Scien Directvibration base fault dianogis of spur bevel gear box using fuzzy technique

Available online at www.sciencedirect.com Expert Systems with Applications Expert Systems with Applications 36 (2009) 3119–3135 www.elsevier.com/locate/eswa Vibration-based fault diagnosis of spur bevel gear box using fuzzy technique N Saravanan *, S Cholairajan, K.I Ramachandran Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu 641105, India Abstract To determine the condition of an inaccessible gear in an operating machine the vibration signal of the machine can be continuously monitored by placing a sensor close to the source of the vibrations These signals can be further processed to extract the features and identify the status of the machine The vibration signal acquired from the operating machine has been used to effectively diagnose the condition of inaccessible moving components inside the machine Suitable sensors are kept at various locations to pick up the signals produced by machinery and these signals are very meaningful in condition diagnosis surveillance To determine the important characteristics and to unravel the significance of these signals, further analysis or processing is required This paper presents the use of decision tree for selecting best statistical features that will discriminate the fault conditions of the gear box from the signals extracted These features are extracted from vibration signals A rule set is formed from the extracted features and fed to a fuzzy classifier The rule set necessary for building the fuzzy classifier is obtained largely by intuition and domain knowledge This paper also presents the usage of decision tree to generate the rules automatically from the feature set The vibration signal from a piezo-electric transducer is captured for the following conditions – good bevel gear, bevel gear with tooth breakage (GTB), bevel gear with crack at root of the tooth (GTC), and bevel gear with face wear of the teeth (TFW) for various loading and lubrication conditions The statistical features were extracted and good features that discriminate the different fault conditions of the gearbox were selected using decision tree The rule set for fuzzy classifier is obtained by once using the decision tree again A fuzzy classifier is built and tested with representative data The results are found to be encouraging Ó 2008 Elsevier Ltd All rights reserved Keywords: Feature selection; Statistical features; Decision tree; Gear box; Fuzzy; Fault detection Introduction A faulty gear system could result in serious damage if defects occur to one of the gears during operation condition Early detection of the defects, therefore, is crucial to prevent the system from malfunction that could cause damage or entire system halt Diagnosing a gear system by examining the vibration signals is the most commonly used method for detecting gear failures The conventional methods for processing measured data contain the frequency * Corresponding author Tel.: +91 4222656422; fax: +91 4222656274 E-mail addresses: n_saravanan@ettimadai.amrita.edu, nsaro_2000@ yahoo.com (N Saravanan) 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd All rights reserved doi:10.1016/j.eswa.2008.01.010 domain technique, time domain technique, and time– frequency domain technique These methods have been widely employed to detect gear failures The use of vibration analysis for gear fault diagnosis and monitoring has been widely investigated and its application in industry is well established (Cameron & Stuckey, 1994; Gadd & Mitchell, 1984; Leblanc, Dube, & Devereux, 1990) This is particularly reflected in the aviation industry where the helicopter engine, drive trains and rotor systems are fitted with vibration sensors for component health monitoring The raw vibration signal in any mode from a single point on a machine is not a good indicator of the health or condition of a machine Vibration is a vectorial parameter with three dimensions and requires to be measured at several carefully selected points 3120 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Vibration Signals Feature Selection Using J 48 Algorithm Rule Generation Test data set Modeling Fuzzy system Fuzzy inference engine Fuzzy output Bevel Gear Box Machine Condition Diagnosis Sensor Fig Fault simulator setup Fig Flowchart for bevel gear box health diagnosis Vibration analysis can be carried out using Fourier transform techniques like Fourier series expansion (FSE), Fourier integral transform (FIT) and discrete Fourier transform (DFT) (Collacott, xxxx) After the development of large-scale integration (LSI) and the associated microprocessor technology, fast Fourier transform (FFT) analyzers became cost effective for general applications The raw signatures acquired through a vibration sensor needed further processing and classification of the data for any meaningful surveillance of the condition of the system being monitored Artificial neural network (ANN), support vector machine (SVM) and Fuzzy classifier are widely used as classification tool and reported in literature (Burgess, 1998; Jack & Nandi, 2000a; Nandi, 2000; Samanta & AlBaulshi, 2003; Samanta, Al-Baulshi, & Al-Araimi, 2003; Shi et al., 1988) Among them, ANN has limitations on generalization of the results in models that can over fit the data (Samanta et al., 2003) SVM has high classification accuracy and good generalization capabilities for crisp data (Burgess, 1998; Jack & Nandi, 2000a; Shi et al., 1988) In the problem at hand, the nature of the fault itself is fuzzy in nature Fuzzy classifier models the physical problem under study more closely The flow chart of the fault diagnostic system is shown in Fig 1.1 Different phases of present work The signals obtained are processed further for machine condition diagnosis as explained in the flow chart Fig Experimental studies The fault simulator with sensor is shown in Fig and the pinion and gear shown in Fig A variable speed DC motor (0.5 hp) with speed up to 3000 rpm is the basic Electromagnetic spring loaded disc brake Pinion Wheel Gear Wheel Fig Inner view of the bevel gear box drive A short shaft of 30 mm diameter is attached to the shaft of the motor through a flexible coupling; this is to minimize effects of misalignment and transmission of vibration from the motor The shaft is supported at its ends through two roller bearings From this shaft the drive is transmitted to the bevel gear box by means of a belt drive The gear box is of dimension 150 mm  170 mm  120 mm and the full lubrication level is 110 mm and half lubrication level is 60 mm SAE 40 oil was used as a lubricant An electromagnetic spring-loaded disc brake was used to load the gear wheel A torque level of N-m was applied at the full-load condition The various defects are created in the pinion wheels and the mating gear wheel is not disturbed With the sensor mounted on top of the gear box vibrations signals are obtained for various conditions The selected area on the top of the gearbox for mounting the sensor is made flat and smooth to ensure effective coupling between the sensor and the gearbox The sensor used is a piezoelectric accelerometer (Dytran model) which is mounted on the flat N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 surface using direct adhesive mounting technique The accelerometer is connected to the signal-conditioning unit (DACTRAN FFT analyzer), where the signal goes through the charge amplifier and an analogue-to-digital converter (ADC) The vibration signal in digital form is fed to the computer through a USB port The software RT Pro-series that accompanies the signal-conditioning unit is used for Table Details of faults under investigation Gears Fault description Dimension (mm) G1 G2 G3 G4 Good Gear tooth breakage (GTB) Gear with crack at root (GTC) Gear with face wear – 0.8  0.5 0.5 Table Gear wheel and pinion details Parameters Gear wheel Pinion wheel No of teeth Module Normal pressure angle (°) Shaft angle (°) Top clearance (mm) Addendum (mm) Whole depth (mm) Chordal tooth thickness (mm) Chordal tooth height (mm) Material 35 2.5 20 90 0.5 2.5 5.5 3.93À0.150 2.53 EN8 25 2.5 20 90 0.5 2.5 5.5 3.92À0.110 2.55 EN8 a 3121 recording the signals directly in the computer’s secondary memory The signal is then read from the memory and processed to extract different features 2.1 Experimental procedure In the present study, four pinion wheels whose details are as mentioned in Table were used One was a new wheel and was assumed to be free from defects In the other three pinion wheels, defects were created using electron discharge machine (EDM) in order to keep the size of the defect under control The details of the various defects are depicted in Table and its views are shown in Fig The size of the defects is in-line with work reported in literature (Gadd & Mitchell, 1984) The vibration signal from the piezoelectric pickup mounted on the test bearing was taken, after allowing initial running of the bearing for sometime The sampling frequency was 12,000 Hz and sample length was 8192 for all speeds and all conditions The sample length was chosen arbitrarily, however, the following points were considered Statistical measures are more meaningful, when the number of samples is more On the other hand, as the number of samples increases the computation time increases To strike a balance, sample length of around 10000 was chosen In some feature extraction techniques, which will be used with the same data, the number of samples is to be 2n The nearest 2n–10,000 is 8192 and hence, it was taken as sample length Many trials were taken at the set speed and vibration signal was stored b c Fig (a)View of good pinion wheel (b) View of pinion wheel with face wear (GFW) (c) View of pinion wheel with tooth breakage (GTB) N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 -0.2 6000 -0.4 -0.4 8000 0 2000 4000 6000 -0.2 8000 -0.2 4000 6000 -0.2 2000 d 2000 4000 6000 Amplitude -0.1 -0.1 8000 Sample No GTC-HalfLub-Unload 2000 4000 6000 -0.1 4000 6000 -0.1 8000 2000 4000 6000 -0.1 2000 4000 Sample No 6000 8000 -0.1 2000 4000 6000 2000 8000 Sample No 4000 6000 8000 2000 4000 6000 -0.2 -0.4 8000 2000 TFW-Dry-Unload 4000 6000 -0.2 -0.2 6000 -0.2 4000 6000 Sample 6000 8000 -0.2 2000 4000 6000 8000 Sample TFW-FullLub-FullLoad 2000 4000 0.2 8000 0.2 2000 Sample TFW-HalfLub-FullLoad 4000 8000 0.2 8000 0.2 2000 6000 TFW-Dry-FullLoad -0.2 2000 4000 Sample No Sample TFW-FullLub-Unload 0 Sample No GTB-FullLub-FullLoad 0.2 Amplitude Amplitude 0 -0.2 -0.4 8000 -0.2 8000 0.1 8000 0.2 Sample No GTC-FullLub-FullLoad 0.1 6000 6000 0.2 Sample TFW-HalfLub-Unload Sample No GTC-FullLub-Unload 4000 0 Amplitude Amplitude 2000 4000 Sample No GTB-HalfLub-FullLoad 0.2 8000 0.1 2000 Sample No GTC-HalfLub-FullLoad 0.1 -0.4 2000 Sample No GTC-Dry-fullLoad 0 Sample No GTB-FullLub-Unload 8000 0.1 Amplitude Amplitude 6000 -0.2 -0.4 8000 -0.2 Sample No GTC-Dry-Unload Amplitude 4000 6000 -0.4 8000 4000 0.2 8000 0.2 Sample No c 0.1 6000 Amplitude Amplitude Amplitude 2000 4000 2000 0.2 Sample No GTB-HalfLub-Unload Sample No Good-Full-FullLoad 0.2 2000 8000 Sample No Good-FullLub-Unload Amplitude 6000 0.2 -0.2 -0.4 4000 Sample No Good-HalfLub-FullLoad 0.2 Amplitude Amplitude Sample No Good-HalfLub-Unload 2000 Amplitude 4000 -0.2 Amplitude 2000 -0.2 Amplitude 0 GTB-Dry-FullLoad Amplitude GTB-Dry-Unload 0.2 Amplitude 0.2 Amplitude Amplitude 0.2 -0.4 b Good-Dry-FullLoad Amplitude Good-Dry-Unload Amplitude a Amplitude 3122 8000 0.2 -0.2 2000 4000 6000 8000 Sample Fig (a) Vibration signal for good pinion wheel under different lubrication and loading conditions (b) Vibration signal for pinion wheel with teeth breakage under different lubrication and loading conditions (c) Vibration signal for pinion wheel with crack at root under different lubrication and loading conditions (d) Vibration signals for pinion wheel with teeth face wear under different lubrication and loading conditions in the data file The raw vibration signals acquired for various experimental conditions form the gearbox using FFT are shown in Fig conditions and fed as an input to J 48 algorithm for selecting the best features which classify the different fault conditions Feature extraction Descriptive statistics Statistical analysis of vibration signals yields different primary and secondary Parameters Research work reported (James Li & Wu, 1989) use these in combinations to elicit information regarding bearing faults Such procedures use allied logic often based on physical Considerations A fairly wide set of these parameters is selected as a basis for our study, as detailed below a Mean b Standard error c Median d Standard deviation e Sample variance f Kurtosis g Skewness h Range i Minimum j Maximum k Sum All the above mentioned statistical features were extracted for the vibration signals obtained for various The statistical features are explained below 4.1 Standard deviation This is a measure of the effective energy or power content of the vibration signal and clearly indicates deterioration in the bearing condition The following formula was used for computation of standard deviation sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P 2ffi n x2 À ð xÞ : Standard deviation ¼ nðn À 1Þ N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 3123 4.2 Skewness 4.8 Maximum value Skewness characterizes the degree of asymmetry of a distribution around its mean The below shown expression was used to calculate the skewness, where ‘n’ is the sample size and ‘s’ is the sample standard deviation X xi À x3 n : Skewness ¼ ðn À 1Þðn À 2Þ s It refers to the maximum signal point value in a given signal 4.9 Sum It is the sum of all signal point values in a given signal Using J 48 algorithm in the present work 4.3 Kurtosis Kurtosis indicates the flatness or the spikiness of the signal Its value is very low for good bevel gearbox and high for faulty gearbox due to the spiky nature of the signal ( Kurtosis ¼ ) X xi À x4 nðn þ 1Þ ðn À 1Þðn À 2Þðn À 3Þ s À 3ðn À 1Þ : ðn À 2Þðn À 3Þ where ‘s’ is the sample standard deviation 4.4 Standard error Standard error is a measure of the amount of error in the prediction of y for an individual x in the regression, where x and y are the sample means and ‘n’ is the sample size Standard error of the predicted vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " #ffi u P X u   ½ ðx À x Þðy À y Þ Š ðy À y Þ À : y¼t P ðn À 2Þ ðx À xÞ 4.5 Sample variance It is variance of the signal points and the following formula was used for computation of standard variance Sample variance ¼ n P P x2 À ð xÞ : nðn À 1Þ 4.6 Range It refers to the difference in maximum and minimum signal point values for a given signal A standard tree induced with c5.0 (or possibly ID3 or c4.5) consists of a number of branches, one root, a number of nodes and a number of leaves One branch is a chain of nodes from root to a leaf; and each node involves one attribute The occurrence of an attribute in a tree provides the information about the importance of the associated attribute as explained by Peng, Flach, Brazdil, and Soares (2002) A Decision Tree is a tree based knowledge representation methodology used to represent classification rules J48 algorithm (A WEKA implementation of c4.5 Algorithm) is a widely used one to construct Decision Trees as explained by Sugumaran, Muralidharan, and Ramachandran (2006) The Decision Tree algorithm has been applied to the problem under discussion Input to the algorithm is set of statistical features of vibration signatures It is clear that the top node is the best node for classification The other features in the nodes of Decision Tree appear in descending order of importance It is to be stressed here that only features that contribute to the classification appear in the Decision Tree and others not Features, which have less discriminating capability, can be consciously discarded by deciding on the threshold This concept is made use for selecting good features The algorithm identifies the good features for the purpose of classification from the given training data set, and thus reduces the domain knowledge required to select good features for pattern classification problem The decision trees shown in Figs 7, 13, 18, 22, 27 and 31 are for various lubrication and loading conditions of different faults compared with good conditions of the pinion gear wheel Based on the output of J 48 algorithm, the decision tree various statistical parameters are selected for the various conditions of the gearbox The values appearing between various nodes in the decision tree are used for generating the fuzzy rules to classify the various conditions of the gearbox under study 5.1 Application of decision tree for feature selection 4.7 Minimum value It refers to the minimum signal point value in a given signal As the gear parts (crack, breakage, face wear) get degraded, the vibration levels seem to go high Therefore, it can be used to detect faulty gears The algorithm has been applied to the problem under discussion for feature selection Input to the algorithm is the set of statistical features described in Section extracted from raw vibration signatures, the output is the Decision Tree It is clear there from that the top node is the best node for classification The other features appear 3124 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 in the nodes in Decision Tree in descending order of importance It is to be stressed here that only features that contribute to the classification appear in the Decision Tree and others not The level of contribution is not same and all statistical features are not equally important The level of contribution by individual feature is given by a statistical measure within the parenthesis in the Decision Tree The first number in the parenthesis indicates the number of data points that can be classified using that feature set The second number indicates the number of samples against this action If the first number is very small compared to the total number of samples, then the corresponding features can be considered as outliers and hence ignored Features that have less discriminating capability can be consciously discarded by deciding on the threshold This concept is made use of in selecting good features The algorithm identifies the good features for the purpose of classification from the given training data set and thus reduces the domain knowledge required to select good features for pattern classification problem Methodology adopted for fuzzy classification See Fig Fuzzy logic (classifier) Fuzzy Logic provides a precise approach for dealing with uncertainty Fuzzy inference is a method that interprets the values in the input vector and, based on some set of rules, assigns values to the output vector The point of fuzzy logic is to map an input space to an output space, and the primary mechanism for doing this is a list of ‘if-then’ statements called rules Rules are the inputs for building a fuzzy inference engine The methodology adopted for fuzzy classification is shown in Fig All rules are evaluated in parallel, and the order of the rules is unimportant The real world data not have sharply defined boundaries where information is often incomplete or sometimes unreliable In quest for precision, scientists have generally attempted to manipulate the real world into artificial mathematical models that make no provision for gradation Because Fuzzy Logic provides the tools to classify information into broad, coarse categorizations or groupings, it has infinite possi- bilities for application which have proven to be much cheaper, simpler and more effective than other systems in handling complex information (Cox, 1994) For the problem at hand, the condition of the gearbox, good or faulty is basically fuzzy in nature All the faults not occur in the gearbox instantly It comes gradually In that case, there is no threshold value (crisp data) based on which the decision on the condition of the gearbox can be taken (Whether gearbox is now good or faulty) The problems of this kind can be modeled using fuzzy logic more closely (Huang, 1997; Rao, 1996; Zeng & Wang, 1991) Membership function A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between and Observing the values of the feature, based on which the branches of the Decision Tree are created for different conditions of the gearbox, the membership functions for the corresponding features are defined There are four possible outcomes from a fuzzy classifier, namely: good bevel gear, bevel gear with tooth breakage (GTB), bevel gear with crack at root of the tooth (GTC), and bevel gear with face wear of the teeth (TFW) for various loading and lubrication conditions Hence, four membership functions are defined with equal range for the output Rule generation from decision tree Artificial neural network and support vector machine are used to generate rule for classification problems (Andrews et al., 1995; Haydemar, Cecilio, & Andreu, xxxx) In this study, Decision Tree is used for that purpose Decision Tree shows the relation between features and the condition of the gearbox Tracing a branch from the root node leads to a condition of the gearbox (Refer Figs 7, 13, 18, 22, 27 and 31) and decoding the information available in a branch in the form of ‘if-then’ statement gives the rules for classification using fuzzy for Dry/Half/Full No Load Full Load GOOD/GTC/ GTB/TFW Fig Methodology of classification using Fuzzy Fig Decision tree from J 48 Algorithm for dry-lub no-load condition N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 various conditions of the gearbox Hence the usefulness of the decision tree in forming the rules for fuzzy classification is established 10 Generation of rules for various gearbox conditions and discussions The preceding section describes how the classification has been carried out using fuzzy technique 3125 10.1 Dry-lubrication and no-load condition From Fig we can see that standard error, kurtosis and variance play a decisive role in classifying the various gearbox faults under dry lubrication and no-load condition This output of the decision tree is used to design the membership function for fuzzy classifier as shown in Fig 8–10 A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership Fig Membership function for ‘‘standard error” Fig Membership function for ‘‘kurtosis” Fig 10 Membership function for ‘‘variance” 3126 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 11 Membership functions for condition (output) value (or degree of membership) between and In the present study, trapezoidal membership function is used The selection of this membership function is to some extent arbitrary However, the following points were considered while selecting membership function The Decision Tree for the selected three features is shown in Fig Observing the values of the feature, based on which the branches of the Decision Tree is created, the membership functions for all three features are defined for standard error, kurtosis and variance, respectively 10.1.1 Rules designed for the dry-lubrication and no-load condition Figs 14–16 If (stderr is not stderr) then (Output1 is GTC) If (stderr is stderr) and (kurtosis is Kur) then (Output1 is GOOD) If (stderr is stderr) and (kurtosis is not Kur) and (variance is Var) then (Output1 is GTB) If (stderr is stderr) and (kurtosis is not Kur) and (variance is not Var) then (Output1 is TFW) The membership value of the condition being GTC is when the standard error value is less than or equal to 0.000175 (from Fig 7) which is the threshold value Hence, up to this threshold value the membership function generates the value ‘0’ and afterwards it increases linearly (assumption) The trapezoidal membership function suits this phenomenon and hence it was selected to map each point in the input space to a membership value To review, the threshold values are given by decision tree and the slope is defined by the user through heuristics The threshold value (0.000175) is defined based on the representative training dataset If standard error value is less than or equal to 0.000175, a membership function which is defined on a 0–1 scale gives a value of which means that it is not a standard error If threshold value is greater than 0.000175, the membership function generates a value of Similarly membership functions for other features are designed accordingly and shown in Figs and 10 There are four possible outcomes from a fuzzy classifier, namely: Good, GTC, GTB and TFW Hence, four membership functions are defined with equal range and shown in Fig 11 10.1.2 Fuzzy inference engine After defining membership functions and generating the ‘if-then’ rules, the next step is to build the fuzzy inference engine The fuzzy toolbox available in MATLAB was used for building fuzzy inference engine Each rule was taken at a time and using membership functions and fuzzy operators the rules were entered The rules were obtained from a training data set (150 trials in each condition) For testing the built model a portion of the data (100 trials in each condition) called testing data was kept aside Using the testing data, the fuzzy inference engine was evaluated and its performance was presented as confusion matrix in Table The diagonal elements in the confusion matrix table (3) show the number of correctly classified instances In the first row, the first element shows the number of data points belonging to ‘good’ class and classified by fuzzy logic as ‘good’ The second element shows the number of data points belonging to ‘GTC’ class and classified by fuzzy logic as ‘GTC’ The third element shows the number of data points belonging to ‘GTB’ class and classified by fuzzy logic as ‘GTB’ The fourth element shows the number of data points belonging to ‘TFW’ class and classified by fuzzy logic as ‘TFW’ Table illustrates the powerfulness of the fuzzy rules designed with the aid of the decision trees by the authors Fig 12 illustrates the application of the rules designed Here each row corresponds to each rule as discussed in Table Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 100 0 0 100 0 0 100 0 0 100 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 3127 Fig 12 Rule viewer for one of the test data section 6.4.2 The first three blocks in rows represents the membership function of standard error, kurtosis, variance, respectively The fourth block corresponds to the membership functions for output as shown in Fig 11 With the help of sample inputs for standard error, kurtosis and variance the rules are tested as follows, for a sample input of standard error as 0.0005, kurtosis as 10 and variance as 0.005 which satisfies the second rule completely and the corresponding output condition is GOOD, which is shown in the output block of the second row in the rule viewer shown in Fig 12 10.2.1 Rules designed for the dry-lubrication and full-load condition See Figs 14–16 10.1.3 Confusion matrix In lieu with the above discussions the fuzzy rules, membership functions, confusion matrix and rule viewer are shown in Sections 10.2–10.5 and 10.6 Here there are three membership functions to represent three threshold values of variance in the decision tree Fig 17 is the rule viewer for the following test data.If stderr = 0.0005, kurtosis = 10, Variance = 0.005, then the output is 6.25, i.e., the condition is GTB If (stderr is stderr) then (output1 is GTC) If (stderr is not stderr) and (variance is var3) then (output1 is GTB) If (kurtosis is kur) and (variance is var2) then (output1 is GOOD) If (kurtosis is not kur) and (variance is var1) then (output1 is TFW) 10.2 Dry-lubrication and full-load condition See Fig 13 10.2.2 Confusion matrix Table Fig 13 Decision tree from J 48 Algorithm for dry-lub full-load condition 3128 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 14 Membership function for ‘‘stderr” Fig 15 Membership function for ‘‘kurtosis” Fig 16 Membership functions for ‘‘variance” 10.3 Half-lubrication and no-load condition If (stderr is stderr2) and (kurtosis is not kur) then (output1 is TFW) See Fig 18 10.3.2 Confusion matrix Table 10.3.1 Rules designed for half -lubrication and no-load condition See Figs 19–21 10.4 Half-lubrication and full-load condition See Fig 22 If (stderr is stderr1) then (output1 is GTC) If (stderr is not stderr2) then (output1 is GOOD) If (stderr is stderr2) and (kurtosis is kur) then (output1 is GTB) 10.4.1 Rules designed for half-lubrication and full-load condition Figs 23–26 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 3129 Fig 17 Rule viewer for one of the test data Table Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 100 0 0 100 0 0 100 0 0 100 If (stderr is stderr1) then (output1 is GTC) If (stderr is not stderr2) then (output1 is GOOD) If (stderr is stderr2) and (kurtosis is not kur) then (output1 is TFW) If (stderr is stderr2) and (kurtosis is kur) and (minimum is min) then (output1 is GTB) Fig 18 Decision tree from J 48 Algorithm for half-lub no-load condition Fig 19 Membership functions for ‘‘stderr” 3130 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 20 Membership function for ‘‘kurtosis” Fig 21 Rule viewer for one of the test data If stderr = 0.0005, kurtosis = 10 The output is 6.25, hence the condition is GTB Table Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 100 0 0 100 0 0 100 0 0 100 If (stderr is stderr2) and (variance is var) then (output1 is GTB) If (stderr is stderr2) and (variance is not var) then (output1 is TFW) 10.5.2 Confusion matrix Table If (stderr is stderr2) and (kurtosis is kur) and (minimum is not min) then (output1 is TFW) 10.6 Full-lubrication and full-load condition See Fig 31 10.4.2 Confusion matrix Table 10.5 Full-lubrication and no-load condition 10.6.1 Rules designed for full-lubrication and full-load condition Figs 32 and 33 See Fig 27 10.5.1 Rules designed for full-lubrication and no-load condition Figs 28–30 If If If If (stderr (stderr (stderr (stderr is is is is stderr1) then (output1 is GTC) not stderr3) then (output1 is GOOD) stderr2) then (output1 is GTB) stderr3) then (output1 is TFW) If (stderr is stderr1) then (output1 is GTC) If (stderr is not stderr2) then (output1 is GOOD) 10.6.2 Confusion matrix Table N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 22 Decision tree from J 48 Algorithm for half-lub full-load condition Fig 23 Membership functions for ‘‘stderr” Fig 24 Membership functions for ‘‘kurtosis” 3131 3132 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 25 Membership functions for ‘‘minimum” Fig 26 Rule viewer for one of the test data If Stderr = 0.0005, kurtosis = 10, minimum = 0, output1 = 6.25, i.e., the condition is GTB Table 11 Conclusion Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 100 0 0 100 0 0 100 0 0 100 Fault diagnosis of Gear box is one of the core research areas in the field of condition monitoring of rotating machines The work conducted, proposing the method of Fig 27 Decision tree from J 48 Algorithm for full-lub no-load condition N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 3133 Fig 28 Membership function for ‘‘stderr.” Fig 29 Membership function for ‘‘variance” Fig 30 Rule viewer for one of the test data.If stderr = 0.0005, variance = 0.005, then output1 = 6.25 Table Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 96 10 0 100 0 0 90 0 100 the gearbox fault identification based on fuzzy logic technique, shows the great potentiality and the strong ability to classify and identify machinery faults This work has investigated the use of basic fuzzy logic principle as a fault diagnostic technique for spur bevel gearbox The work conducted has demonstrated the potential of fuzzy logic to 3134 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 31 Decision tree from J 48 Algorithm for full-lub full-load condition Fig 32 Membership function for ‘‘stderr” Fig 33 Rule viewer for one of the test data If stderr = 0.0002 then output1 = 1.25, ie, the condition is Good N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Table Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 100 0 0 100 0 0 100 0 0 100 classify the likely fault conditions which are represent in rotating machinery From the study carried out and presented in this paper, the diagnosis technique based on the fuzzy logic principle is found to be practical for the condition recognition of the gearbox Also this work brings out the potential of decision trees to generate the rules automatically from the feature set which proves to be a great asset in generating fuzzy rules This work has outlined the procedure of fuzzy diagnosis technique by using the characteristic variables which represent a particular running condition of the gearbox to determine the fuzzy membership function References Andrews, R., Diederich, J., & Tickle, A (1995) A survey and critique of techniques for extracting rules from trained artificial neural networks Knowledge-Based Systems, 8(6), 373–389 Burgess, C J C (1998) A tutorial on support vector machines for pattern recognition Data Mining and Knowledge Discovery, 2, 955–974 Cameron, B G., & Stuckey, M J (1994) A review of transmission vibration monitoring at Westland Helicopter Ltd In Proceedings of the 20th European rotorcraft forum (pp 16/1–116/16) paper 116 Collacott, R A Mechanical fault diagnosis and condition monitoring Chapman & Hall Cox, E (1994) The fuzzy systems handbook – a practitioner’s guide to building, using, and maintaining fuzzy systems New York: Academic Press Gadd, P., & Mitchell, P J (1984) Condition monitoring of helicopter gearboxes using automatic vibration analysis techniques, AGARD CP 369 Gears and power transmission system for helicopter turboprops, 29/ 1–29/10 3135 Haydemar, N., Cecilio, A., & Andreu C Rule extraction from support vector machines In ESANN’2002 proceedings – European symposium on artificial neural networks (pp 107–112) Huang, Y C., Yang, H T., & Huang, C L (1997) Developing a new transformer fault diagnosis system through evolutionary fuzzy logic IEEE Transactions on Power Delivery 12 Jack, L B., & Nandi, A K (2000) Comparison of neural networks and support vector machines in condition monitoring application In Proceedings of COMADEM 2000 (pp 721–730) Houston, TX, USA James Li, C., & Wu, S M (1989) Online detection of localized defects in bearing by pattern recognition analysis ASME Journal of Engineering Industry, 111, 331–336 Leblanc, J F A., Dube, J R F., & Devereux, B (1990) Helicopter gearbox vibration analysis in the Canadian forces – applications and lessons In Proceedings of the first international conference, gearbox noise and vibration (pp 173–177) IMechE Cambridge, UK, C404/023 Nandi, A K (2000) Advanced digital vibration signal processing for condition monitoring In Proceedings of COMADEM2000 (pp 129– 143) Houston, TX, USA Peng, Y H., Flach, P A., Brazdil, P., & Soares, C (2002) Decision treebased data characterization for meta-learning In ECML/PKDD-2002 workshop IDDM-2002 Helsinki, Finland Rao, B K N (1996) The handbook of condition monitoring London: Elsevier Samanta, B., & Al-Baulshi, K R (2003) Artificial neural network based fault diagnostics of rolling element bearings using time domain features Mechanical Systems and Signal Processing, 17(2), 317–328 Samanta, B., Al-Baulshi, K R., & Al-Araimi, S A (2003) Artificial neural networks and support vector machines with genetic algorithm for bearing fault detection Engineering Applications of Artificial Intelligence, 16, 657–665 Shi, X Z., Xu, Z Q & Xu (1988) A study on the automatic recognition of vibration signal for ball bearing faults – The FFTAR feature extraction and classification methods In Proceedings of IEEE international workshop on applied time series analysis (pp 318–321) World Scientific Sugumaran, V., Muralidharan, V., & Ramachandran, K I (2006) Feature selection using decision tree and classification through proximal support vector machine for fault diagnostics of roller bearing Mechanical Systems and Signal Processing, 21, 930–942 Zeng, L., & Wang, Z., (1991) Machine-fault classification: A fuzzy approach The International Journal of Advanced Manufacturing Technology 6, 83–94 [...]... generating fuzzy rules This work has outlined the procedure of fuzzy diagnosis technique by using the characteristic variables which represent a particular running condition of the gearbox to determine the fuzzy membership function References Andrews, R., Diederich, J., & Tickle, A (1995) A survey and critique of techniques for extracting rules from trained artificial neural networks Knowledge-Based Systems,... one of the test data.If stderr = 0.0005, variance = 0.005, then output1 = 6.25 Table 7 Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 96 0 10 0 0 100 0 0 0 0 90 0 4 0 0 100 the gearbox fault identification based on fuzzy logic technique, shows the great potentiality and the strong ability to classify and identify machinery faults This work has investigated the use of basic fuzzy logic principle as a fault. .. viewer for one of the test data If Stderr = 0.0005, kurtosis = 10, minimum = 0, output1 = 6.25, i.e., the condition is GTB Table 6 11 Conclusion Condition GOOD GTC GTB TFW GOOD GTC GTB TFW 100 0 0 0 0 100 0 0 0 0 100 0 0 0 0 100 Fault diagnosis of Gear box is one of the core research areas in the field of condition monitoring of rotating machines The work conducted, proposing the method of Fig 27 Decision... 100 0 0 0 0 100 0 0 0 0 100 0 0 0 0 100 classify the likely fault conditions which are represent in rotating machinery From the study carried out and presented in this paper, the diagnosis technique based on the fuzzy logic principle is found to be practical for the condition recognition of the gearbox Also this work brings out the potential of decision trees to generate the rules automatically from... fuzzy logic principle as a fault diagnostic technique for spur bevel gearbox The work conducted has demonstrated the potential of fuzzy logic to 3134 N Saravanan et al / Expert Systems with Applications 36 (2009) 3119–3135 Fig 31 Decision tree from J 48 Algorithm for full-lub full-load condition Fig 32 Membership function for ‘‘stderr” Fig 33 Rule viewer for one of the test data If stderr = 0.0002 then... B G., & Stuckey, M J (1994) A review of transmission vibration monitoring at Westland Helicopter Ltd In Proceedings of the 20th European rotorcraft forum (pp 16/1–116/16) paper 116 Collacott, R A Mechanical fault diagnosis and condition monitoring Chapman & Hall Cox, E (1994) The fuzzy systems handbook – a practitioner’s guide to building, using, and maintaining fuzzy systems New York: Academic Press... handbook – a practitioner’s guide to building, using, and maintaining fuzzy systems New York: Academic Press Gadd, P., & Mitchell, P J (1984) Condition monitoring of helicopter gearboxes using automatic vibration analysis techniques, AGARD CP 369 Gears and power transmission system for helicopter turboprops, 29/ 1–29/10 3135 Haydemar, N., Cecilio, A., & Andreu C Rule extraction from support vector machines... detection of localized defects in bearing by pattern recognition analysis ASME Journal of Engineering Industry, 111, 331–336 Leblanc, J F A., Dube, J R F., & Devereux, B (1990) Helicopter gearbox vibration analysis in the Canadian forces – applications and lessons In Proceedings of the first international conference, gearbox noise and vibration (pp 173–177) IMechE Cambridge, UK, C404/023 Nandi, A K (2000)... Proceedings of COMADEM2000 (pp 129– 143) Houston, TX, USA Peng, Y H., Flach, P A., Brazdil, P., & Soares, C (2002) Decision treebased data characterization for meta-learning In ECML/PKDD-2002 workshop IDDM-2002 Helsinki, Finland Rao, B K N (1996) The handbook of condition monitoring London: Elsevier Samanta, B., & Al-Baulshi, K R (2003) Artificial neural network based fault diagnostics of rolling element... vibration signal for ball bearing faults – The FFTAR feature extraction and classification methods In Proceedings of IEEE international workshop on applied time series analysis (pp 318–321) World Scientific Sugumaran, V., Muralidharan, V., & Ramachandran, K I (2006) Feature selection using decision tree and classification through proximal support vector machine for fault diagnostics of roller bearing Mechanical