Health Assessment of Electronic Products using Mahalanobis Distance and Projection Pursuit Analysis

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1 Health Assessment of Electronc Products usng Mahalanobs Dstance and Projecton Pursut Analyss Sachn Kumar, Vasls Sotrs, and Mchael Pecht Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 Abstract Wth ncreasng complexty n electronc systems there s a need for system level anomaly detecton and fault solaton. Anomaly detecton based on vector smlarty to a tranng set s used n ths paper through two approaches, one the preserves the orgnal nformaton, Mahalanobs Dstance (MD), and the other that compresses the data nto ts prncpal components, Projecton Pursut Analyss. These methods have been used to detect devatons n system performance from normal operaton and for crtcal parameter solaton n multvarate envronments. The study evaluates the detecton capablty of each approach on a set of test data wth known faults aganst a baselne set of data representatve of such healthy systems.. Keywords Mahalanobs dstance, Prncple components, Projecton pursut, Health assessment, Anomaly. I. INTRODUCTION ROGNOSTICS and health management (PHM) s a process Pof predctng the future relablty of the system by assessng the extent of devaton or degradaton of a product from ts expected normal operatng condtons n a preemptve and opportunstc manner to the antcpaton of falures. Ths can enable contnuous, autonomous, real tme montorng of the health condtons of a system by means of embedded or attached sensors wth mnmum manual nterventon to evaluate ts actual lfe-cycle condtons, to determne the advent of falure, and to mtgate system rsks. The term dagnostcs refers to the detecton and solaton of faults or falures and prognostcs refers to the process of predctng a future state (of relablty) of the system based on ts current and hstorc condtons. The am of falure prognoss s ntended to dentfy and estmate the advancement of fault condtons to system falure. Quantfcaton of degradaton and the progresson from faults to falure n electronc products s a challengng task. Gu et. al. [2] dentfes sx levels of prognostcs S. Kumar s wth the Center for Advanced Lfe Cycle Engneerng (CALCE), Unversty of Maryland, College Park, MD USA (phone: ; fax: ; e-mal: skumar@ calce.umd.edu). V. Sotrs wth the Center for Advanced Lfe Cycle Engneerng (CALCE), Unversty of Maryland, College Park, MD USA (e-mal: vsotrs@ calce.umd.edu). M. Pecht wth the Center for Advanced Lfe Cycle Engneerng (CALCE), Unversty of Maryland, College Park, MD USA (e-mal: pecht@ calce.umd.edu). mplementaton for electroncs, from on chp packagng to complete products of products. They provded an approach for prognostcs mplementaton at the varous levels of electroncs, based on falure modes, mechansms and effects analyss. Zhang et. al. [3] proposed a model to assess ntermttent as well as hard falures. The model s a fuson of two predcton algorthms based on lfe consumpton montorng and uncertanty adjusted prognostcs. Vchare et. al. [1][4][5] proposed methods for montorng and recordng n-stu temperature loads. Ths ncludes methods for embeddng data reducton and load parameter extracton algorthms nto the sensor modules to enable reducton n on-board storage space, low power consumpton, and unnterrupted data collecton. Two approaches for detecton and fault solaton based on classfcaton theory are presented n ths paper. Both are capable of system level anomaly detecton n multvarate, data-rch envronments. One methodology uses the Mahalanobs Dstance (MD) and the other uses a projecton pursut analyss (PPA) to analyze on-lne system data. Both approaches are used to montor the health of the system and dentfy onsets and perods of abnormaltes. Parameter contrbuton s performed by both approaches as a means of dentfyng domnant and potentally faulty parameters [8] [9] [12]. Experments were performed on notebook computers to generate data and valdate the analyss approaches. The expermental detals, the algorthmc approach to anomaly detecton, and a case study are dscussed. II. METHODOLOGY TO IDENTIFY ABNORMALITIES IN ELECTRONIC PRODUCTS The Mahalanobs Dstance (MD) methodology s a process of dstngushng data groups [6][10]. The MD measures dstances n mult-dmensonal spaces by consderng correlatons among parameters. The dstance s senstve to the correlaton matrx of the healthy group. The MD values are used to construct a normal operatng doman also known as Mahalanobs space to montor the condton of a multdmensonal system. Health of a system s defned by several performance parameters. These parameters are standardzed and the MDs are calculated for the normal group. These MD values defne the Mahalanobs space, whch s used as a 282

2 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 reference set for the MD measurement scale. The parameters collected from a system are denoted as X, where = 1,2,,m. The observaton of the th parameter on the j th nstance s denoted by X j, where =1, 2,, m, and j = 1, 2,,n. Thus the (m x 1) data vectors for the normal group are denoted by X j, where j = 1, 2,, n. Here m s the number of parameters and n s the number of observatons. Each ndvdual parameter n each data vector s standardzed by subtractng the mean of the parameter and dvdng t by the standard devaton. These mean and standard devaton are calculated from the data collected for normal or healthy system. Thus, the standardzed values are: X j X Zj, = 1, 2 m, j=1, 2 n, (1) S where, 1 X n X j n j1 and S n j1 X X j n 1 Next, the values of the MDs are calculated for the normal tems usng: 1 T 1 MD j z j C z j (2) m where, z T j =[z 1j,z 2j,,z mj ] s a vector comprses of z j, z j s transpose of z T j and C s correlaton matrx calculated as: n 1 T C z j z j (3) (n 1) j1 Next, the test system s consdered to determne ts health. The MDs for the test system are calculated after the parameters are standardzed usng the mean and standard devaton for normal-group. The resultng MD values from test system are compared wth the MD values of the normal or healthy system to determne test system s health. A. Sgnfcant Parameter Identfcaton Usng Mahalanobs Dstance Analyss Crtcal parameters usng MD output can be acheved by dentfyng parameters that contrbute more to the MD value. In other words, the parameters that have sgnfcant mpact on the MD value should be dentfed. The effect of ndvdual parameters or combnaton of parameters on MD output values can be observed through a leave-one-out approach where a reduced set of parameters s used to compute the MD values, n effort to understand the effect of the excluded parameter. The leave-one-out approach can be expressed by an orthogonal array (OA) and a sgnal-to-nose (S/N) rato that can be used for quantfy the mpact of selected combnatons. An OA s a desgn matrx that reflects the presence or absence of parameters nvolved n the leave-one-out approach for all experments. Each parameter s assgned to a column and each row represents an expermental run for the leave-one-out approach. Intally all parameters are consdered and later wth each run one parameter s removed from consderaton to observe the effect of that parameter. The MD values correspondng to each leave-one-out run are then used to calculate the S/N rato values, whch are the correspondng 2 responses for each run. Many dfferent S/N ratos are used n Taguch s desgn of experment. One opton mentoned s to use Taguch s [9] larger-s better S/N rato, defned as (4) 2 q 1 10 log (1/ q) (4) j1 MD j where, q s the number of observaton for an leave-one-out run. For a gven parameter X, the average value of the S/N rato s determned over all runs wth that parameter present (S/N p ) and absent (S/N a ). If the dfference between (S/N) ratos S/N p (X ) - S/N a (X ) s postve then ths parameter has hgher responses when t s part of the system and therefore the parameter X, s retaned and consdered crtcal. B. Projecton Pursut Analyss The Projecton Pursut Analyss uses a Prncpal Components Analyss (PCA), least squares optmzaton (LS) and a Sngular Value Decomposton (SVD) treatment of the data. PCA s used n a wde array of applcatons to reduce a large data set to a smaller one whle mantanng the majorty of the varablty present n the orgnal data. It s also very useful n provdng compact representaton of temporal and spatal correlatons n the felds of data beng analyzed. PCA facltates a multvarate statstcal control to detect when abnormal processes exst and can solate the source of the process abnormaltes down to the component level. Two statstcal ndces, the Hotellng Squared (T 2 ) and squared predcton error (SPE) are used n the PCA. The SPE statstc s related to the resduals of process varables that are not llustrated by the PCA statstcal model, and s a relable ndcator to a change n the correlaton structure of the process varables. The SPE physcally tests the ft of new data to the establshed PCA models and s effcent at dentfyng outlers from the PCA model [7]. The Hotellng T 2 score measures the Mahalanobs dstance from the projected sample data pont to the orgn n the sgnal space defned by the PCA model. The prmary objectves of prncpal component analyss are data summarzaton, classfcaton of varables, outler detecton, early warnng of potental malfunctons and solaton of fault. PCA seeks to fnd a few lnear combnatons whch can be used to summarze the data wth a mnmal loss of nformaton. Let X = x 1, x 2, x 3,..,x m be an m dmensonal data set descrbng the system varables. The frst prncpal component s the lnear combnaton of the columns of X,.e. the varables, whch descrbes the greatest varablty n X, t 1 =X p1 subject to p 1 =1. In the m-dmensonal space p 1 defnes the drecton of greatest varablty, and t 1 represents the projecton of each sample data pont onto p 1. The second prncpal component s the lnear combnaton defned by t 2 =X p2 whch has the next greatest varance subject to p 2 =1 and subject to the condton that t s orthogonal to the frst prncpal component, t 1 [11]. Essentally PCA decomposes the orgnal sgnal X, as 283

3 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 m X=TP T T = t p (5) 1 where p s chosen to be an egenvector of the covarance matrx of X. P s defned as the prncpal component loadng matrx and T s defned to be the matrx of prncpal component scores. The loadngs provde nformaton as to whch varables contrbute the most to ndvdual prncpal components, and can help solate the domnant faulty varables. In the approach used n ths paper, each varable s separately scaled to zero mean and unt varance. One mportant feature of the PCA model s that t gves nformaton about the nose structure of the orgnal data whch means that t can tell somethng about varables that do not domnate on the varance level but are ndeed degradng or faulty. Consequently, t s desrable to exclude less nfluental prncpal components from the sgnal space defned by the PCA model, whch leads to the decomposton of X nto the sgnal and resdual subspaces. The sgnal subspace s ntended to capture the varables that are contrbutng to any abnormal process varablty and the resdual subspace wll complement ths by examnng the varables that are effectvely overshadowed by domnant varables n the sgnal subspace. It s mportant to note that faulty varables aren t always the ones that exhbt the greatest varablty. An example of ths phenomenon s presented n the data analyss and dscusson secton of ths paper. C. Prncpal Component Subspace Decomposton Subspace decomposton nto Prncpal Components can be accomplshed usng sngular value decomposton of matrx X. The SVD of data matrx X, s expressed as X=USV T, where S=dag(s 1,,s m ) R n x m, and s 1 >s 2 > >s m. The two orthogonal matrces U and V are called the left and rght egen-matrces of X. Based on the sngular value decomposton, the subspace decomposton of X s expressed as: X=X s +X r =U s S s V T s + U r S r V T r (6) The sgnal space S s s defned by the PCA model and the resdual subspace S r s taken as the resdual space [12]. The dagonal S s are the sngular values {s 1,,s k }, and {s k+1,,s m } belong to the dagonals of S r. The set of orthonormal vectors U s =[u 1,u 2,,u k ] form the bases of sgnal space S s. The projecton matrx P s onto the sgnal subspace s gven by: P s =U s U s T The resdual subspace s the orthogonal complement of the sgnal subspace and the projecton of the orgnal data onto t can be expressed as: (7) P r =I-P s (8) Any vector X can be represented by a summaton of two projecton vectors from subspaces S s and S r. X=X s +X r =P s x + (I-P s )x (9) The subspace decomposton can also be accomplshed by the egen analyss of the correlaton matrx of X, C, whch s expressed as follows, where the columns of U are actually the egenvectors of C, and the egen values of C are the squared sngular values of the dagonal matrx S. The egen values provde a measure of the varance of each of the egenvectors and determne the selecton of the prncpal components and the number of prncpal components to choose. C=(1/n)XX T =(1/n)US 2 U T (10) D. Fault Detecton Usng Projecton Pursut Analyss From the normal hstorcal data one can derve the nomnal normal system behavor statstcs, mean, varance and from the above analyss the sgnal and resdual subspaces. From the subspaces, we extract some statstcs to descrbe the data dstrbutons n two subspaces[13]. One s the Hotellng T 2 whch measures the varaton of each sample s the sgnal subspace. For a new sample vector x, t s expressed as: T 2 =x T U s S -1 U s T x (11) where S s the covarance of X, and s equal to U T U. Another statstc, the squared predcton error (SPE), ndcates how well each sample conforms to the PCA model, measured by the projecton of the sample vector onto the resdual space SPE= P r x 2 =r= (I P s )x 2 (12) The process s consdered normal f SPE 2 and T 2 2 (13) where 2 and 2 are the control lmts for the SPE and T 2 statstcs, respectvely, gven a 1- confdence level. These lmts assume that x follows a normal dstrbuton and T 2 follows a 2 dstrbuton wth k degrees of freedom, where k s defned to be the cut off for the number of prncpal components used n the PCA model. Because SPE s a measure of the devaton n the resdual space, t can be used to dentfy when the current operaton devates from the expected n terms of parameters that are not domnant but stll abnormal. On the other hand, the T 2 wll be more senstve to the regular fluctuatons that move the process away from normal based on the projectons n the model subspace. The two statstcs functon ndependently n ths analyss, although a combned ndex has been developed for process montorng. Yue and Qn [14] proposed a convenent alternatve for mergng the nformaton from SPE and T 2. For the purpose of ths analyss though, each statstc wll be examned separately. E. Fault Isolaton and Contrbuton Plots After a fault has been detected, there are several methods that can be used to determne the crtcal system parameters. Contrbuton plots contnue to be a wdely used for fault dagnoss. Durng montorng of the system each new observaton that s projected on the model and resdual subspaces wll have a unque mpact onto each subspace respectvely as dscussed earler. The mpact s quantfed by 284

4 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 calculatng the contrbutons to the SPE and T 2. The larger the contrbuton of an ndvdual parameter, the more lkely t s that the parameter s the reason for the changes or faults. The contrbuton of the m th parameter to the SPE s found by takng the squared resdual assocated wth that parameter x m by: SPE m =r m 2 (14) The contrbuton of all parameter to T 2 s gven (n terms of the SVD) by: T 2 = XUS -1/2 U T (15) III. E XPERIMENTAL SETUP To demonstrate the feasblty of the proposed methodology, experments were conducted to defne a baselne for healthy products and to dentfy specfc parameter behavor. Notebook computers were exposed to a set of envronmental condtons representatve of the extremes of ther lfe cycle profles. The performance parameters, the fan speed, CPU temperature, motherboard temperature, vdeocard temperature, %C2 state, %C3 state, %CPU usage, and %CPU throttle were montored n-stu durng the experments. The baselne of healthy products was used to dfferentate unhealthy products from healthy ones. The proposed anomaly detecton methodology was verfed by njectng an artfcal fault nto the system. Results from the study demonstrate the potental of the approach for system dagnostcs and prognostcs. Operatonal and envronmental ranges and profles that consttute a healthy system were used to replcate the real tme usage of the notebook computer. Software was nstalled on the computer to be used. A set of user actvtes was defned and smulated usng scrpt fle to run on notebook computers. An artfcal fault was njected nto the notebook computers to create and detect any change n system dynamcs. Power Settng AC adapter (when battery s fully charged) AC adapter (when battery s ntally fully dscharged) TABLE I ENVIRONMENTAL CONDITIONS Temperature- Humdty 5ºC wth uncontrolled RH 25ºC wth 55% RH (room ) 25ºC wth 93% RH 50ºC wth 20% RH 50ºC wth 55% RH 50ºC wth 93% RH TABLE II EXPERIMENTS PERFORMED Usage Level Envronmental Condton Battery only Experments were performed on ten dentcal notebook computers, representatve of the state-of-the-art n (2007) notebook computer performance and battery lfe (nearly three and half an hours on a sngle battery). For the experment, sx dfferent envronmental condtons were consdered as shown n Table I. For each temperature/humdty combnaton, four usage condtons and three power supply condtons were consdered. Factoral experment was desgned to study the effect of each factor on the response varable, as well as the effects of nteractons between factors on the response varable. Table II shows the lst of all 72 experments. Each computer was turned on for 30 mnutes before startng the experment. The software for n-stu montorng was nstalled on the notebook computers, along wth Wndows XP Professonal operatng system, Mcrosoft Offce, Front page, WnRunner, Spybot, Wnamp, Real Player, Vsual Studo, Java 5, Mntab, Tunes, Adobe Photoshop, MATLAB, Wnzp and McAfee Antvrus. Selecton of ths software was based on the authors dscreton and experence. A scrpt fle was wrtten usng WnRunner software to smulate user actvty. Antvrus applcaton McAfee v8.0 was confgured to run on the laptop all the tme. A set of fles (.doc,.mp3,.ppt,.pdf,.xls) was kept n a folder to be used durng smulaton. Notebook computers were kept at room temperature between each test condton. When the laptop was powered by the AC adapter (when the battery was fully charged), the test duraton was 3.5 hours. When the laptop was powered by an AC adapter (when the battery was fully dscharged), the test duraton was determned by the tme t took for the battery to fully charge. When the laptop was powered by ts battery only, the test duraton was determned by the tme t took for the battery to fully dscharge. Same usage condtons were appled on all notebook computers to acheve tme synchronzaton between computer and software applcaton responses. The notebook computer s power mode was always set to ON. The screen saver and hbernaton opton were dsabled to prevent these functons from occurrng durng an experment. The wreless capablty of notebook computer was dsabled due to the lmted wreless connectvty nsde the temperature-humdty chambers. Four level of notebook computer usage were chosen: 1. Idle system - In ths category the operatng system s loaded, all wndows are closed, user nput from the keyboard or mouse, optcal drve are dsabled. USB or Frewre perpherals are not attached. 2. Offce productvty - In ths category, the usage condton s desgned to smulate an offce work envronment. The smulator work s desgned to read a word document as well as prepare a new word document. The smulator opens the fle explorer and locates a fle to be opened. The smulator opens a technology benchmark report word document of 88 pages and sze of 2.6MB. The smulator reads through the document and uses arrow keys to move page up, page down and selects 285

5 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 a paragraph to copy. The smulator opens a new document from the word toolbar and pastes thee coped secton to a new document. The smulator reszes both documents to make t easy to toggle between the two documents. The smulator swtches to the orgnal document and reads through pages and copes addtonal paragraphs and pastes agan nto the new document as new paragraphs. The smulator also types a new paragraph nto the new document. Wth these actvtes, the smulator creates a fve-page summary and saves t by pressng the save button n the word toolbar. Then t saves the fle through nvokng the save as fle explorer and provdng a fle name for the new document. The smulator does a cleanup by reszng and closng all opened document. The smulator removes the new fles from the desktop and pastes nto another folder. Fnally, the smulator closes all opened fle explorer wndows. 3. Meda center In ths category, the usage condton s desgned to smulate an entertanment need. Wnamp (v5.24) meda player started from the start menu. The fle explorer wndow s opened by pressng the open button n Wnamp. MP3 musc fles are stored on the hard drve and selected to play n Wnamp. Musc s stopped after 4 mnutes followed by shuttng down the Wnamp player wndow. Real meda player (v10.5) s started from the start menu. The fle explorer wndow s opened to select vdeo fles by pressng the open button n Real player. Vdeo fles from a DVD are selected by maneuverng through the fle explorer wndow and then played n Real player. Move screens are reszed to full screen. The move s turned off after 90 mnutes and Real player closed. 4. Game mode In ths category, the usage condton s desgned to smulate gammng. Quake Arena II was started from the start menu and sngle player opton s selected to start the game. After an hour of play, the game s stopped and exted. The followng secton provdes dscusson on the data analyss and provdes results on the data collected durng these experments. Data analyss s performed by the methodology dscussed n the prevous secton. IV. DATA ANALYSIS AND DISCUSSION The experments were performed on ten new notebook computers wth an assumpton that these products are representatve of normal/healthy products. The MD value obtaned from these datasets called Mahalanobs space s used to dentfy anomales present n the product. Fve thousand data ponts are selected from the experments performed at CALCE. An effort was made to demonstrate the capablty of the MD method to detect anomales present n a test notebook computer and characterzaton of ths computer model based on the baselne experments. In Fg. 1, MD values are plotted to graphcally present the performance of the test computer n comparson to the CALCE baselne. From Fg. 1, the test computer shows problems from the begnnng, a fact verfed by observng the actual data fle for the test computer n whch the fan was not operatng and the three montored temperatures were unusually hgh. The drop n MD value for the test computer at the 2700 th and 3600 th observatons are an ndcaton that the computer were shutdown and then restarted, whch caused a temporary drop n these temperatures. Ths can be verfed by lookng at the actual data fle. Based on our results, we have seen that a test computer can be characterzed usng expermental data representatve of healthy computers. It s observed that the MD values for the test computer are dfferent from the MD values correspondng to the baselne. Metrcs correspondng to the analyss are gven n Table III. The table gves the statstcs of MD values for the test computer and the baselne. The test computer shows hgher MD values as compared to the baselne. Fg. 1 Comparson of MD values of abnormal test computer wth baselne TABLE III STATISTICS OF MD VALUE BASED ON EXPERIMENTAL DATA System/Stats Mean Std Dev 1st Quartle 3rd Quartle Baselne Test Abnormal Orthogonal array analyss s used to dentfy the sgnfcant parameters out of the eght orgnal parameters. The leaveone-out expermental runs are shown n Table IV. The parameters are lsted n the columns and the leave-one-out runs n the rows. An entry of 1 n the cell ndcates that the parameter s ncluded and 2 ndcates that t s excluded. In total, nne leave-one-out runs were conducted, one wth all parameters present and then the remanng eght excludng one parameter respectvely each tme to nvestgate the effect of that parameter on the MD output values. The S/N rato s used as a measure of performance for each leave-one-out run and calculated usng equaton

6 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 S/N rato P1 P2 P3 P4 P5 P6 P7 P8 Fg. 2: Graphs of factoral effects In Fg. 2, the dfference n the (S/N) rato s represented n Fg. 2 as a vector, and hghlghts parameters that have a vectors wth a negatve slope. These parameters are TABLE IV ORTHOGONAL ARRAY Performance Parameters Vdeo card %C2 Temp State consdered sgnfcant ones. The level of mportance for each parameter s then further defned by the magntude of ther vector slopes. Parameters that show postve slopes are not consdered sgnfcant because elmnaton of these parameters does not result nto nformaton loss. Snce removal of these parameters result nto hgher S/N rato these parameters are not dentfed as sgnfcant once, snce larger the better S/N rato s the crtera for parameter selecton. Ths analyss dentfes four mportant parameters: the fan s the most crtcal parameter out of these four, and the three temperature parameters are also shown to be mportant. They are affected by the falure of the fan and temperature ncrease of ~10 degrees centgrade as experenced by the temperature components. The followng paragraphs dscuss the Projecton Pursut analyss approach. No. CPU Mother %C3 %CPU %CPU Fan Speed Temp board Temp State Usage Throttle Fg. 3 Comparson of SPE scores of abnormal test computer wth baselne The goal of the Projecton Pursut analyss was to use Hotellng T 2 and SPE statstcs from a healthy computer and successfully classfy and detect faults n a new computer of the same model. Two healthy baselne sets of T 2 and SPE statstcs were derved from two sources: one from a CALCE baselne set, based on 10 healthy computers of a dfferent model, and the other based on one computer of the same model. From the analyss, the known faulty computer was dentfed as abnormal based on both comparsons. Fg. 3 and Fg. 4 are used as example plots to show the analyss results by plottng the SPE and Hotellng T 2 statstcs for the above two scenaros versus the number of sample ponts. The lower pnk lne ndcates baselne healthy values for each statstc and the upper blue lne ndcates the test values for each S/N rato statstc for the abnormal test computer. It s clear from the plots that the abnormal test computer statstcs are dfferent from the baselne computer for both scenaros. The frst fve prncpal components were used to form the model space and the remanng three for the resdual space. From these results we see that the varablty of the process n both the PCA model and resdual subspaces can be used to capture abnormal system behavor. The detecton s based on the geometry of the problem whose dmensons are establshed by the PCA model and resdual subspaces. The subspaces as dscussed are constructed from the healthy data and represent a fxed frame of reference used to compare ncomng new observatons. New observatons are taken as a pont n the mult-dmensonal space and are projected onto the PCA model and resdual subspaces respectvely. Wth the projecton the new observaton s reduced from ts orgnal dmenson R 1xm to the lower dmenson of the PCA model, R 1xk, where k s the number of prncpal components used to form the model subspace. If the projecton of the observaton falls wthn the statstcal control lmts 2 and 2, of the model and resdual subspaces respectvely, then t s taken as normal or healthy, otherwse t s treated as abnormal or un-healthy. The PCA model can mask faults. Ths can occur for example when the new computer starts to exhbt abnormal behavor yet the varablty of test data n both the model and resdual subspaces fall wthn the healthy control lmts for the system. 287

7 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 Fg. 4: Comparson of Hotellng T 2 scores of abnormal test computer wth baselne For the baselne, the statstcs are modeled wth patterns that are smlar for both comparsons. One of the explanatons for ths s that the baselne for the computers captures the necessary range and varablty of normal operatng condtons of such computer models. Wthout the use of the control lmts ths analyss s left to dentfy the presence of abnormaltes between test and tranng data and also to dentfy the crtcal system parameters. A. Fault Isolaton Domnant Varables Usng Projecton Pursut Analyss The model space s desgned to capture the data that vares the most, whereas the resdual space s desgned to capture the data that does not vary but contrbutes to a faulty state. The resdual space can therefore detect changes n the dstrbuton from varables that are degradng or have faults and are not effectng the varance. Below are the prncpal components for the entre subspace S. Each prncpal component s composed of the eght parameters wth a partcular weghtng as shown n Table IV. The model/sgnal subspace s composed of the frst four prncpal components. Ths was chosen based on teratve expermentaton to best capture the faults. The decson of how many prncpal components are chosen to represent the model/sgnal space s based on experence and understandng of the data at hand. There are computatonal/statstcal technques that can provde estmates for the selecton of the number of PCs to optmzed results. The remanng columns span the resdual subspace. TABLE V PRINCIPAL COMPONENT OF SUBSPACE S AND PARAMETER CONTRIBUTION [S] PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 Fan Speed CPU Temp Motherboard Temp Vdeocard Temp %C2 State %C3 State %CPU Usage %CPU Throttle Each varable s represented by each respectve row of matrx [S]. The frst row shows the contrbutons of the fan speed, and the rest show the CPU temperature, motherboard temperature, vdeo card temperature, %C2 state, %C3 state, %CPU usage and %CPU throttle from top to bottom n matrx [S]. From the decomposton of [S] we can see that the model space varatons should be domnated by the fan speed followed by %C3 state, %CPU throttle and usage. In the resdual subspace the temperature components are domnant. We expect that the temperature varables to be hghly domnant. Changes n the temperature are expected n turn to be less obvous to changes n system varance and should contrbute to the shape of the multvarate data dstrbuton. Such a dstrbuton can be modeled as Gaussan mxtures, but n general a hard task. Intutvely, f the fan speed s not functonng, we expect that the temperature of the system wll rse and become abnormally hgh. Ths s at frst hand valdated by the domnance of the temperatures components as observed n the resdual subspace n [S]. Mathematcally, ths s also valdated through the parameter contrbuton plots to the T 2 and SPE respectvely as llustrated n the contrbuton plots shown n Fg. 5 and Fg. 6. The contrbuton plots tell us whch parameter s contrbutng the most to the projecton onto each subspace. It s shown that on the model space the fan speed s hghly domnant and vares the most n terms of standard devaton. Ths phenomenon masks the effect on parameters that are also exhbtng abnormaltes but are overpowered by domnant parameters such as the fan speed. The resdual space statstc, SPE, captures the nverse nformaton and dentfes the parameters that are ndeed abnormal but are not domnatng n terms of varance. Also nterestng s the fact that the mathematcs valdates our ntuton that because the fan s not functonng properly, the temperature sensors would be experencng unusual readngs. Note that these results are based on pckng the model space usng k = 4, that s the frst four PCs n matrx [S]. The selecton of more PCs for the model space and consequently fewer PCs for the resdual space wll change the results slghtly. If all eght PCs are used to construct the model space then the SPE wll be rendered neffectve although the results for the Hotellng T 2 wll mprove. Even though the results from the Hotellng T 2 mprove wth the selecton of more PCs the nformaton avalable through the SPE s lost. There are ways to select the optmum number of PCs necessary to optmze the nformaton captured from both subspaces, often the selecton 288

8 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 s purely based on experence or expermentaton, although there are statstcal methods such as the maxmum lkelhood estmator (MLE) whch can estmate the optmum number of PCs to use. % Contrbuton % Contrbuton Fan Motherboard Temp Vdeo Card Temp CPU Temp %C2 %C3 %CPU Usage %CPU Throttle Parameters Fg. 5 Contrbuton plot of each parameter towards T Fan %Motherboard Temp %Vdeo Card Temp %CPU Temp %C2 %C3 %CPU Usage %CPU Throttle Parameters Fg. 6 Contrbuton plot of each parameter towards SPE V. CONCLUSIONS A set of experments n dfferent usages and envronmental condtons were conducted to establsh the baselne healthy or normal operaton on a set of notebook computers. A test computer was then subjected to the feld use condton and t was evaluated usng Mahalanobs Dstance (MD), and Projecton Pursut analyss (PPA) technques. In ths study, PPA and MD were ndependently used to dentfy the smlarty of new observatons to healthy data, detect system anomales and dentfy crtcal components. PPA performed ths analyss n a reduced dmenson based on an optmzaton crteron (maxmum varance). The strength of PPA les n the ablty to decompose the sgnal and extract addtonal nformaton not orgnally avalable, used to dentfy faults n the system. PPA overcomes maskng effects when workng wth hghly correlated data. The strength of the MD method s that t preserves all the nformaton avalable because t does not reduce the orgnal dmensonalty of the data but t s susceptble to maskng effects. Usng an S/N rato analyss based on Taguch s technque the MD analyss was also used to dentfy the crtcal components. Four crtcal parameters were dentfed through both methods: the fan speed and the three temperature components (CPU temperature, motherboard temperature, and vdeocard temperature). The fan speed s dentfed as the most domnant, whereas the three temperature parameters were dentfed less domnant but stll contrbutng to a faulty state. Ths fndng valdated the actual problem wth the test computer, namely that ts fan was malfunctonng. REFERENCES [1] N. Vchare, P. Rodgers; V. Eveloy; and M. Pecht; Envronment and Usage Montorng of Electronc Products for Health Assessment and Product Desgn, Internatonal Journal of Qualty Technology and Quanttatve Management. vol. 2, no. 4, 2007, pp [2] J. Gu; N. Vchare; T. Tracy; and M. Pecht; Prognostcs Implementaton Methods for Electroncs, 53rd Annual Relablty and Mantanablty Symposum (RAMS), Florda, [3] G. Zhang, C. Kwan; R. Xu; N. Vchare; and M. Pecht; An Enhanced Prognostc Model for Intermttent Falures n Dgtal Electroncs, IEEE Aerospace Conference, Bg Sky, MT, March [4] N. Vchare; and M. Pecht; Enablng Electronc Prognostcs Usng Thermal Data, Proceedngs of the 12th Internatonal Workshop on Thermal Investgaton of ICs and Products, Nce, Côte d'azur, France, September [5] N. Vchare, P. Rodgers; and M. Pecht; Methods for Bnnng and Densty Estmaton of Load Parameters for Prognostcs and Health Management, Internatonal Journal of Performablty Engneerng, vol. 2, no. 2, Aprl [6] A. Fraser; N. Hengartner; K. Vxe; and B. Wohlberg; Incorporatng Invarants n Mahalanobs Dstance based Classfers: Applcaton to Face Recognton, n Internatonal Jont Conference on Neural Networks (IJCNN), (Portland, OR, USA), Jul [7] J. E. Jackson; and G. S. Mudholkar; Control Procedures for Resduals Assocated Wth Prncpal Component Analyss, Technometrcs, vol. 21, no. 3, [8] J. Lu, K. Lm; R. Srnvasan; and X. Doan; On-Lne Process Montorng and Fault Isolaton Usng PCA, Proceedngs of the 2005 IEEE Internatonal Symposum on, Medterranean Conference on Control and Automaton, 2005, pp [9] G. Taguch, and R. Jugulum; The Mahalanobs-Taguch Strategy: A Pattern Technology System, Wley, [10] G. Taguch, S. Chowdhury; and Y. Wu; The Mahalanobs Taguch System, New York: McGraw-Hll [11] E. B. Martn, A. J. Morrs; and J. Zhang; Process Performance Montorng Usng Multvarate Statstcal Process Control, IEEE Proceedng of Control Theory Applcaton, vol. 143, no.2, March [12] H. Chen, G. Jang; C. Ungureanu; and K. Yoshhra; Falure Detecton and Localzaton n Component Based Products by Onlne Trackng, KDD, [13] H. Wang, Z. Song; and P. L; Fault Detecton Behavor and Performance Analyss of Prncpal Component Analyss Based Process Montorng Methods, Amercan Chemcal Socety, vol. 41, 2002, pp [14] H. Yue, and S. J. Qn; Reconstructon-Based Fault Identfcaton Usng a Combned Index, Amercan Chemcal Socety, vol. 40, 2001, pp Sachn Kumar receved the B.S. degree n Metallurgcal Engneerng from the Bhar Insttute of Technology and the M.Tech. degree n Relablty Engneerng from the Indan Insttute of Technology, Kharagpur. He s currently pursung the Ph.D. degree n Mechancal Engneerng at the Unversty of Maryland, College Park. Hs research nterests nclude relablty, electronc system prognostcs, and health and usage montorng of systems. Vasls Sotrs receved the B.S. degree n Aerospace Engneerng from Rutgers Unversty n New Brunswck, New Jersey and the M.S. degree n Mechancal Engneerng from Columba Unversty n New York. He worked as a Systems Engneer for Lockheed Martn Corporaton concentratng on software development projects for the Federal Avaton Admnstraton. He s currently pursung the Ph.D. degree n Appled Mathematcs at the Unversty of Maryland, College Park. Hs research nterests are n the feld of appled statstcs and computatonal mathematcs related to dagnostcs and prognostcs for electronc systems. 289

9 Internatonal Scence Index, Electroncs and Communcaton Engneerng waset.org/publcaton/8544 Mchael Pecht has a B.S. n Acoustcs, an M.S. n Electrcal Engneerng and an M.S. and Ph.D. n Engneerng Mechancs from the Unversty of Wsconsn at Madson. He s a Professonal Engneer, an IEEE Fellow and an ASME Fellow. He has receved the 3M Research Award for electroncs packagng, the IEEE Award for charng key Relablty Standards, and the IMAPS Wllam D. Ashman Memoral Achevement Award for hs contrbutons n electroncs relablty analyss. He has wrtten over twenty books on electronc products development, use and supply chan management. He served as chef edtor of the IEEE Transactons on Relablty for eght years and on the advsory board of IEEE Spectrum. He has been the chef edtor for Mcroelectroncs Relablty for over eleven years and an assocate edtor for the IEEE Transactons on Components and Packagng Technology. He s a Char Professor and the founder of the Center for Advanced Lfe Cycle Engneerng (CALCE) and the Electronc Products and Systems Consortum at the Unversty of Maryland. He has also been leadng a research team n the area of prognostcs, and formed the Prognostcs and Health Management Consortum at the Unversty of Maryland. He has consulted for over 50 major nternatonal electroncs companes, provdng expertse n strategc plannng, desgn, test, prognostcs, IP and rsk assessment of electronc products and systems. 290