Estimation of Remaining Useful Life of Bearings Based on Nested ...

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Estimation of Remaining Useful Life of Bearings Based on Nested Dichotomy Classifier – A Machine Learning Approach R. Satishkumar1, V.Sugumaran2 School of Mechanical &Building Sciences, VIT University, Chennai- Campus, Chennai, India 1 [email protected], [email protected] Abstract - Rolling element bearings play a vital role for maintaining the reliability metrics in all rotating machineries. The downtime due to these bearing failures are now in increasing trend. In general manufacturing environment most of the time the bearings are replaced only after an indication or symptom due to the complexities of deployments for condition monitoring techniques. This paper emphasis on estimating the remaining useful life of bearing using Nested dichotomy classifier. Vibration signals were acquired for a bearing from day one of its operation till it fails naturally through a piezoelectric accelerometer and the features are extracted using the defined statistical features. The best contributing features are selected and classified using the Nested dichotomy, data near balanced nested dichotomy and class balanced nested dichotomy classifiers. The effectiveness of these classifiers was analyzed and compared. Keywords : Remaining Useful Life (RUL) ; Nested Dichotomy (ND), Statistical Features I. INTRODUCTION In a manufacturing industry a high amount of capital cost is incurred on improving the uptime of the machineries. Preventive maintenance is a common tool deployed across the industries to reduce the downtime and improve the health condition of the machines. However there are instances that the breakdowns occur due to variable unpredicted conditions. Bearing failures alone contributes to a reasonable sum in the total breakdowns. This failures shows up usually in the quality parameters. There are already number of conditional monitoring techniques for assessing the health condition of the bearings under study. However, these techniques have their own limitations to the real time applications. A bearing failure is associated with various reasons like misalignment,temperature, load conditions,lubrications etc., however,the present study is focused on assessing the health condition of a bearing under real time conditions. Palmgren. A and G.Lundberg [1]-[3] have laid the basics in estimating the lifetime of the bearing. This has given way to establish the standard for predicting the lifetime of the bearings with respect to the loads and speed of the application [4]-[6].Zhigang Tian,Lorna Wong and NimaSafaei [7] has detailed the deployment of Artificial Neural Networks (ANN) for estimating the remaining useful life of a bearing with age and condition monitoring data as input and the remaining life as the resultant output. This model was built with the past failure histories. The main drawback of using ANN is the associated complexities in designing all the failure histories in the real time applications. Nathan Bolander,Haiqiu and Neil Eklund [8] summarizes a physics based remaining useful life predictions for a aircraft engine bearing. The model was built with spall propogation theories by which the remaining life is assessed based on the future operating conditions and the spall propogation. Francesco Di Maio, et.al., [9] used a Naïve baysian classifier for estimating the remaining useful life of bearings. This method is based on the bearing degradation patterns that are already stored in the database. The new acquired vibration signals are compared with reference to the similar degradation patterns and the remaining useful life is predicted. Paula J. Dempsey, et.al.,[10] presented the remaining life by correlating it with the condition indicators. Spall propogation data was used to generate the condition indicators. A damage progression model was thus built with the said data. Data fusion analysis technique was used to map the condition indicator to the damage level and thus the current state of the transmission component is assessed. Sugumaran V. andRamachandran K. I [11]-[13] and V.Muralidharan and V. Sugumaran [14],[15] detailed the process of acquiring the vibration signals, feature extraction ,feature selection and feature classification through a machine learning approach. Statistical parameters like standard deviation, mean average, minimum and maximum values forms a set of features and the best contributing features are selected and further classified using various classifiers. Decision tree was used as one of the tool for selecting the best contrubting feature for the given data set.

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This paper presents a predictive meethod to estim mate the remaaining useful life of the bearings based on nested my clasifiers. This T method is based on thhe supervised dmachine learrning approachh. Run-to-failure tests dichotom were connducted on thee bearings thaat are similar to t real time ap pplications. The T vibration ssignals thus accquired at defined inntervals were used for featuure extraction through descrriptive statistiical methods. II METHODOL M LOGY This paper proposes thhe step by steep process to estimate the remaining r useeful life of thee bearings as shown in ws data drivenn approach wh herein the data collected froom the experiiments are Fig. 1. Thhe said methoodology follow used to leearn about thee systems andd to infer the current c state of the system. The experimeents were con nducted on dedicatedd test rigs withh real time conditions. The selected bearrings were testted on these eexperimental setups s and the vibrattion signals arre acquired at defined intervvals. The sign nals are later converted to daata for furtherr analysis.

Featurre  Extraction

Feature  Selection

Model  Co onstruction

Pred dict the  RUL

Fig. 1. Metthodology of RUL L estimation

Statisticaal features werre deployed foor feature extrraction. Thesee features are dealt in detaill in the next sections s in this papeer. From the liisted features the best perfoorming and co ontributing feeatures are sellected. This seelection is done usinng decision treee algorithm. The selected features are fu urther used for constructingg a model which will be used for assessing the current state of the bearinggs and thus esstimating the remaining r useeful life of thee bearings i initially connstructed withh training dataa set and furthher validated ffor precise ressults. This in the tesst.The model is paper dettails about thee effectivenesss of Nested Dichotomy Claassifiers for moodel constructtion. Nested dichotomy d (ND) is a method useed for studyinng a multi claass classificattion problem. A nested dicchotomy orgaanizes the s of classes can be organiized in a diffeerent ways classes inn a tree , eachh internal nodee has a binary classifier. A set in an nessted dichotom my. An ensembble of nested dichotomy d is formed by sevveral dichotom mies. Hence an a attempt has beenn made in the present studyy to classify thhe selected feeatures using different typees of nested dichotomy d classifierrs. III EXPE ERIMENTAL L STUDIES The maiin objective of o this experim ment is to asseess the health h condition off the bearing aat defined inteervals.The experimeents were condducted with thhe selected beearings in a co ontrolled envirronment andruun-to-failure test data is aquired to t validate thee effectiveness of the propoosed model fo or predicting the remainingg life of the bearing. b In general, most m of the beearing tests will be done in an accelerated conditions toshorten t the test time. Thiis paper is built arouund to overcoome the limittations set in the previouss studies. Thee experiments on these beaarings are continuedd at real timee environmentts till the bearring fails natu urally. The coomplete experrimental setup p used for data acquuisition is shown in Fig. 2. 2 This setupp consists of a bearing, acccelerometer, motor, DAQ card and LABVIE EW software looaded into a computer c to accquire the vibrration signals..

Fig. 2. Experimental setup

The bearrings are mounnted on a shaft with housinng and in-turn n connected too a variable sppeed motor. Few F major parameteers like speed,, load, temperrature, lubrication, etc., are simulated at real time conditions. The brand b new bearing (ball ( bearing 6205) 6 was madde to run to faailure at rated speeds (1400 RPM)and ratted radial load d (0.2 kN). The vibration signals from the beaarings are colllected through h the piezo ellectric accelerrometers placced on the Q system (Mo odel NI USB 4432).The 4 carrd has a 5 ano olog input either sidde of the houssings and acquuired via DAQ slots withh a sampling rate of 102.44 kilo sampless per second and a 24 bit ressolution. Thesse accelerometers(40Hz p-ISSN : 2319-8613

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Amplitude

Amplitude

resonant frequency) have h a large frrequency respoonse and it caan detect very small vibratioons. These sig gnals were VIEW. The vibration v signnals acquired from the expperimental sett-up follows the t below processedd in the LabV samplingg parameters. Sample length : 1024 Samplingg frequency :224 kHz Number of samples : 200 2 samples evvery 08 hrsoff running The expeeriment was run r in real tim me conditions matching to the said bearring applicatioon. Adequate measures were takken to avoid bearing faultss or damagess due to fitm ments, misalignnments etc,.A All researchess done on bearing life time mostlly opts with Vibration V signaalas it is mostt effective andd suitable for rreflectingactual bearing T are othher methods other than vibration siggnals such aas temperaturre, oil or running condition. There debris,accoustic methodds etc., to asssess the healthh condition off the bearings. However vibbration signalls are less complex when compaared to otherss. The amplituude of the vib bration signalls is monitoreed on a daily basis for b The amplitude reeflects the agee of the bearing under estimatinng the currentt health condiition of the bearings. study. Thhe amplitude of the vibratiion is small and a smooth when w the beariing is under nnormal condittion. The amplitudde of the vibraation signal gradually increaases with resp pect to the tim me as shown inn Fig.2. Meanwhile any defects or o damages onn the bearingss during the process p can alsso be easily identified, if thhe acquired signals are contuniouusly monitoreed. Thus, vibbration signall becomes thee suitable variable to asses teh health con ndition of the bearinngs. The colleected data from m the bearingss were categorized into diffferent stages w with respect to o the time. The stagees are definedd asstage 1, staage 2, stage 3,, stage 4 and stage s 5 etc.... Signals acquirred from a new w bearing were placced on stage 1. Stage 2 andd 3 includes the t signals thaat are extracteed from the beearing after 10 000 hours and 12500 hours respectively. Stagge 4 includes the signals th hat are extracted after 15000 hours of ru unning the bearing at a rated load and a speed connditions. Signaals from damaaged bearing are placed in stage 5. The variations in signalss, thus acquired from the bearings b in vaarious stages is shown in Fiig. 3 (a), 3 (b)), 3 (c), 3 (d) and 3 (e) respectivvely.

Data point iindex

Data point index

Fig.. 3 (b). Satge-2: Vibration V signals@ @1000 Hrs

Amplitude

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F 3 (a). Satge-1: Vibration Signaals at Start Fig.

Data pooint index

Data point indeex

Fig. 3 (c). Stage-3:Vibration Signals@11250Hrs Fig. 3 (d). ( Stage-4:Vibraation Signals@15500Hrs

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Dataa point index

Fig. 3 (e). Stagee-5: Vibration Sig gnals @1800 Hrs..

IV FEATUR RE EXTRAC CTION AND FEATURE SELECTION S N The signals s acquirred for the experiments e w be too laarge for the algorithm will a to bbe processed and it is suspectedd to be redunddant and hencee they are reduuced set of features. This process is calleed as feature extraction. e Descriptiive statistical parameters suuch as mean, median, mod de, sample vaariance, kurtossis, skewness, standard error, staandard deviatiion, minimum m, maximum, sum, and ran nge were compputed to serve as features. They are named as ‘statistical features’ heree. Brief descrriptions aboutt the extracteed statistical ffeatures as deetailed by Jegadeeshwaran & Suggumaran [16]--[18]. A. Feaature selectionn Featuure selection is the process of selecting well w contributting features among the avvailable featurres. In the present study s 12 descrriptive statisticcal features have been extrracted and outt of 12 featurees the well contributing features have h to be iddentified. Decision tree wass used for feaature selectionn. Satishkumaar and Sugum maran [19] detailed the feature seelection usingg J48 decisionn tree algorith hm. The featuure which apppears on the top t of the m and comingg down the neext level, the next best decision tree is the beest feature forr the classificcation problem w be availaable. In this way w a threshold is cut manu ually to selectt the number oof features req quired for features will classificaation. All 12 features f are ordered in the descending order o of imporrtance. Out off which only 8 features are appeaaring in the decision d tree and a rest of thee 4 features arre taken in thee random ordder. An experiiment was carried out o by using only the top most featurees and classifi fication accuraacy was noteed down, then n top two features were w selectedd and correspoonding classifi fication accuraacy was notedd. The processs was continu ued till the classificaation accuracyy for all the features f weree noted It is found f that 7 features nameely standard deviation, maximum m, minimum,ssum, skewness, kurtosis andd range was fo ound to be thee best contribuuting features. V. FEATU URE CLASSIIFICATION In this paaper, nested dichotomy d claassifiers are used u for featurre classificatioon. The selectted features are a further classifiedd using the below b detailedd nested dichotomy classiffiers. Jegadeeeshwaran and Sugumaran [17] have detailed the t deploymennt of this classsifiers. A. Nested Dichootomy (ND) A systtem of nested dichotomies is a hierarchiccal decomposiition of a multti-class probleem with c classses into c − 1 two--class problem ms and can be b representedd as a tree strructure. Ensem mbles of randdomlygeneratted nested dichotom mies have provven to be an efffective approoach to multi-cclass learning problems. Thhe decomposittion canbe representted as a binarry tree (Figurre. 4). Each node n of the treee stores a seet of class labbels, the correesponding training data d and a binnary classifierr. At the very beginning, th he root node contains c the w whole set of th he original class labeels correspondding to the muulti-class classsification prob blem. This sett is then split iinto two subseets. These two subssets of class labels l are treaated as two “m meta” classess and a binaryy classifier is learned for predicting p them. Thhe training daataset is split into two subssets correspon nding to the two t meta classses and one subset of training data d is regardded as the possitive examplees while the other o subset iss regarded as the negative examples. e The two successor noddes of the rooot inherit the tw wo subsets off the original class c labels w with their correesponding ursively. The process finallly reaches a leeaf node if trainingddatasets and a tree is built byy applying thiis process recu the node contains onlyy one class laabel.It is obvioous that for an ny given c-claass problem, the tree contaains c leaf nal node contaains a binary classifier. Do ong, Frank nodes (onne for each cllass) and c−1 internal nodees. Each intern andKram mmer [20-21] explicitly e detaailed the nesteed dichotomy classifier. c

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[ a, b, c, d]

[a, c]

[a]

Root Level

[b, d]

[c]

[b]

Inner Node Level

[d]

Leaf Level

Fig. 4. Nested Dichotomy Tree

B. Class-balanced nested dichotomies In light of these observations considered two different sampling strategies inthis paper. The first method is based on balancing the number of classes ateach node. Instead of sampling from the space of all possible trees, sample from the space of all balanced trees, and build an ensemble of balanced trees.The advantage of this method is that the depth of the tree is guaranteed to belogarithmic in the number of classes. This is referred as an ensemble of class-balancednested dichotomies (ECBND).The number of possible class-balanced nested dichotomies is obviously smallerthan the total number of nested dichotomies. The following recurrence relationdefines the number of possible class-balanced trees:

whereT (1) = 1 and T (2) = 1. Dong, Frank &Krammer [20] has explicitly detailed the algorithm for building a system of class-balanced nested dichotomies as below. if|C| = 1 then return P = subset of C, randomly chosen from all subsets of size [|C|/2] N=C\P Dp= all instances in D apart from those pertaining to classes in P buildClassBalancedNestedDichotomies(Dp, P) Dn= all instances in D apart from those pertaining to classes in N buildClassBalancedNestedDichotomies(Dn, N) D’ = a two-class version of D created based on N and P classifierForNode = buildClassifier(D’) C. Data-balanced nested dichotomies The most common problem with the class-balanced approach is that some multi-class problems are very unbalanced and some are much more populated thanothers. In that case a class-balanced tree does not infer that it is also databalanced.This can negatively affect runtime if thebase learning algorithm has time complexity worse than linear in the number ofinstances. The data-balanced nested dichotomies randomly assignsthe classes to two subsets until the size of thetraining data in one of the subsets exceeds half the total amount of trainingdata at the node. One motivation for using this simple algorithm was that it isimportant to maintain a degree of randomness in the assignment of classes tosubsets in order to preserve diversity in the committee of randomly generatedsystems of nested dichotomies. Dong, Frank &Krammer [20] has explicitly detailed the algorithm for building a system of data-balanced nested dichotomies. Even with our simple algorithm diversitysuffers when the class distribution is very unbalanced. However, it is difficult toderive a general expression for the number of trees that can potentially generated by this method because this number depends on the class distribution in thedataset. if|C| = 1 then return C = random permutation of C Dp= ∅, Dn= ∅ do if(|C| >1) then add all instances from D pertaining to first class in C to Dp p-ISSN : 2319-8613

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add all instances from D pertaining to last class in C to Dn remove first and last class from C else add all instances from D pertaining to remaining class in C to Dp remove remaining class from C while(|Dp|