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

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Health Assessment of Electronic Products Using Mahalanobis Distance and Projection Pursuit Analysis International Journal of Computer, Information, and Systems Science, and Engineering 2;3 © www.waset.org Fall 2008 Health Assessment of Electronic Products using Mahalanobis Distance and Projection Pursuit Analysis Sachin Kumar, Vasilis Sotiris, and Michael Pecht implementation for electronics, from on–chip packaging to Abstract—With increasing complexity in electronic systems complete products of products. They provided an approach for there is a need for system level anomaly detection and fault isolation. prognostics implementation at the various levels of Anomaly detection based on vector similarity to a training set is used electronics, based on failure modes, mechanisms and effects in this paper through two approaches, one the preserves the original analysis. information, Mahalanobis Distance (MD), and the other that compresses the data into its principal components, Projection Pursuit Zhang et. al. [3] proposed a model to assess intermittent as Analysis. These methods have been used to detect deviations in well as hard failures. The model is a fusion of two prediction system performance from normal operation and for critical parameter algorithms based on life consumption monitoring and isolation in multivariate environments. The study evaluates the uncertainty adjusted prognostics. detection capability of each approach on a set of test data with known Vichare et. al. [1][4][5] proposed methods for monitoring faults against a baseline set of data representative of such “healthy” and recording in-situ temperature loads. This includes systems.. methods for embedding data reduction and load parameter extraction algorithms into the sensor modules to enable Keywords—Mahalanobis distance, Principle components, Projection pursuit, Health assessment, Anomaly. reduction in on-board storage space, low power consumption, and uninterrupted data collection. I. INTRODUCTION Two approaches for detection and fault isolation based on classification theory are presented in this paper. Both are ROGNOSTICS and health management (PHM) is a process capable of system level anomaly detection in multivariate, of predicting the future reliability of the system by P data-rich environments. One methodology uses the assessing the extent of deviation or degradation of a product Mahalanobis Distance (MD) and the other uses a projection from its expected normal operating conditions in a preemptive pursuit analysis (PPA) to analyze on-line system data. Both and opportunistic manner to the anticipation of failures. This approaches are used to monitor the health of the system and can enable continuous, autonomous, real time monitoring of identify onsets and periods of abnormalities. Parameter the health conditions of a system by means of embedded or contribution is performed by both approaches as a means of attached sensors with minimum manual intervention to identifying dominant and potentially faulty parameters [8] [9] evaluate its actual life-cycle conditions, to determine the [12]. Experiments were performed on notebook computers to advent of failure, and to mitigate system risks. The term generate data and validate the analysis approaches. The “diagnostics” refers to the detection and isolation of faults or experimental details, the algorithmic approach to anomaly failures and “prognostics” refers to the process of predicting a detection, and a case study are discussed. future state (of reliability) of the system based on its current and historic conditions. The aim of failure prognosis is II. METHODOLOGY TO IDENTIFY ABNORMALITIES IN intended to identify and estimate the advancement of fault ELECTRONIC PRODUCTS conditions to system failure. Quantification of degradation and the progression from The Mahalanobis Distance (MD) methodology is a process faults to failure in electronic products is a challenging task. of distinguishing data groups [6][10]. The MD measures Gu et. al. [2] identifies six levels of prognostics distances in multi-dimensional spaces by considering correlations among parameters. The distance is sensitive to the correlation matrix of the healthy group. The MD values are S. Kumar is with the Center for Advanced Life Cycle Engineering (CALCE), University of Maryland, College Park, MD 20742 USA (phone: used to construct a normal operating domain also known as 301-405-5324; fax: 301-314-9269; e-mail: skumar@ calce.umd.edu). Mahalanobis space to monitor the condition of a multi- V. Sotiris with the Center for Advanced Life Cycle Engineering dimensional system. Health of a system is defined by several (CALCE), University of Maryland, College Park, MD 20742 USA (e-mail: vsotiris@ calce.umd.edu). performance parameters. These parameters are standardized M. Pecht with the Center for Advanced Life Cycle Engineering (CALCE), and the MDs are calculated for the normal group. These MD University of Maryland, College Park, MD 20742 USA (e-mail: pecht@ values define the Mahalanobis space, which is used as a calce.umd.edu). 242 International Journal of Computer, Information, and Systems Science, and Engineering 2;3 © www.waset.org Fall 2008 reference set for the MD measurement scale. responses for each run. The parameters collected from a system are denoted as Xi, Many different S/N ratios are used in Taguchi’s design of where i = 1,2,…,m. The observation of the ith parameter on experiment. One option mentioned is to use Taguchi’s [9] th the j instance is denoted by Xij, where i =1, 2,…, m, and j = larger-is better S/N ratio, defined as (4) 1, 2,…,n. Thus the (m x 1) data vectors for the normal group 2 ⎡ q ⎛ 1 ⎞ ⎤ are denoted by X , where j = 1, 2,…, n. Here m is the number −10log⎢(1/ q) ⎜ ⎟ ⎥ (4) j ⎢ ∑⎜ MD ⎟ ⎥ of parameters and n is the number of observations. Each ⎣ j=1 ⎝ j ⎠ ⎦ individual parameter in each data vector is standardized by where, q is the number of observation for an leave-one-out subtracting the mean of the parameter and dividing it by the run. standard deviation. These mean and standard deviation are For a given parameter Xi, the average value of the S/N ratio calculated from the data collected for normal or healthy is determined over all runs with that parameter present (S/Np) system. Thus, the standardized values are: and absent (S/Na). If the difference between (S/N) ratios S/Np (X − X ) (Xi) - S/Na (Xi) is positive then this parameter has higher ij i , i = 1, 2… m, j=1, 2… n, Zij = (1) responses when it is part of the system and therefore the Si parameter Xi, is retained and considered critical. n 2 B. Projection Pursuit Analysis n ∑()Xij − Xi 1 where, X = X and S = j=1 The Projection Pursuit Analysis uses a Principal i n ∑ ij i j=1 ()n −1 Components Analysis (PCA), least squares optimization (LS) Next, the values of the MDs are calculated for the normal and a Singular Value Decomposition (SVD) treatment of the items using: data. PCA is used in a wide array of applications to reduce a 1 large data set to a smaller one while maintaining the majority MD = zTC−1z (2) j m j j of the variability present in the original data. It’s also very T useful in providing compact representation of temporal and where, zj =[z1j,z2j,…,zmj] is a vector comprises of zij , zj is T spatial correlations in the fields of data being analyzed. PCA transpose of zj and C is correlation matrix calculated as: n facilitates a multivariate statistical control to detect when 1 T C = z jz j (3) abnormal processes exist and can isolate the source of the (n −1) ∑ j=1 process abnormalities down to the component level. Next, the test system is considered to determine its health. Two statistical indices, the Hotelling Squared (T2) and The MDs for the test system are calculated after the squared prediction error (SPE) are used in the PCA. The SPE parameters are standardized using the mean and standard statistic is related to the residuals of process variables that are deviation for normal-group. The resulting MD values from not illustrated by the PCA statistical model, and is a reliable test system are compared with the MD values of the normal or indicator to a change in the correlation structure of the process healthy system to determine test system’s health. variables. The SPE physically tests the fit of new data to the A. Significant Parameter Identification Using Mahalanobis established PCA models and is efficient at identifying outliers 2 Distance Analysis from the PCA model [7]. The Hotelling T score measures the Critical parameters using MD output can be achieved by Mahalanobis distance from the projected sample data point to identifying parameters that contribute more to the MD value. the origin in the signal space defined by the PCA model. In other words, the parameters that have significant impact on The primary objectives of principal component analysis are the MD value should be identified. The effect of individual data summarization, classification of variables, outlier parameters or combination of parameters on MD output detection, early warning of potential malfunctions and values can be observed through a leave-one-out approach isolation of fault. PCA seeks to find a few linear combinations where a reduced set of parameters is used to compute the MD which can be used to summarize the data with a minimal loss values, in effort to understand the effect of the excluded of information. Let X = x1, x2, x3,..,xm be an m – dimensional parameter. The leave-one-out approach can be expressed by data set describing the system variables. The first principal an orthogonal array (OA) and a signal-to-noise (S/N) ratio that component is the linear combination of the columns of X, i.e. can be used for quantify the impact of selected combinations. the variables, which describes the greatest variability in X, An OA is a design matrix that reflects the presence or absence t1=Xp1 subject to |p1|=1.
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