Keynote Presentation Feature Extraction and Health ... - IEEE Xplore

Keynote Presentation Feature Extraction and Health Monitoring using Image Correlation for Survivability of Leadfree Packaging under Shock and Vibration Pradeep Lall, Deepti Iyengar, Sandeep Shantaram, Prashant Gupta, Dhananjay Panchagade, Jeff Suhling Auburn University Department of Mechanical Engineering and Center for Advanced Vehicle Electronics Auburn, AL 36849 Tele: (334) 844-3424 E-mail: [email protected] Abstract In this paper, the feature extraction for health monitoring based on optical measurements of transientstrain from digital image correlation (DIC) in conjunction with ultra high-speed imaging has been investigated. Full-field measurement of transient strain have been made in various board assemblies subjected to shock in various orientations. Feature-extraction for health monitoring of leadfree area array architectures based on statistical pattern recognition has been presented. Previous researchers have measured the transient-dynamics of board assemblies with high-speed imaging in conjunction with high-speed image analysis for measurement of relative displacement, angle, velocity, and acceleration [Lall 2006, Che 2006], high-speed data-acquisition systems with discrete strain gages [Lall 2004, 2005, Liang 2005] and with accelerometers for measurement of transient acceleration [Dunford 2004, Goyal 2000, Seah 2005]. Degradation in confidence value gives a leading indication of component failure. Package architectures examined include-flex ball-grid arrays, tape-array ballgrid arrays, and metal lead-frame packages. Statistical Pattern Recognition Techniques including, mahalanobisdistance approach, wavelet packet energy decomposition, and time-frequency (TFA) techniques have been investigated for system identification, condition monitoring, and fault detection and diagnosis in electronic systems. Explicit finite element models have been developed and various kinds of failure modes have been simulated such as solder ball cracking, package fall off and solder ball failure. Models developed include, smeared property models, Timoshenko-beam models, and explicit sub-models. Explicit finite-element models have been correlated with experimental data. The presented approach does not depend on continuity and therefore does not need daisy-chained devices for detection of failure. 1. Introduction Early indicators of system degradation can signal impending failure. Diagnosing impending loss of functionality provides a window for the identification of potential failures and trigger repair or replacement significantly prior to failure. In this paper, a feature

C 2008 IEEE 978-1-4244-2128-2/08/$25.00

extraction approach to health monitoring using drop and shock survivability models and optical high-speed data in conjunction with statistical pattern recognition has been presented for leadfree solder systems. While, structural health monitoring is popularly used in various fields, its application to the field of reliability of electronic structures is relatively new. Currently the failure monitoring methodologies performed on electronic assemblies undergoing drop and shock utilize the resistive continuity of daisy chained circuits [Lall 2004, 2005, 2006a,b], Shear testing [Hanabe 2004] and ball pull testing [Newman 2005]. The JEDEC drop test is based on the JESD-B2111 test standards, and targets the board-level evaluation of shock reliability of components. Electronic packages on the printed-circuit board are typically daisy chained and the failure detection techniques relies on measurement of electrical resistance. Ball-pull testing and Shear testing has also been applied to test structures to study the reliability of electronic assemblies to shock and vibration. In addition, the impact toughness of solder joints using Charpy test [Date 2004], Shear test, and the package to board interconnection shear strength (PBISS) technique [Hanabe 2004] has been used as damage proxy. Continuity-based test procedures are not scalable for product-level damage monitoring during shock and vibration. The Built in self test (BIST) approach is currently being applied to the testing of Digital chips and various other digital devices [Steininger 2000, Harris 2002, Hashempour 2004, Suthar 2006], but the current version of BIST approach is focused on reactive failure detection and provides limited insight in to solder joint reliability and residual life. Previously, health monitoring and prognostication of electronic assemblies has been investigated using statistical pattern recognition based on wavelet packet decomposition and Mahalanobis distance approach using transient strain data from strain gages [Lall 2006c]. Structural health monitoring has found application in various fields, like shaft crack detection [Lebold 2004, Gyekenyesi 2003], aircraft maintenance [Hedley 2004, Hickman 1991, Castanien 1996], and Machinery systems [Lee 1995, Chuang 2004, Wegerich 2003]. In electronics industry, digital image correlation has been used to study the stresses in solder interconnects of BGA packages under thermal loading [Zhou 2001, Yogel

—1—

9th. Int. Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2008

2001, Rajendra 2002, Zhang 2004, Zhang 2005, Xu 2006, Bieler 2006, Sun 2006], material characterization under thermal loading [Srinivasan 2005, Gu 2006], parametric study of speckle size [Gu 2006], dynamic testing to study deformation for flexible bodies [Reu 2006], material characterization at high strain rate [Tiwari 2005], stresses and strain in flip-chip die under thermal loading [Kehoe 2006], fracture toughness of underfill/chip interface due to temperature and aging conditions [Song 2006]. The use of digital image correlation for health monitoring of electronic assemblies is new. In this paper, deformation kinematics has been measured with the help of ultra highspeed data acquisition and video systems. Various test board assemblies have been drop tested in 00 JEDEC and 900 vertical drop orientations. Continuity of the daisy chained packages is measured for all the packages during the transient event. Experimental data has been correlated to the finite element models. Explicit finite element models have been used to assess reliability and performance of the electronic boards. Failure modes have been studied for various packaging architectures including flex-BGA and Tarray BGA. Influence of thermal cycling, board surface finish (ImSn, ImAg, ENIG), and drop severity has been studied on the development of failure modes. Weibull plots are used for reliability prediction of the fine-pitch packages. In this paper, damage proxies have been developed to serve as a component integration guideline to ensure survivability in shock and vibration environments at a user-specified confidence level. The approach is scalable to a wide variety of electronic applications. The reliability of packages of different leadfree architectures including PBGA, CABGA, BGA, CSP, PQFN and MLF has been investigated. Four different surface finishes, ImAg, ENIG, ImSn and Cu-OSP on six different PCBs have been compared. The reliability of Sn4Ag0.5Cu lead free solder alloy system has been evaluated under impact loading conditions in the JEDEC orientation. In addition, the effect of thermal stresses has been studied by subjecting two sets of test boards to thermal cycling from -40°C to +125° C for 25 cycles, and thermal aging for 100 hrs at 125° C respectively. Full field strain and displacement data has been acquired using Digital Image Processing (DIC) in conjunction with high speed cameras capable of working at a speed of 275,000 frames per second. The results obtained from this method have been validated by experimental data obtained from strain gages mounted at different locations on the test boards in concurrence with high speed data acquisition systems. Explicit finite element models have been created for all the test boards using different techniques such as smeared model, conventional as well as continuum shellTimoshenko beam element model to predict the reliability of these systems. These results have been validated by comparing them to the experimental data obtained from both the DIC technique and the strain gages. Failure analysis has been done on the failed packages to assess damage and determine the failure modes. Confidence

value of the transient-strain response computed using Wavelet Packet Energy Decomposition, Mahalanobis distance approach, and Joint Time-Frequency Analysis have also been investigated. A methodology has been devised for identifying the damage progression versus number of drops by studying the transient strain history of electronic assemblies from DIC. 2. Test Vehicle Three test structures targeting various packaging architectures were used in this study. Test board A has 10 mm ball-grid array, 0.8 mm pitch, 100 I/O on one side and 8mm flex-substrate chip scale packages, 0.5 mm pitch, 132 I/O. Only one side has been populated in any test vehicle. The test board has ten-components on each side of the board (Figure 1, Table 1). Both 8 mm, 132 I/O CSPs and 10 mm 100 I/O CSPs have lead-free solder balls with 95.5Sn4.0Ag0.5Cu solder alloy. Test boards A is made of FR-4, based on standard PCB technology with no build-up or HDI layers. Test Boards A is 2.95" by 7.24" by 0.042" thick.

10 mm, 100 I/O BGA 8mm 132 I/O BGA Figure 1: Interconnect array configuration 95.5Sn4.0Ag0.5Cu Test Vehicles. Table 1: Test Vehicles 10mm 95.5Sn4.0Ag 0.5Cu Ball Count 100 Ball Pitch 0.8 mm Die Size 5x5 Substrate Thickness 0.5 mm Substrate Pad Dia. 0.3 mm Substrate Pad Type SMD Ball Dia. 0.46 mm

for

8mm 95.5Sn4.0Ag 0.5Cu 132 0.5 mm 3.98 x 3.98 0.1 mm 0.28 mm Thru-Flex 0.3 mm

Test Board B has package architectures including, plastic ball-grid arrays, chip-array ball-grid arrays, tape-array ball-grid arrays, and flex-substrate ball-grid arrays. The experimental matrix has ball counts in the range of 64 to 676 I/O, pitch sizes are in the range of 0.5mm to 1mm, and package sizes are in the range of 6mm to 27mm (Table 1). The test boards are made of FR4-06. These test boards were based on standard PCB technology with six trace layers. Test Boards are 8” x 5.5” x 0.06” thick. All the packages used in the test configuration were daisychained. In all cases, multiple boards were tested in each test-configuration. Test boards were exposed to sequential thermo-mechanical stresses followed by shock impact to determine the effect of cumulative damage on the interconnect reliability.

—2— 9th. Int. Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2008

27mm, 676 I/O PBGA

16 mm, 280 I/O Flex BGA

10 mm, 144 I/O Tape Array

Tracking of a geometric point before and after deformation gives the displacement field [Zhou 2001, Amodio 2003, Srinivasan 2005, Kehoe 2006]. The tracking is achieved using image processing of speckle pattern on the specimen surface. Speckle pattern of the image before and after deformation are captured using high speed camera and digitized into digital images (Figure 3). The two images are called reference image I1 (r) and the deformed image I2 (r) respectively, which are related as follows:

15 mm, 196 I/O PBGA

7mm, 84 I/O CABGA

6 mm, 64 I/O Tape Array

Figure 2: Interconnect array configuration for Test Vehicles. Table 2: Test Vehicles

I/O Pitch (mm) Die Size (mm) Substrate Thick (mm) Pad Dia. (mm) Substrate Pad Ball Dia. (mm)

6 mm Tape Array 64

7 mm 10 mm 15 16 mm 27 Chip Tape mm Flex mm Array array PBGA BGA PBGA 84 144 196 280 676

0.5

0.5

0.8

1

0.8

1

4

5.4

7

6.35

10

6.35

0.36

0.36

0.36

0.36

0.36

0.36

(1)

(2) Where U(r) is the displacement vector at pixel r = (x, y)T . The difference of the positions of the current pixel and the reference pixel gives the in-plane displacement U(r) of this reference pixel. Full-field in-plane displacement can thus be found out by changing the reference pixel and following the same procedure described above. A subimage around a reference pixel O in the reference image is then compared with the subimages corresponding to different pixels in the current image using a predefined correlation function to describe the difference of the two digital subimages. Three typical correlation functions are defined as follows: [Zhou 2001] Absolute difference:

0.28

0.28

0.30

0.38

0.30

0.38

CA ( r ' ) = 1 −

NSMD NSMD NSMD SMD NSMD SMD 0.32

0.48

0.48

0.5

0.48

0.63

3. Digital Image Correlation Data is scarce for the behavior of the printed circuit board transient dynamics in shock, which is a major reliability issue to study the failures at the solder. Health monitoring of electronic assemblies has never been studied using DIC technique when subjected to drop in vertical and JEDEC orientations. M pixels r

I 2 (r ) = I1[r − U (r )] I1 (r ) = I 2 [r + U(r )]

Before Deformation N pixels

Analyzed area (M x N) matrix

O

After Deformation

r O Reference Image I1(r)

Δy U(r) Δx

O`

Current Image I2(r)

Figure 3: Digital Image Correlation Principle

∫∫Ω I2 (r + r ' ) − I1 (r ) dr ∫∫Ω I1 (r )dr

(3)

2 ∫∫Ω [I2 (r + r ' ) − I1 (r )] dr 2 ∫∫Ω I1 (r )dr

(4)

Least square:

CL (r ' ) = 1 −

and Cross-Correlation:

CC (r ' ) = 1 −

[∫∫ I

Ω 1

∫∫Ω I1 (r)I2 (r + r ' )dr 2

(r )dr ∫∫Ω I2 2 (r + r ' )dr

]

1/ 2

(5)

where Ω (M x N) is the area of the subimage around reference pixel r, r` is the current pixel, CA(r`) is the current absolute correlation function, CL(r`) is the current least square correlation function, and CC(r`) is the current cross-correlation function. The cross-correlation functions provide the correspondence between matching subsets in images of the undeformed and deformed states. It is an iterative spatial-domain cross-correlation method. This method maximizes the cross-correlation coefficient between a subset in the reference image I1 and the deformed image I2. In practice, the absolute and least square correlation functions require less computation. They assume constant brightness. In order to handle illumination changes, Normalized cross-correlation is used, which is more computationally demanding. Correlation functions determine the current pixel O’ from the reference pixel O, by matching the two subimages.


during drop. Strain, displacement, orientation angle, velocity, acceleration, and continuity data has been acquired simultaneously. An image tracking software was used to quantitatively measure displacements during the drop event. Figure 4 shows a typical relative displacement plot measured during the drop event. The position of the vertical line in the plot represents the present location of the board (i.e. just prior to impact in this case) in the plot with “pos (m)” as the ordinate axis. The plot trace subsequent to the white scan is the relative displacement of the board targets w.r.t. to the specified reference. Figure 5 shows the board instrumentation for strain and relative displacement during horizontal JEDEC drop. In addition to relative displacement, velocity, and acceleration of the board prior to impact was measured. This additional step was necessary since, the boards were subjected to a controlled drop, in order to reduce variability in drop orientation.

Strain (Microstrain)

1500

10 8

1000

6 4

500

2 0 -0.04 -0.02 -500

0

0.02

0.04

0 0.06 -2

Voltage (Volts)

4. Detection of Damage Progression The test boards were subjected to a controlled drop. Repeatability of drop orientation is critical to measuring a repeatable response. Small variations in the drop orientation can produce vastly varying transient-dynamic board responses. Significant effort was invested in developing a repeatable drop set-up. The drop height was varied to obtain shock pulses of various magnitudes, in addition to the 1500 Gs, 0.5 millisecond duration, halfsine input pulse. Component locations on the test boards were instrumented with strain sensors (Figure 5). Strain and continuity data was acquired during the drop event using a high-speed data acquisition system at 2.5 to 5 million samples per second.

Strain Continuity

-4

-1000

-6 Time (Seconds)

Figure 6: Package Strain and continuity transient history in JEDEC drop-shock. Figure 6 shows the package-strain history during JEDEC drop-shock. Failure in the device has been identified as an increase in voltage drop. Different locations on the test board exhibit different strain histories during the same drop and different number of drops to failure. However, the strain histories are very consistent and repeatable at the same component location on the test board for various drops. The strain history is also very repeatable for the same component location across various test boards.

Figure 4: Relative Displacement during Shock, TestBoard-A (JEDEC Drop)

Figure 5: Experimental Set-up for Controlled Drop, Test Board-B. The drop-event was simultaneously monitored with ultra high-speed video camera operating at 30,000 frames per second. Targets were mounted on the edge of the board to allow high-speed measurement of relative displacement

5. Development of Training Signal and High-Speed Measurement of Transient-Response Strains were measured using two techniques including digital image correlation in conjunction with ultra-high speed video and strain gages in conjunction with highspeed data-acquisition systems. Strain gages were mounted at different locations on the test board on both the package and the board side. Package continuity was monitored during the transient-dynamic shock event. Figure 7 shows the speckle pattern on the four boards. Effort has been made to get a close and consistent speckle patterns on all the test boards. It has been shown in the past that speckle size and distribution affects accuracy [Zhou 2001, Gu 2006]. The test boards A, B are shown in the Figure 8.


Test Board A B

Test Board B D

Figure 7: Speckle Pattern for various test boards

Calibration involves positioning the two cameras at a certain angle in front of the calibration grid (target). Figure 10 shows the picture of the target at various positions during calibration. The images of the target are roughly centered in the field of view for each camera. Exposure from each camera is approximately kept same while capturing target images. Target consists of 9x9 grid points with 15 mm pitch. The two cameras are synced together with one camera as master and the other as slave. A series of images are taken from both the cameras. Approximately 15-20 images per camera are sufficient for calibration. Both the cameras are triggered simultaneously and the images are recorded and analyzed using software from Correlated Solutions.

Figure 8: Test Boards A, B Figure 10: Calibration Repeatability of drop orientation is critical to measuring a repeatable response. Small variations in the drop orientation can produce vastly varying transient-dynamic board responses. Significant effort was invested in developing a repeatable drop set-up. However, the strain histories are very consistent and repeatable at the same component location on the test board for various drops (Figure 11). The strain history is also very repeatable for the same component location across various test boards.

Microstrain

The experimental setup consists of two cameras rested on the rigid floor as shown in Figure 9. The test boards are dropped from 3 ft height in vertical orientation. A mass of steel weighing 31.8 gms is attached on the top edge of the board to accelerate the experiment. The test board is attached to the fixture on the drop tower with the help of fishing lines. Test board falls freely from a predefined height and hits the rigid floor. This event is captured by two high speed cameras at 40,000 fps. The two cameras make an angle of 25 degrees with each other when facing the speckled test board. [Gu 2006] 200, [Helm 1996] 600. It was observed that an angle in the range of 20-40 degrees gave good results. The cameras are calibrated before the start of the experiment.

Drop Tower

1000 800 600 400 200 0 -200 -0.005 -400 -600 -800

Drop2 Drop3 Drop4 Drop5

0.005

0.015

0.025

0.035

Drop6 Drop7 Drop8 Drop9 Drop10 Drop11

Time (Seconds)

Figure 11: Strain Repeatability for Test-Board A.

CCD 250 Rigid Floor CCD

Figure 9: Vertical Drop Test Setup

6. Correlation of Speckle Data with Strain Gages Strain from DIC technique is correlated with the strain from strain gages at various locations on the test board B (Figure 12). Drop results for vertical drop orientation from 3 ft height are shown in Figure 12. The strains are correlated from strain gage sensors and DIC at location A3, and A6 on the Test Board-B. DIC results obtained were accurate and consistent with the strain gage sensors for vertical drop. Figure 13 shows the 2-D contour of


strain in the longitudinal direction from DIC for twodifferent test boards in the 90-degree vertical configuration. DIC Strain Gage

PCB Strain at A3

Microstrain

integration in time without changing the form of dynamic equations as done in modal methods. PCB Stand-off

2000 1000 0 -1000 -2000 -3000 -4000

Drop Table

Rigid Floor

-0.005

0

0.005

0.01

0.015

0.02

Adhesive Copper Pad

Time (Seconds)

DIC Strain Gage

PCB Strain at A6 2000

BT Substrate

Encapsulant Solder Ball

1000 Microstrain

Die

0 -1000 -2000

Test Board C (Zero-Degree Configuration)

-3000

Figure 14: Explicit-Finite Element Model for Test BoardC in JEDEC Configuration.

-4000 -0.005

0

0.005

0.01

0.015

0.02

The modeling effort has focused on prediction of transient dynamic drop response using explicit finite-element theory with reduced integration elements. An explicit algorithm uses a difference expression of the general form,

Time (Seconds)

Figure 12: Strain Correlation on Test Board-C (Vertical Drop)

{D}n +1 = f [{D}n , {D}n , {D}n , {D}n −1 , ....]

Test-Board A Test-Board B

Figure 13: 2-D Strain Contour. 7. Explicit Finite Element Models Transient dynamic deformation of the test boards was modeled using Explicit Finite Element Models. The effect of board drop orientation on global response of printed circuit assembly has been predicted and correlated with digital image correlation measurements. Previously, the JEDEC JESD22-B111 has been modeled has been modeled using the input-G method [Tee 2004]. In this paper, the use of explicit finite elements has been investigated. The use of explicit finite elements enables the calculation of response history using step-by-step

(6)

where {D} is the d.o.f. vector, the “.” on top represents time differentiation, and subscript “n” represents the timestep. The equation contains only historical information on the right hand side. The difference expression is combined with the equation of motion at time step “n” for the simulation. 1 ⎛ 1 [C]⎞⎟{D}n +1 ⎜ 2 [M ] + t 2 t Δ Δ ⎝ ⎠ 2 1 ⎛ 1 ext int = {R }n − {R }n + 2 [M ]{D}n − ⎜ 2 [M ] − [C]⎞⎟{D}n−1 Δt 2Δt ⎠ ⎝ Δt (7) The degree of freedom vector at the n-1 time-step is given by a taylor series, 2 3 {D}n −1 = {D}n − Δt{D}n + Δt {D}n − Δt {D}n + ... (8) 6 2 2 {D}−1 = {D}0 − Δt{D}0 + Δt {D}0 for n = 0, 2 The coefficient matrix of {Dn+1} can be made diagonal using lumped mass-matrix or diagonalization of the consistent mass matrix, [m ] = ∫ ρ [N ]T [N ] dV through techniques such as HRZ lumping. Therefore, {Dn+1} can be cheaply calculated for each time step.


90° free-drop. Linear elastic material properties were assumed for solder interconnects. Drop height required for an 1500 Gs, 0.5 millisecond duration, half-sine input pulse has been determined. An initial velocity of {D}0 , equivalent of the required drop has been assigned to the board, components and the weight at the top edge of the board (Equation 3). The model was simulated between 6ms to 20 ms as the peak deformation and strain was observed during this period. Using beam elements for solder interconnects saved 10x of time as compared to conventional solid elements (C3D8R) for the solder balls.

Test Board A (Zero-Degree Configuration) Figure 15: Explicit-Finite Element Model for Test BoardA in JEDEC Configuration Figure 14 to Figure 16 show the various explicit finite element models for Test Boards A, B, in both zero-degree JEDEC and 90-degree vertical drop configurations. Reduced integration elements have been used to formulate the transient event. Fewer integration points are used as compared to the implicit formulation hence it saves computational time. Shell-elements (S4R) are used to model the PCB which accounts for large strains. The solder interconnects has been modeled using threedimensional, linear, Timoshenko-beam element (B31) elements. Three-dimensional beams have six degrees of freedom at each node including three translational and three rotational degrees of freedom. The rotational degrees-of-freedom has been constrained to model the interconnect behavior. The B31 elements allow for shear deformation. It is assumed that the strain in the beam is constant throughout the beam. Various component layers for the packages such as substrate die-adhesive, silicon die, encapsulant, copper pads have been modeled with C3D8R elements. The concrete floor has been modeled as rigid floor using R3D4 elements. Reduced integration elements have been used for computational efficiency because evaluation of internal force vector, {rint}n requires the same order of quadrature as element stiffness matrix [K]. A reference node has been placed behind the rigid wall for application of constraints. Contact has been monitored between any PCB surface, CSP surface or Weight surface and only on the positive side of the floor. Node to surface contact has been used. The Gerschgorin Bound has been used to provide an estimate of highest natural frequency, ωmax, which is used for calculation of the critical time step size. For a lumped diagonal mass matrix, it may be stated as follows, ⎛ 1 n ⎞ (9) K ij ⎟⎟ ω2max ≤ max⎜⎜ ∑ i ⎝ M ii j=1 ⎠ where, i = 1, 2, 3,….,n, and n is the matrix order of number of degrees of freedom, K and M are the stiffness and mass matrices respectively. Node to surface contact has been employed between PCB and rigid floor. The drop orientation has been varied from 0° JEDEC drop to

Test Board A (90° Vertical Drop) Figure 16: Explicit-Finite Element Model for Test BoardA in 90-degree Vertical Drop Configuration 8. Feature Vector Extraction In this paper, statistical pattern recognition has been applied to study the degradation of reliability in an electronic assemblies, due to shock and drop using FastFourier Transform (FFT) and Time-Frequency Analysis (TFA) for feature extraction. The time frequency analysis using a RID kernel provides the specific time or frequency localized information of the signal which can not be obtained from a wavelet packet spectrum or by using the Mahalanobis distance approach. The health monitoring of the assembly is done by monitoring the confidence values computed by applying statistical pattern recognition techniques to the pertinent data such as strain values, and the vibration mode shapes and frequencies of the electronic assembly under shock and drop. Prior application areas of statistical pattern recognition include image analysis, character recognition, speech analysis, man and machine diagnostics, person identification and industrial inspection. Examples include neural networks applied to faults in gas turbine engines [Atlas 1996, Sick 1998, Chuang 2004], hidden markov models applied to speech recognition and machine tool wear [Wang 2001, Heck 1991], multivariate similarity models applied to machine health monitoring [Wegerich 2003], auto-regression models applied to machine health monitoring [Logan 2003, Shao 2000, Lei 2003, Casoetto


2003, Yan 2004, Engel 2000], wavelet packet approach applied to tool wear [Yan 2005], FFT based frequencydomain analysis applied to machine monitoring [Yuan 2004], time-series methods applied to machine tool monitoring [Zheng 1992, Djurdjanovic 2002], and statistical data comparison applied to railway bearing diagnostics [National Research Council Canada 1999]. Application of statistical pattern recognition to health monitoring of electronic assemblies subjected to shock and vibration environments is new. Mahalanobis Distance Approach The Mahalanobis Distance classification is similar to the Maximum Likelihood classification except for the class covariances which are all assumed to be equal, hence the method is more efficient. It is based on correlations between variables by which different patterns can be identified and analyzed. It is a useful way of determining similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set. The Mahalanobis distance from a group of values with mean μ = (μ1 , μ 2 , μ 3 , μ 4 … , μ n ) and covariance matrix Σ for a

multivariate vector x = ( x 1, x 2 , x 3 , x 4 … , x n ) is,

T (10) D M ( x ) = (x − μ ) Σ −1 (x − μ ) Mahalanobis distance can also be defined as dissimilarity measure between two random vectors x and y of the same distribution with the covariance matrix Σ ,

T (11) d ( x , y) = (x − y ) Σ −1 (x − y ) The Mahalanobis distance approach has been chosen over other classification approaches as it considers the variance and covariance of the variables as opposed to only the average value. The distance measure is taken as a basis for the calculation of the confidence values for prognostics.

Wavelet Packet Energy Wavelets has been used in wide range of applications such as data and image processing [Martin 2001], geophysics [Kumar 1994], power signal studies [Santoso 1996], meteorological studies [Lau 1995], speech recognition [Favero 1994], medicine [Akay 1997], and motor vibration [Fu 2003, Yen1999]. A wavelet transform is defined by

Wf (u,s) = f , ψ u,s =

1 s

+∞

∫ f (t) ψ

−∞

*

⎛t−u⎞ ⎜ ⎟ dt ⎝ s ⎠

(12) where the base atom ψ* is the complex conjugate of the wavelet function which is a zero average function, centered around zero with a finite energy. ‘s’ and ‘u’ represent the scale and translation factors which are used to decompose function f(t) into a set of basis functions called the wavelets. This transform is used to study transient strains histories. The decomposition of different frequency bands

at different resolutions is carried out to obtain coarse approximation and detail information of the signal. This dissemination of signal in different frequency bands is equivalent to, successive filtering the time domain signal using lowpass and highpass filters. The original strain signal is first passed through a halfband highpass filter g[n] and a lowpass filter h[n]. After the filtering, half of the samples are eliminated according to the Nyquist’s rule, since the signal now has a highest frequency of p/2 radians instead of p. Hence sub-sampling of signal by 2 takes place as other samples are disregarded. This is level-1 decomposition of the signal whose mathematical representation is as follows:

y high [k] = ∑ signal[n] ⋅ g[2k − n] n

y low [k] = ∑ signal[n] ⋅ h[2k − n]

(13)

n

Here yhigh[k] and ylow[k] are the outputs of the highpass and lowpass filters, respectively, after sub-sampling by 2. Such compression and de-noising in wavelet packet transform is equivalent to wavelet transform framework. The advantage with wavelet packets approach is, it offer a more complex and flexible analysis, as the details as well as the approximations of the signal are split. An entropy-based criterion is used to decide the level of decomposition needed for a given signal. This leads to quantification of information at each node in the decomposition tree. Simple and efficient algorithms exist for both wavelet packet decomposition and optimal decomposition selection. An optimal tree, is such that a node is split into two nodes, if and only if the sum of entropy of the two nodes is lower than the sum of entropy of the initial node. After the wavelet packet transform, the wavelet packet energy is calculated at each node of the decomposition tree. Wavelet packet energy is given by:

E=

1 N 2 ∑ Ci N i =1

(14)

Here N is the total number of points in the signal at a given node in the wavelet packet tree and Ci is the wavelet packet coefficients obtained during the wavelet packet transform at the particular node where energy is being calculated. These packet energy obtained from wavelet packet approach form feature vector which is used for confidence value computation for monitoring health of electronics subjected to shock and vibration in drop event. Joint Time Frequency Analysis Transient response of the circuit board assemblies have frequency content that varies over time in the signal. Using a joint time frequency analysis (JTFA) on such a signal provides the exact behavior of the frequency content and its variation over time. This provides an opportunity to study the energy density of a signal simultaneously in time and frequency and also helps in removing noise and interference from the signal. The


joint time frequency is classified into two categories, the Linear Time-Frequency Transforms and the Bilinear Time-Frequency Transforms. [Wigner 1932, Ville 1948, Grossmann 1984, Cohen 1995] The quadratic time frequency transforms are computed by the multiplicative comparison of the signal with itself which is expanded in various directions about each point in time. The representation is in the form of a two dimensional distribution of energy over the timefrequency spectrum. As the quadratic transforms do not use windowing functions hence the resolution problems faced in linear transforms are eliminated. The transient strain signal obtained during a drop event contains component signals of different frequency values and can be broken into a number of parts based on frequency content. The quadratic nature of the Wigner-Ville transforms creates cross-terms whenever multiple frequencies are superimposed [Wigner 1932, Ville 1948, Mark 1970]. The Wigner distribution for a sum of two signals, is given by

been applied to study the drop and shock characteristics of an electronic assembly. The binomial time-frequency Distribution defined by [Jeong 1992a,b] is defined as, TFR (n , ν) =

τ =∞

ν =+ τ

τ= −∞

ν =− τ

∑ h (τ) ∑

g (ν ) ⎛ 2 τ ⎞ ⎜ ⎟f (n + ν + τ )f ∗ (n + ν − τ )e −i 4 πωτ 2τ 2 ⎜⎝ τ + ν ⎟⎠

(20) where h (τ) and g(ν ) is the time smoothing window and the frequency smoothing window respectively and f (n ) represents the signal where n = 1,2 N . The frequency smoothing window

g(ν )

and the time smoothing

* W12 = W21 Due to this property of the cross Wigner distribution the sum of the two cross terms give a real value, i.e.

window h (τ ) used here is a hamming window of size(N) as outlined in [Jeong 1991, Jeong 1992a,b, Williams 1994]. The binomial distribution provides an efficient and fast computation method for computing Time Frequency distributions. The Time frequency moments are used in our study to represent the time frequency distribution of the transient signals obtained during the shock and drop testing of electronic assemblies. In this study the individual time moments and frequency moments of the signal are computed and used as a feature vector to study the damage progression in electronics in a shock and drop event. The above approach has also been applied to the transient-strain response, the transient-displacement response, vibration modeshapes and frequencies of the electronic assembly under drop and shock. The time frequency analysis of the signal provides the frequency content of the transient strain signal at each given time instant. The time moment represents an estimation of instantaneous frequency at a given time instant during the drop event [Boashash 1989, Cohen 1995, Tacer 1995]. The frequency moment represents an estimation of the group delay of the signal for each frequency in the signal. [Cohen 1995, Tacer 1996, Georgopoulos 1997]. As the time moment and frequency moment feature vectors are unique for each signal they are an appropriate choice for prognostics of electronic assemblies in drop and shock.

W12 + W21 = 2 Re{W12 ( t , ω)}

First Time-moment

W ( t , ω) = W11 ( t , ω) + W22 ( t , ω) + W12 ( t , ω) + W21 ( t , ω) (15) where the signal is composed of two signals, i.e. (16) f ( t ) = f1 ( t ) + f 2 ( t ) and the independent Wigner distributions of the signals f1(t) and f2(t) are given by 1 τ τ W11 ( t , ω) = f1* ( t − )f1 ( t − )e − iτωdτ 2π ∫ 2 2 (17a, b) 1 τ τ W22 ( t , ω) = f 2* ( t − )f 2 ( t − )e− iτωdτ 2π ∫ 2 2 and the cross Wigner distribution is given by

1 τ τ (18) f1* ( t − )f 2 ( t − )e −iτωdτ 2π ∫ 2 2 As the Wigner distribution is complex in nature hence W12 ( t , ω) =

(19) W ( t , ω) = W11 ( t , ω) + W22 ( t , ω) + 2 Re{W12 ( t , ω)} This causes the correlation term to be present in the distribution and this term is not unique and can cause errors while studying the signal distributions. This is overcome by using the Cohen Class of Distributions. The Cohen class of transforms apply the approach of computing the time frequency analysis using a kernel, which is a auxiliary function [Cohen 1989, 1995, Williams 1994]. The kernel can be defined so as to represent the properties and requirements of the particular distribution. The cross terms can be reduced by developing kernels that reduce the interference or the cross reference terms, such kernel are defined as the Reduced Interference Distribution (RID) kernels. In this study the binomial time-frequency kernel proposed by [Jeong 1992a,b] has

∞

fm

∫ (t) = ∫

−∞ ∞

f tfr ( t , f ) df

−∞

(21)

tfr ( t , f )df

First Frequency-moment ∞

tm

∫ (f ) = ∫

−∞ ∞

t tfr ( t , f ) dt

−∞

(22)

tfr ( t , f ) dt

9. Model Based Assessment of Underlying Damage To provide a physical relevance to the above approach an explicit finite element model for the free drop and horizontal drop of a 0.5 mm pitch, 132 I/O, 8 mm flexsubstrate CSP has been created. A reduced integration shell elements (S4R) is used for the PCB, and the various component layers such as the substrate, die attach, silicon


die, mold compound have been modeled with C3D8R elements. The interconnects are modeled using two-node beam elements (B31) in place of solder balls as shown in Figure 17. Smeared properties have been derived for the CSP considering all the individual components mentioned above. The concrete floor has been modeled using rigid R3D4 elements. A weight has been attached on the top edge of the board. The explicit models created for the study for the Vertical free drop and the Horizontal drop are shown in Figure 18 and Figure 19 respectively. Some of the common faults that occur in an electronic assembly due to a drop and shock event have been modeled, and by applying the Statistical Pattern recognition techniques the degradation in confidence value is physically correlated to the occurrence of damage in an assembly. The faults simulated in this study are Solder ball cracking, solder ball failure, chip cracking, chip delamination and Package Fall off. The faults have been simulated for both the vertical and horizontal drops.

Solder Ball Cracking and Failure The above described model for the free drop was analyzed several times, with all solder beams intact and with the various corner solder beams damaged (cracked) and failed. The statistical pattern recognition methods described in this study have been applied to the time history output of the strain signal obtained at the PCB surface below the centre of the package, where the sensor would have been mounted in an experimental setup. The solder beam array in the failure simulations for solder ball failure is shown in Figure 20 and the various solder beams missing have been marked and shown for the models developed.

Figure 17: Package with Solder Beam Array

(a) One Interconnect Missing

(b) Two Interconnects Missing

(c) Three Interconnects Missing

(d) Four Interconnects Missing

Figure 20: Model Configurations for Correlation of Interconnect Failure to Confidence Value Degradation. 1.0 Wavelet Packet Energy

Confidence Value

Detailed Package

Packages based on calculated Smeared Properties

0.8

Mahalanobis Distance

0.6

FFT Frequency Band Energy Time Moments

0.4

Frequency Moments

0.2 0.0

Figure 18: Vertical Drop Model developed for the Study.

0

1

2

3

4

Number of Corner Interconnect Failure

Figure 21: Confidence Value degradation in Transient PCB Strain with Solder Ball Failure for VERTICAL Drop.

Figure 19: Horizontal Drop Model developed for the Study

The failure of corner solder balls has been simulated by removing the corner interconnects as the corner solder balls have the most stress concentration and hence are mostly the first to fail in a solder array. The cracking of the solder ball has been simulated by reducing the cross sectional area of the corner solder beams and the model has been simulated for up to all four corner ball damaged, for both vertical and horizontal drop. The confidence


values computed for solder ball failure are shown in Figure 21, for a vertical drop and in Figure 22, for a horizontal drop orientation. The damage monitoring of solder ball damage is shown in Figure 23, for a vertical drop and in Figure 24, for a horizontal drop orientation. The confidence value shows a drop in confidence with the degradation of reliability, thus showing the applicability of the above stated damage monitoring methods to the reliability studies of Electronic assemblies. 1

Confidence Value

Wavelet Packet Analysis 0.8


0.6


0.4

Frequency Moments

0.2 0 0

1

2

3

4

Number of Corner Interconnect Failure

10. Model Validation Transient dynamic strains have been predicted for 0degree JEDEC drop and 3ft, 90-degree vertical drop respectively and correlated with high-speed digital-image correlation measurements. Transient mode shapes at different time intervals has been shown Figure 25 for Test-Board A. Correlation is for the 0-degree JEDEC configuration between high-speed digital image correlation and explicit finite elements. Transient mode shapes have been plotted at 1.4ms, 4.29ms. The predicted mode shapes show good correlation with experimental data. Figure 26 demonstrates the relative confidence value degradation in the transient strain feature vector calculated from Mahalanobis distance and the Wavelet Packet Energy feature vectors for pristine, thermallyaged, and thermally-cycled assemblies after the 1st shockimpact. Figure 27 shows the relative confidence value of the transient strain feature vector for pristine, thermallyaged and the thermally cycled electronic assemblies after 50 shock-impacts.

Figure 22: Confidence Value degradation in Transient PCB Strain with Solder Ball Failure for HORIZONTAL Drop.

Confidence Value

1 0.9

Wavelet Packet Energy

0.8


1.4 ms

Time Moments

0.7

FFT Frequency Band Energy

0.6 0.5 0

1

2

3

4

Number of Corner Interconnects Damaged

Figure 23: Confidence Value degradation in Transient PCB Strain with Solder Ball Damage for VERTICAL Drop.

4.29 ms Figure 25: Correlation of DIC and FEM Full Field 3D Strain Contour of Test Board A (0-degree JEDEC Drop)

D1 C5

1.1 Wavelet Packet Analysis

0.9

Confidence Value

Confidence Value

1


0.8


0.7 0.6

Frequency Moments

0.5 0.4 0

1

2

3

4

Number of Corner Interconnects Damaged

Wavelet Packet

1 0.8 0.6 0.4 0.2 0 Pristine

Figure 24: Confidence Value degradation in Transient PCB Strain with Solder Ball Damage for HORIZONTAL Drop.

Mahalanobis

TA

TC

Figure 26: Relative Confidence Value Degradation for pristine, thermally-aged and thermally-cycled Assemblies after first shock-impact.


Confidence Value

D50 C1

feature vectors versus number of drops for thermally aged and thermally-cycled assemblies respectively, after 1, 25, and 50 drops. The transient strain feature vector shows a significant degradation in the feature vector at 25 drops. The graphs demonstrate that the transient strain signal feature vector constructed from full-field DIC measurements have the ability to identify the onset of degradation in the presence of multiple failure modes.

Mahalanobis Wavelet Packet

1 0.8 0.6 0.4 0.2 0 Pristine

TA

TC

Figure 27: Relative Confidence Value of the Pristine, Thermally Aged and Thermally-Cycled Assemblies after 50-Shock-Impacts.

Confidence Value

TA C5


1 0.8 0.6 0.4 0.2 0 Drop 1

Drop 25

Drop 50

Figure 28: Confidence Value Degradation for THERMALLY AGED Assemblies versus Number of Drops.

Confidence Value

TC C3


1 0.8 0.6 0.4 0.2 0 Drop 1

Drop 25

Drop 50

Figure 29: Confidence Value Degradation for THERMALLY CYCLED Assemblies versus Number of Drops. A different training-signal has been selected for each relative CV calculation, as appropriate, in Figure 26 to Figure 29. For example, in Figure 27, the pristine assemblies subjected to 50 shock-impacts have been taken as the training signal for the analysis. Figure 28 and Figure 29 demonstrate the confidence value degradation in the transient strain feature vector calculated from Mahalanobis distance and the Wavelet Packet Energy

11. Summary and Conclusions In this paper, full-field strain measurement using digital image correlation (DIC) has been investigated for shock and vibration of electronic assemblies. It has been shown that accurate full-field measurements can be made using DIC in conjunction with high-speed imaging for twoelectronic assemblies with various packaging architectures. Transient impact strain histories have been measured in two orientation including 0-degree JEDEC shock and the 90-degree Vertical drop. Full-field strain data from DIC has been correlated with high-speed strain measurements at discrete electronic assembly locations. Explicit finite element models have been constructed for all the electronic assemblies to simulate transient-impact.. Model predictions show good correlation with experimental data. The transient strain measurements have been analyzed using statistical pattern recognition and the ability to monitor in-situ health of the electronic assemblies studied. Results show that the confidence value degradation of the transient strains feature vector from DIC can be used as leading indicator of failure. Acknowledgments The work presented here in this paper has been supported by a research grant from the Semiconductor Research Corporation (SRC), Research ID 1283. References Akay, M.; Wavelet Applications in Medicine; IEEE Spectrum, Vol: 34 , Issue: 5, pp. 50 – 56, 1997. Amodio, D., Broggiato, G., Campana, F., Newaz, G., Digital Speckle Correlation for Strain Measurement by Image Analysis, Society for Experimental Mechanics, Vol. 43, No. 4, December 2003. Atlas, L., G. D. Bernard, S. B. Narayanan, Applications of Time-Frequency Analysis to Manufacturing Sensor Signals, Proceedings of the IEEE, Vol. 84, No. 9, pp. 1319-1329, 1996. Bieler, T., Jiang, H., Influence of Sn Grain Size and Orientation on the Thermomechanical Response and Reliability of Pb-free Solder Joints, Electronic Components and Technology Conference, pp. 146214671, May 2006. Boashash, B., Lovell, B., Kootsookos, P., TimeFrequency Signal Analysis and Instantaneous Frequency Estimation: Methodology, Relationships And Implementations, International Symposium on Circuits and Systems, Vol.2, pp. 1237 - 1242, 1989. Casoetto, N., Djurdjanovic, D., Mayor, R., Lee, J., Ni, J., Multisensor Process Performance Assessment through the Use of Autoregressive Modeling and Feature


Maps, Transactions of SME/NAMRI, also in the SME Journal of Manufacturing Systems, Vol. 31, pp.48390. 2003. Castanien, K. E., Liang, C., Application of Active Structural Health Monitoring Technique to Aircraft Fuselage Structures, Proc. Smart Structures and Materials (SPIE), Vol. 2721, pp. 38-49, 1996. Che, F.X., Pang, H. L., Modeling Board-Level Four-Point Bend Fatigue and Impact Drop Tests, Proceedings of the 56th Electronic Components and Technology Conference, San Diego, CA, pp. 443-448, 2006. Chuang, F., Luqing, Y., Yongqian, L., Ren, Y., Benoit, I, Yuanchu, C., Yuming, Z., Predictive Maintenance in Intelligent Control Maintenance Management System for Hydroelectric Generating Unit, IEEE Transactions on Energy Conversion, Volume 19, Issue 1, pp. 179 – 186, 2004. Cohen, L., Time-Frequency Analysis, Prentice-Hall, Englewood Cliffs,. NJ, 1995. Cohen, L., Time-Frequency Distributions-a Review, Proceedings of the IEEE, Vol. 77, Issue 7, pp. 941 – 981, 1989. Date, M., Shoji, T., Fujiyoshi, M., Sato, K., Tu, K.N., Impact Reliability of Solder Joints, Proceedings of the Electronic Components and Technology, Vol. 1, pp.668-674, 2004. Djurdjanovic, D., Ni, J., Lee, J., Time–Frequency Based Sensor Fusion in the Assessment and Monitoring of Machine Performance Degradation., Proceedings of ASME International Mechanical Engineering Congress and Exposition, Paper Number IMECE2002-2032, New Orleans, Louisiana, 2002. Dunford, S., Okura, J., JEDEC Drop Test Preparations For Qualification of Ceramic LGAs, Proceedings of the SMTA International, Chicago, IL, pp. 314-318, 2004. Engel, S. J., Gilmartin, B. J., Bongort, K., Hess, A., Prognostics, The Real Issues Involved With Predicting Life Remaining, IEEE Aerospace Conference Proceedings, Vol. 6, pp. 457-469, 2000. Favero, R.F.; Compound Wavelets: Wavelets For Speech Recognition, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, pp. 600 – 603; 1994. Fu, Y., Wen-Sheng Li; Guo-Hua Xu; Wavelets and singularities in bearing vibration signals; International Conference on Machine Learning and Cybernetics, Vol. 4, Pages:2433 - 2436, 2003. Georgopoulos, V.C., Preis, D., A Non-Negative Approximate Wigner Distribution With Accurate Low-Order Moments, International Conference on Digital Signal Processing Vol. 2, pp. 769 – 772, 1997. Goyal, S., Buratynski, E., Methods for Realistic DropTesting, The International Journal of Microcircuits and Electronic Packaging, Volume 23, Number 1, pp. 45-52, 2000. Grossmann, A., J. Morlet, Decomposition of Hardy Functions into Square-Integrable Wavelets of

Constant Shape, SIAM J. Appl. Math., vol. 15, pp. 723-736, 1984. Gu, J., Cooreman, S., et al., Full-Field Optical Measurement For Material Parameter Identification With Inverse Methods, WIT Transactions on The Built Environment, Vol. 85, 2006. Gu, J., Cooreman, Steven., Full-Field Optical Measurement For Material Parameter Identification With Inverse Methods, Proceedings of the 2006 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 4-7, 2006. Gyekenyesi, A. L., Sawicki, J. T., and Baaklini, G. Y., Vibration Based Crack Detection in a Rotating Disk: Part 1--An Analytical Study., Report Number NASA/TM-2003-212624, 2003. Hanabe, M., Canumalla, S., Package to Board Interconnection Shear Strength (PBISS) Behavior at High Strain Rates Approaching Mechanical Drop, Proceedings of the Electronic Components and Technology, Vol. 2, pp.1263-1270, 2004. Harris, I. G., Tessier, R., Testing and Diagnosis of Interconnect Faults in Cluster-Based FPGA Architectures, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 21, No. 11, pp.1337-1343, 2002. Hashempour, H., Meyer, F.J., Lombardi, F., Analysis and Measurement of Fault Coverage in a Combined ATE and BIST Environment, IEEE Transactions on Instrumentation and Measurement, Vol. 53, No. 2, 300- 307, 2004. Heck, L. P. and McClellan, J. H., Mechanical System Monitoring Using Hidden Markov Models, Proceedings of International Conference on Acoustics, Speech and Signal Processing, Vol. 3, pp. 1697-1700, 1991. Hedley, M., Hoschke, N., Johnson, M., Lewis, C., Murdoch, A., Price, D., Prokopenko, M., Scott, A., Wang, P., Farmer, A., Sensor Network for Structural Health Monitoring, Processing Conference Intelligent Sensors, Sensor Networks and Information, pp.361 – 366, 2004. Helm, J., McNeill, S., Sutton, M., Improved ThreeDimensional Image Correlation For Surface Displacement Measurement, Society of Photo-Optical Instrumentation Engineers, Vol. 35, No. 7, pp. 19111920, July 1996. Hickman, G. A., Gerardi, J. J., Feng, Y., “Application of Smart Structures to Aircraft Health Monitoring”, Journal of Intelligent Material Systems and Structures, Vol. 2, pp. 411-430, 1991. Jeong, J., Williams, W.J., A New Formulation of Generalized Discrete-Time Time-Frequency Distributions, International Conference on Acoustics, Speech, and Signal Processing, Vol. 5, pp. 3189 – 3192, 1991. Jeong, J., Williams, W.J., Alias-free Generalized Discrete-Time Time-Frequency Distributions, IEEE Transactions on Signal Processing, Vol. 40, Issue 11, pp. 2757 – 2765, 1992b.


Jeong, J., Williams, W.J., Kernel Design For Reduced Interference Distributions, IEEE Transactions on Signal Processing, Vol. 40, Issue 2, pp. 402 – 412, 1992a. Kehoe, L., Lynch, P., Guénebaut, V., Measurement of Deformation and Strain in First Level C4 Interconnect and Stacked Die using Optical Digital Image Correlation, Electronic Components and Technology Conference, pp. 1874-1881, May 2006. Kumar, P, Georgiou, E. F. , Wavelets in Geophysics, Wavelets and its Applications, Academia Press, 1994. Lall, P., Choudhary, P., Gupte, S., Health Monitoring for Damage Initiation & Progression during Mechanical Shock in Electronic Assemblies, Proceedings of the 56th IEEE Electronic Components and Technology Conference, San Diego, California, pp.85-94, May 30June 2, 2006c. Lall, P., Panchagade, D., Iyengar, D., Suhling, J., Life Prediction and Damage Equivalency for Shock Survivability of Electronic Components, Proceedings of the ITherm 2006, 10th Intersociety Conference on Thermal and Thermo-mechanical Phenomena, San Diego, California, pp.804-816, May 30-June 2, 2006b. Lall, P., Gupte, S., Choudhary, P., Suhling, J., SolderJoint Reliability in Electronics Under Shock and Vibration using Explicit Finite Element Submodeling, Proceedings of the 56th IEEE Electronic Components and Technology Conference, San Diego, California, pp.428-435, May 30-June 2, 2006a. Lall, P., Panchagade, D., Choudhary, P., Suhling, J., Gupte, S., Failure-Envelope Approach to Modeling Shock and Vibration Survivability of Electronic and MEMS Packaging, 55th Electronic Components and Technology Conference, Orlando, FL, pp. 480-490, June 1-3, 2005. Lall, P., Panchagade, D., Liu, Y., Johnson, W., Suhling, J., Models for Reliability Prediction of Fine-Pitch BGAs and CSPs in Shock and Drop-Impact, 54th Electronic Components and Technology Conference, pp. 1296 – 1303, 2004. Lau, K.-M., and H.-Y. Weng, Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing, Bulletin of the American Meteorological Society, No. 76, pp. 2391–2402, 1995. Lebold, M. S., Maynard, K., Reichard, K., Trethewey, M., Bieryla, D., Lissenden, C., Dobbins, D., Using Torsional Vibration Analysis as a Synergistic Method for Crack Detection in Rotating Equipment, Proceedings of the Aerospace Conference, Vol. 6, pp. 3517-3527, 2004. Lee, J., Machine Performance Monitoring and Proactive Maintenance in Computer-Integrated Manufacturing: Review and Perspective, International Journal of Computer Integrated Manufacturing, Vol. 8, No. 5, pp. 370-380, 1995. Lei,.Y., Kiremidjian, A. S., Nair, K. K., Lynch, J. P., Law, K. H., An Enhanced Statistical Damage Detection Algorithm Using Time Series Analysis, Proceedings of the 4th International Workshop on

Structural Health Monitoring, Stanford, Sept 15-17, pp. 1-7, 2003. Liang, F. Z., Williams, R. L., and Hsieh, G., Board Strain States Method and FCBGA Mechanical Shock Analysis, Proceedings of First International Conference and Exhibition on Device Packaging, Scottsdale, AZ, March 2005 Logan, K. P., Prognostic Software Agents for Machinery Health Monitoring, Proceedings of the IEEE Aerospace Conference, Vol. 7, pp. 3213- 3225, 2003. Mark, W.D., Spectral Analysis of the Convolution and Filtering of Non-Stationary Stochastic Processes, Journal of Sound and Vibration, Vol. 11, pp. 19-63, 1970. Martin, M.B.; Bell, A.E.; New Image Compression Techniques Using Multiwavelets and Multiwavelet Packets; IEEE Transactions on Image Processing, Vol: 10, Issue: 4, Pages: 500 – 510; 2001 National Research Council Canada, Railway Bearing Diagnostics: Laboratory Data Analysis, 1999. Newman, K., Brittle Fracture – Alternative Solder Joint Integrity Test Methods, Proceedings of the 55th IEEE Electronic Components and Technology Conference, Orlando, FL, pp. 1194-1201, 2005. Rajendra, Pendse, D., Zhou, P., Methodology For Predicting Solder Joint Reliability In Semiconductor Packages, Microelectronics Reliability, Vol. 42, pp. 301-305, 2002. Reu, P., Miller, T., High-speed Multi-camera DIC for Finite Element Model Validation, Part 1, SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 4-7, 2006. Santoso, S.; Powers, E.J.; Grady, W.M.; Hofmann, P.; Power quality assessment via Wavelet transform analysis; IEEE Transactions on Power Delivery, Volume: 11 , Issue: 2, Pages: 924 – 930; 1996. Seah, S.K.W., Wong, E.H., Ranjan, R., Lim C.T., Mai, Y.-W., Understanding and Testing For Drop Impact Failure, ASME, pp. 1-6, 2005. Shao,Y., Nezu, K., Prognosis of Remaining Bearing Life Using Neural Networks, Proceedings of the Institution of Mechanical Engineers, Vol. 214, Part I, 2000. Sick, B., Online Tool Wear Monitoring In Turning Using Time-Delay Neural Networks, Proceedings of International Conference On Acoustics, Speech and Signal Processing, Volume. 1, pp. 445-448, 1998. Song, F., Lee, S., Investigation of IMC Thickness Effect on the Lead-free Solder Ball Attachment Strength: Comparison between Ball Shear Test and Cold Bump Pull Test Results, Electronic Components and Technology Conference, pp.1196-1203, May 2006 Song, G., Shi, X., Qin, F., He, C., Effect Of Loading Mode, Temperature And Moisture On Interface Fracture Toughness Of Silicon/Underfill/Silicon Sandwitched System, Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems, pp. 1147-1152, May 2006. Srinivasan, V., Radhakrishnan, S., Zhang, X., Subbarayan, G., Baughn, T., Nguyen, L., High


Resolution Characterization of Materials Used In Packages Through Digital Image Correlation, InterPACK Conference Proceedings, July 17-22, 2005. Steininger, A., Testing and Built-in-Self-Test - A Survey, Journal of Systems Architecture, Elsevier Science Publishers, Vol. 46, Issue 9, pp. 721-747, 2000. Sun, Y., Pang, J., Shi, X., Tew, J., Thermal Deformation Measurement by Digital Image Correlation Method, Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems, pp. 921-927, May 2006. Suthar, V., Dutt, S., Mixed PLB and Interconnect BIST for FPGAs without Fault-Free Assumptions, 24th IEEE VLSI Test Symposium, pp. 36-43, 2006. Tacer, B., Loughlin, P.J., Instantaneous Frequency and Time-Frequency Distributions, International Conference on Acoustics, Speech, and Signal Processing, Vol. 2, pp. 1013 - 1016, 1995. Tacer, B., Loughlin, P.J., What are the Joint TimeFrequency Moments of a Signal?, International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, pp. 1427 – 1430, 1996. Tee, T. Y., Luan, J., Pek, E., Lim, C. T., Zhing, Z., Advanced Experimental and Simulation Techniques for Analysis of Dynamic Responses during Drop Impact, Electronic Components and technology Conference, Las Vegas, Nevada, pp. 1088-1094, June 1-4, 2004 Tiwari, V., Williams, S., Sutton, M., McNeill, S., Application of Digital Image Correlation in Impact Testing, Proceedings of the 2005 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 7-9, 2005. Ville, J., Theorie et Applications de la Notion de Signal Analytique, Cablet et Transmission, Vol. 2A, pp. 6174, 1948. Wang, L., Mostafa G. Mehrabi, Elijah Kannatey-Asibu, Jr.; Hidden Markov Model-based Tool Wear Monitoring in Turning ; Journal of Manufacturing Science and Engineering, 2001. Wegerich, S. W., Similarity Based Modeling of Time Synchronous Averaged Vibration Signals for Machinery Health Monitoring, Proceedings of the IEEE Aerospace Conference, Big Sky, MT, pp. 36543662, March 6-13, 2003 Wigner, E., On the Quantum Correction for Thermodynamic Equilibrium, Physics Rev, Vol. 40, pp. 749, 1932. Williams, W.J., Tzuhsien, S., Adaptive RID Kernels Which Minimize Time-Frequency Uncertainty, IEEESP International Symposium on Time-Frequency and Time-Scale Analysis, pp. 96 – 99, 1994. Xu, L., Pang, H., Combined Thermal and Electromigration Exposure Effect on SnAgCu BGA Solder Joint Reliability, Electronic Components and Technology Conference, pp. 1154-1159, May 2006. Yan, J., Koc, M., Lee, J., A Prognostic Algorithm For Machine Performance Assessment and its

Application, Production Planning and Control, Vol. 15, No. 8, pp. 796–801, 2004. Yan, J., Lee J., Degradation Assessment And Fault Modes Classification Using Logistic Regression, Journal of Manufacturing Science and Engineering, Vol. 127, Issue 4, pp. 912-914, November 2005. Yen, G.Y.; Kuo-Chung Lin; Wavelet packet feature extraction for vibration monitoring; Proceedings of the 1999 IEEE International Conference on Control Applications, Vol.2, Pages:1573 - 1578, 1999. Yogel, D., Grosser, V., Schubert, A., Michel, B., MicroDAC Strain Measurement for Electronics Packaging Structures, Optics and Lasers in Engineering, Vol. 36, pp. 195-211, 2001. Yuan, S., Ge, M., Qiu, H., Lee, J., Xu, Y., Intelligent Diagnosis in Electromechanical Operations Systems, Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2267–2272, 2004. Zhang, F., Li, M., Xiong, C., Fang, F., Yi, S., Thermal Deformation Analysis of BGA Package by Digital Image Correlation Technique, Microelectronics International, Vol. 22, No. 1, pp. 34-42, 2005. Zhang, Y., Shi, X., Zhou, W., Effect of Hygrothermal Aging on Interfacial Reliability of Flip Chip on Board (FCOB) Assembly, Electronic Packaging Technology Conference, pp. 404-409, 2004. Zheng, K. and Whitehouse, D. J., The Application of the Wigner Distribution to Machine Tool Monitoring, Proceedings of the Institution of Mechanical Engineers, Vol. 206, pp 249-264, 1992. Zhou, P., Goodson, K. E., Sub-pixel Displacement and Deformation Gradient Measurement Using Digital Image-Speckle Correlation (DISC), Optical Engineering, Vol. 40, No. 8, pp 1613-1620, August 2001.
