is the modelling stage, which mainly decides the success. Two points need special attention: first, the model built should include several measuring point variables to obtain more possible solutions for selection, as far as possible to close the actual application; additionally, variables reflecting the faults are needed in the model, which should include common faults of interest. 5.2 Two wind turbine gear fault diagnosis application Detection and isolation all gear faults in wind turbine gearbox is difficult, common fault diagnosis is aimed to one gear fault in wind turbine gearbox. Next, two examples of gear fault diagnosis are shown to demonstrate the effectiveness of our sensor configuration solution. To detect gearbox fault early, Chen et al. [23] propose a method for an effective fault diagnosis by using improved ensemble empirical mode decomposition and Hilbert square demodulation. The method was verified numerically by implementing the scheme on the vibration signals measured form bearing and gear test rigs. The experimental results demonstrate the merit of the proposed method in gearbox fault diagnosis. In the gear experimental evaluation, two acceleration sensors were mounted on the top of the gearbox, and their average value is used to detect gear crack fault in gear g2. The position where the acceleration sensors are placed is accord with this paper's analysis. In this paper, senor signal at that place is measured by x28, to identify fault of gear g2, only one variable in {x21, x22, x23, x27, x28, x29} is measured. Chen et al. [23] used x28 to detect gear crack of g2 successfully, that is accord with one of our solution, and shows that our solution is effective. In [24], to detect gear g4 pitting fault, four sensors are installed on the gearbox. With no modal analysis to determine the best sensor location, they glue four acceleration transducers on the casing of the gearbox from low- to high-speed stages, two sensors (no. 1 and no. 2) in the front of the gearbox and two (no. 3 and no. 4) in the rear of the gearbox. Vibration signals from all the four acceleration transducers are analysed using empirical mode decomposition (EMD). The analysis results show that the sensor of no. 4 represents big fault feature, no. 1 has no fault feature, and no. 3 has few fault feature. Teng et al. [24] give the reason that the sensor of no. 1 is installed on the ribbed slab of the casing where it is not overly sensitive to the excitation of the high-speed stage. This view is consistent with our research. According to the above structure analysis method, the location of sensor no. 1 is to measure variable x19 or x20, it is fit to detect fault of carrier and planetary gear, but not suitable to detect fault of high-speed shaft gear. While the sensor of no. 4 (located above the high-speed shaft gear and measuring variable x39, x40, or x41) is recommended to detect high-speed shaft gear by the structural analysis, and good effectiveness is shown in [24]. The sensor of no. 3 shows less fault feature, the reason is that, its location is close to the sensor of no. 4, but not right on the high-speed shaft gear, so it captures less fault feature. 6 Conclusion This paper studies various models for the wind turbine gearbox and gear tooth faults, and builds a vibration model involving the tooth faults of a wind turbine gearbox. Using structure analysis method, based on the vibration model, optimal sensor configuration solutions are achieved to render all faults detectable of isolable with a minimum number of sensors. The solutions are consistent with typical sensor configuration solutions and give theoretical support. The structural analysis method can also be used to deal with sensor configuration solution rendering one or some fault detection or isolation. This sensor configuration procedure can also be applied to sensor configuration of other machinery fields. 7 Acknowledgments This paper is supported by the National Key Technology Research and Development Program (no. 2015BAA06B03), the National Natural Science Foundation (no. 51277074) and North Electric Power University of Central Universities Fundamental Research (no. 13MS103). 9 Appendix (55) (56) (57) (58) (59) (60) (61) 8 References 1Sheng, S., Veers, P.: ' Wind turbine drive train condition monitoring-an overview'. 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